/***************************************************************************
                          SparseMatrix.h -  description
                             -------------------
    begin                : Nov 29, 2019
    copyright            : (C) 2019 by Tomas Oberhuber
    email                : tomas.oberhuber@fjfi.cvut.cz
 ***************************************************************************/

/* See Copyright Notice in tnl/Copyright */

#pragma once

#include <map>
#include <TNL/Matrices/Matrix.h>
#include <TNL/Matrices/MatrixType.h>
#include <TNL/Allocators/Default.h>
#include <TNL/Algorithms/Segments/CSR.h>
#include <TNL/Matrices/SparseMatrixRowView.h>
#include <TNL/Matrices/SparseMatrixView.h>
#include <TNL/Matrices/DenseMatrix.h>

namespace TNL {
namespace Matrices {

/**
 * \brief Implementation of sparse matrix, i.e. matrix storing only non-zero elements.
 *
 * \tparam Real is a type of matrix elements. If \e Real equals \e bool the matrix is treated
 *    as binary and so the matrix elements values are not stored in the memory since we need
 *    to remember only coordinates of non-zero elements( which equal one).
 * \tparam Device is a device where the matrix is allocated.
 * \tparam Index is a type for indexing of the matrix elements.
 * \tparam MatrixType specifies a symmetry of matrix. See \ref MatrixType. Symmetric
 *    matrices store only lower part of the matrix and its diagonal. The upper part is reconstructed on the fly.
 *    GeneralMatrix with no symmetry is used by default.
 * \tparam Segments is a structure representing the sparse matrix format. Depending on the pattern of the non-zero elements
 *    different matrix formats can perform differently especially on GPUs. By default \ref CSR format is used. See also
 *    \ref Ellpack, \ref SlicedEllpack, \ref ChunkedEllpack or \ref BiEllpack.
 * \tparam ComputeReal is the same as \e Real mostly but for binary matrices it is set to \e Index type. This can be changed
 *    by the user, of course.
 * \tparam RealAllocator is allocator for the matrix elements values.
 * \tparam IndexAllocator is allocator for the matrix elements column indexes.
 */
template< typename Real =  double,
          typename Device = Devices::Host,
          typename Index = int,
          typename MatrixType = GeneralMatrix,
          template< typename Device_, typename Index_, typename IndexAllocator_ > class Segments = Algorithms::Segments::CSRDefault,
          typename ComputeReal = typename ChooseSparseMatrixComputeReal< Real, Index >::type,
          typename RealAllocator = typename Allocators::Default< Device >::template Allocator< Real >,
          typename IndexAllocator = typename Allocators::Default< Device >::template Allocator< Index > >
class SparseMatrix : public Matrix< Real, Device, Index, RealAllocator >
{
   static_assert(
         ! MatrixType::isSymmetric() ||
         ! std::is_same< Device, Devices::Cuda >::value ||
         ( std::is_same< Real, float >::value || std::is_same< Real, double >::value || std::is_same< Real, int >::value || std::is_same< Real, long long int >::value ),
         "Given Real type is not supported by atomic operations on GPU which are necessary for symmetric operations." );

   public:

      // Supporting types - they are not important for the user
      using BaseType = Matrix< Real, Device, Index, RealAllocator >;
      using ValuesVectorType = typename Matrix< Real, Device, Index, RealAllocator >::ValuesType;
      using ValuesViewType = typename ValuesVectorType::ViewType;
      using ConstValuesViewType = typename ValuesViewType::ConstViewType;
      using ColumnsIndexesVectorType = Containers::Vector< typename TNL::copy_const< Index >::template from< Real >::type, Device, Index, IndexAllocator >;
      using ColumnsIndexesViewType = typename ColumnsIndexesVectorType::ViewType;
      using ConstColumnsIndexesViewType = typename ColumnsIndexesViewType::ConstViewType;
      using RowsCapacitiesType = Containers::Vector< std::remove_const_t< Index >, Device, Index, IndexAllocator >;
      using RowsCapacitiesView = Containers::VectorView< std::remove_const_t< Index >, Device, Index >;
      using ConstRowsCapacitiesView = typename RowsCapacitiesView::ConstViewType;

