Template Numerical Library: TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator

Implementation of sparse matrix, i.e. matrix storing only non-zero elements. More...

#include <TNL/Matrices/SparseMatrix.h>

Inheritance diagram for TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >:

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Collaboration diagram for TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >:

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Public Types
using	BaseType = Matrix< Real, Device, Index, RealAllocator >

using	ColumnsIndexesVectorType = Containers::Vector< typename TNL::copy_const< Index >::template from< Real >::type, Device, Index, IndexAllocator >

using	ColumnsIndexesViewType = typename ColumnsIndexesVectorType::ViewType

using	ComputeRealType = ComputeReal

using	ConstColumnsIndexesViewType = typename ColumnsIndexesViewType::ConstViewType

using	ConstRowsCapacitiesView = typename RowsCapacitiesView::ConstViewType

using	ConstRowView = typename ViewType::ConstRowView
	Type for accessing constant matrix rows.

using	ConstValuesViewType = typename ValuesViewType::ConstViewType

using	ConstViewType = SparseMatrixView< std::add_const_t< Real >, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >
	Matrix view type for constant instances. More...

using	DeviceType = Device
	The device where the matrix is allocated.

using	IndexAllocatorType = IndexAllocator
	The allocator for matrix elements column indexes.

using	IndexType = Index
	The type used for matrix elements indexing.

using	RealAllocatorType = RealAllocator
	The allocator for matrix elements values.

using	RealType = std::remove_const_t< Real >
	The type of matrix elements.

using	RowsCapacitiesType = Containers::Vector< std::remove_const_t< Index >, Device, Index, IndexAllocator >

using	RowsCapacitiesView = Containers::VectorView< std::remove_const_t< Index >, Device, Index >

using	RowView = typename ViewType::RowView
	Type for accessing matrix rows.

template<typename Device_ , typename Index_ , typename IndexAllocator_ >
using	SegmentsTemplate = Segments< Device_, Index_, IndexAllocator_ >
	Templated type of segments, i.e. sparse matrix format.

using	SegmentsType = Segments< Device, Index, IndexAllocator >
	Type of segments used by this matrix. It represents the sparse matrix format.

template<typename Device_ , typename Index_ >
using	SegmentsViewTemplate = typename SegmentsType::template ViewTemplate< Device_, Index >
	Templated view type of segments, i.e. sparse matrix format.

using	SegmentsViewType = typename SegmentsType::ViewType
	Type of segments view used by the related matrix view. It represents the sparse matrix format.

template<typename _Real = Real, typename _Device = Device, typename _Index = Index, typename _MatrixType = MatrixType, template< typename, typename, typename > class _Segments = Segments, typename _ComputeReal = ComputeReal, typename _RealAllocator = typename Allocators::Default< _Device >::template Allocator< _Real >, typename _IndexAllocator = typename Allocators::Default< _Device >::template Allocator< _Index >>
using	Self = SparseMatrix< _Real, _Device, _Index, _MatrixType, _Segments, _ComputeReal, _RealAllocator, _IndexAllocator >
	Helper type for getting self type or its modifications.

using	ValuesVectorType = typename Matrix< Real, Device, Index, RealAllocator >::ValuesType

using	ValuesViewType = typename ValuesVectorType::ViewType

using	ViewType = SparseMatrixView< Real, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >
	Type of related matrix view. More...

Public Types inherited from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >
using	ConstRowsCapacitiesView = typename RowsCapacitiesView::ConstViewType

using	ConstValuesType = Containers::Vector< std::add_const_t< double >, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >
	Type of constant vector holding values of matrix elements.

using	ConstValuesView = typename ViewType::ConstValuesView
	Type of constant vector view holding values of matrix elements.

using	ConstViewType = typename MatrixView< double, Devices::Host, int >::ConstViewType
	Type of base matrix view for constant instances.

using	DeviceType = Devices::Host
	The device where the matrix is allocated.

using	IndexType = int
	The type used for matrix elements indexing.

using	RealAllocatorType = typename Allocators::Default< Devices::Host >::template Allocator< double >

using	RealType = double
	The type of matrix elements.

using	RowsCapacitiesType = Containers::Vector< int, Devices::Host, int >

using	RowsCapacitiesView = Containers::VectorView< int, Devices::Host, int >

using	ValuesType = Containers::Vector< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >
	Type of vector holding values of matrix elements.

using	ValuesView = typename ViewType::ValuesView
	Type of vector view holding values of matrix elements.

using	ViewType = MatrixView< double, Devices::Host, int >
	Type of base matrix view.

Public Member Functions
	SparseMatrix (const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor only with values and column indexes allocators. More...

template<typename RowCapacitiesVector , std::enable_if_t< TNL::IsArrayType< RowCapacitiesVector >::value, int > = 0>
	SparseMatrix (const RowCapacitiesVector &rowCapacities, IndexType columns, const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor with matrix rows capacities given as a vector and number of columns. More...

	SparseMatrix (const SparseMatrix &matrix)
	Copy constructor. More...

template<typename ListIndex >
	SparseMatrix (const std::initializer_list< ListIndex > &rowCapacities, IndexType columns, const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor with matrix rows capacities and number of columns. More...

template<typename Index_t , std::enable_if_t< std::is_integral< Index_t >::value, int > = 0>
	SparseMatrix (Index_t rows, Index_t columns, const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor with matrix dimensions. More...

	SparseMatrix (IndexType rows, IndexType columns, const std::initializer_list< std::tuple< IndexType, IndexType, RealType > > &data, const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor with matrix dimensions and data in initializer list. More...

template<typename MapIndex , typename MapValue >
	SparseMatrix (IndexType rows, IndexType columns, const std::map< std::pair< MapIndex, MapIndex >, MapValue > &map, const RealAllocatorType &realAllocator=RealAllocatorType(), const IndexAllocatorType &indexAllocator=IndexAllocatorType())
	Constructor with matrix dimensions and data in std::map. More...

	SparseMatrix (SparseMatrix &&matrix) noexcept=default
	Move constructor. More...

__cuda_callable__ void	addElement (IndexType row, IndexType column, const RealType &value, const RealType &thisElementMultiplicator)
	Add element at given row and column to given value. More...

template<typename Function >
void	forAllElements (Function &&function)
	Method for parallel iteration over all matrix elements for non-constant instances. More...

template<typename Function >
void	forAllElements (Function &&function) const
	Method for parallel iteration over all matrix elements for constant instances. More...

template<typename Function >
void	forAllRows (Function &&function)
	Method for parallel iteration over all matrix rows. More...

template<typename Function >
void	forAllRows (Function &&function) const
	Method for parallel iteration over all matrix rows for constant instances. More...

template<typename Function >
void	forElements (IndexType begin, IndexType end, Function &&function)
	Method for parallel iteration over all matrix elements of given rows for non-constant instances. More...

template<typename Function >
void	forElements (IndexType begin, IndexType end, Function &&function) const
	Method for parallel iteration over matrix elements of given rows for constant instances. More...

template<typename Function >
void	forRows (IndexType begin, IndexType end, Function &&function)
	Method for parallel iteration over matrix rows from interval [ begin, end). More...

template<typename Function >
void	forRows (IndexType begin, IndexType end, Function &&function) const
	Method for parallel iteration over matrix rows from interval [ begin, end) for constant instances. More...

ColumnsIndexesVectorType &	getColumnIndexes ()
	Getter of column indexes for nonconstant instances. More...

const ColumnsIndexesVectorType &	getColumnIndexes () const
	Getter of column indexes for constant instances. More...

template<typename Vector >
void	getCompressedRowLengths (Vector &rowLengths) const
	Computes number of non-zeros in each row. More...

ConstViewType	getConstView () const
	Returns a non-modifiable view of the sparse matrix. More...

__cuda_callable__ RealType	getElement (IndexType row, IndexType column) const
	Returns value of matrix element at position given by its row and column index. More...

IndexType	getNonzeroElementsCount () const override
	Returns number of non-zero matrix elements. More...

__cuda_callable__ IndexType	getPaddingIndex () const
	Returns a padding index value. More...

__cuda_callable__ RowView	getRow (const IndexType &rowIdx)
	Non-constant getter of simple structure for accessing given matrix row. More...

__cuda_callable__ const ConstRowView	getRow (const IndexType &rowIdx) const
	Constant getter of simple structure for accessing given matrix row. More...

template<typename Vector >
void	getRowCapacities (Vector &rowCapacities) const
	Compute capacities of all rows. More...

__cuda_callable__ IndexType	getRowCapacity (IndexType row) const
	Returns capacity of given matrix row. More...

SegmentsType &	getSegments ()
	Getter of segments for non-constant instances. More...

const SegmentsType &	getSegments () const
	Getter of segments for constant instances. More...

std::string	getSerializationTypeVirtual () const override
	Returns string with serialization type. More...

template<typename Real2 , typename Index2 , template< typename, typename, typename > class Segments2>
void	getTransposition (const SparseMatrix< Real2, Device, Index2, MatrixType, Segments2 > &matrix, const ComputeRealType &matrixMultiplicator=1.0)

ViewType	getView () const
	Returns a modifiable view of the sparse matrix. More...

void	load (const String &fileName)
	Method for loading the matrix from the file with given filename. More...

void	load (File &file) override
	Method for loading the matrix from a file. More...

template<typename Matrix >
bool	operator!= (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type. More...

template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization, typename RealAllocator_ >
SparseMatrix &	operator= (const DenseMatrix< Real_, Device_, Index_, Organization, RealAllocator_ > &matrix)
	Assignment of dense matrix. More...

template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization, typename RealAllocator_ >
SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > &	operator= (const DenseMatrix< Real_, Device_, Index_, Organization, RealAllocator_ > &matrix)

template<typename RHSMatrix >
SparseMatrix &	operator= (const RHSMatrix &matrix)
	Assignment of any matrix type other then this and dense. More...

template<typename RHSMatrix >
SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > &	operator= (const RHSMatrix &matrix)

SparseMatrix &	operator= (const SparseMatrix &matrix)
	Copy-assignment of exactly the same matrix type. More...

SparseMatrix &	operator= (SparseMatrix &&matrix) noexcept(false)
	Move-assignment of exactly the same matrix type. More...

template<typename Matrix >
bool	operator== (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type. More...

void	print (std::ostream &str) const override
	Method for printing the matrix to output stream. More...

