TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization > Class Template Reference

A common base class for TridiagonalMatrix and TridiagonalMatrixView. More...

#include <TNL/Matrices/TridiagonalMatrixBase.h>

Inheritance diagram for TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >:

Collaboration diagram for TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >:

Public Types
using	ConstRowView = typename RowView::ConstRowView
	Type for accessing constant matrix rows.
using	DeviceType = Device
	The device where the matrix is allocated.
using	IndexerType = details::TridiagonalMatrixIndexer< Index, Organization >
using	IndexType = Index
	The type used for matrix elements indexing.
using	RealType = typename Base::RealType
	The type of matrix elements.
using	RowView = TridiagonalMatrixRowView< typename Base::ValuesViewType, IndexerType >
	Type for accessing matrix rows.
Public Types inherited from TNL::Matrices::MatrixBase< Real, Device, Index, GeneralMatrix, Organization >
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__	TridiagonalMatrixBase ()=default
	Constructor with no parameters.
__cuda_callable__	TridiagonalMatrixBase (const TridiagonalMatrixBase &)=default
	Copy constructor.
__cuda_callable__	TridiagonalMatrixBase (TridiagonalMatrixBase &&) noexcept=default
	Move constructor.
__cuda_callable__	TridiagonalMatrixBase (typename Base::ValuesViewType values, IndexerType indexer)
	Constructor with all necessary data and views.
__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.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_>
void	addMatrix (const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &matrix, const RealType &matrixMultiplicator=1.0, const RealType &thisMatrixMultiplicator=1.0)
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.
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.
__cuda_callable__ IndexerType &	getIndexer ()
	This method returns matrix elements indexer used by this matrix.
__cuda_callable__ const IndexerType &	getIndexer () const
	This method returns matrix elements indexer used by this matrix.
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.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_>
bool	operator!= (const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &matrix) const
	Comparison operator with another multidiagonal matrix.
TridiagonalMatrixBase &	operator= (const TridiagonalMatrixBase &)=delete
	Copy-assignment operator.
TridiagonalMatrixBase &	operator= (TridiagonalMatrixBase &&)=delete
	Move-assignment operator.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_>
bool	operator== (const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &matrix) const
	Comparison operator with another tridiagonal matrix.
void	print (std::ostream &str) const
	Method for printing the matrix to output stream.
template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceAllRows (Fetch &fetch, Reduce &reduce, Keep &keep, const FetchReal &identity) const
	Method for performing general reduction on all matrix rows for constant instances.
template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceRows (IndexType begin, IndexType end, Fetch &fetch, Reduce &reduce, Keep &keep, const FetchReal &identity) 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	setValue (const RealType &value)
	Set all matrix elements to given value.
template<typename InVector , typename OutVector >
void	vectorProduct (const InVector &inVector, OutVector &outVector, RealType matrixMultiplicator=1.0, RealType outVectorMultiplicator=0.0, IndexType begin=0, IndexType end=0) const
	Computes product of matrix and vector.
Public Member Functions inherited from TNL::Matrices::MatrixBase< Real, Device, Index, GeneralMatrix, Organization >
__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, GeneralMatrix, Organization >
static constexpr ElementsOrganization	getOrganization ()
	Matrix elements organization getter.
static constexpr bool	isBinary ()
	Test of binary matrix type.
static constexpr bool	isMatrix ()
	Test of matrix type.
static constexpr bool	isSymmetric ()
	Test of symmetric matrix type.

Protected Member Functions
__cuda_callable__ void	bind (typename Base::ValuesViewType values, IndexerType indexer)
	Re-initializes the internal attributes of the base class.
__cuda_callable__ IndexType	getElementIndex (IndexType row, IndexType column) const
Protected Member Functions inherited from TNL::Matrices::MatrixBase< Real, Device, Index, GeneralMatrix, Organization >
__cuda_callable__ void	bind (IndexType rows, IndexType columns, ValuesViewType values)
	Re-initializes the internal attributes of the base class.

