TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index > Class Template Reference

"Matrix-free matrix" based on lambda functions. More...

#include <TNL/Matrices/LambdaMatrix.h>

Public Types
using	CompressedRowLengthsLambdaType = CompressedRowLengthsLambda
	Type of the lambda function returning the number of non-zero elements in each row.
using	ConstRowView = RowView
	Type of constant Lambda matrix row view.
using	DeviceType = Device
	The device where the matrix is allocated.
using	IndexType = Index
	The type used for matrix elements indexing.
using	MatrixElementsLambdaType = MatrixElementsLambda
	Type of the lambda function returning the matrix elements.
using	RealType = Real
	The type of matrix elements.
using	RowView = LambdaMatrixRowView< MatrixElementsLambdaType, CompressedRowLengthsLambdaType, RealType, IndexType >
	Type of Lambda matrix row view.

Public Member Functions
	LambdaMatrix (const LambdaMatrix &matrix)=default
	Copy constructor.
	LambdaMatrix (IndexType rows, IndexType columns, MatrixElementsLambda &matrixElements, CompressedRowLengthsLambda &compressedRowLengths)
	Constructor with matrix dimensions and lambda functions defining the matrix elements.
	LambdaMatrix (LambdaMatrix &&matrix) noexcept=default
	Move constructor.
	LambdaMatrix (MatrixElementsLambda &matrixElements, CompressedRowLengthsLambda &compressedRowLengths)
	Constructor with lambda functions defining the matrix elements.
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) const
	Method for parallel iteration over all matrix rows for 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) const
	Method for parallel iteration over matrix rows from interval [ begin, end) for constant instances.
__cuda_callable__ IndexType	getColumns () const
	Returns a number of matrix columns.
template<typename RowLengthsVector >
void	getCompressedRowLengths (RowLengthsVector &rowLengths) const
	Computes number of non-zeros in each row.
template<typename Vector >
void	getCompressedRowLengths (Vector &rowLengths) const
__cuda_callable__ const CompressedRowLengthsLambda &	getCompressedRowLengthsLambda () const
	Get reference to the lambda function returning number of non-zero elements in each row.
RealType	getElement (IndexType row, IndexType column) const
	Returns value of matrix element at position given by its row and column index.
__cuda_callable__ const MatrixElementsLambda &	getMatrixElementsLambda () const
	Get reference to the lambda function returning the matrix elements values and column indexes.
IndexType	getNonzeroElementsCount () const
	Returns number of non-zero matrix elements.
__cuda_callable__ ConstRowView	getRow (IndexType rowIdx) const
	Getter of simple structure for accessing given matrix row.
template<typename Vector >
void	getRowCapacities (Vector &rowCapacities) const
	Compute capacities of all rows.
__cuda_callable__ IndexType	getRows () const
	Returns a number of matrix rows.
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, const Reduce &reduce, Keep &&keep, const FetchReal &identity) const
	Method for performing general reduction on ALL matrix rows.
template<typename Fetch , typename Reduce , typename Keep , typename FetchReal >
void	reduceRows (IndexType begin, IndexType end, Fetch &&fetch, const Reduce &reduce, Keep &&keep, const FetchReal &identity) const
	Method for performing general reduction on matrix rows.
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) const
	Method for sequential iteration over all matrix rows for constant instances.
void	setDimensions (IndexType rows, IndexType columns)
	Set number of rows and columns of this matrix.
template<typename InVector , typename OutVector >
void	vectorProduct (const InVector &inVector, OutVector &outVector, const RealType &matrixMultiplicator=1.0, const RealType &outVectorMultiplicator=0.0, IndexType begin=0, IndexType end=0) const
	Computes product of matrix and vector.

Static Public Member Functions
static constexpr bool	isBinary ()
static constexpr bool	isSymmetric ()

Protected Attributes
IndexType	columns
CompressedRowLengthsLambda	compressedRowLengthsLambda
MatrixElementsLambda	matrixElementsLambda
IndexType	rows

Detailed Description

template<typename MatrixElementsLambda, typename CompressedRowLengthsLambda, typename Real = double, typename Device = Devices::Host, typename Index = int>
class TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >

"Matrix-free matrix" based on lambda functions.

The elements of this matrix are not stored explicitly in memory but implicitly on a form of lambda functions.

