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

Implementation of sparse tridiagonal matrix. More...

#include <TNL/Matrices/TridiagonalMatrix.h>

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

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

Public Types
using	ConstViewType = typename ViewType::ConstViewType
	Matrix view type for constant instances.
using	RealAllocatorType = RealAllocator
	The allocator for matrix elements values.
template<typename _Real = Real, typename _Device = Device, typename _Index = Index, ElementsOrganization _Organization = Algorithms::Segments::DefaultElementsOrganization< _Device >::getOrganization(), typename _RealAllocator = typename Allocators::Default< _Device >::template Allocator< _Real >>
using	Self = TridiagonalMatrix< _Real, _Device, _Index, _Organization, _RealAllocator >
	Helper type for getting self type or its modifications.
using	ValuesVectorType = Containers::Vector< Real, Device, Index, RealAllocator >
	Type of vector holding values of matrix elements.
using	ViewType = TridiagonalMatrixView< Real, Device, Index, Organization >
	Type of related matrix view.
Public Types inherited from TNL::Matrices::TridiagonalMatrixBase< double, Devices::Host, int, Algorithms::Segments::DefaultElementsOrganization< Devices::Host >::getOrganization() >
using	ConstRowView
	Type for accessing constant matrix rows.
using	DeviceType
	The device where the matrix is allocated.
using	IndexerType
using	IndexType
	The type used for matrix elements indexing.
using	RealType
	The type of matrix elements.
using	RowView
	Type for accessing matrix rows.
Public Types inherited from TNL::Matrices::MatrixBase< double, Devices::Host, int, 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
	TridiagonalMatrix ()=default
	Constructor with no parameters.
	TridiagonalMatrix (const TridiagonalMatrix &matrix)
	Copy constructor.
template<typename ListReal >
	TridiagonalMatrix (Index columns, const std::initializer_list< std::initializer_list< ListReal > > &data)
	Constructor with matrix dimensions, diagonals offsets and matrix elements.
	TridiagonalMatrix (Index rows, Index columns)
	Constructor with matrix dimensions.
	TridiagonalMatrix (TridiagonalMatrix &&) noexcept=default
	Move constructor.
ConstViewType	getConstView () const
	Returns a non-modifiable view of the tridiagonal matrix.
template<typename Real2 , typename Index2 >
void	getTransposition (const TridiagonalMatrix< Real2, Device, Index2 > &matrix, const Real &matrixMultiplicator=1.0)
ViewType	getView ()
	Returns a modifiable view of the tridiagonal matrix.
void	load (const String &fileName)
	Method for loading the matrix from the file with given filename.
void	load (File &file) override
	Method for loading the matrix from a file.
TridiagonalMatrix &	operator= (const TridiagonalMatrix &matrix)
	Assignment of exactly the same matrix type.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_, typename RealAllocator_ >
TridiagonalMatrix &	operator= (const TridiagonalMatrix< Real_, Device_, Index_, Organization_, RealAllocator_ > &matrix)
	Assignment of another tridiagonal matrix.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_, typename RealAllocator_ >
TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator > &	operator= (const TridiagonalMatrix< Real_, Device_, Index_, Organization_, RealAllocator_ > &matrix)
void	reset ()
	Resets the matrix to zero dimensions.
void	save (const String &fileName) const
	Method for saving the matrix to the file with given filename.
void	save (File &file) const override
	Method for saving the matrix to a file.
void	setDimensions (Index rows, Index columns)
	Set matrix dimensions.
template<typename ListReal >
void	setElements (const std::initializer_list< std::initializer_list< ListReal > > &data)
	Set matrix elements from an initializer list.
template<typename Real_ , typename Device_ , typename Index_ , ElementsOrganization Organization_, typename RealAllocator_ >
void	setLike (const TridiagonalMatrix< Real_, Device_, Index_, Organization_, RealAllocator_ > &matrix)
	Setup the matrix dimensions and diagonals offsets based on another tridiagonal matrix.
template<typename RowCapacitiesVector >
void	setRowCapacities (const RowCapacitiesVector &rowCapacities)
	This method is for compatibility with SparseMatrix.
Public Member Functions inherited from TNL::Object
virtual	~Object ()=default
	Destructor.
virtual std::string	getSerializationTypeVirtual () const
void	load (const String &fileName)
	Method for restoring the object from a file.
void	save (const String &fileName) const
	Method for saving the object to a file as a binary data.
Public Member Functions inherited from TNL::Matrices::TridiagonalMatrixBase< double, Devices::Host, int, Algorithms::Segments::DefaultElementsOrganization< Devices::Host >::getOrganization() >
__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.
void	addMatrix (const TridiagonalMatrixBase< Real_, Device_, Index_, Organization_ > &matrix, const RealType &matrixMultiplicator=1.0, const RealType &thisMatrixMultiplicator=1.0)
void	forAllElements (Function &function)
	This method calls forElements for all matrix rows.
void	forAllElements (Function &function) const
	This method calls forElements for all matrix rows (for constant instances).
void	forAllRows (Function &&function)
	Method for parallel iteration over all matrix rows.
void	forAllRows (Function &&function) const
	Method for parallel iteration over all matrix rows for constant instances.
void	forElements (IndexType begin, IndexType end, Function &function)
	Method for iteration over all matrix rows for non-constant instances.
void	forElements (IndexType begin, IndexType end, Function &function) const
	Method for iteration over all matrix rows for constant instances.
void	forRows (IndexType begin, IndexType end, Function &&function)
	Method for parallel iteration over matrix rows from interval [begin, end).
void	forRows (IndexType begin, IndexType end, Function &&function) const
	Method for parallel iteration over matrix rows from interval [begin, end) for constant instances.
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.
void	getRowCapacities (Vector &rowCapacities) const
	Compute capacities of all rows.
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.
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.
void	reduceAllRows (Fetch &&fetch, const Reduce &reduce, Keep &&keep, const FetchReal &identity) const
	Method for performing general reduction on all matrix rows for constant instances.
void	reduceRows (IndexType begin, IndexType end, Fetch &&fetch, const Reduce &reduce, Keep &&keep, const FetchReal &identity) const
	Method for performing general reduction on matrix rows for constant instances.
void	sequentialForAllRows (Function &function)
	This method calls sequentialForRows for all matrix rows.
void	sequentialForAllRows (Function &function) const
	This method calls sequentialForRows for all matrix rows (for constant instances).
void	sequentialForRows (IndexType begin, IndexType end, Function &function)
	Method for sequential iteration over all matrix rows for non-constant instances.
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.
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< double, Devices::Host, int, 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::Object
static std::string	getSerializationType ()
	Static serialization type getter.
Static Public Member Functions inherited from TNL::Matrices::TridiagonalMatrixBase< double, Devices::Host, int, Algorithms::Segments::DefaultElementsOrganization< Devices::Host >::getOrganization() >
static std::string	getSerializationType ()
	Returns string with serialization type.
Static Public Member Functions inherited from TNL::Matrices::MatrixBase< double, Devices::Host, int, GeneralMatrix, Organization >
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 Attributes
ValuesVectorType	values
	Vector containing the allocated matrix elements.
Protected Attributes inherited from TNL::Matrices::TridiagonalMatrixBase< double, Devices::Host, int, Algorithms::Segments::DefaultElementsOrganization< Devices::Host >::getOrganization() >
IndexerType	indexer
Protected Attributes inherited from TNL::Matrices::MatrixBase< double, Devices::Host, int, GeneralMatrix, Organization >
IndexType	columns
IndexType	rows
ValuesViewType	values