Protected Attributes
IndexerType	indexer
Protected Attributes inherited from TNL::Matrices::MatrixBase< Real, Device, Index, GeneralMatrix, Organization >
IndexType	columns
IndexType	rows
ValuesViewType	values

Detailed Description

template<typename Real, typename Device, typename Index, ElementsOrganization Organization>
class TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >

A common base class for TridiagonalMatrix and TridiagonalMatrixView.

Template Parameters

Real	is a type of matrix elements.
Device	is a device where the matrix is allocated.
Index	is a type for indexing of the matrix elements.
Organization	tells the ordering of matrix elements. It is either RowMajorOrder or ColumnMajorOrder.

Constructor & Destructor Documentation

TridiagonalMatrixBase()

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

__cuda_callable__ TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::TridiagonalMatrixBase	(	typename Base::ValuesViewType	values,
		IndexerType	indexer )

Constructor with all necessary data and views.

Parameters

values	is a vector view with matrix elements values
indexer	is an indexer of matrix elements

Member Function Documentation

addElement()

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

__cuda_callable__ void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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. TridiagonalMatrix::getRow or TridiagonalMatrix::forElements and TridiagonalMatrix::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
 
template< typename Device >
void
addElements()
{
   const int matrixSize( 5 );
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( matrixSize,  // number of rows
                                                              matrixSize   // number of columns
   );
   auto view = matrix.getView();
 
   for( int i = 0; i < matrixSize; i++ )
      view.setElement( i, i, i );  // or matrix.setElement
 
   std::cout << "Initial matrix is: " << std::endl << matrix << std::endl;
 
   for( int i = 0; i < matrixSize; i++ ) {
      if( i > 0 )
         view.addElement( i, i - 1, 1.0, 5.0 );  // or matrix.addElement
      view.addElement( i, i, 1.0, 5.0 );         // or matrix.addElement
      if( i < matrixSize - 1 )
         view.addElement( i, i + 1, 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   
Row: 1 ->     0:1       1:6       2:1   
Row: 2 ->     1:1       2:11      3:1   
Row: 3 ->     2:1       3:16      4:1   
Row: 4 ->     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   
Row: 1 ->     0:1       1:6       2:1   
Row: 2 ->     1:1       2:11      3:1   
Row: 3 ->     2:1       3:16      4:1   
Row: 4 ->     3:1       4:21  
 

bind()

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

__cuda_callable__ void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::bind ( typename Base::ValuesViewType values, IndexerType indexer )

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.

forAllElements() [1/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::forAllElements

(

Function &

function

)

This method calls forElements for all matrix rows.

See TridiagonalMatrix::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forAllElementsExample()
{
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    * 0 / 1  3  .  .  . \   -> { 0, 1, 3 }
    *   | 2  1  3  .  . |   -> { 2, 1, 3 }
    *   | .  2  1  3  . |   -> { 2, 1, 3 }
    *   | .  .  2  1  3 |   -> { 2, 1, 3 }
    *   \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( 5,    // number of matrix rows
                                                              5 );  // number of matrix columns
   auto view = matrix.getView();
 
   auto f = [] __cuda_callable__( int rowIdx, int localIdx, int columnIdx, double& value )
   {
      /***
       * 'forElements' method iterates only over matrix elements lying on given subdiagonals
       * and so we do not need to check anything. The element value can be expressed
       * by the 'localIdx' variable, see the following figure:
       *
       *                           0  1  2  <- localIdx values
       *                           -------
       * 0 / 1  3  .  .  . \   -> { 0, 1, 3 }
       *   | 2  1  3  .  . |   -> { 2, 1, 3 }
       *   | .  2  1  3  . |   -> { 2, 1, 3 }
       *   | .  .  2  1  3 |   -> { 2, 1, 3 }
       *   \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
       *
       */
      value = 3 - localIdx;
   };
   view.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 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 
Creating matrix on CUDA device: 
Row: 0 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 

forAllElements() [2/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::forAllElements