Template Parameters

MatrixElementsLambda	is a lambda function returning matrix elements values and positions.
MatrixElementsLambda	is a lambda function returning matrix elements values and positions.

It has the following form:

auto matrixElements = [] __cuda_callable__ ( Index rows, Index columns, Index rowIdx, Index localIdx, Index& columnIdx, Real&
value ) { ... }

where rows is the number of matrix rows, columns is the number of matrix columns, rowIdx is the index of matrix row being queried, localIdx is the rank of the non-zero element in given row, columnIdx is a column index of the matrix element computed by this lambda and value is a value of the matrix element computed by this lambda.

Template Parameters

CompressedRowLengthsLambda

is a lambda function returning a number of non-zero elements in each row.

It has the following form:

auto rowLengths = [] __cuda_callable__ ( Index rows, Index columns, Index rowIdx ) -> IndexType { ...  }

where rows is the number of matrix rows, columns is the number of matrix columns and rowIdx is an index of the row being queried.

Template Parameters

Real	is a type of matrix elements values.
Device	is a device on which the lambda functions will be evaluated.
Index	is a type to be used for indexing.

Constructor & Destructor Documentation

LambdaMatrix() [1/4]

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

TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::LambdaMatrix	(	MatrixElementsLambda &	matrixElements,
		CompressedRowLengthsLambda &	compressedRowLengths )

Constructor with lambda functions defining the matrix elements.

Note: It might be difficult to express the types of the lambdas. For easier creation of LambdaMatrix you may use LambdaMatrixFactory.

Parameters

matrixElements	is a lambda function giving matrix elements position and value.
compressedRowLengths	is a lambda function returning how many non-zero matrix elements are in given row.

Example

#include <iostream>
#include <TNL/Matrices/LambdaMatrix.h>
 
int
main( int argc, char* argv[] )
{
   /***
    * Lambda functions defining the matrix.
    */
   auto compressedRowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return 1;
   };
   auto matrixElements1 =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = rowIdx;
      value = 1.0;
   };
   auto matrixElements2 =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = rowIdx;
      value = rowIdx;
   };
 
   const int size = 5;
 
   /***
    * Matrix construction with explicit type definition.
    */
   using MatrixType = decltype( TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create(
      matrixElements1, compressedRowLengths ) );
   MatrixType m1( size, size, matrixElements1, compressedRowLengths );
 
   /***
    * Matrix construction using 'auto'.
    */
   auto m2 =
      TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create( matrixElements2, compressedRowLengths );
   m2.setDimensions( size, size );
 
   std::cout << "The first lambda matrix: " << std::endl << m1 << std::endl;
   std::cout << "The second lambda matrix: " << std::endl << m2 << std::endl;
}

Output

The first lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
 
The second lambda matrix: 
Row: 0 -> 
Row: 1 ->     1:1   
Row: 2 ->     2:2   
Row: 3 ->     3:3   
Row: 4 ->     4:4   
 

LambdaMatrix() [2/4]

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

TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::LambdaMatrix	(	IndexType	rows,
		IndexType	columns,
		MatrixElementsLambda &	matrixElements,
		CompressedRowLengthsLambda &	compressedRowLengths )

Constructor with matrix dimensions and lambda functions defining the matrix elements.

Note: It might be difficult to express the types of the lambdas. For easier creation of LambdaMatrix you may use LambdaMatrixFactory.

Parameters

rows	is a number of the matrix rows.
columns	is a number of the matrix columns.
matrixElements	is a lambda function giving matrix elements position and value.
compressedRowLengths	is a lambda function returning how many non-zero matrix elements are in given row.