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceAllRows (Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity)
	Method for performing general reduction on all matrix rows. More...

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceAllRows (Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity) const
	Method for performing general reduction on all matrix rows for constant instances. More...

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceRows (IndexType begin, IndexType end, Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity)
	Method for performing general reduction on matrix rows. More...

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceRows (IndexType begin, IndexType end, Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity) const
	Method for performing general reduction on matrix rows for constant instances. More...

template<typename Fetch , typename Reduce , typename Keep , typename FetchValue >
void	reduceRows (IndexType begin, IndexType end, Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchValue &identity)

template<typename Fetch , typename Reduce , typename Keep , typename FetchValue >
void	reduceRows (IndexType begin, IndexType end, Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchValue &identity) const

void	reset ()
	Resets the matrix to zero dimensions.

void	save (const String &fileName) const
	Method for saving the matrix to the file with given filename. More...

void	save (File &file) const override
	Method for saving the matrix to a file. More...

template<typename Function >
void	sequentialForAllRows (Function &function)
	This method calls sequentialForRows for all matrix rows. More...

template<typename Function >
void	sequentialForAllRows (Function &function) const
	This method calls sequentialForRows for all matrix rows (for constant instances). More...

template<typename Function >
void	sequentialForRows (IndexType begin, IndexType end, Function &function)
	Method for sequential iteration over all matrix rows for non-constant instances. More...

template<typename Function >
void	sequentialForRows (IndexType begin, IndexType end, Function &function) const
	Method for sequential iteration over all matrix rows for constant instances. More...

virtual void	setColumnsWithoutReset (IndexType columns)
	Set number of columns of this matrix. More...

void	setDimensions (IndexType rows, IndexType columns) override
	Set number of rows and columns of this matrix. More...

__cuda_callable__ void	setElement (IndexType row, IndexType column, const RealType &value)
	Sets element at given row and column to given value. More...

void	setElements (const std::initializer_list< std::tuple< IndexType, IndexType, RealType > > &data)
	This method sets the sparse matrix elements from initializer list. More...

template<typename MapIndex , typename MapValue >
void	setElements (const std::map< std::pair< MapIndex, MapIndex >, MapValue > &map)
	This method sets the sparse matrix elements from std::map. More...

template<typename Matrix >
void	setLike (const Matrix &matrix)
	Set the number of matrix rows and columns by the given matrix. More...

template<typename Matrix_ >
void	setLike (const Matrix_ &matrix)

template<typename RowsCapacitiesVector >
void	setRowCapacities (const RowsCapacitiesVector &rowCapacities)
	Allocates memory for non-zero matrix elements. More...

template<typename InVector , typename OutVector >
void	vectorProduct (const InVector &inVector, OutVector &outVector, ComputeRealType matrixMultiplicator=1.0, ComputeRealType outVectorMultiplicator=0.0, IndexType begin=0, IndexType end=0) const
	Computes product of matrix and vector. More...

Public Member Functions inherited from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >
	Matrix (const RealAllocatorType &allocator=RealAllocatorType())
	Construct a new Matrix object possibly with user defined allocator of the matrix values. More...

	Matrix (IndexType rows, IndexType columns, const RealAllocatorType &allocator=RealAllocatorType())
	Construct a new Matrix object with given dimensions and possibly user defined allocator of the matrix values. More...

IndexType	getAllocatedElementsCount () const
	Tells the number of allocated matrix elements. More...

__cuda_callable__ IndexType	getColumns () const
	Returns number of matrix columns. More...

virtual IndexType	getNonzeroElementsCount () const
	Computes a current number of nonzero matrix elements. More...

__cuda_callable__ IndexType	getRows () const
	Returns number of matrix rows. More...

ValuesType &	getValues ()
	Returns a reference to a vector with the matrix elements values. More...

const ValuesType &	getValues () const
	Returns a constant reference to a vector with the matrix elements values. More...

void	load (File &file) override
	Method for loading the matrix from a file. More...

bool	operator!= (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type. More...

bool	operator!= (const MatrixT &matrix) const

bool	operator== (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type. More...

bool	operator== (const MatrixT &matrix) const

virtual void	print (std::ostream &str) const
	Method for printing the matrix to output stream. More...

void	reset ()
	Reset the matrix. More...

void	save (File &file) const override
	Method for saving the matrix to a file. More...

virtual void	setDimensions (IndexType rows, IndexType columns)
	Method for setting or changing of the matrix dimensions. More...

void	setLike (const Matrix_ &matrix)
	Set the matrix dimensions to be equal to those of the input matrix. More...

Public Member Functions inherited from TNL::Object
virtual	~Object ()=default
	Destructor. More...

virtual std::string	getSerializationTypeVirtual () const

void	load (const String &fileName)
	Method for restoring the object from a file. More...

virtual void	load (File &file)
	Method for restoring the object from a file. More...

void	save (const String &fileName) const
	Method for saving the object to a file as a binary data. More...

virtual void	save (File &file) const
	Method for saving the object to a file as a binary data. More...

Static Public Member Functions
static std::string	getSerializationType ()
	Returns string with serialization type. More...

static constexpr bool	isBinary ()
	Test of binary matrix type. More...

static constexpr bool	isSymmetric ()
	Test of symmetric matrix type. More...

Static Public Member Functions inherited from TNL::Object
static std::string	getSerializationType ()
	Static serialization type getter. More...

Protected Attributes
ColumnsIndexesVectorType	columnIndexes

IndexAllocator	indexAllocator

SegmentsType	segments

ViewType	view

Protected Attributes inherited from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >
IndexType	columns

IndexType	rows

ValuesType	values
	Array containing the allocated matrix elements.

Detailed Description

template<typename Real = double, typename Device = Devices::Host, typename Index = int, typename MatrixType = GeneralMatrix, template< typename Device_, typename Index_, typename IndexAllocator_ > class Segments = Algorithms::Segments::CSRDefault, typename ComputeReal = typename ChooseSparseMatrixComputeReal< Real, Index >::type, typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >, typename IndexAllocator = typename Allocators::Default< Device >::template Allocator< Index >>
class TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >

Implementation of sparse matrix, i.e. matrix storing only non-zero elements.

Template Parameters

Real	is a type of matrix elements. If Real equals bool the matrix is treated as binary and so the matrix elements values are not stored in the memory since we need to remember only coordinates of non-zero elements( which equal one).
Device	is a device where the matrix is allocated.
Index	is a type for indexing of the matrix elements.
MatrixType	specifies a symmetry of matrix. See MatrixType. Symmetric matrices store only lower part of the matrix and its diagonal. The upper part is reconstructed on the fly. GeneralMatrix with no symmetry is used by default.
Segments	is a structure representing the sparse matrix format. Depending on the pattern of the non-zero elements different matrix formats can perform differently especially on GPUs. By default Algorithms::Segments::CSR format is used. See also Algorithms::Segments::Ellpack, Algorithms::Segments::SlicedEllpack, Algorithms::Segments::ChunkedEllpack, and Algorithms::Segments::BiEllpack.
ComputeReal	is the same as Real mostly but for binary matrices it is set to Index type. This can be changed by the user, of course.
RealAllocator	is allocator for the matrix elements values.
IndexAllocator	is allocator for the matrix elements column indexes.

Member Typedef Documentation

◆ ConstViewType

using TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::ConstViewType = SparseMatrixView< std::add_const_t< Real >, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >

Matrix view type for constant instances.

See SparseMatrixView.

◆ ViewType

using TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::ViewType = SparseMatrixView< Real, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >

Type of related matrix view.

See SparseMatrixView.

Constructor & Destructor Documentation

◆ SparseMatrix() [1/8]

template<typename Real , typename Device , typename Index , typename MatrixType , template< typename, typename, typename > class Segments, typename ComputeReal , typename RealAllocator , typename IndexAllocator >

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

Constructor only with values and column indexes allocators.

Parameters

realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

◆ SparseMatrix() [2/8]

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix ( const SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > & matrix )

explicit

Copy constructor.

Parameters

matrix is the source matrix

◆ SparseMatrix() [3/8]

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix ( SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > && matrix )

defaultnoexcept

Move constructor.

Parameters

matrix is the source matrix

◆ SparseMatrix() [4/8]

template<typename Index_t , std::enable_if_t< std::is_integral< Index_t >::value, int > >

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	Index_t	rows,
		Index_t	columns,
		const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

Constructor with matrix dimensions.

Parameters

rows	is number of matrix rows.
columns	is number of matrix columns.
realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

◆ SparseMatrix() [5/8]

template<typename ListIndex >

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	const std::initializer_list< ListIndex > &	rowCapacities,
		IndexType	columns,
		const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

explicit

Constructor with matrix rows capacities and number of columns.

The number of matrix rows is given by the size of rowCapacities list.

Template Parameters

ListIndex is the initializer list values type.

Parameters

rowCapacities	is a list telling how many matrix elements must be allocated in each row.
columns	is the number of matrix columns.
realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void initializerListExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix {

{ 1, 2, 3, 4, 5 }, // row capacities

6 }; // number of matrix columns

for( int row = 0; row < matrix.getRows(); row++ )

for( int column = 0; column <= row; column++ )

matrix.setElement( row, column, row - column + 1 );

std::cout << "General sparse matrix: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrices on CPU ... " << std::endl;

initializerListExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrices on CUDA GPU ... " << std::endl;

initializerListExample< TNL::Devices::Cuda >();

#endif

}

std::cout

TNL::Matrices::SparseMatrix
Implementation of sparse matrix, i.e. matrix storing only non-zero elements.
Definition: SparseMatrix.h:57

TNL::Matrices::SparseMatrix::setElement
__cuda_callable__ void setElement(IndexType row, IndexType column, const RealType &value)
Sets element at given row and column to given value.
Definition: SparseMatrix.hpp:505

std::endl
T endl(T... args)

Output: Creating matrices on CPU ...

General sparse matrix:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

Creating matrices on CUDA GPU ...

General sparse matrix:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

◆ SparseMatrix() [6/8]

template<typename RowCapacitiesVector , std::enable_if_t< TNL::IsArrayType< RowCapacitiesVector >::value, int > >

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	const RowCapacitiesVector &	rowCapacities,
		IndexType	columns,
		const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

explicit

Constructor with matrix rows capacities given as a vector and number of columns.

