TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > Class Template Reference

Implementation of sparse matrix view. More...

#include <TNL/Matrices/SparseMatrixBase.h>

Inheritance diagram for TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >:

Collaboration diagram for TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >:

Public Types
using	ColumnIndexesViewType
using	ComputeRealType = ComputeReal
using	ConstRowView = typename RowView::ConstRowView
	Type for accessing constant matrix rows.
using	DefaultSegmentsReductionKernel = typename Algorithms::SegmentsReductionKernels::DefaultKernel< SegmentsView >::type
	Type of the kernel used for parallel reductions on segments.
using	DeviceType = Device
	The device where the matrix is allocated.
using	IndexType = Index
	The type used for matrix elements indexing.
using	RealType = typename Base::RealType
	The type of matrix elements.
using	RowView
	Type for accessing matrix rows.
using	SegmentsViewType = SegmentsView
	Type of segments view used by this matrix. It represents the sparse matrix format.
Public Types inherited from TNL::Matrices::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >
using	ConstValuesViewType
	Type of constant vector view holding values of matrix elements.
using	DeviceType
	The device where the matrix is allocated.
using	IndexType
	The type used for matrix elements indexing.
using	RealType
	The type of matrix elements.
using	RowCapacitiesType
using	ValuesViewType
	Type of vector view holding values of matrix elements.