Example

#include <iostream>
#include <TNL/Matrices/LambdaMatrix.h>
 
int
main( int argc, char* argv[] )
{
   /***
    * Lambda functions defining the matrix.
    */
   auto compressedRowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return 1;
   };
   auto matrixElements1 =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = rowIdx;
      value = 1.0;
   };
   auto matrixElements2 =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = rowIdx;
      value = rowIdx;
   };
 
   const int size = 5;
 
   /***
    * Matrix construction with explicit type definition.
    */
   using MatrixType = decltype( TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create(
      matrixElements1, compressedRowLengths ) );
   MatrixType m1( size, size, matrixElements1, compressedRowLengths );
 
   /***
    * Matrix construction using 'auto'.
    */
   auto m2 =
      TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create( matrixElements2, compressedRowLengths );
   m2.setDimensions( size, size );
 
   std::cout << "The first lambda matrix: " << std::endl << m1 << std::endl;
   std::cout << "The second lambda matrix: " << std::endl << m2 << std::endl;
}

Output

The first lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
 
The second lambda matrix: 
Row: 0 -> 
Row: 1 ->     1:1   
Row: 2 ->     2:2   
Row: 3 ->     3:3   
Row: 4 ->     4:4   
 

LambdaMatrix() [3/4]

template<typename MatrixElementsLambda , typename CompressedRowLengthsLambda , typename Real = double, typename Device = Devices::Host, typename Index = int>

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

default

Copy constructor.

Parameters

matrix

is input matrix.

LambdaMatrix() [4/4]

template<typename MatrixElementsLambda , typename CompressedRowLengthsLambda , typename Real = double, typename Device = Devices::Host, typename Index = int>

TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::LambdaMatrix ( LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index > && matrix )

defaultnoexcept

Move constructor.

Parameters

matrix

is input matrix.

Member Function Documentation

forAllElements()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::forAllElements

(

Function &

function

)

const

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

See LambdaMatrix::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/DenseMatrix.h>
#include <TNL/Matrices/LambdaMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forAllElementsExample()
{
   /***
    * Lambda functions defining the matrix.
    */
   auto compressedRowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   using MatrixFactory = TNL::Matrices::LambdaMatrixFactory< double, Device, int >;
   auto matrix = MatrixFactory::create( 5, 5, matrixElements, compressedRowLengths );
 
   TNL::Matrices::DenseMatrix< double, Device > denseMatrix( 5, 5 );
   auto denseView = denseMatrix.getView();
 
   auto f = [ = ] __cuda_callable__( int rowIdx, int localIdx, int columnIdx, double value ) mutable
   {
      denseView.setElement( rowIdx, columnIdx, value );
   };
 
   matrix.forAllElements( f );
   std::cout << "Original lambda matrix:" << std::endl << matrix << std::endl;
   std::cout << "Dense matrix:" << std::endl << denseMatrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Copying matrix on host: " << std::endl;
   forAllElementsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Copying matrix on CUDA device: " << std::endl;
   forAllElementsExample< TNL::Devices::Cuda >();
#endif
}

Output

Copying matrix on host: 
Original lambda matrix:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Dense matrix:
Row: 0 ->     0:1       1:0       2:0       3:0       4:0   
Row: 1 ->     0:2       1:1       2:0       3:0       4:0   
Row: 2 ->     0:3       1:2       2:1       3:0       4:0   
Row: 3 ->     0:4       1:3       2:2       3:1       4:0   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
Copying matrix on CUDA device: 
Original lambda matrix:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Dense matrix:
Row: 0 ->     0:1       1:0       2:0       3:0       4:0   
Row: 1 ->     0:2       1:1       2:0       3:0       4:0   
Row: 2 ->     0:3       1:2       2:1       3:0       4:0   
Row: 3 ->     0:4       1:3       2:2       3:1       4:0   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   

forAllRows()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::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 LambdaMatrix::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::LambdaMatrix::RowView.

Example

#include <iostream>
#include <TNL/Matrices/LambdaMatrix.h>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forRowsExample()
{
   /***
    * Set  matrix representing approximation of the Laplace operator on regular
    * grid using the finite difference method.
    */
   const int gridSize( 4 );
   const int matrixSize = gridSize * gridSize;
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
         return 1;
      return 5;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
      {
         columnIdx = rowIdx;  // diagonal element ....
         value = 1.0;         // ... is set to 1
      }
      else  // interior grid node
      {
         switch( localIdx )  // set diagonal element to 4
         {                   // and the others to -1
            case 0:
               columnIdx = rowIdx - gridSize;
               value = 1;
               break;
            case 1:
               columnIdx = rowIdx - 1;
               value = 1;
               break;
            case 2:
               columnIdx = rowIdx;
               value = -4;
               break;
            case 3:
               columnIdx = rowIdx + 1;
               value = 1;
               break;
            case 4:
               columnIdx = rowIdx + gridSize;
               value = 1;
               break;
         }
      }
   };
   auto matrix =
      TNL::Matrices::LambdaMatrixFactory< double, Device, int >::create( matrixSize, matrixSize, matrixElements, rowLengths );
   using MatrixType = decltype( matrix );
   using RowView = typename MatrixType::RowView;
 