The number of matrix rows is given by the size of rowCapacities vector.

Template Parameters

RowCapacitiesVector is the row capacities vector type. Usually it is some of TNL::Containers::Array, TNL::Containers::ArrayView, TNL::Containers::Vector or TNL::Containers::VectorView.

Parameters

rowCapacities	is a vector telling how many matrix elements must be allocated in each row.
columns	is the number of matrix columns.
realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Containers/Vector.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void initializerListExample()

{

TNL::Containers::Vector< int, Device > rowCapacities{ 1, 2, 3, 4, 5 };

TNL::Matrices::SparseMatrix< double, Device > matrix {

rowCapacities, // row capacities

6 }; // number of matrix columns

for( int row = 0; row < matrix.getRows(); row++ )

for( int column = 0; column <= row; column++ )

matrix.setElement( row, column, row - column + 1 );

std::cout << "General sparse matrix: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrices on CPU ... " << std::endl;

initializerListExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrices on CUDA GPU ... " << std::endl;

initializerListExample< TNL::Devices::Cuda >();

#endif

}

TNL::Containers::Vector
Vector extends Array with algebraic operations.
Definition: Vector.h:40

Output: Creating matrices on CPU ...

General sparse matrix:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

Creating matrices on CUDA GPU ...

General sparse matrix:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

◆ SparseMatrix() [7/8]

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	IndexType	rows,
		IndexType	columns,
		const std::initializer_list< std::tuple< IndexType, IndexType, RealType > > &	data,
		const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

explicit

Constructor with matrix dimensions and data in initializer list.

The matrix elements values are given as a list data of triples: { { row1, column1, value1 }, { row2, column2, value2 }, ... }.

Parameters

rows	is number of matrix rows.
columns	is number of matrix columns.
data	is a list of matrix elements values.
realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void initializerListExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix (

5, // number of matrix rows

5, // number of matrix columns

{ // matrix elements definition

{ 0, 0, 2.0 },

{ 1, 0, -1.0 }, { 1, 1, 2.0 }, { 1, 2, -1.0 },

{ 2, 1, -1.0 }, { 2, 2, 2.0 }, { 2, 3, -1.0 },

{ 3, 2, -1.0 }, { 3, 3, 2.0 }, { 3, 4, -1.0 },

{ 4, 4, 2.0 } } );

std::cout << "General sparse matrix: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrices on CPU ... " << std::endl;

initializerListExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrices on CUDA GPU ... " << std::endl;

initializerListExample< TNL::Devices::Cuda >();

#endif

}

Output: Creating matrices on CPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

Creating matrices on CUDA GPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

◆ SparseMatrix() [8/8]

template<typename MapIndex , typename MapValue >

TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::SparseMatrix	(	IndexType	rows,
		IndexType	columns,
		const std::map< std::pair< MapIndex, MapIndex >, MapValue > &	map,
		const RealAllocatorType &	realAllocator = `RealAllocatorType()`,
		const IndexAllocatorType &	indexAllocator = `IndexAllocatorType()`
	)

explicit

Constructor with matrix dimensions and data in std::map.

The matrix elements values are given as a map data where keys are std::pair of matrix coordinates ( {row, column} ) and value is the matrix element value.

Template Parameters

MapIndex	is a type for indexing rows and columns.
MapValue	is a type for matrix elements values in the map.

Parameters

rows	is number of matrix rows.
columns	is number of matrix columns.
map	is std::map containing matrix elements.
realAllocator	is used for allocation of matrix elements values.
indexAllocator	is used for allocation of matrix elements column indexes.

Example: #include <iostream>

#include <map>

#include <utility>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void initializerListExample()

{

std::map< std::pair< int, int >, double > map;

map.insert( std::make_pair( std::make_pair( 0, 0 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 0 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 1 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 2 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 1 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 2 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 3 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 2 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 3 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 4 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 4, 4 ), 2.0 ) );

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5, map );

std::cout << "General sparse matrix: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrices on CPU ... " << std::endl;

initializerListExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrices on CUDA GPU ... " << std::endl;

initializerListExample< TNL::Devices::Cuda >();

#endif

}

std::map::insert
T insert(T... args)

std::make_pair
T make_pair(T... args)

std::map

Output: Creating matrices on CPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

Creating matrices on CUDA GPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

Member Function Documentation

◆ addElement()

__cuda_callable__ void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::addElement	(	IndexType	row,
		IndexType	column,
		const RealType &	value,
		const RealType &	thisElementMultiplicator
	)

Add element at given row and column to given value.

This method can be called from the host system (CPU) no matter where the matrix is allocated. If the matrix is allocated on GPU this method can be called even from device kernels. If the matrix is allocated in GPU device this method is called from CPU, it transfers values of each matrix element separately and so the performance is very low. For higher performance see. SparseMatrix::getRow or SparseMatrix::forElements and SparseMatrix::forAllElements. The call may fail if the matrix row capacity is exhausted.

Parameters

row	is row index of the element.
column	is columns index of the element.
value	is the value the element will be set to.
thisElementMultiplicator	is multiplicator the original matrix element value is multiplied by before addition of given value.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void addElements()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( { 5, 5, 5, 5, 5 }, 5 );

for( int i = 0; i < 5; i++ )

matrix.setElement( i, i, i );

std::cout << "Initial matrix is: " << std::endl << matrix << std::endl;

for( int i = 0; i < 5; i++ )

for( int j = 0; j < 5; j++ )

matrix.addElement( i, j, 1.0, 5.0 );

std::cout << "Matrix after addition is: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Add elements on host:" << std::endl;

addElements< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Add elements on CUDA device:" << std::endl;

addElements< TNL::Devices::Cuda >();

#endif

}

Output: Add elements on host:

Initial matrix is:

Row: 0 ->

Row: 1 -> 1:1

Row: 2 -> 2:2

Row: 3 -> 3:3

Row: 4 -> 4:4

Matrix after addition is:

Row: 0 -> 0:1 1:1 2:1 3:1 4:1

Row: 1 -> 0:1 1:6 2:1 3:1 4:1

Row: 2 -> 0:1 1:1 2:11 3:1 4:1

Row: 3 -> 0:1 1:1 2:1 3:16 4:1

Row: 4 -> 0:1 1:1 2:1 3:1 4:21

Add elements on CUDA device:

Initial matrix is:

Row: 0 ->

Row: 1 -> 1:1

Row: 2 -> 2:2

Row: 3 -> 3:3

Row: 4 -> 4:4

Matrix after addition is:

Row: 0 -> 0:1 1:1 2:1 3:1 4:1

Row: 1 -> 0:1 1:6 2:1 3:1 4:1

Row: 2 -> 0:1 1:1 2:11 3:1 4:1

Row: 3 -> 0:1 1:1 2:1 3:16 4:1

Row: 4 -> 0:1 1:1 2:1 3:1 4:21

◆ forAllElements() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forAllElements ( Function && function )

Method for parallel iteration over all matrix elements for non-constant instances.

See SparseMatrix::forElements.

Template Parameters

Function is a type of lambda function that will operate on matrix elements.

Parameters

function is an instance of the lambda function to be called for each matrix element.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forElementsExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 2, 3, 4, 5 }, 5 );

auto f = [=] __cuda_callable__ ( int rowIdx, int localIdx, int& columnIdx, double& value ) {

if( rowIdx >= localIdx ) // This is important, some matrix formats may allocate more matrix elements

// than we requested. These padding elements are processed here as well.

{

columnIdx = localIdx;

value = rowIdx + localIdx + 1;

}

};

matrix.forElements( 0, matrix.getRows(), f );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrix on host: " << std::endl;

forElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrix on CUDA device: " << std::endl;

forElementsExample< TNL::Devices::Cuda >();

#endif

}

__cuda_callable__
#define __cuda_callable__
Definition: CudaCallable.h:22

Output: Creating matrix on host:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

Creating matrix on CUDA device:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

◆ forAllElements() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forAllElements ( Function && function ) const

Method for parallel iteration over all matrix elements for constant instances.

See SparseMatrix::forElements.

Template Parameters

Function is a type of lambda function that will operate on matrix elements.

Parameters

function is an instance of the lambda function to be called for each matrix element.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forElementsExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 2, 3, 4, 5 }, 5 );

auto f = [=] __cuda_callable__ ( int rowIdx, int localIdx, int& columnIdx, double& value ) {

if( rowIdx >= localIdx ) // This is important, some matrix formats may allocate more matrix elements

// than we requested. These padding elements are processed here as well.

{

columnIdx = localIdx;

value = rowIdx + localIdx + 1;

}

};

matrix.forElements( 0, matrix.getRows(), f );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrix on host: " << std::endl;

forElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrix on CUDA device: " << std::endl;

forElementsExample< TNL::Devices::Cuda >();

#endif

}

Output: Creating matrix on host:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

Creating matrix on CUDA device:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

◆ forAllRows() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forAllRows ( Function && function )

Method for parallel iteration over all matrix rows.

In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method SparseMatrix::forAllElements where more than one thread can be mapped to each row.

Template Parameters

Function is type of the lambda function.

Parameters

function is an instance of the lambda function to be called for each row.

auto function = [] __cuda_callable__ ( RowView& row ) mutable { ... };

TNL::Matrices::SparseMatrix::RowView

typename ViewType::RowView RowView

Type for accessing matrix rows.

Definition: SparseMatrix.h:167

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forRowsExample()

{

/***

* Set the following matrix (dots represent zero matrix elements):

*

* / 2 . . . . \

* | 1 2 1 . . |

* | . 1 2 1. . |

* | . . 1 2 1 |

* \ . . . . 2 /

*/

const int size( 5 );

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

MatrixType matrix( { 1, 3, 3, 3, 1 }, size );

using RowView = typename MatrixType::RowView;

/***

* Set the matrix elements.

*/

auto f = [=] __cuda_callable__ ( RowView& row ) mutable {

const int rowIdx = row.getRowIndex();

if( rowIdx == 0 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else if( rowIdx == size - 1 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else

{

row.setElement( 0, rowIdx - 1, 1.0 ); // elements below the diagonal

row.setElement( 1, rowIdx, 2.0 ); // diagonal element

row.setElement( 2, rowIdx + 1, 1.0 ); // elements above the diagonal

}

};

matrix.forAllRows( f );

std::cout << matrix << std::endl;

/***

* Divide each matrix row by a sum of all elements in the row - with use of iterators.