Additional Inherited Members
Protected Member Functions inherited from TNL::Matrices::TridiagonalMatrixBase< double, Devices::Host, int, Algorithms::Segments::DefaultElementsOrganization< Devices::Host >::getOrganization() >
__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< double, Devices::Host, int, GeneralMatrix, Organization >
__cuda_callable__ void	bind (IndexType rows, IndexType columns, ValuesViewType values)
	Re-initializes the internal attributes of the base class.

Detailed Description

template<typename Real = double, typename Device = Devices::Host, typename Index = int, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization(), typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >>
class TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >

Implementation of sparse tridiagonal matrix.

Use this matrix type for storing of tridiagonal matrices i.e., matrices having non-zero matrix elements only on its diagonal and immediately above and bellow the diagonal. This is an example:

\[ \left( \begin{array}{ccccccc} 4 & -1 & . & . & . & . \\ -1 & 4 & -1 & . & . & . \\ . & -1 & 4 & -1 & . & . \\ . & . & -1 & 4 & -1 & . \\ . & . & . & -1 & 4 & -1 \\ . & . & . & . & -1 & 4 \end{array} \right) \]

Advantage is that we do not store the column indexes explicitly as it is in SparseMatrix. This can reduce significantly the memory requirements which also means better performance. See the following table for the storage requirements comparison between TridiagonalMatrix and SparseMatrix.