Public Member Functions
__cuda_callable__	SparseMatrixBase ()=default
	Constructor with no parameters.
__cuda_callable__	SparseMatrixBase (const SparseMatrixBase &matrix)=default
	Copy constructor.
__cuda_callable__	SparseMatrixBase (IndexType rows, IndexType columns, typename Base::ValuesViewType values, ColumnIndexesViewType columnIndexes, SegmentsViewType segments)
	Constructor with all necessary data and views.
__cuda_callable__	SparseMatrixBase (SparseMatrixBase &&matrix) noexcept=default
	Move constructor.
__cuda_callable__ void	addElement (IndexType row, IndexType column, const RealType &value, const RealType &thisElementMultiplicator=1.0)
	Add element at given row and column to given value.
__cuda_callable__ IndexType	findElement (IndexType row, IndexType column) const
	Finds element in the matrix and returns its position in the arrays with values and columnIndexes.
template<typename Function >
void	forAllElements (Function &&function)
	This method calls forElements for all matrix rows.
template<typename Function >
void	forAllElements (Function &&function) const
	This method calls forElements for all matrix rows (for constant instances).
template<typename Function >
void	forAllRows (Function &&function)
	Method for parallel iteration over all matrix rows.
template<typename Function >
void	forAllRows (Function &&function) const
	Method for parallel iteration over all matrix rows for constant instances.
template<typename Function >
void	forElements (IndexType begin, IndexType end, Function &&function)
	Method for iteration over all matrix rows for non-constant instances.
template<typename Function >
void	forElements (IndexType begin, IndexType end, Function &&function) const
	Method for iteration over all matrix rows for constant instances.
template<typename Function >
void	forRows (IndexType begin, IndexType end, Function &&function)
	Method for parallel iteration over matrix rows from interval [begin, end).
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.
ColumnIndexesViewType &	getColumnIndexes ()
	Getter of column indexes for nonconstant instances.
const ColumnIndexesViewType &	getColumnIndexes () const
	Getter of column indexes for constant instances.
template<typename Vector >
void	getCompressedRowLengths (Vector &rowLengths) const
	Computes number of non-zeros in each row.
__cuda_callable__ RealType	getElement (IndexType row, IndexType column) const
	Returns value of matrix element at position given by its row and column index.
IndexType	getNonzeroElementsCount () const override
	Returns number of non-zero matrix elements.
__cuda_callable__ RowView	getRow (IndexType rowIdx)
	Non-constant getter of simple structure for accessing given matrix row.
__cuda_callable__ ConstRowView	getRow (IndexType rowIdx) const
	Constant getter of simple structure for accessing given matrix row.
template<typename Vector >
void	getRowCapacities (Vector &rowCapacities) const
	Compute capacities of all rows.
__cuda_callable__ IndexType	getRowCapacity (IndexType row) const
	Returns capacity of given matrix row.
SegmentsViewType &	getSegments ()
	Getter of segments for non-constant instances.
const SegmentsViewType &	getSegments () const
	Getter of segments for constant instances.
template<typename Matrix >
bool	operator!= (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type.
SparseMatrixBase &	operator= (const SparseMatrixBase &)=delete
	Copy-assignment operator.
SparseMatrixBase &	operator= (SparseMatrixBase &&)=delete
	Move-assignment operator.
template<typename Matrix >
bool	operator== (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix type.
void	print (std::ostream &str) const
	Method for printing the matrix to output stream.
template<typename Fetch , typename Reduce , typename Keep , typename FetchValue , typename SegmentsReductionKernel = DefaultSegmentsReductionKernel>
void	reduceAllRows (Fetch &&fetch, const Reduce &reduce, Keep &&keep, const FetchValue &identity, const SegmentsReductionKernel &kernel=SegmentsReductionKernel{}) const
	Method for performing general reduction on all matrix rows for constant instances.
template<typename Fetch , typename Reduce , typename Keep , typename FetchValue , typename SegmentsReductionKernel = DefaultSegmentsReductionKernel>
void	reduceRows (IndexType begin, IndexType end, Fetch &&fetch, const Reduce &reduce, Keep &&keep, const FetchValue &identity, const SegmentsReductionKernel &kernel=SegmentsReductionKernel{}) const
	Method for performing general reduction on matrix rows for constant instances.
template<typename Function >
void	sequentialForAllRows (Function &&function)
	This method calls sequentialForRows for all matrix rows.
template<typename Function >
void	sequentialForAllRows (Function &&function) const
	This method calls sequentialForRows for all matrix rows (for constant instances).
template<typename Function >
void	sequentialForRows (IndexType begin, IndexType end, Function &&function)
	Method for sequential iteration over all matrix rows for non-constant instances.
template<typename Function >
void	sequentialForRows (IndexType begin, IndexType end, Function &&function) const
	Method for sequential iteration over all matrix rows for constant instances.
__cuda_callable__ void	setElement (IndexType row, IndexType column, const RealType &value)
	Sets element at given row and column to given value.
void	sortColumnIndexes ()
	Sort matrix elements in each row by column indexes in ascending order.
template<typename InVector , typename OutVector >
void	transposedVectorProduct (const InVector &inVector, OutVector &outVector, ComputeReal matrixMultiplicator=1.0, ComputeReal outVectorMultiplicator=0.0, Index begin=0, Index end=0) const
	Computes product of transposed matrix and vector.
template<typename InVector , typename OutVector , typename SegmentsReductionKernel = DefaultSegmentsReductionKernel>
void	vectorProduct (const InVector &inVector, OutVector &outVector, ComputeRealType matrixMultiplicator=1.0, ComputeRealType outVectorMultiplicator=0.0, IndexType begin=0, IndexType end=0, const SegmentsReductionKernel &kernel=SegmentsReductionKernel{}) const
	Computes product of matrix and vector.
template<typename InVector , typename OutVector , typename SegmentsReductionKernel , typename... , std::enable_if_t< ! std::is_convertible_v< SegmentsReductionKernel, ComputeRealType >, bool > = true>
void	vectorProduct (const InVector &inVector, OutVector &outVector, const SegmentsReductionKernel &kernel) const
Public Member Functions inherited from TNL::Matrices::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >
__cuda_callable__	MatrixBase ()=default
	Basic constructor with no parameters.
__cuda_callable__	MatrixBase (const MatrixBase &view)=default
	Shallow copy constructor.
__cuda_callable__	MatrixBase (IndexType rows, IndexType columns, ValuesViewType values)
	Constructor with matrix dimensions and matrix elements values.
__cuda_callable__	MatrixBase (MatrixBase &&view) noexcept=default
	Move constructor.
IndexType	getAllocatedElementsCount () const
	Tells the number of allocated matrix elements.
__cuda_callable__ IndexType	getColumns () const
	Returns number of matrix columns.
__cuda_callable__ IndexType	getRows () const
	Returns number of matrix rows.
__cuda_callable__ ValuesViewType &	getValues ()
	Returns a reference to a vector with the matrix elements values.
__cuda_callable__ const ValuesViewType &	getValues () const
	Returns a constant reference to a vector with the matrix elements values.
bool	operator!= (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix view type.
bool	operator!= (const MatrixT &matrix) const
__cuda_callable__ MatrixBase &	operator= (const MatrixBase &)=delete
	Copy-assignment operator.
__cuda_callable__ MatrixBase &	operator= (MatrixBase &&)=delete
	Move-assignment operator.
bool	operator== (const Matrix &matrix) const
	Comparison operator with another arbitrary matrix view type.
bool	operator== (const MatrixT &matrix) const

Static Public Member Functions
static std::string	getSerializationType ()
	Returns string with serialization type.
Static Public Member Functions inherited from TNL::Matrices::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >
static constexpr ElementsOrganization	getOrganization ()
	Matrix elements organization getter.
static constexpr bool	isBinary ()
	Test of binary matrix type.
static constexpr bool	isSymmetric ()
	Test of symmetric matrix type.