*/

matrix.forAllRows( [=] __cuda_callable__ ( RowView& row ) mutable {

double sum( 0.0 );

for( auto element : row )

sum += element.value();

for( auto element: row )

element.value() /= sum;

} );

std::cout << "Divide each matrix row by a sum of all elements in the row ... " << std::endl;

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

forRowsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

forRowsExample< TNL::Devices::Cuda >();

#endif

}

Output: Getting matrix rows on host:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

Getting matrix rows on CUDA device:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

◆ forAllRows() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forAllRows ( Function && function ) const

Method for parallel iteration over all matrix rows for constant instances.

In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method SparseMatrix::forAllElements where more than one thread can be mapped to each row.

Template Parameters

Function is type of the lambda function.

Parameters

function is an instance of the lambda function to be called for each row.

auto function = [] __cuda_callable__ ( RowView& row ) { ... };

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forRowsExample()

{

/***

* Set the following matrix (dots represent zero matrix elements):

*

* / 2 . . . . \

* | 1 2 1 . . |

* | . 1 2 1. . |

* | . . 1 2 1 |

* \ . . . . 2 /

*/

const int size( 5 );

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

MatrixType matrix( { 1, 3, 3, 3, 1 }, size );

using RowView = typename MatrixType::RowView;

/***

* Set the matrix elements.

*/

auto f = [=] __cuda_callable__ ( RowView& row ) mutable {

const int rowIdx = row.getRowIndex();

if( rowIdx == 0 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else if( rowIdx == size - 1 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else

{

row.setElement( 0, rowIdx - 1, 1.0 ); // elements below the diagonal

row.setElement( 1, rowIdx, 2.0 ); // diagonal element

row.setElement( 2, rowIdx + 1, 1.0 ); // elements above the diagonal

}

};

matrix.forAllRows( f );

std::cout << matrix << std::endl;

/***

* Divide each matrix row by a sum of all elements in the row - with use of iterators.

*/

matrix.forAllRows( [=] __cuda_callable__ ( RowView& row ) mutable {

double sum( 0.0 );

for( auto element : row )

sum += element.value();

for( auto element: row )

element.value() /= sum;

} );

std::cout << "Divide each matrix row by a sum of all elements in the row ... " << std::endl;

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

forRowsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

forRowsExample< TNL::Devices::Cuda >();

#endif

}

Output: Getting matrix rows on host:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

Getting matrix rows on CUDA device:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

◆ forElements() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forElements	(	IndexType	begin,
		IndexType	end,
		Function &&	function
	)

Method for parallel iteration over all matrix elements of given rows for non-constant instances.

Template Parameters

Function is type of lambda function that will operate on matrix elements.

Parameters

begin	defines beginning of the range [ begin,end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called for each element of given rows.

The lambda function function should be declared like follows:

auto function = [] __cuda_callable__ ( IndexType rowIdx, IndexType localIdx, IndexType& columnIdx, const RealType& value )

mutable { ... }

TNL::Matrices::SparseMatrix::IndexType

Index IndexType

The type used for matrix elements indexing.

Definition: SparseMatrix.h:115

TNL::Matrices::SparseMatrix::RealType

std::remove_const_t< Real > RealType

The type of matrix elements.

Definition: SparseMatrix.h:103

The localIdx parameter is a rank of the non-zero element in given row.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forElementsExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 2, 3, 4, 5 }, 5 );

auto f = [=] __cuda_callable__ ( int rowIdx, int localIdx, int& columnIdx, double& value ) {

if( rowIdx >= localIdx ) // This is important, some matrix formats may allocate more matrix elements

// than we requested. These padding elements are processed here as well.

{

columnIdx = localIdx;

value = rowIdx + localIdx + 1;

}

};

matrix.forElements( 0, matrix.getRows(), f );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrix on host: " << std::endl;

forElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrix on CUDA device: " << std::endl;

forElementsExample< TNL::Devices::Cuda >();

#endif

}

Output: Creating matrix on host:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

Creating matrix on CUDA device:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

◆ forElements() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forElements	(	IndexType	begin,
		IndexType	end,
		Function &&	function
	)		const

Method for parallel iteration over matrix elements of given rows for constant instances.

Template Parameters

Function is type of lambda function that will operate on matrix elements.

Parameters

begin	defines beginning of the range [ begin, end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called for element of given rows.

The lambda function function should be declared like follows:

auto function = [] __cuda_callable__ ( IndexType rowIdx, IndexType localIdx, IndexType columnIdx, const RealType& value )

{ ... };

The localIdx parameter is a rank of the non-zero element in given row.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forElementsExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 2, 3, 4, 5 }, 5 );

auto f = [=] __cuda_callable__ ( int rowIdx, int localIdx, int& columnIdx, double& value ) {

if( rowIdx >= localIdx ) // This is important, some matrix formats may allocate more matrix elements

// than we requested. These padding elements are processed here as well.

{

columnIdx = localIdx;

value = rowIdx + localIdx + 1;

}

};

matrix.forElements( 0, matrix.getRows(), f );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrix on host: " << std::endl;

forElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrix on CUDA device: " << std::endl;

forElementsExample< TNL::Devices::Cuda >();

#endif

}

Output: Creating matrix on host:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

Creating matrix on CUDA device:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:3 1:4 2:5

Row: 3 -> 0:4 1:5 2:6 3:7

Row: 4 -> 0:5 1:6 2:7 3:8 4:9

◆ forRows() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forRows	(	IndexType	begin,
		IndexType	end,
		Function &&	function
	)

Method for parallel iteration over matrix rows from interval [ begin, end).

In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method SparseMatrix::forElements where more than one thread can be mapped to each row.

Template Parameters

Function is type of the lambda function.

Parameters

begin	defines beginning of the range [ begin,end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called for each row.

auto function = [] __cuda_callable__ ( RowView& row ) mutable { ... };

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forRowsExample()

{

/***

* Set the following matrix (dots represent zero matrix elements):

*

* / 2 . . . . \

* | 1 2 1 . . |

* | . 1 2 1. . |

* | . . 1 2 1 |

* \ . . . . 2 /

*/

const int size( 5 );

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

MatrixType matrix( { 1, 3, 3, 3, 1 }, size );

using RowView = typename MatrixType::RowView;

/***

* Set the matrix elements.

*/

auto f = [=] __cuda_callable__ ( RowView& row ) mutable {

const int rowIdx = row.getRowIndex();

if( rowIdx == 0 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else if( rowIdx == size - 1 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else

{

row.setElement( 0, rowIdx - 1, 1.0 ); // elements below the diagonal

row.setElement( 1, rowIdx, 2.0 ); // diagonal element

row.setElement( 2, rowIdx + 1, 1.0 ); // elements above the diagonal

}

};

matrix.forAllRows( f );

std::cout << matrix << std::endl;

/***

* Divide each matrix row by a sum of all elements in the row - with use of iterators.

*/

matrix.forAllRows( [=] __cuda_callable__ ( RowView& row ) mutable {

double sum( 0.0 );

for( auto element : row )

sum += element.value();

for( auto element: row )

element.value() /= sum;

} );

std::cout << "Divide each matrix row by a sum of all elements in the row ... " << std::endl;

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

forRowsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

forRowsExample< TNL::Devices::Cuda >();

#endif

}

Output: Getting matrix rows on host:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

Getting matrix rows on CUDA device:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

◆ forRows() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::forRows	(	IndexType	begin,
		IndexType	end,
		Function &&	function
	)		const

Method for parallel iteration over matrix rows from interval [ begin, end) for constant instances.

In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method SparseMatrix::forElements where more than one thread can be mapped to each row.

Template Parameters

Function is type of the lambda function.

Parameters

begin	defines beginning of the range [ begin,end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called for each row.

auto function = [] __cuda_callable__ ( RowView& row ) { ... };

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void forRowsExample()

{

/***

* Set the following matrix (dots represent zero matrix elements):

*

* / 2 . . . . \

* | 1 2 1 . . |

* | . 1 2 1. . |

* | . . 1 2 1 |

* \ . . . . 2 /

*/

const int size( 5 );

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

MatrixType matrix( { 1, 3, 3, 3, 1 }, size );

using RowView = typename MatrixType::RowView;

/***

* Set the matrix elements.

*/

auto f = [=] __cuda_callable__ ( RowView& row ) mutable {

const int rowIdx = row.getRowIndex();

if( rowIdx == 0 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else if( rowIdx == size - 1 )

row.setElement( 0, rowIdx, 2.0 ); // diagonal element

else

{

row.setElement( 0, rowIdx - 1, 1.0 ); // elements below the diagonal

row.setElement( 1, rowIdx, 2.0 ); // diagonal element

row.setElement( 2, rowIdx + 1, 1.0 ); // elements above the diagonal

}

};

matrix.forAllRows( f );

std::cout << matrix << std::endl;

/***

* Divide each matrix row by a sum of all elements in the row - with use of iterators.

*/

matrix.forAllRows( [=] __cuda_callable__ ( RowView& row ) mutable {

double sum( 0.0 );

for( auto element : row )

sum += element.value();

for( auto element: row )

element.value() /= sum;

} );

std::cout << "Divide each matrix row by a sum of all elements in the row ... " << std::endl;

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

forRowsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

forRowsExample< TNL::Devices::Cuda >();

#endif

}

Output: Getting matrix rows on host:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

Getting matrix rows on CUDA device:

Row: 0 -> 0:2

Row: 1 -> 0:1 1:2 2:1

Row: 2 -> 1:1 2:2 3:1

Row: 3 -> 2:1 3:2 4:1

Row: 4 -> 4:2

Divide each matrix row by a sum of all elements in the row ...

Row: 0 -> 0:1

Row: 1 -> 0:0.25 1:0.5 2:0.25

Row: 2 -> 1:0.25 2:0.5 3:0.25

Row: 3 -> 2:0.25 3:0.5 4:0.25

Row: 4 -> 4:1

◆ getColumnIndexes() [1/2]

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getColumnIndexes

Getter of column indexes for nonconstant instances.

Returns: Reference to a vector with matrix elements column indexes.

◆ getColumnIndexes() [2/2]

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getColumnIndexes

Getter of column indexes for constant instances.