      /**
       * \brief Test of symmetric matrix type.
       *
       * \return \e true if the matrix is stored as symmetric and \e false otherwise.
       */
      static constexpr bool isSymmetric() { return MatrixType::isSymmetric(); };

      /**
       * \brief Test of binary matrix type.
       *
       * \return \e true if the matrix is stored as binary and \e false otherwise.
       */
      static constexpr bool isBinary() { return std::is_same< Real, bool >::value; };

      /**
       * \brief The type of matrix elements.
       */
      using RealType = std::remove_const_t< Real >;

      using ComputeRealType = ComputeReal;

      /**
       * \brief The device where the matrix is allocated.
       */
      using DeviceType = Device;

      /**
       * \brief The type used for matrix elements indexing.
       */
      using IndexType = Index;

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

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

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

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

      /**
       * \brief The allocator for matrix elements values.
       */
      using RealAllocatorType = RealAllocator;

      /**
       * \brief The allocator for matrix elements column indexes.
       */
      using IndexAllocatorType = IndexAllocator;

      /**
       * \brief Type of related matrix view.
       *
       * See \ref SparseMatrixView.
       */
      using ViewType = SparseMatrixView< Real, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >;

      /**
       * \brief Matrix view type for constant instances.
       *
       * See \ref SparseMatrixView.
       */
      using ConstViewType = SparseMatrixView< std::add_const_t< Real >, Device, Index, MatrixType, SegmentsViewTemplate, ComputeRealType >;

      /**
       * \brief Type for accessing matrix rows.
       */
      using RowView = typename ViewType::RowView;

      /**
       * \brief Type for accessing constant matrix rows.
       */
      using ConstRowView = typename ViewType::ConstRowView;

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

      /**
       * \brief Constructor only with values and column indexes allocators.
       *
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       */
      SparseMatrix( const RealAllocatorType& realAllocator = RealAllocatorType(),
                    const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Copy constructor.
       *
       * \param matrix is the source matrix
       */
      SparseMatrix( const SparseMatrix& matrix1 ) = default;

      /**
       * \brief Move constructor.
       *
       * \param matrix is the source matrix
       */
      SparseMatrix( SparseMatrix&& matrix ) = default;