(

Function &

function

)

const

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

See TridiagonalMatrix::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forAllElementsExample()
{
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    * 0 / 1  3  .  .  . \   -> { 0, 1, 3 }
    *   | 2  1  3  .  . |   -> { 2, 1, 3 }
    *   | .  2  1  3  . |   -> { 2, 1, 3 }
    *   | .  .  2  1  3 |   -> { 2, 1, 3 }
    *   \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( 5,    // number of matrix rows
                                                              5 );  // number of matrix columns
   auto view = matrix.getView();
 
   auto f = [] __cuda_callable__( int rowIdx, int localIdx, int columnIdx, double& value )
   {
      /***
       * 'forElements' method iterates only over matrix elements lying on given subdiagonals
       * and so we do not need to check anything. The element value can be expressed
       * by the 'localIdx' variable, see the following figure:
       *
       *                           0  1  2  <- localIdx values
       *                           -------
       * 0 / 1  3  .  .  . \   -> { 0, 1, 3 }
       *   | 2  1  3  .  . |   -> { 2, 1, 3 }
       *   | .  2  1  3  . |   -> { 2, 1, 3 }
       *   | .  .  2  1  3 |   -> { 2, 1, 3 }
       *   \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
       *
       */
      value = 3 - localIdx;
   };
   view.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 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 
Creating matrix on CUDA device: 
Row: 0 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 

forAllRows() [1/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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 TridiagonalMatrixBase::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::TridiagonalMatrixBase::RowView.

Example

#include <iostream>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forRowsExample()
{
   using MatrixType = TNL::Matrices::TridiagonalMatrix< double, Device >;
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    *    0 /  2  .  .  .  . \  -> { 0, 0, 1 }
    *      | -1  2 -1  .  . |  -> { 0, 2, 1 }
    *      |  . -1  2 -1. . |  -> { 3, 2, 1 }
    *      |  .  . -1  2 -1 |  -> { 3, 2, 1 }
    *      \  .  .  .  .  2 /  -> { 3, 2, 1 }
    *
    * The diagonals offsets are { -1, 0, 1 }.
    */
   const int size = 5;
   MatrixType matrix( size, size );
   auto view = matrix.getView();
 
   auto f = [] __cuda_callable__( typename MatrixType::RowView & row )
   {
      const int& rowIdx = row.getRowIndex();
      if( rowIdx > 0 )
         row.setElement( 0, -1.0 );  // elements below the diagonal
      row.setElement( 1, 2.0 );      // elements on the diagonal
      if( rowIdx < size - 1 )        // elements above the diagonal
         row.setElement( 2, -1.0 );
   };
   view.forAllRows( f );  // or matrix.forAllRows
   std::cout << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating matrix on host: " << std::endl;
   forRowsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating matrix on CUDA device: " << std::endl;
   forRowsExample< TNL::Devices::Cuda >();
#endif
}

Output

Creating matrix on host: 
Row: 0 ->     0:2       1:-1  
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 ->     3:-1      4:2   
 
Creating matrix on CUDA device: 
Row: 0 ->     0:2       1:-1  
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 ->     3:-1      4:2   
 

forAllRows() [2/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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 TridiagonalMatrixBase::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::TridiagonalMatrixBase::ConstRowView.

forElements() [1/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forElementsExample()
{
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    * 0 / 2  1  .  .  . \   -> { 0, 2, 1 }
    *   | 3  2  1  .  . |   -> { 3, 2, 1 }
    *   | .  3  2  1  . |   -> { 3, 2, 1 }
    *   | .  .  3  2  1 |   -> { 3, 2, 1 }
    *   \ .  .  .  3  2 / 0 -> { 3, 2, 0 }
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( 5,    // number of matrix rows
                                                              5 );  // number of matrix columns
   auto view = matrix.getView();
 
   auto f = [] __cuda_callable__( int rowIdx, int localIdx, int columnIdx, double& value )
   {
      /***
       * 'forElements' method iterates only over matrix elements lying on given subdiagonals
       * and so we do not need to check anything. The element value can be expressed
       * by the 'localIdx' variable, see the following figure:
       *
       *                           0  1  2  <- localIdx values
       *                           -------
       * 0 / 2  1  .  .  . \   -> { 0, 2, 1 }
       *   | 3  2  1  .  . |   -> { 3, 2, 1 }
       *   | .  3  2  1  . |   -> { 3, 2, 1 }
       *   | .  .  3  2  1 |   -> { 3, 2, 1 }
       *   \ .  .  .  3  2 / 0 -> { 3, 2, 0 }
       *
       */
      value = 3 - localIdx;
   };
   view.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 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 
Creating matrix on CUDA device: 
Row: 0 ->     0:2       1:1   
Row: 1 ->     0:3       1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     3:3       4:2   
 

forElements() [2/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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, 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 , ElementsOrganization Organization>

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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 TridiagonalMatrixBase::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::TridiagonalMatrixBase::RowView.