Returns: Constant reference to a vector with matrix elements column indexes.

◆ getCompressedRowLengths()

template<typename Vector >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getCompressedRowLengths ( Vector & rowLengths ) const

Computes number of non-zeros in each row.

Parameters

rowLengths is a vector into which the number of non-zeros in each row will be stored.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void getCompressedRowLengthsExample()

{

TNL::Matrices::SparseMatrix< double, Device > triangularMatrix( 5, 5 );

triangularMatrix.setElements( {

{ 0, 0, 1 },

{ 1, 0, 2 }, { 1, 1, 3 },

{ 2, 0, 4 }, { 2, 1, 5 }, { 2, 2, 6 },

{ 3, 0, 7 }, { 3, 1, 8 }, { 3, 2, 9 }, { 3, 3, 10 },

{ 4, 0, 11 }, { 4, 1, 12 }, { 4, 2, 13 }, { 4, 3, 14 }, { 4, 4, 15 } } );

std::cout << triangularMatrix << std::endl;

TNL::Containers::Vector< int, Device > rowLengths;

triangularMatrix.getCompressedRowLengths( rowLengths );

std::cout << "Compressed row lengths are: " << rowLengths << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting compressed row lengths on host: " << std::endl;

getCompressedRowLengthsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting compressed row lengths on CUDA device: " << std::endl;

getCompressedRowLengthsExample< TNL::Devices::Cuda >();

#endif

}

Output: Getting compressed row lengths on host:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:4 1:5 2:6

Row: 3 -> 0:7 1:8 2:9 3:10

Row: 4 -> 0:11 1:12 2:13 3:14 4:15

Compressed row lengths are: [ 1, 2, 3, 4, 5 ]

Getting compressed row lengths on CUDA device:

Row: 0 -> 0:1

Row: 1 -> 0:2 1:3

Row: 2 -> 0:4 1:5 2:6

Row: 3 -> 0:7 1:8 2:9 3:10

Row: 4 -> 0:11 1:12 2:13 3:14 4:15

Compressed row lengths are: [ 1, 2, 3, 4, 5 ]

◆ getConstView()

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getConstView

Returns a non-modifiable view of the sparse matrix.

See SparseMatrixView.

Returns: sparse matrix view.

◆ getElement()

__cuda_callable__ auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getElement	(	IndexType	row,
		IndexType	column
	)		const

Returns value of matrix element at position given by its row and column index.

Parameters

row	is a row index of the matrix element.
column	i a column index of the matrix element.

Returns: value of given matrix element.

Example: #include <iostream>

#include <iomanip>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void getElements()

{

TNL::Matrices::SparseMatrix< double, Device > matrix (

5, // number of matrix rows

5, // number of matrix columns

{ // matrix elements definition

{ 0, 0, 2.0 },

{ 1, 0, -1.0 }, { 1, 1, 2.0 }, { 1, 2, -1.0 },

{ 2, 1, -1.0 }, { 2, 2, 2.0 }, { 2, 3, -1.0 },

{ 3, 2, -1.0 }, { 3, 3, 2.0 }, { 3, 4, -1.0 },

{ 4, 4, 2.0 } } );

for( int i = 0; i < 5; i++ )

{

for( int j = 0; j < 5; j++ )

std::cout << std::setw( 5 ) << matrix.getElement( i, j );

std::cout << std::endl;

}

}

int main( int argc, char* argv[] )

{

std::cout << "Get elements on host:" << std::endl;

getElements< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Get elements on CUDA device:" << std::endl;

getElements< TNL::Devices::Cuda >();

#endif

}

std::setw
T setw(T... args)

Output: Get elements on host:

2 0 0 0 0

-1 2 -1 0 0

0 -1 2 -1 0

0 0 -1 2 -1

0 0 0 0 2

Get elements on CUDA device:

2 0 0 0 0

-1 2 -1 0 0

0 -1 2 -1 0

0 0 -1 2 -1

0 0 0 0 2

◆ getNonzeroElementsCount()

Index TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getNonzeroElementsCount

overridevirtual

Returns number of non-zero matrix elements.

This method really counts the non-zero matrix elements and so it returns zero for matrix having all allocated elements set to zero.

Returns: number of non-zero matrix elements.

Reimplemented from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >.

◆ getPaddingIndex()

__cuda_callable__ Index TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getPaddingIndex

Returns a 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.

Returns: value of the padding index.

◆ getRow() [1/2]

__cuda_callable__ auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getRow ( const IndexType & rowIdx )

Non-constant getter of simple structure for accessing given matrix row.

Parameters

rowIdx is matrix row index.

Returns: RowView for accessing given matrix row.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

#include <TNL/Pointers/SharedPointer.h>

template< typename Device >

void getRowExample()

{

auto rowCapacities = { 1, 1, 1, 1, 1 }; // Variadic templates in SharedPointer

// constructor do not recognize initializer

// list so we give it a hint.

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

TNL::Pointers::SharedPointer< MatrixType > matrix( rowCapacities, 5 );

auto f = [=] __cuda_callable__ ( int rowIdx ) mutable {

auto row = matrix->getRow( rowIdx );

row.setElement( 0, rowIdx, 10 * ( rowIdx + 1 ) );

};

/***

* For the case when Device is CUDA device we need to synchronize smart

* pointers. To avoid this you may use SparseMatrixView. See

* SparseMatrixView::getRow example for details.

*/

TNL::Pointers::synchronizeSmartPointersOnDevice< Device >();

/***

* Set the matrix elements.

*/

TNL::Algorithms::ParallelFor< Device >::exec( 0, matrix->getRows(), f );

std::cout << *matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

getRowExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

getRowExample< TNL::Devices::Cuda >();

#endif

}

TNL::Pointers::SharedPointer
Cross-device shared smart pointer.
Definition: SharedPointer.h:49

TNL::Algorithms::ParallelFor::exec
static void exec(Index start, Index end, Function f, FunctionArgs... args)
Static method for the execution of the loop.
Definition: ParallelFor.h:87

Output: Getting matrix rows on host:

Row: 0 -> 0:10

Row: 1 -> 1:20

Row: 2 -> 2:30

Row: 3 -> 3:40

Row: 4 -> 4:50

Getting matrix rows on CUDA device:

Row: 0 -> 0:10

Row: 1 -> 1:20

Row: 2 -> 2:30

Row: 3 -> 3:40

Row: 4 -> 4:50

See SparseMatrixRowView.

◆ getRow() [2/2]

__cuda_callable__ auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getRow ( const IndexType & rowIdx ) const

Constant getter of simple structure for accessing given matrix row.

Parameters

rowIdx is matrix row index.

Returns: RowView for accessing given matrix row.

Example: #include <iostream>

#include <functional>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

#include <TNL/Pointers/SharedPointer.h>

template< typename Device >

void getRowExample()

{

using MatrixType = TNL::Matrices::SparseMatrix< double, Device >;

TNL::Pointers::SharedPointer< MatrixType > matrix ( 5, 5 );

matrix->setElements(

{ { 0, 0, 1 },

{ 1, 0, 1 }, { 1, 1, 2 },

{ 2, 0, 1 }, { 2, 1, 2 }, { 2, 2, 3 },

{ 3, 0, 1 }, { 3, 1, 2 }, { 3, 2, 3 }, { 3, 3, 4 },

{ 4, 0, 1 }, { 4, 1, 2 }, { 4, 2, 3 }, { 4, 3, 4 }, { 4, 4, 5 } } );

/***

* Fetch lambda function returns diagonal element in each row.

*/

auto fetch = [=] __cuda_callable__ ( int rowIdx ) mutable -> double {

auto row = matrix->getRow( rowIdx );

return row.getValue( rowIdx );

};

/***

* For the case when Device is CUDA device we need to synchronize smart

* pointers. To avoid this you may use SparseMatrixView. See

* SparseMatrixView::getConstRow example for details.

*/

TNL::Pointers::synchronizeSmartPointersOnDevice< Device >();

/***

* Compute the matrix trace.

*/

int trace = TNL::Algorithms::reduce< Device >( 0, matrix->getRows(), fetch, std::plus<>{}, 0 );

std::cout << "Matrix trace is " << trace << "." << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Getting matrix rows on host: " << std::endl;

getRowExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Getting matrix rows on CUDA device: " << std::endl;

getRowExample< TNL::Devices::Cuda >();

#endif

}

std::plus

Output: Getting matrix rows on host:

Matrix trace is 15.

Getting matrix rows on CUDA device:

Matrix trace is 15.

See SparseMatrixRowView.

◆ getRowCapacities()

template<typename Vector >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getRowCapacities ( Vector & rowCapacities ) const

Compute capacities of all rows.

The row capacities are not stored explicitly and must be computed.

Parameters

rowCapacities is a vector where the row capacities will be stored.

◆ getRowCapacity()

__cuda_callable__ Index TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getRowCapacity ( IndexType row ) const

Returns capacity of given matrix row.

Parameters

row	index of matrix row.

Returns: number of matrix elements allocated for the row.

◆ getSegments() [1/2]

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getSegments

Getter of segments for non-constant instances.

Segments are a structure for addressing the matrix elements columns and values. In fact, Segments represent the sparse matrix format.

Returns: Non-constant reference to segments.

◆ getSegments() [2/2]

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getSegments

Getter of segments for constant instances.

Segments are a structure for addressing the matrix elements columns and values. In fact, Segments represent the sparse matrix format.

Returns: Constant reference to segments.

◆ getSerializationType()

std::string TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getSerializationType

static

Returns string with serialization type.

The string has a form Matrices::SparseMatrix< RealType, [any_device], IndexType, General/Symmetric, Format, [any_allocator] >.

Returns: String with the serialization type.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void getSerializationTypeExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix;

std::cout << "Matrix type is: " << matrix.getSerializationType();

}

int main( int argc, char* argv[] )

{

std::cout << "Get serialization type on CPU ... " << std::endl;

getSerializationTypeExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Get serialization type on CUDA GPU ... " << std::endl;

getSerializationTypeExample< TNL::Devices::Cuda >();

#endif

}

TNL::Matrices::SparseMatrix::getSerializationType
static std::string getSerializationType()
Returns string with serialization type.
Definition: SparseMatrix.hpp:196

Output: Get serialization type on CPU ...