      /**
       * \brief Constructor with matrix dimensions.
       *
       * \param rows is number of matrix rows.
       * \param columns is number of matrix columns.
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       */
      template< typename Index_t, std::enable_if_t< std::is_integral< Index_t >::value, int > = 0 >
      SparseMatrix( const Index_t rows,
                    const Index_t columns,
                    const RealAllocatorType& realAllocator = RealAllocatorType(),
                    const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Constructor with matrix rows capacities and number of columns.
       *
       * The number of matrix rows is given by the size of \e rowCapacities list.
       *
       * \tparam ListIndex is the initializer list values type.
       * \param rowCapacities is a list telling how many matrix elements must be
       *    allocated in each row.
       * \param columns is the number of matrix columns.
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_Constructor_init_list_1.cpp
       * \par Output
       * \include SparseMatrixExample_Constructor_init_list_1.out
       */
      template< typename ListIndex >
      explicit SparseMatrix( const std::initializer_list< ListIndex >& rowCapacities,
                             const IndexType columns,
                             const RealAllocatorType& realAllocator = RealAllocatorType(),
                             const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Constructor with matrix rows capacities given as a vector and number of columns.
       *
       * The number of matrix rows is given by the size of \e rowCapacities vector.
       *
       * \tparam RowCapacitiesVector is the row capacities vector type. Usually it is some of
       *    \ref TNL::Containers::Array, \ref TNL::Containers::ArrayView, \ref TNL::Containers::Vector or
       *    \ref TNL::Containers::VectorView.
       * \param rowCapacities is a vector telling how many matrix elements must be
       *    allocated in each row.
       * \param columns is the number of matrix columns.
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_Constructor_rowCapacities_vector.cpp
       * \par Output
       * \include SparseMatrixExample_Constructor_rowCapacities_vector.out
       */
      template< typename RowCapacitiesVector, std::enable_if_t< TNL::IsArrayType< RowCapacitiesVector >::value, int > = 0 >
      explicit SparseMatrix( const RowCapacitiesVector& rowCapacities,
                             const IndexType columns,
                             const RealAllocatorType& realAllocator = RealAllocatorType(),
                             const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Constructor with matrix dimensions and data in initializer list.
       *
       * The matrix elements values are given as a list \e data of triples:
       * { { row1, column1, value1 },
       *   { row2, column2, value2 },
       * ... }.
       *
       * \param rows is number of matrix rows.
       * \param columns is number of matrix columns.
       * \param data is a list of matrix elements values.
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_Constructor_init_list_2.cpp
       * \par Output
       * \include SparseMatrixExample_Constructor_init_list_2.out
       */
      explicit SparseMatrix( const IndexType rows,
                             const IndexType columns,
                             const std::initializer_list< std::tuple< IndexType, IndexType, RealType > >& data,
                             const RealAllocatorType& realAllocator = RealAllocatorType(),
                             const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Constructor with matrix dimensions and data in std::map.
       *
       * The matrix elements values are given as a map \e data where keys are
       * std::pair of matrix coordinates ( {row, column} ) and value is the
       * matrix element value.
       *
       * \tparam MapIndex is a type for indexing rows and columns.
       * \tparam MapValue is a type for matrix elements values in the map.
       *
       * \param rows is number of matrix rows.
       * \param columns is number of matrix columns.
       * \param map is std::map containing matrix elements.
       * \param realAllocator is used for allocation of matrix elements values.
       * \param indexAllocator is used for allocation of matrix elements column indexes.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_Constructor_std_map.cpp
       * \par Output
       * \include SparseMatrixExample_Constructor_std_map.out
       */
      template< typename MapIndex,
                typename MapValue >
      explicit SparseMatrix( const IndexType rows,
                             const IndexType columns,
                             const std::map< std::pair< MapIndex, MapIndex >, MapValue >& map,
                             const RealAllocatorType& realAllocator = RealAllocatorType(),
                             const IndexAllocatorType& indexAllocator = IndexAllocatorType() );

      /**
       * \brief Returns a modifiable view of the sparse matrix.
       *
       * See \ref SparseMatrixView.
       *
       * \return sparse matrix view.
       */
      ViewType getView() const; // TODO: remove const

      /**
       * \brief Returns a non-modifiable view of the sparse matrix.
       *
       * See \ref SparseMatrixView.
       *
       * \return sparse matrix view.
       */
      ConstViewType getConstView() const;

      /**
       * \brief Returns string with serialization type.
       *
       * The string has a form `Matrices::SparseMatrix< RealType,  [any_device], IndexType, General/Symmetric, Format, [any_allocator] >`.
       *
       * \return \ref String with the serialization type.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getSerializationType.cpp
       * \par Output
       * \include SparseMatrixExample_getSerializationType.out
       */
      static String getSerializationType();

      /**
       * \brief Returns string with serialization type.
       *
       * See \ref SparseMatrix::getSerializationType.
       *
       * \return \e String with the serialization type.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getSerializationType.cpp
       * \par Output
       * \include SparseMatrixExample_getSerializationType.out
       */
      virtual String getSerializationTypeVirtual() const override;

      /**
       * \brief Set number of rows and columns of this matrix.
       *
       * \param rows is the number of matrix rows.
       * \param columns is the number of matrix columns.
       */
      virtual void setDimensions( const IndexType rows,
                                  const IndexType columns ) override;