Example

#include <iostream>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forRowsExample()
{
   using MatrixType = TNL::Matrices::TridiagonalMatrix< double, Device >;
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    *    0 /  2  .  .  .  . \  -> { 0, 0, 1 }
    *      | -1  2 -1  .  . |  -> { 0, 2, 1 }
    *      |  . -1  2 -1. . |  -> { 3, 2, 1 }
    *      |  .  . -1  2 -1 |  -> { 3, 2, 1 }
    *      \  .  .  .  .  2 /  -> { 3, 2, 1 }
    *
    * The diagonals offsets are { -1, 0, 1 }.
    */
   const int size = 5;
   MatrixType matrix( size, size );
   auto view = matrix.getView();
 
   auto f = [] __cuda_callable__( typename MatrixType::RowView & row )
   {
      const int& rowIdx = row.getRowIndex();
      if( rowIdx > 0 )
         row.setElement( 0, -1.0 );  // elements below the diagonal
      row.setElement( 1, 2.0 );      // elements on the diagonal
      if( rowIdx < size - 1 )        // elements above the diagonal
         row.setElement( 2, -1.0 );
   };
   view.forAllRows( f );  // or matrix.forAllRows
   std::cout << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating matrix on host: " << std::endl;
   forRowsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating matrix on CUDA device: " << std::endl;
   forRowsExample< TNL::Devices::Cuda >();
#endif
}

Output

Creating matrix on host: 
Row: 0 ->     0:2       1:-1  
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 ->     3:-1      4:2   
 
Creating matrix on CUDA device: 
Row: 0 ->     0:2       1:-1  
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 ->     3:-1      4:2   
 

forRows() [2/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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 TridiagonalMatrixBase::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::TridiagonalMatrixBase::ConstRowView.

getCompressedRowLengths()

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

template<typename Vector >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
laplaceOperatorMatrix()
{
   const int gridSize( 6 );
   const int matrixSize = gridSize;
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( matrixSize,  // number of rows
                                                              matrixSize   // number of columns
   );
   matrix.setElements( {
      // clang-format off
      {  0.0, 1.0 },
      { -1.0, 2.0, -1.0 },
      { -1.0, 2.0, -1.0 },
      { -1.0, 2.0, -1.0 },
      { -1.0, 2.0, -1.0 },
      {  0.0, 1.0 }
      // clang-format on
   } );
   auto view = matrix.getView();
 
   TNL::Containers::Vector< int, Device > rowLengths;
   view.getCompressedRowLengths( rowLengths );  // or matrix.getCompressedRowLengths
   std::cout << "Laplace operator matrix: " << std::endl << matrix << std::endl;
   std::cout << "Compressed row lengths: " << rowLengths << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating Laplace operator matrix on CPU ... " << std::endl;
   laplaceOperatorMatrix< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating Laplace operator matrix on CUDA GPU ... " << std::endl;
   laplaceOperatorMatrix< TNL::Devices::Cuda >();
#endif
}

Output

Creating Laplace operator matrix on CPU ... 
Laplace operator matrix: 
Row: 0 ->     0:1   
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 ->     3:-1      4:2       5:-1  
Row: 5 ->     5:1   
 
Compressed row lengths: [ 1, 3, 3, 3, 3, 1 ]
Creating Laplace operator matrix on CUDA GPU ... 
Laplace operator matrix: 
Row: 0 ->     0:1   
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 ->     3:-1      4:2       5:-1  
Row: 5 ->     5:1   
 
Compressed row lengths: [ 1, 3, 3, 3, 3, 1 ]

getElement()

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

__cuda_callable__ auto TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getElement	(	IndexType	row,
		IndexType	column ) const