Matrix type is: Matrices::SparseMatrix< double, CSR< [any_device], int, TNL::Algorithms::Segments::CSRScalarKernel<int, TNL::Devices::Host> >, [any_device], int, General, [any_allocator], [any_allocator] >Get serialization type on CUDA GPU ...

Matrix type is: Matrices::SparseMatrix< double, CSR< [any_device], int, TNL::Algorithms::Segments::CSRScalarKernel<int, TNL::Devices::Cuda> >, [any_device], int, General, [any_allocator], [any_allocator] >

◆ getSerializationTypeVirtual()

std::string TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getSerializationTypeVirtual

overridevirtual

Returns string with serialization type.

See SparseMatrix::getSerializationType.

Returns: String with the serialization type.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void getSerializationTypeExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix;

std::cout << "Matrix type is: " << matrix.getSerializationType();

}

int main( int argc, char* argv[] )

{

std::cout << "Get serialization type on CPU ... " << std::endl;

getSerializationTypeExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Get serialization type on CUDA GPU ... " << std::endl;

getSerializationTypeExample< TNL::Devices::Cuda >();

#endif

}

Output: Get serialization type on CPU ...

Matrix type is: Matrices::SparseMatrix< double, CSR< [any_device], int, TNL::Algorithms::Segments::CSRScalarKernel<int, TNL::Devices::Host> >, [any_device], int, General, [any_allocator], [any_allocator] >Get serialization type on CUDA GPU ...

Matrix type is: Matrices::SparseMatrix< double, CSR< [any_device], int, TNL::Algorithms::Segments::CSRScalarKernel<int, TNL::Devices::Cuda> >, [any_device], int, General, [any_allocator], [any_allocator] >

Reimplemented from TNL::Object.

◆ getView()

auto TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::getView

Returns a modifiable view of the sparse matrix.

See SparseMatrixView.

Returns: sparse matrix view.

◆ isBinary()

static constexpr bool TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::isBinary ( )

inlinestaticconstexpr

Test of binary matrix type.

Returns: true if the matrix is stored as binary and false otherwise.

◆ isSymmetric()

static constexpr bool TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::isSymmetric ( )

inlinestaticconstexpr

Test of symmetric matrix type.

Returns: true if the matrix is stored as symmetric and false otherwise.

◆ load() [1/2]

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::load ( const String & fileName )

Method for loading the matrix from the file with given filename.

Parameters

fileName is name of the file.

◆ load() [2/2]

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::load ( File & file )

overridevirtual

Method for loading the matrix from a file.

Parameters

file	is the input file.

Reimplemented from TNL::Object.

◆ operator!=()

template<typename Matrix >

bool TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator!= ( const Matrix & matrix ) const

Comparison operator with another arbitrary matrix type.

Parameters

matrix is the right-hand side matrix.

Returns: true if the RHS matrix is equal, false otherwise.

◆ operator=() [1/4]

template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization, typename RealAllocator_ >

SparseMatrix & TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator= ( const DenseMatrix< Real_, Device_, Index_, Organization, RealAllocator_ > & matrix )

Assignment of dense matrix.

Parameters

matrix is input matrix for the assignment.

Returns: reference to this matrix.

◆ operator=() [2/4]

template<typename RHSMatrix >

SparseMatrix & TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator= ( const RHSMatrix & matrix )

Assignment of any matrix type other then this and dense.

Warning: Assignment of symmetric sparse matrix to general sparse matrix does not give correct result, currently. Only the diagonal and the lower part of the matrix is assigned.

Parameters

matrix is input matrix for the assignment.

Returns: reference to this matrix.

◆ operator=() [3/4]

SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > & TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator= ( const SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > & matrix )

Copy-assignment of exactly the same matrix type.

Parameters

matrix is input matrix for the assignment.

Returns: reference to this matrix.

◆ operator=() [4/4]

SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > & TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator= ( SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator > && matrix )

noexcept

Move-assignment of exactly the same matrix type.

Parameters

matrix is input matrix for the assignment.

Returns: reference to this matrix.

◆ operator==()

template<typename Matrix >

bool TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::operator== ( const Matrix & matrix ) const

Comparison operator with another arbitrary matrix type.

Parameters

matrix is the right-hand side matrix.

Returns: true if the RHS matrix is equal, false otherwise.

◆ print()

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::print ( std::ostream & str ) const

overridevirtual

Method for printing the matrix to output stream.

Parameters

str	is the output stream.

Reimplemented from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >.

◆ reduceAllRows() [1/2]

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::reduceAllRows	(	Fetch &	fetch,
		const Reduce &	reduce,
		Keep &	keep,
		const FetchReal &	identity
	)

Method for performing general reduction on all matrix rows.

Template Parameters

Fetch is a type of lambda function for data fetch declared as

auto fetch = [=] __cuda_callable__ ( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue { ...

};

The return type of this lambda can be any non void.

Template Parameters

Reduce is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callable__ ( const FetchValue& v1, const FetchValue& v2 ) -> FetchValu { ... };

TNL::Algorithms::reduce

Result reduce(Index begin, Index end, Fetch &&fetch, Reduction &&reduction, const Result &identity)

reduce implements (parallel) reduction for vectors and arrays.

Definition: reduce.h:71

Template Parameters

Keep	is a type of lambda function for storing results of reduction in each row. It is declared as

auto keep = [=] __cuda_callable__ ( const IndexType rowIdx, const double& value ) { ... };

Template Parameters

FetchValue is type returned by the Fetch lambda function.

Parameters

fetch	is an instance of lambda function for data fetch.
reduce	is an instance of lambda function for reduction.
keep	in an instance of lambda function for storing results.
identity	is the identity element for the reduction operation, i.e. element which does not change the result of the reduction.

Example: #include <iostream>

#include <iomanip>

#include <functional>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void reduceAllRows()

{

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5, {

{ 0, 0, 1 },

{ 1, 1, 1 }, { 1, 2, 8 },

{ 2, 2, 1 }, { 2, 3, 9 },

{ 3, 3, 1 }, { 3, 4, 9 },

{ 4, 4, 1 } } );

/***

* Find largest element in each row.

*/

TNL::Containers::Vector< double, Device > rowMax( matrix.getRows() );

/***

* Prepare vector view and matrix view for lambdas.

*/

auto rowMaxView = rowMax.getView();

/***

* Fetch lambda just returns absolute value of matrix elements.

*/

auto fetch = [=] __cuda_callable__ ( int rowIdx, int columnIdx, const double& value ) -> double {

return TNL::abs( value );

};

/***

* Reduce lambda return maximum of given values.

*/

auto reduce = [=] __cuda_callable__ ( double& a, const double& b ) -> double {

return TNL::max( a, b );

};

/***

* Keep lambda store the largest value in each row to the vector rowMax.

*/

auto keep = [=] __cuda_callable__ ( int rowIdx, const double& value ) mutable {

rowMaxView[ rowIdx ] = value;

};

/***

* Compute the largest values in each row.

*/

matrix.reduceAllRows( fetch, reduce, keep, std::numeric_limits< double >::lowest() );

std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;

std::cout << "Max. elements in rows are: " << rowMax << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "All rows reduction on host:" << std::endl;

reduceAllRows< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "All rows reduction on CUDA device:" << std::endl;

reduceAllRows< TNL::Devices::Cuda >();

#endif

}

TNL::Matrices::SparseMatrix::reduceAllRows
void reduceAllRows(Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity)
Method for performing general reduction on all matrix rows.
Definition: SparseMatrix.hpp:628

TNL::abs
__cuda_callable__ T abs(const T &n)
This function returns absolute value of given number n.
Definition: Math.h:87

TNL::max
constexpr ResultType max(const T1 &a, const T2 &b)
This function returns maximum of two numbers.
Definition: Math.h:61

std::numeric_limits

Output: All rows reduction on host:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

All rows reduction on CUDA device:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

◆ reduceAllRows() [2/2]

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::reduceAllRows	(	Fetch &	fetch,
		const Reduce &	reduce,
		Keep &	keep,
		const FetchReal &	identity
	)		const

Method for performing general reduction on all matrix rows for constant instances.

Template Parameters

Fetch is a type of lambda function for data fetch declared as

auto fetch = [=] __cuda_callable__ ( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue { ...

};

The return type of this lambda can be any non void.

Template Parameters

Reduce is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callable__ ( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue { ... };

Template Parameters

Keep	is a type of lambda function for storing results of reduction in each row. It is declared as

auto keep = [=] __cuda_callable__ ( const IndexType rowIdx, const double& value )

Template Parameters

FetchValue is type returned by the Fetch lambda function.

Parameters

fetch	is an instance of lambda function for data fetch.
reduce	is an instance of lambda function for reduction.
keep	in an instance of lambda function for storing results.
identity	is the identity element for the reduction operation, i.e. element which does not change the result of the reduction.

Example: #include <iostream>

#include <iomanip>

#include <functional>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void reduceAllRows()

{

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5, {

{ 0, 0, 1 },

{ 1, 1, 1 }, { 1, 2, 8 },

{ 2, 2, 1 }, { 2, 3, 9 },

{ 3, 3, 1 }, { 3, 4, 9 },

{ 4, 4, 1 } } );

/***

* Find largest element in each row.

*/

TNL::Containers::Vector< double, Device > rowMax( matrix.getRows() );

/***

* Prepare vector view and matrix view for lambdas.

*/

auto rowMaxView = rowMax.getView();

/***

* Fetch lambda just returns absolute value of matrix elements.

*/

auto fetch = [=] __cuda_callable__ ( int rowIdx, int columnIdx, const double& value ) -> double {

return TNL::abs( value );

};

/***

* Reduce lambda return maximum of given values.

*/

auto reduce = [=] __cuda_callable__ ( double& a, const double& b ) -> double {

return TNL::max( a, b );

};

/***

* Keep lambda store the largest value in each row to the vector rowMax.

*/

auto keep = [=] __cuda_callable__ ( int rowIdx, const double& value ) mutable {

rowMaxView[ rowIdx ] = value;

};

/***

* Compute the largest values in each row.