      /**
       * \brief Set the number of matrix rows and columns by the given matrix.
       *
       * \tparam Matrix is matrix type. This can be any matrix having methods
       *  \ref getRows and \ref getColumns.
       *
       * \param matrix in the input matrix dimensions of which are to be adopted.
       */
      template< typename Matrix >
      void setLike( const Matrix& matrix );

      /**
       * \brief Allocates memory for non-zero matrix elements.
       *
       * The size of the input vector must be equal to the number of matrix rows.
       * The number of allocated matrix elements for each matrix row depends on
       * the sparse matrix format. Some formats may allocate more elements than
       * required.
       *
       * \tparam RowsCapacitiesVector is a type of vector/array used for row
       *    capacities setting.
       *
       * \param rowCapacities is a vector telling the number of required non-zero
       *    matrix elements in each row.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_setRowCapacities.cpp
       * \par Output
       * \include SparseMatrixExample_setRowCapacities.out
       */
      template< typename RowsCapacitiesVector >
      void setRowCapacities( const RowsCapacitiesVector& rowCapacities );

      /**
       * \brief Compute capacities of all rows.
       *
       * The row capacities are not stored explicitly and must be computed.
       *
       * \param rowCapacities is a vector where the row capacities will be stored.
       */
      template< typename Vector >
      void getRowCapacities( Vector& rowCapacities ) const;

      /**
       * \brief This method sets the sparse matrix elements from initializer list.
       *
       * The number of matrix rows and columns must be set already.
       * The matrix elements values are given as a list \e data of triples:
       * { { row1, column1, value1 },
       *   { row2, column2, value2 },
       * ... }.
       *
       * \param data is a initializer list of initializer lists representing
       * list of matrix rows.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_setElements.cpp
       * \par Output
       * \include SparseMatrixExample_setElements.out
       */
      void setElements( const std::initializer_list< std::tuple< IndexType, IndexType, RealType > >& data );

      /**
       * \brief This method sets the sparse matrix elements from std::map.
       *
       * The matrix elements values are given as a map \e data where keys are
       * std::pair of matrix coordinates ( {row, column} ) and value is the
       * matrix element value.
       *
       * \tparam MapIndex is a type for indexing rows and columns.
       * \tparam MapValue is a type for matrix elements values in the map.
       *
       * \param map is std::map containing matrix elements.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_setElements_map.cpp
       * \par Output
       * \include SparseMatrixExample_setElements_map.out
       */
      template< typename MapIndex,
                typename MapValue >
      void setElements( const std::map< std::pair< MapIndex, MapIndex > , MapValue >& map );

      /**
       * \brief Computes number of non-zeros in each row.
       *
       * \param rowLengths is a vector into which the number of non-zeros in each row
       * will be stored.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getCompressedRowLengths.cpp
       * \par Output
       * \include SparseMatrixExample_getCompressedRowLengths.out
       */
      template< typename Vector >
      void getCompressedRowLengths( Vector& rowLengths ) const;


      /**
       * \brief Returns capacity of given matrix row.
       *
       * \param row index of matrix row.
       * \return number of matrix elements allocated for the row.
       */
      __cuda_callable__
      IndexType getRowCapacity( const IndexType row ) const;

      /**
       * \brief Returns number of non-zero matrix elements.
       *
       * This method really counts the non-zero matrix elements and so
       * it returns zero for matrix having all allocated elements set to zero.
       *
       * \return number of non-zero matrix elements.
       */
      IndexType getNonzeroElementsCount() const;

      /**
       * \brief Resets the matrix to zero dimensions.
       */
      void reset();