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. TridiagonalMatrix::getRow or TridiagonalMatrix::forElements and TridiagonalMatrix::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
 
template< typename Device >
void
getElements()
{
   const int matrixSize( 5 );
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( matrixSize,  // number of matrix columns
                                                              {            // matrix elements definition
                                                                { 0.0, 2.0, -1.0 },
                                                                { -1.0, 2.0, -1.0 },
                                                                { -1.0, 2.0, -1.0 },
                                                                { -1.0, 2.0, -1.0 },
                                                                { -1.0, 2.0, 0.0 } } );
   auto view = matrix.getView();
 
   for( int i = 0; i < matrixSize; i++ ) {
      for( int j = 0; j < matrixSize; j++ )
         std::cout << std::setw( 5 ) << view.getElement( i, j );  // or matrix.getElement
      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   -1    0    0    0
   -1    2   -1    0    0
    0   -1    2   -1    0
    0    0   -1    2   -1
    0    0    0   -1    2
Get elements on CUDA device:
    2   -1    0    0    0
   -1    2   -1    0    0
    0   -1    2   -1    0
    0    0   -1    2   -1
    0    0    0   -1    2

getIndexer() [1/2]

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

__cuda_callable__ auto TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getIndexer

(

)

This method returns matrix elements indexer used by this matrix.

Returns

non-constant reference to the indexer.

getIndexer() [2/2]

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

__cuda_callable__ auto TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getIndexer

(

)

const

This method returns matrix elements indexer used by this matrix.

Returns

constant reference to the indexer.

getNonzeroElementsCount()

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

Index TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getNonzeroElementsCount ( ) const

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::MatrixBase< Real, Device, Index, GeneralMatrix, Organization >.

getRow() [1/2]

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

__cuda_callable__ auto TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getRow

(

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/TridiagonalMatrix.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 and zeros are
    * padding zeros for memory alignment):
    *
    *    0 /  2 -1  .  .  . \  -> { 0, 0, 1 }
    *      | -1  2 -1  .  . |  -> { 0, 2, 1 }
    *      |  . -1  2 -1. . |  -> { 3, 2, 1 }
    *      |  .  . -1  2 -1 |  -> { 3, 2, 1 }
    *      \  .  .  . -1  2 /  -> { 3, 2, 1 }
    *
    */
 
   const int matrixSize( 5 );
   using MatrixType = TNL::Matrices::TridiagonalMatrix< double, Device >;
   MatrixType matrix( matrixSize,  // number of matrix rows
                      matrixSize   // number of matrix columns
   );
   auto view = matrix.getView();
 
   auto f = [ = ] __cuda_callable__( int rowIdx ) mutable
   {
      auto row = view.getRow( rowIdx );
 
      if( rowIdx > 0 )
         row.setElement( 0, -1.0 );  // elements below the diagonal
      row.setElement( 1, 2.0 );      // elements on the diagonal
      if( rowIdx < matrixSize - 1 )  // elements above the diagonal
         row.setElement( 2, -1.0 );
   };
 
   /***
    * Set the matrix elements.
    */
   TNL::Algorithms::parallelFor< Device >( 0, view.getRows(), f );
   std::cout << std::endl << 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       1:-1  
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 ->     3:-1      4:2   
 
Getting matrix rows on CUDA device: 
 
Row: 0 ->     0:2       1:-1  
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 ->     3:-1      4:2   
 

See TridiagonalMatrixRowView.

getRow() [2/2]

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

__cuda_callable__ auto TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getRow

(

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/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
getRowExample()
{
   const int matrixSize = 5;
   using MatrixType = TNL::Matrices::TridiagonalMatrix< double, Device >;
   MatrixType matrix( matrixSize,           // number of matrix columns
                      { { 0.0, 2.0, 1.0 },  // matrix elements
                        { 0.0, 2.0, 1.0 },
                        { 3.0, 2.0, 1.0 },
                        { 3.0, 2.0, 1.0 },
                        { 0.0, 2.0, 1.0 } } );
   auto view = matrix.getView();
 
   /***
    * Fetch lambda function returns diagonal element in each row.
    */
   auto fetch = [ = ] __cuda_callable__( int rowIdx ) mutable -> double
   {
      auto row = view.getRow( rowIdx );
      return row.getValue( 2 );  // get value from subdiagonal with index 2, i.e. the main diagonal
   };
 