*/

matrix.reduceAllRows( fetch, reduce, keep, std::numeric_limits< double >::lowest() );

std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;

std::cout << "Max. elements in rows are: " << rowMax << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "All rows reduction on host:" << std::endl;

reduceAllRows< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "All rows reduction on CUDA device:" << std::endl;

reduceAllRows< TNL::Devices::Cuda >();

#endif

}

Output: All rows reduction on host:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

All rows reduction on CUDA device:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

◆ reduceRows() [1/2]

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::reduceRows	(	IndexType	begin,
		IndexType	end,
		Fetch &	fetch,
		const Reduce &	reduce,
		Keep &	keep,
		const FetchReal &	identity
	)

Method for performing general reduction on matrix rows.

Template Parameters

Fetch is a type of lambda function for data fetch declared as

auto fetch = [=] __cuda_callable__ ( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue { ...

};

The return type of this lambda can be any non void.

Template Parameters

Reduce is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callable__ ( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue { ... };

Template Parameters

Keep	is a type of lambda function for storing results of reduction in each row. It is declared as

auto keep = [=] __cuda_callable__ ( const IndexType rowIdx, const double& value ) { ... };

Template Parameters

FetchValue is type returned by the Fetch lambda function.

Parameters

begin	defines beginning of the range [ begin, end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
fetch	is an instance of lambda function for data fetch.
reduce	is an instance of lambda function for reduction.
keep	in an instance of lambda function for storing results.
identity	is the identity element for the reduction operation, i.e. element which does not change the result of the reduction.

Example: #include <iostream>

#include <iomanip>

#include <functional>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void reduceRows()

{

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5, {

{ 0, 0, 1 },

{ 1, 1, 1 }, { 1, 2, 8 },

{ 2, 2, 1 }, { 2, 3, 9 },

{ 3, 3, 1 }, { 3, 4, 9 },

{ 4, 4, 1 } } );

/***

* Find largest element in each row.

*/

TNL::Containers::Vector< double, Device > rowMax( matrix.getRows() );

/***

* Prepare vector view for lambdas.

*/

auto rowMaxView = rowMax.getView();

/***

* Fetch lambda just returns absolute value of matrix elements.

*/

auto fetch = [=] __cuda_callable__ ( int rowIdx, int columnIdx, const double& value ) -> double {

return TNL::abs( value );

};

/***

* Reduce lambda return maximum of given values.

*/

auto reduce = [=] __cuda_callable__ ( double& a, const double& b ) -> double {

return TNL::max( a, b );

};

/***

* Keep lambda store the largest value in each row to the vector rowMax.

*/

auto keep = [=] __cuda_callable__ ( int rowIdx, const double& value ) mutable {

rowMaxView[ rowIdx ] = value;

};

/***

* Compute the largest values in each row.

*/

matrix.reduceRows( 0, matrix.getRows(), fetch, reduce, keep, std::numeric_limits< double >::lowest() );

std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;

std::cout << "Max. elements in rows are: " << rowMax << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Rows reduction on host:" << std::endl;

reduceRows< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Rows reduction on CUDA device:" << std::endl;

reduceRows< TNL::Devices::Cuda >();

#endif

}

TNL::Matrices::SparseMatrix::reduceRows
void reduceRows(IndexType begin, IndexType end, Fetch &fetch, const Reduce &reduce, Keep &keep, const FetchReal &identity)
Method for performing general reduction on matrix rows.

Output: Rows reduction on host:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

Rows reduction on CUDA device:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

◆ reduceRows() [2/2]

template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::reduceRows	(	IndexType	begin,
		IndexType	end,
		Fetch &	fetch,
		const Reduce &	reduce,
		Keep &	keep,
		const FetchReal &	identity
	)		const

Method for performing general reduction on matrix rows for constant instances.

Template Parameters

Fetch is a type of lambda function for data fetch declared as

auto fetch = [=] __cuda_callable__ ( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue { ...

};

The return type of this lambda can be any non void.

Template Parameters

Reduce is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callable__ ( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue { ... }

Template Parameters

Keep	is a type of lambda function for storing results of reduction in each row. It is declared as

auto keep = [=] __cuda_callable__ ( const IndexType rowIdx, const double& value ) { ... };

Template Parameters

FetchValue is type returned by the Fetch lambda function.

Parameters

begin	defines beginning of the range [ begin, end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
fetch	is an instance of lambda function for data fetch.
reduce	is an instance of lambda function for reduction.
keep	in an instance of lambda function for storing results.
identity	is the identity element for the reduction operation, i.e. element which does not change the result of the reduction.

Example: #include <iostream>

#include <iomanip>

#include <functional>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void reduceRows()

{

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5, {

{ 0, 0, 1 },

{ 1, 1, 1 }, { 1, 2, 8 },

{ 2, 2, 1 }, { 2, 3, 9 },

{ 3, 3, 1 }, { 3, 4, 9 },

{ 4, 4, 1 } } );

/***

* Find largest element in each row.

*/

TNL::Containers::Vector< double, Device > rowMax( matrix.getRows() );

/***

* Prepare vector view for lambdas.

*/

auto rowMaxView = rowMax.getView();

/***

* Fetch lambda just returns absolute value of matrix elements.

*/

auto fetch = [=] __cuda_callable__ ( int rowIdx, int columnIdx, const double& value ) -> double {

return TNL::abs( value );

};

/***

* Reduce lambda return maximum of given values.

*/

auto reduce = [=] __cuda_callable__ ( double& a, const double& b ) -> double {

return TNL::max( a, b );

};

/***

* Keep lambda store the largest value in each row to the vector rowMax.

*/

auto keep = [=] __cuda_callable__ ( int rowIdx, const double& value ) mutable {

rowMaxView[ rowIdx ] = value;

};

/***

* Compute the largest values in each row.

*/

matrix.reduceRows( 0, matrix.getRows(), fetch, reduce, keep, std::numeric_limits< double >::lowest() );

std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;

std::cout << "Max. elements in rows are: " << rowMax << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Rows reduction on host:" << std::endl;

reduceRows< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Rows reduction on CUDA device:" << std::endl;

reduceRows< TNL::Devices::Cuda >();

#endif

}

Output: Rows reduction on host:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

Rows reduction on CUDA device:

The matrix reads as:

Row: 0 -> 0:1

Row: 1 -> 1:1 2:8

Row: 2 -> 2:1 3:9

Row: 3 -> 3:1 4:9

Row: 4 -> 4:1

Max. elements in rows are: [ 1, 8, 9, 9, 1 ]

◆ save() [1/2]

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::save ( const String & fileName ) const

Method for saving the matrix to the file with given filename.

Parameters

fileName is name of the file.

◆ save() [2/2]

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::save ( File & file ) const

overridevirtual

Method for saving the matrix to a file.

Parameters

file	is the output file.

Reimplemented from TNL::Object.

◆ sequentialForAllRows() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::sequentialForAllRows ( Function & function )

This method calls sequentialForRows for all matrix rows.

See SparseMatrix::sequentialForAllRows.

Template Parameters

Function is a type of lambda function that will operate on matrix elements.

Parameters

function is an instance of the lambda function to be called in each row.

◆ sequentialForAllRows() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::sequentialForAllRows ( Function & function ) const

This method calls sequentialForRows for all matrix rows (for constant instances).

See SparseMatrix::sequentialForRows.

Template Parameters

Function is a type of lambda function that will operate on matrix elements.

Parameters

function is an instance of the lambda function to be called in each row.

◆ sequentialForRows() [1/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::sequentialForRows	(	IndexType	begin,
		IndexType	end,
		Function &	function
	)

Method for sequential iteration over all matrix rows for non-constant instances.

Template Parameters

Function is type of lambda function that will operate on matrix elements. It is should have form like

auto function = [] __cuda_callable__ ( RowView& row ) { ... };

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Parameters

begin	defines beginning of the range [ begin, end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called in each row.

◆ sequentialForRows() [2/2]

template<typename Function >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::sequentialForRows	(	IndexType	begin,
		IndexType	end,
		Function &	function
	)		const

Method for sequential iteration over all matrix rows for constant instances.

Template Parameters

Function is type of lambda function that will operate on matrix elements. It is should have form like

auto function = [] __cuda_callable__ ( RowView& row ) { ... };

RowView represents matrix row - see TNL::Matrices::SparseMatrix::RowView.

Parameters

begin	defines beginning of the range [ begin, end ) of rows to be processed.
end	defines ending of the range [ begin, end ) of rows to be processed.
function	is an instance of the lambda function to be called in each row.

◆ setColumnsWithoutReset()

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setColumnsWithoutReset ( IndexType columns )

virtual

Set number of columns of this matrix.

Unlike setDimensions, the storage is not reset in this operation. It is the user's responsibility to update the column indices stored in the matrix to be consistent with the new number of columns.

Parameters

columns is the number of matrix columns.

◆ setDimensions()

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setDimensions	(	IndexType	rows,
		IndexType	columns
	)

overridevirtual

Set number of rows and columns of this matrix.

Parameters

rows	is the number of matrix rows.
columns	is the number of matrix columns.

Reimplemented from TNL::Matrices::Matrix< double, Devices::Host, int, typename Allocators::Default< Devices::Host >::template Allocator< double > >.

◆ setElement()

__cuda_callable__ void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setElement	(	IndexType	row,
		IndexType	column,
		const RealType &	value
	)

Sets element at given row and column to given value.

Parameters

row	is row index of the element.
column	is columns index of the element.
value	is the value the element will be set to.

Example: #include <iostream>

#include <TNL/Algorithms/ParallelFor.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

#include <TNL/Pointers/SharedPointer.h>

#include <TNL/Pointers/SmartPointersRegister.h>

template< typename Device >

void setElements()

{

auto rowCapacities = { 1, 1, 1, 1, 1 };

TNL::Pointers::SharedPointer< TNL::Matrices::SparseMatrix< double, Device > > matrix( rowCapacities, 5 );

/***

* Calling the method setElements from host (CPU).

*/

for( int i = 0; i < 5; i++ )

matrix->setElement( i, i, i );

std::cout << "Matrix set from the host:" << std::endl;

std::cout << *matrix << std::endl;

/***

* This lambda function will run on the native device of the matrix which can be CPU or GPU.

*/

auto f = [=] __cuda_callable__ ( int i ) mutable {

matrix->setElement( i, i, -i );

};

/***

* For the case when Device is CUDA device we need to synchronize smart

* pointers. To avoid this you may use SparseMatrixView. See

* SparseMatrixView::getRow example for details.