   TNL::Matrices::DenseMatrix< double, Device > denseMatrix( matrixSize, matrixSize );
   denseMatrix.setValue( 0.0 );
   auto dense_view = denseMatrix.getView();
   auto f = [ = ] __cuda_callable__( const RowView& row ) mutable
   {
      auto dense_row = dense_view.getRow( row.getRowIndex() );
      for( int localIdx = 0; localIdx < row.getSize(); localIdx++ )
         dense_row.setValue( row.getColumnIndex( localIdx ), row.getValue( localIdx ) );
   };
   matrix.forAllRows( f );
 
   std::cout << "Laplace operator lambda matrix: " << std::endl << matrix << std::endl;
   std::cout << "Laplace operator dense matrix: " << std::endl << denseMatrix << std::endl;
 
   /***
    * Compute sum of elements in each row and store it into a vector.
    */
   TNL::Containers::Vector< double, Device > sum_vector( matrixSize );
   auto sum_view = sum_vector.getView();
   matrix.forAllRows(
      [ = ] __cuda_callable__( const RowView& row ) mutable
      {
         double sum( 0.0 );
         for( auto element : row )
            sum += TNL::abs( element.value() );
         sum_view[ row.getRowIndex() ] = sum;
      } );
 
   std::cout << "Sums in matrix rows = " << sum_vector << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Running example on CPU ... " << std::endl;
   forRowsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Running example on CUDA GPU ... " << std::endl;
   forRowsExample< TNL::Devices::Cuda >();
#endif
}

Output

Running example on CPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   
Sums in matrix rows = [ 1, 1, 1, 1, 1, 8, 8, 1, 1, 8, 8, 1, 1, 1, 1, 1 ]
Running example on CUDA GPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   
Sums in matrix rows = [ 1, 1, 1, 1, 1, 8, 8, 1, 1, 8, 8, 1, 1, 1, 1, 1 ]

forElements()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::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 is should have form like

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

The column index repeats twice only for compatibility with sparse matrices.

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/DenseMatrix.h>
#include <TNL/Matrices/LambdaMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forElementsExample()
{
   /***
    * Lambda functions defining the matrix.
    */
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   using MatrixFactory = TNL::Matrices::LambdaMatrixFactory< double, Device, int >;
   auto matrix = MatrixFactory::create( 5, 5, matrixElements, rowLengths );
 
   TNL::Matrices::DenseMatrix< double, Device > denseMatrix( 5, 5 );
   auto denseView = denseMatrix.getView();
 
   auto f = [ = ] __cuda_callable__( int rowIdx, int localIdx, int columnIdx, double value ) mutable
   {
      denseView.setElement( rowIdx, columnIdx, value );
   };
 
   matrix.forElements( 0, matrix.getRows(), f );
   std::cout << "Original lambda matrix:" << std::endl << matrix << std::endl;
   std::cout << "Dense matrix:" << std::endl << denseMatrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Copying matrix on host: " << std::endl;
   forElementsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Copying matrix on CUDA device: " << std::endl;
   forElementsExample< TNL::Devices::Cuda >();
#endif
}

Output

Copying matrix on host: 
Original lambda matrix:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Dense matrix:
Row: 0 ->     0:1       1:0       2:0       3:0       4:0   
Row: 1 ->     0:2       1:1       2:0       3:0       4:0   
Row: 2 ->     0:3       1:2       2:1       3:0       4:0   
Row: 3 ->     0:4       1:3       2:2       3:1       4:0   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
Copying matrix on CUDA device: 
Original lambda matrix:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Dense matrix:
Row: 0 ->     0:1       1:0       2:0       3:0       4:0   
Row: 1 ->     0:2       1:1       2:0       3:0       4:0   
Row: 2 ->     0:3       1:2       2:1       3:0       4:0   
Row: 3 ->     0:4       1:3       2:2       3:1       4:0   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   

forRows()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::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 LambdaMatrix::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::LambdaMatrix::RowView.