Real	Index	SparseMatrix	TridiagonalMatrix	Ratio
float	32-bit int	8 bytes per element	4 bytes per element	50%
double	32-bit int	12 bytes per element	8 bytes per element	75%
float	64-bit int	12 bytes per element	4 bytes per element	30%
double	64-bit int	16 bytes per element	8 bytes per element	50%

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.
RealAllocator	is allocator for the matrix elements.

Member Typedef Documentation

ConstViewType

template<typename Real = double, typename Device = Devices::Host, typename Index = int, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization(), typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >>

using TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::ConstViewType = typename ViewType::ConstViewType

Matrix view type for constant instances.

See TridiagonalMatrixView.

ViewType

template<typename Real = double, typename Device = Devices::Host, typename Index = int, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization(), typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >>

using TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::ViewType = TridiagonalMatrixView< Real, Device, Index, Organization >

Type of related matrix view.

See TridiagonalMatrixView.

Constructor & Destructor Documentation

TridiagonalMatrix() [1/2]

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

TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::TridiagonalMatrix	(	Index	rows,
		Index	columns )

Constructor with matrix dimensions.

Parameters

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

TridiagonalMatrix() [2/2]

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

template<typename ListReal >

TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::TridiagonalMatrix	(	Index	columns,
		const std::initializer_list< std::initializer_list< ListReal > > &	data )

Constructor with matrix dimensions, diagonals offsets and matrix elements.

The number of matrix rows is deduced from the size of the initializer list data.

Template Parameters

ListReal

is type used in the initializer list defining matrix elements values.

Parameters

columns	is number of matrix columns.
data	is initializer list holding matrix elements. The size of the outer list defines the number of matrix rows. Each inner list defines values of each sub-diagonal and so its size should be lower or equal to three. Values of sub-diagonals which do not fit to given row are omitted.

Example

#include <iostream>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
createTridiagonalMatrix()
{
   const int matrixSize = 6;
 
   /***
    * Setup the following matrix (dots represent zeros):
    *
    * /  2 -1 .   .  .  . \
    * | -1  2 -1  .  .  . |
    * |  . -1  2 -1  .  . |
    * |  .  . -1  2 -1  . |
    * |  .  .  . -1  2 -1 |
    * \  .  .  .  . -1  2 /
    *
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix(
      matrixSize,
      { /***
         * To set the matrix elements we first extend the diagonals to their full
         * lengths even outside the matrix (dots represent zeros and zeros are
         * artificial zeros used for memory alignment):
         *
         * 0 /  2 -1 .   .  .  . \    -> {  0,  2, -1 }
         *   | -1  2 -1  .  .  . |    -> { -1,  2, -1 }
         *   |  . -1  2 -1  .  . |    -> { -1,  2, -1 }
         *   |  .  . -1  2 -1  . |    -> { -1,  2, -1 }
         *   |  .  .  . -1  2 -1 |    -> { -1,  2, -1 }
         *   \  .  .  .  . -1  2 / 0  -> { -1,  2,  0 }
         *
         */
        { 0, 2, -1 },
        { -1, 2, -1 },
        { -1, 2, -1 },
        { -1, 2, -1 },
        { -1, 2, -1 },
        { -1, 2, 0 } } );
   std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating tridiagonal matrix on CPU ... " << std::endl;
   createTridiagonalMatrix< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating tridiagonal matrix on CUDA GPU ... " << std::endl;
   createTridiagonalMatrix< TNL::Devices::Cuda >();
#endif
}

Output

Creating tridiagonal matrix on CPU ... 
The matrix reads as: 
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       5:-1  
Row: 5 ->     4:-1      5:2   
 
Creating tridiagonal matrix on CUDA GPU ... 
The matrix reads as: 
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       5:-1  
Row: 5 ->     4:-1      5:2   
 

Member Function Documentation

getConstView()

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

auto TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::getConstView ( ) const

nodiscard

Returns a non-modifiable view of the tridiagonal matrix.

See TridiagonalMatrixView.

Returns

tridiagonal matrix view.

getSerializationType()

template<typename Real = double, typename Device = Devices::Host, typename Index = int, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization(), typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >>

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

staticnodiscard

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.

getView()

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

auto TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::getView ( )

nodiscard

Returns a modifiable view of the tridiagonal matrix.

See TridiagonalMatrixView.

Returns

tridiagonal matrix view.

load() [1/2]

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::load

(

const String &

fileName

)

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

Parameters

fileName

is name of the file.

load() [2/2]

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::load ( File & file )

overridevirtual

Method for loading the matrix from a file.

Parameters

file	is the input file.

Reimplemented from TNL::Object.

operator=() [1/2]

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

TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator > & TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::operator=

(

const TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator > &

matrix

)

Assignment of exactly the same matrix type.