*/

TNL::Pointers::synchronizeSmartPointersOnDevice< Device >();

TNL::Algorithms::ParallelFor< Device >::exec( 0, 5, f );

std::cout << "Matrix set from its native device:" << std::endl;

std::cout << *matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Set elements on host:" << std::endl;

setElements< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Set elements on CUDA device:" << std::endl;

setElements< TNL::Devices::Cuda >();

#endif

}

TNL::Matrices::SparseMatrix::setElements
void setElements(const std::initializer_list< std::tuple< IndexType, IndexType, RealType > > &data)
This method sets the sparse matrix elements from initializer list.
Definition: SparseMatrix.hpp:333

Output: Set elements on host:

Matrix set from the host:

Row: 0 ->

Row: 1 -> 1:1

Row: 2 -> 2:2

Row: 3 -> 3:3

Row: 4 -> 4:4

Matrix set from its native device:

Row: 0 ->

Row: 1 -> 1:-1

Row: 2 -> 2:-2

Row: 3 -> 3:-3

Row: 4 -> 4:-4

Set elements on CUDA device:

Matrix set from the host:

Row: 0 ->

Row: 1 -> 1:1

Row: 2 -> 2:2

Row: 3 -> 3:3

Row: 4 -> 4:4

Matrix set from its native device:

Row: 0 ->

Row: 1 -> 1:-1

Row: 2 -> 2:-2

Row: 3 -> 3:-3

Row: 4 -> 4:-4

◆ setElements() [1/2]

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setElements ( const std::initializer_list< std::tuple< IndexType, IndexType, RealType > > & data )

This method sets the sparse matrix elements from initializer list.

The number of matrix rows and columns must be set already. The matrix elements values are given as a list data of triples: { { row1, column1, value1 }, { row2, column2, value2 }, ... }.

Parameters

data	is a initializer list of initializer lists representing list of matrix rows.

Example: #include <iostream>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void setElementsExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5 ); // matrix dimensions

matrix.setElements( { // matrix elements definition

{ 0, 0, 2.0 },

{ 1, 0, -1.0 }, { 1, 1, 2.0 }, { 1, 2, -1.0 },

{ 2, 1, -1.0 }, { 2, 2, 2.0 }, { 2, 3, -1.0 },

{ 3, 2, -1.0 }, { 3, 3, 2.0 }, { 3, 4, -1.0 },

{ 4, 4, 2.0 } } );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Setting matrix elements on host: " << std::endl;

setElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Setting matrix elements on CUDA device: " << std::endl;

setElementsExample< TNL::Devices::Cuda >();

#endif

}

Output: Setting matrix elements on host:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

Setting matrix elements on CUDA device:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

◆ setElements() [2/2]

template<typename MapIndex , typename MapValue >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setElements ( const std::map< std::pair< MapIndex, MapIndex >, MapValue > & map )

This method sets the sparse matrix elements from std::map.

The matrix elements values are given as a map data where keys are std::pair of matrix coordinates ( {row, column} ) and value is the matrix element value.

Template Parameters

MapIndex	is a type for indexing rows and columns.
MapValue	is a type for matrix elements values in the map.

Parameters

map	is std::map containing matrix elements.

Example: #include <iostream>

#include <map>

#include <utility>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

template< typename Device >

void setElementsExample()

{

std::map< std::pair< int, int >, double > map;

map.insert( std::make_pair( std::make_pair( 0, 0 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 0 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 1 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 1, 2 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 1 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 2 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 2, 3 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 2 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 3 ), 2.0 ) );

map.insert( std::make_pair( std::make_pair( 3, 4 ), -1.0 ) );

map.insert( std::make_pair( std::make_pair( 4, 4 ), 2.0 ) );

TNL::Matrices::SparseMatrix< double, Device > matrix ( 5, 5 );

matrix.setElements( map );

std::cout << "General sparse matrix: " << std::endl << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrices on CPU ... " << std::endl;

setElementsExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrices on CUDA GPU ... " << std::endl;

setElementsExample< TNL::Devices::Cuda >();

#endif

}

Output: Creating matrices on CPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

Creating matrices on CUDA GPU ...

General sparse matrix:

Row: 0 -> 0:2

Row: 1 -> 0:-1 1:2 2:-1

Row: 2 -> 1:-1 2:2 3:-1

Row: 3 -> 2:-1 3:2 4:-1

Row: 4 -> 4:2

◆ setLike()

template<typename Matrix >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setLike ( const Matrix & matrix )

Set the number of matrix rows and columns by the given matrix.

Template Parameters

Matrix is matrix type. This can be any matrix having methods getRows and getColumns.

Parameters

matrix in the input matrix dimensions of which are to be adopted.

◆ setRowCapacities()

template<typename RowsCapacitiesVector >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::setRowCapacities ( const RowsCapacitiesVector & rowCapacities )

Allocates memory for non-zero matrix elements.

The size of the input vector must be equal to the number of matrix rows. The number of allocated matrix elements for each matrix row depends on the sparse matrix format. Some formats may allocate more elements than required.

Template Parameters

RowsCapacitiesVector is a type of vector/array used for row capacities setting.

Parameters

rowCapacities is a vector telling the number of required non-zero matrix elements in each row.

Example: #include <iostream>

#include <TNL/Containers/Vector.h>

#include <TNL/Matrices/SparseMatrix.h>

#include <TNL/Devices/Host.h>

#include <TNL/Devices/Cuda.h>

template< typename Device >

void setRowCapacitiesExample()

{

TNL::Matrices::SparseMatrix< double, Device > matrix( 5, 5 );

TNL::Containers::Vector< int, Device > rowCapacities{ 1, 2, 3, 4, 5 };

matrix.setRowCapacities( rowCapacities );

for( int row = 0; row < 5; row++ )

for( int column = 0; column <= row; column++ )

matrix.setElement( row, column, row - column + 1 );

std::cout << matrix << std::endl;

}

int main( int argc, char* argv[] )

{

std::cout << "Creating matrix on CPU ... " << std::endl;

setRowCapacitiesExample< TNL::Devices::Host >();

#ifdef HAVE_CUDA

std::cout << "Creating matrix on CUDA GPU ... " << std::endl;

setRowCapacitiesExample< TNL::Devices::Cuda >();

#endif

}

TNL::Containers::Array::setElement
__cuda_callable__ void setElement(IndexType i, ValueType value)
Sets the value of the i-th element to v.
Definition: Array.hpp:356

Output: Creating matrix on CPU ...

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

Creating matrix on CUDA GPU ...

Row: 0 -> 0:1

Row: 1 -> 0:2 1:1

Row: 2 -> 0:3 1:2 2:1

Row: 3 -> 0:4 1:3 2:2 3:1

Row: 4 -> 0:5 1:4 2:3 3:2 4:1

◆ vectorProduct()

template<typename InVector , typename OutVector >

void TNL::Matrices::SparseMatrix< Real, Device, Index, MatrixType, Segments, ComputeReal, RealAllocator, IndexAllocator >::vectorProduct	(	const InVector &	inVector,
		OutVector &	outVector,
		ComputeRealType	matrixMultiplicator = `1.0`,
		ComputeRealType	outVectorMultiplicator = `0.0`,
		IndexType	begin = `0`,
		IndexType	end = `0`
	)		const

Computes product of matrix and vector.

More precisely, it computes:

outVector = matrixMultiplicator * ( * this ) * inVector + outVectorMultiplicator * outVector

Template Parameters

InVector	is type of input vector. It can be TNL::Containers::Vector, TNL::Containers::VectorView, TNL::Containers::Array, TNL::Containers::ArrayView, or similar container.
OutVector	is type of output vector. It can be TNL::Containers::Vector, TNL::Containers::VectorView, TNL::Containers::Array, TNL::Containers::ArrayView, or similar container.

Parameters

inVector	is input vector.
outVector	is output vector.
matrixMultiplicator	is a factor by which the matrix is multiplied. It is one by default.
outVectorMultiplicator	is a factor by which the outVector is multiplied before added to the result of matrix-vector product. It is zero by default.
begin	is the beginning of the rows range for which the vector product is computed. It is zero by default.
end	is the end of the rows range for which the vector product is computed. It is number if the matrix rows by default.

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

src/TNL/Matrices/SparseMatrix.h
src/TNL/Matrices/SparseMatrix.hpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ ConstViewType

◆ ViewType

Constructor & Destructor Documentation

◆ SparseMatrix() [1/8]

◆ SparseMatrix() [2/8]

◆ SparseMatrix() [3/8]

◆ SparseMatrix() [4/8]

◆ SparseMatrix() [5/8]

◆ SparseMatrix() [6/8]

◆ SparseMatrix() [7/8]

◆ SparseMatrix() [8/8]

Member Function Documentation

◆ addElement()

◆ forAllElements() [1/2]

◆ forAllElements() [2/2]

◆ forAllRows() [1/2]

◆ forAllRows() [2/2]

◆ forElements() [1/2]

◆ forElements() [2/2]

◆ forRows() [1/2]

◆ forRows() [2/2]

◆ getColumnIndexes() [1/2]

◆ getColumnIndexes() [2/2]

◆ getCompressedRowLengths()

◆ getConstView()

◆ getElement()

◆ getNonzeroElementsCount()

◆ getPaddingIndex()

◆ getRow() [1/2]

◆ getRow() [2/2]

◆ getRowCapacities()

◆ getRowCapacity()

◆ getSegments() [1/2]

◆ getSegments() [2/2]

◆ getSerializationType()

◆ getSerializationTypeVirtual()

◆ getView()

◆ isBinary()

◆ isSymmetric()

◆ load() [1/2]

◆ load() [2/2]

◆ operator!=()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator==()

◆ print()

◆ reduceAllRows() [1/2]

◆ reduceAllRows() [2/2]

◆ reduceRows() [1/2]

◆ reduceRows() [2/2]

◆ save() [1/2]

◆ save() [2/2]

◆ sequentialForAllRows() [1/2]

◆ sequentialForAllRows() [2/2]

◆ sequentialForRows() [1/2]

◆ sequentialForRows() [2/2]

◆ setColumnsWithoutReset()

◆ setDimensions()

◆ setElement()

◆ setElements() [1/2]

◆ setElements() [2/2]

◆ setLike()

◆ setRowCapacities()

◆ vectorProduct()