Example

#include <iostream>
#include <TNL/Matrices/LambdaMatrix.h>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
forRowsExample()
{
   /***
    * Set  matrix representing approximation of the Laplace operator on regular
    * grid using the finite difference method.
    */
   const int gridSize( 4 );
   const int matrixSize = gridSize * gridSize;
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
         return 1;
      return 5;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
      {
         columnIdx = rowIdx;  // diagonal element ....
         value = 1.0;         // ... is set to 1
      }
      else  // interior grid node
      {
         switch( localIdx )  // set diagonal element to 4
         {                   // and the others to -1
            case 0:
               columnIdx = rowIdx - gridSize;
               value = 1;
               break;
            case 1:
               columnIdx = rowIdx - 1;
               value = 1;
               break;
            case 2:
               columnIdx = rowIdx;
               value = -4;
               break;
            case 3:
               columnIdx = rowIdx + 1;
               value = 1;
               break;
            case 4:
               columnIdx = rowIdx + gridSize;
               value = 1;
               break;
         }
      }
   };
   auto matrix =
      TNL::Matrices::LambdaMatrixFactory< double, Device, int >::create( matrixSize, matrixSize, matrixElements, rowLengths );
   using MatrixType = decltype( matrix );
   using RowView = typename MatrixType::RowView;
 
   TNL::Matrices::DenseMatrix< double, Device > denseMatrix( matrixSize, matrixSize );
   denseMatrix.setValue( 0.0 );
   auto dense_view = denseMatrix.getView();
   auto f = [ = ] __cuda_callable__( const RowView& row ) mutable
   {
      auto dense_row = dense_view.getRow( row.getRowIndex() );
      for( int localIdx = 0; localIdx < row.getSize(); localIdx++ )
         dense_row.setValue( row.getColumnIndex( localIdx ), row.getValue( localIdx ) );
   };
   matrix.forAllRows( f );
 
   std::cout << "Laplace operator lambda matrix: " << std::endl << matrix << std::endl;
   std::cout << "Laplace operator dense matrix: " << std::endl << denseMatrix << std::endl;
 
   /***
    * Compute sum of elements in each row and store it into a vector.
    */
   TNL::Containers::Vector< double, Device > sum_vector( matrixSize );
   auto sum_view = sum_vector.getView();
   matrix.forAllRows(
      [ = ] __cuda_callable__( const RowView& row ) mutable
      {
         double sum( 0.0 );
         for( auto element : row )
            sum += TNL::abs( element.value() );
         sum_view[ row.getRowIndex() ] = sum;
      } );
 
   std::cout << "Sums in matrix rows = " << sum_vector << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Running example on CPU ... " << std::endl;
   forRowsExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Running example on CUDA GPU ... " << std::endl;
   forRowsExample< TNL::Devices::Cuda >();
#endif
}

Output

Running example on CPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   
Sums in matrix rows = [ 1, 1, 1, 1, 1, 8, 8, 1, 1, 8, 8, 1, 1, 1, 1, 1 ]
Running example on CUDA GPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   
Sums in matrix rows = [ 1, 1, 1, 1, 1, 8, 8, 1, 1, 8, 8, 1, 1, 1, 1, 1 ]

getColumns()

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

__cuda_callable__ Index TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getColumns ( ) const

nodiscard

Returns a number of matrix columns.

Returns

number of matrix columns.

getCompressedRowLengths()

template<typename MatrixElementsLambda , typename CompressedRowLengthsLambda , typename Real = double, typename Device = Devices::Host, typename Index = int>

template<typename RowLengthsVector >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getCompressedRowLengths

(

RowLengthsVector &

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/LambdaMatrix.h>
 
int
main( int argc, char* argv[] )
{
   /***
    * Lambda functions defining the matrix.
    */
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   const int size = 5;
   auto matrix =
      TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create( size, size, matrixElements, rowLengths );
 
   TNL::Containers::Vector< int > rowLengthsVector;
   matrix.getCompressedRowLengths( rowLengthsVector );
 
   std::cout << "Matrix looks as:" << std::endl << matrix << std::endl;
   std::cout << "Compressed row lengths are: " << rowLengthsVector << std::endl;
}

Output

Matrix looks as:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Compressed row lengths are: [ 1, 2, 3, 4, 5 ]

getCompressedRowLengthsLambda()

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

__cuda_callable__ const CompressedRowLengthsLambda & TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getCompressedRowLengthsLambda ( ) const

nodiscard

Get reference to the lambda function returning number of non-zero elements in each row.