Protected Member Functions
__cuda_callable__ void	bind (IndexType rows, IndexType columns, typename Base::ValuesViewType values, ColumnIndexesViewType columnIndexes, SegmentsViewType segments)
	Re-initializes the internal attributes of the base class.
Protected Member Functions inherited from TNL::Matrices::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >
__cuda_callable__ void	bind (IndexType rows, IndexType columns, ValuesViewType values)
	Re-initializes the internal attributes of the base class.

Protected Attributes
ColumnIndexesViewType	columnIndexes
SegmentsViewType	segments
Protected Attributes inherited from TNL::Matrices::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >
IndexType	columns
IndexType	rows
ValuesViewType	values

Detailed Description

template<typename Real, typename Device, typename Index, typename MatrixType, typename SegmentsView, typename ComputeReal>
class TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >

Implementation of sparse matrix view.

It serves as an accessor to SparseMatrix for example when passing the matrix to lambda functions. SparseMatrix view can be also created in CUDA kernels.

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.

Member Typedef Documentation

ColumnIndexesViewType

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

using TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::ColumnIndexesViewType

Initial value:

 
      Containers::VectorView< typename TNL::copy_const< Index >::template from< Real >::type, Device, Index >

DefaultSegmentsReductionKernel

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

using TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::DefaultSegmentsReductionKernel = typename Algorithms::SegmentsReductionKernels::DefaultKernel< SegmentsView >::type

Type of the kernel used for parallel reductions on segments.

We are assuming that the default segments reduction kernel provides a static reduceAllSegments method, and thus it does not have to be instantiated and initialized. If the user wants to use a more complicated kernel, such as CSRAdaptive, it must be instantiated and initialized by the user and the object must be passed to the vectorProduct or reduceRows method.

RowView

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

using TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::RowView

Initial value:

 
      SparseMatrixRowView< typename SegmentsViewType::SegmentViewType, typename Base::ValuesViewType, ColumnIndexesViewType >

Type for accessing matrix rows.

Constructor & Destructor Documentation

SparseMatrixBase() [1/3]

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

__cuda_callable__ TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::SparseMatrixBase	(	IndexType	rows,
		IndexType	columns,
		typename Base::ValuesViewType	values,
		ColumnIndexesViewType	columnIndexes,
		SegmentsViewType	segments )

Constructor with all necessary data and views.

Parameters

rows	is a number of matrix rows.
columns	is a number of matrix columns.
values	is a vector view with matrix elements values.
columnIndexes	is a vector view with matrix elements column indexes.
segments	is a segments view representing the sparse matrix format.

SparseMatrixBase() [2/3]

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

__cuda_callable__ TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::SparseMatrixBase ( const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > & matrix )

default

Copy constructor.

Parameters

matrix

is an input sparse matrix view.

SparseMatrixBase() [3/3]

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

__cuda_callable__ TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::SparseMatrixBase ( SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > && matrix )

defaultnoexcept

Move constructor.

Parameters

matrix

is an input sparse matrix view.

Member Function Documentation

addElement()

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

__cuda_callable__ void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::addElement	(	IndexType	row,
		IndexType	column,
		const RealType &	value,
		const RealType &	thisElementMultiplicator = 1.0 )

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 );
   auto matrixView = matrix.getView();
 
   for( int i = 0; i < 5; i++ )
      matrixView.setElement( i, i, i );  // or matrix.setElement
 
   std::cout << "Initial matrix is: " << std::endl << matrix << std::endl;
 
   for( int i = 0; i < 5; i++ )
      for( int j = 0; j < 5; j++ )
         matrixView.addElement( i, j, 1.0, 5.0 );  // or matrix.addElement
 
   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 __CUDACC__
   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  
 

bind()

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

__cuda_callable__ void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::bind ( IndexType rows, IndexType columns, typename Base::ValuesViewType values, ColumnIndexesViewType columnIndexes, SegmentsViewType segments )

protected

Re-initializes the internal attributes of the base class.