Parameters

matrix

is input matrix for the assignment.

Returns

reference to this matrix.

operator=() [2/2]

template<typename Real = double, typename Device = Devices::Host, typename Index = int, ElementsOrganization Organization = Algorithms::Segments::DefaultElementsOrganization< Device >::getOrganization(), typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >>

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

TridiagonalMatrix & TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::operator=

(

const TridiagonalMatrix< Real_, Device_, Index_, Organization_, RealAllocator_ > &

matrix

)

Assignment of another tridiagonal matrix.

Parameters

matrix

is input matrix for the assignment.

Returns

reference to this matrix.

save() [1/2]

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::save

(

const String &

fileName

)

const

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

Parameters

fileName

is name of the file.

save() [2/2]

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::save ( File & file ) const

overridevirtual

Method for saving the matrix to a file.

Parameters

file	is the output file.

Reimplemented from TNL::Object.

setDimensions()

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::setDimensions	(	Index	rows,
		Index	columns )

Set matrix dimensions.

Parameters

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

setElements()

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

template<typename ListReal >

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::setElements

(

const std::initializer_list< std::initializer_list< ListReal > > &

data

)

Set matrix elements from an initializer list.

Template Parameters

ListReal

is data type of the initializer list.

Parameters

data	is initializer list holding matrix elements. The size of the outer list defines the number of matrix rows. Each inner list defines values of each sub-diagonal and so its size should be lower or equal to three. Values of sub-diagonals which do not fit to given row are omitted.

Example

#include <iostream>
#include <TNL/Matrices/TridiagonalMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
createTridiagonalMatrix()
{
   const int matrixSize = 6;
 
   /***
    * Setup the following matrix (dots represent zeros):
    *
    * /  2 -1 .   .  .  . \
    * | -1  2 -1  .  .  . |
    * |  . -1  2 -1  .  . |
    * |  .  . -1  2 -1  . |
    * |  .  .  . -1  2 -1 |
    * \  .  .  .  . -1  2 /
    *
    */
   TNL::Matrices::TridiagonalMatrix< double, Device > matrix( matrixSize, matrixSize );
   matrix.setElements( { /***
                          * To set the matrix elements we first extend the diagonals to their full
                          * lengths even outside the matrix (dots represent zeros and zeros are
                          * artificial zeros used for memory alignment):
                          *
                          * 0 /  2 -1 .   .  .  . \    -> {  0,  2, -1 }
                          *   | -1  2 -1  .  .  . |    -> { -1,  2, -1 }
                          *   |  . -1  2 -1  .  . |    -> { -1,  2, -1 }
                          *   |  .  . -1  2 -1  . |    -> { -1,  2, -1 }
                          *   |  .  .  . -1  2 -1 |    -> { -1,  2, -1 }
                          *   \  .  .  .  . -1  2 / 0  -> { -1,  2,  0 }
                          *
                          */
                         { 0, 2, -1 },
                         { -1, 2, -1 },
                         { -1, 2, -1 },
                         { -1, 2, -1 },
                         { -1, 2, -1 },
                         { -1, 2, 0 } } );
   std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Creating tridiagonal matrix on CPU ... " << std::endl;
   createTridiagonalMatrix< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Creating tridiagonal matrix on CUDA GPU ... " << std::endl;
   createTridiagonalMatrix< TNL::Devices::Cuda >();
#endif
}

Output

Creating tridiagonal matrix on CPU ... 
The matrix reads as: 
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       5:-1  
Row: 5 ->     4:-1      5:2   
 
Creating tridiagonal matrix on CUDA GPU ... 
The matrix reads as: 
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       5:-1  
Row: 5 ->     4:-1      5:2   
 

setLike()

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

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

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::setLike

(

const TridiagonalMatrix< Real_, Device_, Index_, Organization_, RealAllocator_ > &

matrix

)

Setup the matrix dimensions and diagonals offsets based on 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.
RealAllocator_	is RealAllocator of the source matrix.

Parameters

matrix

is the source matrix.

setRowCapacities()

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

template<typename RowCapacitiesVector >

void TNL::Matrices::TridiagonalMatrix< Real, Device, Index, Organization, RealAllocator >::setRowCapacities

(

const RowCapacitiesVector &

rowCapacities

)

This method is for compatibility with SparseMatrix.

It checks if the number of matrix diagonals is compatible with required number of non-zero matrix elements in each row. If not exception is thrown.

Template Parameters

RowCapacitiesVector

is vector-like container type for holding required row capacities.

Parameters

rowCapacities

is vector-like container holding required row capacities.

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

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