   /***
    * Compute the matrix trace.
    */
   int trace = TNL::Algorithms::reduce< Device >( 0, view.getRows(), fetch, std::plus<>{}, 0 );
   std::cout << "Matrix reads as: " << std::endl << matrix << std::endl;
   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 reads as: 
Row: 0 ->     0:2       1:1   
Row: 1 ->     1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     4:2   
 
Matrix trace is: 5.
Getting matrix rows on CUDA device: 
Matrix reads as: 
Row: 0 ->     0:2       1:1   
Row: 1 ->     1:2       2:1   
Row: 2 ->     1:3       2:2       3:1   
Row: 3 ->     2:3       3:2       4:1   
Row: 4 ->     4:2   
 
Matrix trace is: 5.

See TridiagonalMatrixRowView.

getRowCapacities()

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

template<typename Vector >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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.

getSerializationType()

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

std::string TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::getSerializationType ( )

static

Returns string with serialization type.

The string has a form Matrices::TridiagonalMatrix< RealType, [any_device], IndexType, Organization >.

See TridiagonalMatrix::getSerializationType.

Returns

String with the serialization type.

operator!=()

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

template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_>

bool TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::operator!=

(

const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &

matrix

)

const

Comparison operator with another multidiagonal matrix.

Template Parameters

Real_	is Real type of the source matrix.
Device_	is Device type of the source matrix.
Index_	is Index type of the source matrix.
Organization_	is Organization of the source matrix.

Parameters

matrix

is the source matrix view.

Returns

true if both matrices are NOT identical and false otherwise.

operator=()

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

TridiagonalMatrixBase & TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::operator= ( const TridiagonalMatrixBase< Real, Device, Index, Organization > & )

delete

Copy-assignment operator.

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

operator==()

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

template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_>

bool TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::operator==

(

const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &

matrix

)

const

Comparison operator with another tridiagonal matrix.

Template Parameters

Real_	is Real type of the source matrix.
Device_	is Device type of the source matrix.
Index_	is Index type of the source matrix.
Organization_	is Organization of the source matrix.

Parameters

matrix

is the source matrix view.

Returns

true if both matrices are identical and false otherwise.

print()

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

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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 , ElementsOrganization Organization>

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

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::reduceAllRows	(	Fetch &	fetch,
		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__ ( 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.

Example

#include <iostream>
#include <iomanip>
#include <functional>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
 
template< typename Device >
void
reduceRows()
{
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    *  0 / 1  3  .  .  . \   -> { 0, 1, 3 }
    *    | 2  1  3  .  . |   -> { 2, 1, 3 }
    *    | .  2  1  3  . |   -> { 2, 1, 3 }
    *    | .  .  2  1  3 |   -> { 2, 1, 3 }
    *    \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
    *
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( 5,              // number of matrix columns
                                                              { { 0, 1, 3 },  // matrix elements
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 } } );
   auto view = matrix.getView();
 
   /***
    * 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__( const 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.
    */
   view.reduceAllRows( fetch, reduce, keep, std::numeric_limits< double >::lowest() );  // or matrix.reduceAllRows
 
   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       1:3   
Row: 1 ->     0:2       1:1       2:3   
Row: 2 ->     1:2       2:1       3:3   
Row: 3 ->     2:2       3:1       4:3   
Row: 4 ->     3:2       4:1   
 
Max. elements in rows are: [ 3, 3, 3, 3, 2 ]
Rows reduction on CUDA device:
The matrix reads as: 
Row: 0 ->     0:1       1:3   
Row: 1 ->     0:2       1:1       2:3   
Row: 2 ->     1:2       2:1       3:3   
Row: 3 ->     2:2       3:1       4:3   
Row: 4 ->     3:2       4:1   
 
Max. elements in rows are: [ 3, 3, 3, 3, 2 ]

reduceRows()

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

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

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::reduceRows	(	IndexType	begin,
		IndexType	end,
		Fetch &	fetch,
		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__ ( 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.