Note that this function is protected to ensure that the user cannot modify the base class of a matrix. For the same reason, in future code development we also need to make sure that all non-const functions in the base class return by value and not by reference.

findElement()

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

__cuda_callable__ Index TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::findElement ( IndexType row, IndexType column ) const

nodiscard

Finds element in the matrix and returns its position in the arrays with values and columnIndexes.

If the element is not found, the method returns the padding index.

Parameters

row	is the row index of the element.
column	is the column index of the element.

Returns

the position of the element in the arrays with values and columnIndexes or the padding index if the element is not found.

forAllElements() [1/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::forAllElements

(

Function &&

function

)

This method calls forElements for all matrix rows.

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 in each row.

Example

#include <iostream>
#include <TNL/Matrices/SparseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forAllElementsExample()
{
   TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 2, 3, 4, 5 }, 5 );
   auto matrixView = matrix.getView();
 
   auto f = [] __cuda_callable__( int rowIdx, int localIdx, int& columnIdx, double& value )
   {
      // This is important, some matrix formats may allocate more matrix elements
      // than we requested. These padding elements are processed here as well.
      if( rowIdx >= localIdx ) {
         columnIdx = localIdx;
         value = rowIdx + localIdx + 1;
      }
   };
 
   matrixView.forAllElements( f );  // or matrix.forAllElements
   std::cout << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating matrix on host: " << std::endl;
   forAllElementsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating matrix on CUDA device: " << std::endl;
   forAllElementsExample< 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   
 

forAllElements() [2/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::forAllElements

(

Function &&

function

)

const

This method calls forElements for all matrix rows (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 in each row.

forAllRows() [1/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 SparseMatrixBase::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::SparseMatrixBase::RowView.

Example

#include <iostream>
#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 >;
   using RowView = typename MatrixType::RowView;
   MatrixType matrix( { 1, 3, 3, 3, 1 }, size );
   auto matrixView = matrix.getView();
 
   /***
    * Set the matrix elements.
    */
   auto f = [] __cuda_callable__( RowView & row )
   {
      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
      }
   };
   matrixView.forAllRows( f );  // or matrix.forAllRows
   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 )
      {
         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 __CUDACC__
   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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 SparseMatrixBase::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__ ( const ConstRowView& row ) { ... };

ConstRowView represents matrix row - see TNL::Matrices::SparseMatrixBase::ConstRowView.

forElements() [1/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::forElements	(	IndexType	begin,
		IndexType	end,
		Function &&	function )

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

Template Parameters

Function

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

auto function = [] __cuda_callable__ ( IndexType rowIdx, IndexType localIdx, IndexType& columnIdx, RealType& value )
{ ... };

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

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.

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 matrixView = matrix.getView();
 
   auto f = [] __cuda_callable__( int rowIdx, int localIdx, int& columnIdx, double& value )
   {
      // This is important, some matrix formats may allocate more matrix elements
      // than we requested. These padding elements are processed here as well.
      if( rowIdx >= localIdx ) {
         columnIdx = localIdx;
         value = rowIdx + localIdx + 1;
      }
   };
 
   matrixView.forElements( 0, matrix.getRows(), f );  // or matrix.forElements
   std::cout << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating matrix on host: " << std::endl;
   forElementsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::forElements	(	IndexType	begin,
		IndexType	end,
		Function &&	function ) const

Method for iteration over all matrix rows for constant instances.

Template Parameters

Function

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

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

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

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.

forRows() [1/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 SparseMatrixBase::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::SparseMatrixBase::RowView.

Example

#include <iostream>
#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 >;
   using RowView = typename MatrixType::RowView;
   MatrixType matrix( { 1, 3, 3, 3, 1 }, size );
   auto matrixView = matrix.getView();
 
   /***
    * Set the matrix elements.
    */
   auto f = [] __cuda_callable__( RowView & row )
   {
      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
      }
   };
   matrixView.forAllRows( f );  // or matrix.forAllRows
   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 )
      {
         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 __CUDACC__
   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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 SparseMatrixBase::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__ ( const ConstRowView& row ) { ... };

ConstRowView represents matrix row - see TNL::Matrices::SparseMatrixBase::ConstRowView.

getColumnIndexes() [1/2]

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

auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getColumnIndexes ( )

nodiscard

Getter of column indexes for nonconstant instances.

Returns

Reference to a vector with matrix elements column indexes.

getColumnIndexes() [2/2]

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

auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getColumnIndexes ( ) const

nodiscard

Getter of column indexes for constant instances.