Returns

constant reference to CompressedRowLengthsLambda.

getElement()

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

Real TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getElement ( IndexType row, IndexType column ) const

nodiscard

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

Parameters

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

Returns

value of given matrix element.

getMatrixElementsLambda()

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

__cuda_callable__ const MatrixElementsLambda & TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getMatrixElementsLambda ( ) const

nodiscard

Get reference to the lambda function returning the matrix elements values and column indexes.

Returns

constant reference to MatrixElementsLambda.

getNonzeroElementsCount()

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

Index TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getNonzeroElementsCount ( ) const

nodiscard

Returns number of non-zero matrix elements.

Returns

number of all non-zero matrix elements.

Example

#include <iostream>
#include <TNL/Matrices/LambdaMatrix.h>
 
int
main( int argc, char* argv[] )
{
   /***
    * Lambda functions defining the matrix.
    */
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   const int size = 5;
   auto matrix =
      TNL::Matrices::LambdaMatrixFactory< double, TNL::Devices::Host, int >::create( size, size, matrixElements, rowLengths );
 
   std::cout << "Matrix looks as:" << std::endl << matrix << std::endl;
   std::cout << "Non-zero elements count is: " << matrix.getNonzeroElementsCount() << std::endl;
}

Output

Matrix looks as:
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Non-zero elements count is: 15

getRow()

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

__cuda_callable__ auto TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getRow ( IndexType rowIdx ) const

nodiscard

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/LambdaMatrix.h>
#include <TNL/Matrices/DenseMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
getRowExample()
{
   /***
    * Set  matrix representing approximation of the Laplace operator on regular
    * grid using the finite difference method.
    */
   const int gridSize( 4 );
   const int matrixSize = gridSize * gridSize;
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
         return 1;
      return 5;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      const int gridRow = rowIdx / gridSize;  // coordinates in the numerical grid
      const int gridColumn = rowIdx % gridSize;
      if( gridRow == 0 || gridRow == gridSize - 1 ||  // boundary grid node
          gridColumn == 0 || gridColumn == gridSize - 1 )
      {
         columnIdx = rowIdx;  // diagonal element ....
         value = 1.0;         // ... is set to 1
      }
      else  // interior grid node
      {
         switch( localIdx )  // set diagonal element to 4
         {                   // and the others to -1
            case 0:
               columnIdx = rowIdx - gridSize;
               value = 1;
               break;
            case 1:
               columnIdx = rowIdx - 1;
               value = 1;
               break;
            case 2:
               columnIdx = rowIdx;
               value = -4;
               break;
            case 3:
               columnIdx = rowIdx + 1;
               value = 1;
               break;
            case 4:
               columnIdx = rowIdx + gridSize;
               value = 1;
               break;
         }
      }
   };
   auto matrix =
      TNL::Matrices::LambdaMatrixFactory< double, Device, int >::create( matrixSize, matrixSize, matrixElements, rowLengths );
 
   TNL::Matrices::DenseMatrix< double, Device > denseMatrix( matrixSize, matrixSize );
   denseMatrix.setValue( 0.0 );
   auto dense_view = denseMatrix.getView();
   auto f = [ = ] __cuda_callable__( const int& rowIdx ) mutable
   {
      auto row = matrix.getRow( rowIdx );
      auto dense_row = dense_view.getRow( rowIdx );
      for( int localIdx = 0; localIdx < row.getSize(); localIdx++ )
         dense_row.setValue( row.getColumnIndex( localIdx ), row.getValue( localIdx ) );
   };
   TNL::Algorithms::parallelFor< Device >( 0, matrixSize, f );
 
   std::cout << "Laplace operator lambda matrix: " << std::endl << matrix << std::endl;
   std::cout << "Laplace operator dense matrix: " << std::endl << denseMatrix << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Running example on CPU ... " << std::endl;
   getRowExample< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Running example on CUDA GPU ... " << std::endl;
   getRowExample< TNL::Devices::Cuda >();
#endif
}