Example

#include <iostream>
#include <iomanip>
#include <functional>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
 
template< typename Device >
void
reduceRows()
{
   /***
    * Set the following matrix (dots represent zero matrix elements and zeros are
    * padding zeros for memory alignment):
    *
    *  0 / 1  3  .  .  . \   -> { 0, 1, 3 }
    *    | 2  1  3  .  . |   -> { 2, 1, 3 }
    *    | .  2  1  3  . |   -> { 2, 1, 3 }
    *    | .  .  2  1  3 |   -> { 2, 1, 3 }
    *    \ .  .  .  2  1 / 0 -> { 2, 1, 0 }
    *
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( 5,              // number of matrix columns
                                                              { { 0, 1, 3 },  // matrix elements
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 },
                                                                { 2, 1, 3 } } );
   auto view = matrix.getView();
 
   /***
    * 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__( const 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.
    */
   view.reduceRows( 0, view.getRows(), fetch, reduce, keep, std::numeric_limits< double >::lowest() );  // or matrix.reduceRows
 
   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       1:3   
Row: 1 ->     0:2       1:1       2:3   
Row: 2 ->     1:2       2:1       3:3   
Row: 3 ->     2:2       3:1       4:3   
Row: 4 ->     3:2       4:1   
 
Max. elements in rows are: [ 3, 3, 3, 3, 2 ]
Rows reduction on CUDA device:
The matrix reads as: 
Row: 0 ->     0:1       1:3   
Row: 1 ->     0:2       1:1       2:3   
Row: 2 ->     1:2       2:1       3:3   
Row: 3 ->     2:2       3:1       4:3   
Row: 4 ->     3:2       4:1   
 
Max. elements in rows are: [ 3, 3, 3, 3, 2 ]

sequentialForAllRows() [1/2]

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

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::sequentialForAllRows

(

Function &

function

)

This method calls sequentialForRows for all matrix rows.

See TridiagonalMatrixBase::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 , ElementsOrganization Organization>

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::sequentialForAllRows

(

Function &

function

)

const

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

See TridiagonalMatrixBase::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 , ElementsOrganization Organization>

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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::TridiagonalMatrixBase::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 , ElementsOrganization Organization>

template<typename Function >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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::TridiagonalMatrixBase::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 , ElementsOrganization Organization>

__cuda_callable__ void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::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. TridiagonalMatrix::getRow or TridiagonalMatrix::forElements and TridiagonalMatrix::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/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
setElements()
{
   const int matrixSize( 5 );
   using Matrix = TNL::Matrices::TridiagonalMatrix< double, Device >;
   Matrix matrix( matrixSize, matrixSize );
   auto view = matrix.getView();
 
   for( int i = 0; i < 5; i++ )
      view.setElement( i, i, i );  // or matrix.setElement
 
   std::cout << "Matrix set from the host:" << std::endl;
   std::cout << matrix << std::endl;
 
   auto f = [ = ] __cuda_callable__( int i ) mutable
   {
      if( i > 0 )
         view.setElement( i, i - 1, 1.0 );
      view.setElement( i, i, -i );
      if( i < matrixSize - 1 )
         view.setElement( i, i + 1, 1.0 );
   };
 
   TNL::Algorithms::parallelFor< Device >( 0, matrixSize, 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 ->     1:1   
Row: 1 ->     0:1       1:-1      2:1   
Row: 2 ->     1:1       2:-2      3:1   
Row: 3 ->     2:1       3:-3      4:1   
Row: 4 ->     3:1       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 ->     1:1   
Row: 1 ->     0:1       1:-1      2:1   
Row: 2 ->     1:1       2:-2      3:1   
Row: 3 ->     2:1       3:-3      4:1   
Row: 4 ->     3:1       4:-4  
 

setValue()

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

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::setValue

(

const RealType &

value

)

Set all matrix elements to given value.

Parameters

value

is the new value of all matrix elements.

vectorProduct()

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

template<typename InVector , typename OutVector >

void TNL::Matrices::TridiagonalMatrixBase< Real, Device, Index, Organization >::vectorProduct	(	const InVector &	inVector,
		OutVector &	outVector,
		RealType	matrixMultiplicator = 1.0,
		RealType	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/TridiagonalMatrixBase.h
• src/TNL/Matrices/TridiagonalMatrixBase.hpp