Returns

Constant reference to a vector with matrix elements column indexes.

getCompressedRowLengths()

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

template<typename Vector >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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( {
      // clang-format off
      { 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 }
      // clang-format on
   } );
 
   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 __CUDACC__
   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 ]

getElement()

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

__cuda_callable__ auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getElement ( IndexType row, IndexType column ) const

nodiscard

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

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.

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(
      // number of matrix rows
      5,
      // number of matrix columns
      5,
      // matrix elements definition
      {
         // clang-format off
         { 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 }
         // clang-format on
      } );
 
   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 __CUDACC__
   std::cout << "Get elements on CUDA device:" << std::endl;
   getElements< TNL::Devices::Cuda >();
#endif
}

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()

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

Index TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getNonzeroElementsCount ( ) const

nodiscardoverridevirtual

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::MatrixBase< Real, Device, Index, MatrixType, SegmentsView::getOrganization() >.

getRow() [1/2]

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

__cuda_callable__ auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getRow ( IndexType rowIdx )

nodiscard

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>
 
template< typename Device >
void
getRowExample()
{
   /***
    * Set the following matrix (dots represent zero matrix elements):
    *
    *   /  2  .  .  .  . \
    *   |  1  2  1  .  . |
    *   |  .  1  2  1. . |
    *   |  .  .  1  2  1 |
    *   \  .  .  .  .  2 /
    */
   const int size = 5;
   TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 3, 3, 3, 1 }, size );
   auto view = matrix.getView();
 
   /***
    * Set the matrix elements.
    */
   auto f = [ = ] __cuda_callable__( int rowIdx ) mutable
   {
      auto row = view.getRow( rowIdx );
      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
      }
   };
   TNL::Algorithms::parallelFor< Device >( 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 __CUDACC__
   std::cout << "Getting matrix rows on CUDA device: " << std::endl;
   getRowExample< 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   
 
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   
 

See SparseMatrixRowView.

getRow() [2/2]

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

__cuda_callable__ auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getRow ( IndexType rowIdx ) const

nodiscard

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/Matrices/SparseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
getRowExample()
{
   TNL::Matrices::SparseMatrix< double, Device > matrix(
      //
      5,
      5,
      {
         // clang-format off
         { 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 }
         // clang-format on
      } );
   const auto matrixView = matrix.getView();
 
   /***
    * Fetch lambda function returns diagonal element in each row.
    */
   auto fetch = [ = ] __cuda_callable__( int rowIdx ) -> double
   {
      auto row = matrixView.getRow( rowIdx );
      return row.getValue( rowIdx );
   };
 
   /***
    * 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 __CUDACC__
   std::cout << "Getting matrix rows on CUDA device: " << std::endl;
   getRowExample< TNL::Devices::Cuda >();
#endif
}

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

template<typename Vector >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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()

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

__cuda_callable__ Index TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getRowCapacity ( IndexType row ) const

nodiscard

Returns capacity of given matrix row.

Parameters

row	index of matrix row.

Returns

number of matrix elements allocated for the row.

getSegments() [1/2]

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

auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getSegments ( )

nodiscard

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]

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

auto TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getSegments ( ) const

nodiscard

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()

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

std::string TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::getSerializationType ( )

staticnodiscard

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 __CUDACC__
   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< int >, [any_device], int, General, [any_allocator], [any_allocator] >Get serialization type on CUDA GPU ... 
Matrix type is: Matrices::SparseMatrix< double, CSR< int >, [any_device], int, General, [any_allocator], [any_allocator] >

operator!=()

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

template<typename Matrix >

bool TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::operator!= ( const Matrix & matrix ) const

nodiscard

Comparison operator with another arbitrary matrix type.

Parameters

matrix

is the right-hand side matrix.

Returns

false if the RHS matrix is equal, true otherwise.

operator=()

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

SparseMatrixBase & TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::operator= ( const SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal > & )

delete

Copy-assignment operator.

It is a deleted function, because sparse matrix assignment in general requires reallocation.

operator==()

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

template<typename Matrix >

bool TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::operator== ( const Matrix & matrix ) const

nodiscard

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()

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

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::print

(

std::ostream &

str

)

const

Method for printing the matrix to output stream.

Parameters

str	is the output stream.

reduceAllRows()

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

template<typename Fetch , typename Reduce , typename Keep , typename FetchValue , typename SegmentsReductionKernel >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::reduceAllRows	(	Fetch &&	fetch,
		const Reduce &	reduce,
		Keep &&	keep,
		const FetchValue &	identity,
		const SegmentsReductionKernel &	kernel = SegmentsReductionKernel{} ) 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__ ( IndexType rowIdx, const RealType& 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.
kernel	is an instance of the segments reduction kernel to be used for the operation.