Output

Running example on CPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   
Running example on CUDA GPU ... 
Laplace operator lambda matrix: 
Row: 0 ->     0:1   
Row: 1 ->     1:1   
Row: 2 ->     2:1   
Row: 3 ->     3:1   
Row: 4 ->     4:1   
Row: 5 ->     1:1       4:1       5:-4      6:1       9:1   
Row: 6 ->     2:1       5:1       6:-4      7:1      10:1   
Row: 7 ->     7:1   
Row: 8 ->     8:1   
Row: 9 ->     5:1       8:1       9:-4     10:1      13:1   
Row: 10 ->     6:1       9:1      10:-4     11:1      14:1   
Row: 11 ->    11:1   
Row: 12 ->    12:1   
Row: 13 ->    13:1   
Row: 14 ->    14:1   
Row: 15 ->    15:1   
 
Laplace operator dense matrix: 
Row: 0 ->     0:1       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 1 ->     0:0       1:1       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 2 ->     0:0       1:0       2:1       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 3 ->     0:0       1:0       2:0       3:1       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 4 ->     0:0       1:0       2:0       3:0       4:1       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 5 ->     0:0       1:1       2:0       3:0       4:1       5:-4      6:1       7:0       8:0       9:1      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 6 ->     0:0       1:0       2:1       3:0       4:0       5:1       6:-4      7:1       8:0       9:0      10:1      11:0      12:0      13:0      14:0      15:0   
Row: 7 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:1       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 8 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:1       9:0      10:0      11:0      12:0      13:0      14:0      15:0   
Row: 9 ->     0:0       1:0       2:0       3:0       4:0       5:1       6:0       7:0       8:1       9:-4     10:1      11:0      12:0      13:1      14:0      15:0   
Row: 10 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:1       7:0       8:0       9:1      10:-4     11:1      12:0      13:0      14:1      15:0   
Row: 11 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:1      12:0      13:0      14:0      15:0   
Row: 12 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:1      13:0      14:0      15:0   
Row: 13 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:1      14:0      15:0   
Row: 14 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:1      15:0   
Row: 15 ->     0:0       1:0       2:0       3:0       4:0       5:0       6:0       7:0       8:0       9:0      10:0      11:0      12:0      13:0      14:0      15:1   

See LambdaMatrixRowView.

getRowCapacities()

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

template<typename Vector >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::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.

getRows()

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

__cuda_callable__ Index TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::getRows ( ) const

nodiscard

Returns a number of matrix rows.

Returns

number of matrix rows.

print()

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

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::print

(

std::ostream &

str

)

const

Method for printing the matrix to output stream.

Parameters

str	is the output stream.

reduceAllRows()

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

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

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::reduceAllRows	(	Fetch &&	fetch,
		const Reduce &	reduce,
		Keep &&	keep,
		const FetchReal &	identity ) const

Method for performing general reduction on ALL matrix rows.

Template Parameters

Fetch

is a type of lambda function for data fetch declared as

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

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

Template Parameters

Reduce

is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callable__ ( const FetchValue& v1, const FetchValue& v2 ) -> 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/LambdaMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
reduceAllRows()
{
   /***
    * Lambda functions defining the matrix.
    */
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   using MatrixFactory = TNL::Matrices::LambdaMatrixFactory< double, Device, int >;
   auto matrix = MatrixFactory::create( 5, 5, matrixElements, rowLengths );
 
   /***
    * Find largest element in each row.
    */
   TNL::Containers::Vector< double, Device > rowMax( matrix.getRows() );
 
   /***
    * Prepare vector view and matrix view for lambdas.
    */
   auto rowMaxView = rowMax.getView();
 
   /***
    * Fetch lambda just returns absolute value of matrix elements.
    */
   auto fetch = [ = ] __cuda_callable__( int rowIdx, int columnIdx, const double& value ) -> double
   {
      return TNL::abs( value );
   };
 
   /***
    * Reduce lambda return maximum of given values.
    */
   auto reduce = [ = ] __cuda_callable__( double& a, const double& b ) -> double
   {
      return TNL::max( a, b );
   };
 