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(
      // number of matrix rows
      5,
      // number of matrix columns
      5,
      // matrix elements definition
      {
         // clang-format off
         { 0, 0, 1 },
         { 1, 1, 1 }, { 1, 2, 8 },
         { 2, 2, 1 }, { 2, 3, 9 },
         { 3, 3, 1 }, { 3, 4, 9 },
         { 4, 4, 1 }
         // clang-format on
      } );
 
   /***
    * 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 __CUDACC__
   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()

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

template<typename Fetch , typename Reduce , typename Keep , typename FetchValue , typename SegmentsReductionKernel >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::reduceRows	(	IndexType	begin,
		IndexType	end,
		Fetch &&	fetch,
		const Reduce &	reduce,
		Keep &&	keep,
		const FetchValue &	identity,
		const SegmentsReductionKernel &	kernel = SegmentsReductionKernel{} ) 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__ ( IndexType rowIdx, const RealType& 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.
kernel	is an instance of the segments reduction kernel to be used for the operation.

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(
      // number of matrix rows
      5,
      // number of matrix columns
      5,
      // matrix elements definition
      {
         // clang-format off
         { 0, 0, 1 },
         { 1, 1, 1 }, { 1, 2, 8 },
         { 2, 2, 1 }, { 2, 3, 9 },
         { 3, 3, 1 }, { 3, 4, 9 },
         { 4, 4, 1 }
         // clang-format on
      } );
 
   /***
    * 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 __CUDACC__
   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 ]

sequentialForAllRows() [1/2]

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

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::sequentialForAllRows

(

Function &&

function

)

This method calls sequentialForRows for all matrix rows.

See SparseMatrixBase::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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::sequentialForAllRows

(

Function &&

function

)

const

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

See SparseMatrixBase::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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 should have form like

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

RowView represents matrix row - see TNL::Matrices::SparseMatrixBase::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 Real , typename Device , typename Index , typename MatrixType , typename SegmentsView , typename ComputeReal >

template<typename Function >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::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 should have form like

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

ConstRowView represents matrix row - see TNL::Matrices::SparseMatrixBase::ConstRowView.

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.

setElement()

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

__cuda_callable__ void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::setElement	(	IndexType	row,
		IndexType	column,
		const RealType &	value )

Sets 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.

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
setElements()
{
   TNL::Matrices::SparseMatrix< double, Device > matrix( { 1, 1, 1, 1, 1 }, 5 );
 
   /****
    * Get the matrix view.
    */
   auto view = matrix.getView();
   for( int i = 0; i < 5; i++ )
      view.setElement( i, i, i );
 
   std::cout << "Matrix set from the host:" << std::endl;
   std::cout << matrix << std::endl;
 
   auto f = [ = ] __cuda_callable__( int i ) mutable
   {
      view.setElement( i, i, -i );
   };
 
   TNL::Algorithms::parallelFor< Device >( 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 __CUDACC__
   std::cout << "Set elements on CUDA device:" << std::endl;
   setElements< TNL::Devices::Cuda >();
#endif
}

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  
 

transposedVectorProduct()

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

template<typename InVector , typename OutVector >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::transposedVectorProduct	(	const InVector &	inVector,
		OutVector &	outVector,
		ComputeReal	matrixMultiplicator = 1.0,
		ComputeReal	outVectorMultiplicator = 0.0,
		Index	begin = 0,
		Index	end = 0 ) const

Computes product of transposed matrix and vector.

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
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.

vectorProduct()

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

template<typename InVector , typename OutVector , typename SegmentsReductionKernel >

void TNL::Matrices::SparseMatrixBase< Real, Device, Index, MatrixType, SegmentsView, ComputeReal >::vectorProduct	(	const InVector &	inVector,
		OutVector &	outVector,
		ComputeRealType	matrixMultiplicator = 1.0,
		ComputeRealType	outVectorMultiplicator = 0.0,
		IndexType	begin = 0,
		IndexType	end = 0,
		const SegmentsReductionKernel &	kernel = SegmentsReductionKernel{} ) 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.
kernel	is an instance of the segments reduction kernel to be used for the operation.

---

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

• src/TNL/Matrices/SparseMatrixBase.h
• src/TNL/Matrices/SparseMatrixBase.hpp