   /***
    * Keep lambda store the largest value in each row to the vector rowMax.
    */
   auto keep = [ = ] __cuda_callable__( int rowIdx, const double& value ) mutable
   {
      rowMaxView[ rowIdx ] = value;
   };
 
   /***
    * Compute the largest values in each row.
    */
   matrix.reduceAllRows( fetch, reduce, keep, std::numeric_limits< double >::lowest() );
 
   std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;
   std::cout << "Max. elements in rows are: " << rowMax << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "All rows reduction on host:" << std::endl;
   reduceAllRows< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "All rows reduction on CUDA device:" << std::endl;
   reduceAllRows< TNL::Devices::Cuda >();
#endif
}

Output

All rows reduction on host:
The matrix reads as: 
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Max. elements in rows are: [ 1, 2, 3, 4, 5 ]
All rows reduction on CUDA device:
The matrix reads as: 
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Max. elements in rows are: [ 1, 2, 3, 4, 5 ]

reduceRows()

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

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

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::reduceRows	(	IndexType	begin,
		IndexType	end,
		Fetch &&	fetch,
		const Reduce &	reduce,
		Keep &&	keep,
		const FetchReal &	identity ) const

Method for performing general reduction on matrix rows.

Template Parameters

Fetch

is a type of lambda function for data fetch declared as

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

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

Template Parameters

Reduce

is a type of lambda function for reduction declared as

auto reduce = [=] __cuda_callbale__ ( 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/LambdaMatrix.h>
#include <TNL/Devices/Host.h>
#include <TNL/Devices/Cuda.h>
 
template< typename Device >
void
reduceRows()
{
   /***
    * Lambda functions defining the matrix.
    */
   auto rowLengths = [ = ] __cuda_callable__( const int rows, const int columns, const int rowIdx ) -> int
   {
      return columns;
   };
   auto matrixElements =
      [ = ] __cuda_callable__(
         const int rows, const int columns, const int rowIdx, const int localIdx, int& columnIdx, double& value )
   {
      columnIdx = localIdx;
      value = TNL::max( rowIdx - columnIdx + 1, 0 );
   };
 
   using MatrixFactory = TNL::Matrices::LambdaMatrixFactory< double, Device, int >;
   auto matrix = MatrixFactory::create( 5, 5, matrixElements, rowLengths );
 
   /***
    * 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.
    */
   matrix.reduceRows( 0, matrix.getRows(), fetch, reduce, keep, std::numeric_limits< double >::lowest() );
 
   std::cout << "The matrix reads as: " << std::endl << matrix << std::endl;
   std::cout << "Max. elements in rows are: " << rowMax << std::endl;
}
 
int
main( int argc, char* argv[] )
{
   std::cout << "Rows reduction on host:" << std::endl;
   reduceRows< TNL::Devices::Host >();
 
#ifdef __CUDACC__
   std::cout << "Rows reduction on CUDA device:" << std::endl;
   reduceRows< TNL::Devices::Cuda >();
#endif
}

Output

Rows reduction on host:
The matrix reads as: 
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Max. elements in rows are: [ 1, 2, 3, 4, 5 ]
Rows reduction on CUDA device:
The matrix reads as: 
Row: 0 ->     0:1   
Row: 1 ->     0:2       1:1   
Row: 2 ->     0:3       1:2       2:1   
Row: 3 ->     0:4       1:3       2:2       3:1   
Row: 4 ->     0:5       1:4       2:3       3:2       4:1   
 
Max. elements in rows are: [ 1, 2, 3, 4, 5 ]

sequentialForAllRows()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::sequentialForAllRows

(

Function &&

function

)

const

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

See LambdaMatrix::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()

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

template<typename Function >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::sequentialForRows	(	IndexType	begin,
		IndexType	end,
		Function &&	function ) const

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

Template Parameters

Function

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

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

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

setDimensions()

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

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::setDimensions	(	IndexType	rows,
		IndexType	columns )

Set number of rows and columns of this matrix.

Parameters

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

vectorProduct()

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

template<typename InVector , typename OutVector >

void TNL::Matrices::LambdaMatrix< MatrixElementsLambda, CompressedRowLengthsLambda, Real, Device, Index >::vectorProduct	(	const InVector &	inVector,
		OutVector &	outVector,
		const RealType &	matrixMultiplicator = 1.0,
		const 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.

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

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