      /**
       * \brief Constant getter of simple structure for accessing given matrix row.
       *
       * \param rowIdx is matrix row index.
       *
       * \return RowView for accessing given matrix row.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getConstRow.cpp
       * \par Output
       * \include SparseMatrixExample_getConstRow.out
       *
       * See \ref SparseMatrixRowView.
       */
      __cuda_callable__
      const ConstRowView getRow( const IndexType& rowIdx ) const;

      /**
       * \brief Non-constant getter of simple structure for accessing given matrix row.
       *
       * \param rowIdx is matrix row index.
       *
       * \return RowView for accessing given matrix row.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getRow.cpp
       * \par Output
       * \include SparseMatrixExample_getRow.out
       *
       * See \ref SparseMatrixRowView.
       */
      __cuda_callable__
      RowView getRow( const IndexType& rowIdx );

      /**
       * \brief Sets element at given \e row and \e column to given \e value.
       *
       * This method can be called from the host system (CPU) no matter
       * where the matrix is allocated. If the matrix is allocated on GPU this method
       * can be called even from device kernels. If the matrix is allocated in GPU device
       * this method is called from CPU, it transfers values of each matrix element separately and so the
       * performance is very low. For higher performance see. \ref SparseMatrix::getRow
       * or \ref SparseMatrix::forElements and \ref SparseMatrix::forAllElements.
       * The call may fail if the matrix row capacity is exhausted.
       *
       * \param row is row index of the element.
       * \param column is columns index of the element.
       * \param value is the value the element will be set to.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_setElement.cpp
       * \par Output
       * \include SparseMatrixExample_setElement.out
       */
      __cuda_callable__
      void setElement( const IndexType row,
                       const IndexType column,
                       const RealType& value );

      /**
       * \brief Add element at given \e row and \e column to given \e value.
       *
       * This method can be called from the host system (CPU) no matter
       * where the matrix is allocated. If the matrix is allocated on GPU this method
       * can be called even from device kernels. If the matrix is allocated in GPU device
       * this method is called from CPU, it transfers values of each matrix element separately and so the
       * performance is very low. For higher performance see. \ref SparseMatrix::getRow
       * or \ref SparseMatrix::forElements and \ref SparseMatrix::forAllElements.
       * The call may fail if the matrix row capacity is exhausted.
       *
       * \param row is row index of the element.
       * \param column is columns index of the element.
       * \param value is the value the element will be set to.
       * \param thisElementMultiplicator is multiplicator the original matrix element
       *   value is multiplied by before addition of given \e value.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_addElement.cpp
       * \par Output
       * \include SparseMatrixExample_addElement.out
       *
       */
      __cuda_callable__
      void addElement( const IndexType row,
                       const IndexType column,
                       const RealType& value,
                       const RealType& thisElementMultiplicator );

      /**
       * \brief Returns value of matrix element at position given by its row and column index.
       *
       * This method can be called from the host system (CPU) no matter
       * where the matrix is allocated. If the matrix is allocated on GPU this method
       * can be called even from device kernels. If the matrix is allocated in GPU device
       * this method is called from CPU, it transfers values of each matrix element separately and so the
       * performance is very low. For higher performance see. \ref SparseMatrix::getRow
       * or \ref SparseMatrix::forElements and \ref SparseMatrix::forAllElements.
       *
       * \param row is a row index of the matrix element.
       * \param column i a column index of the matrix element.
       *
       * \return value of given matrix element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_getElement.cpp
       * \par Output
       * \include SparseMatrixExample_getElement.out
       *
       */
      __cuda_callable__
      RealType getElement( const IndexType row,
                           const IndexType column ) const;

      /**
       * \brief Method for performing general reduction on matrix rows.
       *
       * \tparam Fetch is a type of lambda function for data fetch declared as
       *          `fetch( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue`.
       *          The return type of this lambda can be any non void.
       * \tparam Reduce is a type of lambda function for reduction declared as
       *          `reduce( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue`.
       * \tparam Keep is a type of lambda function for storing results of reduction in each row.
       *          It is declared as `keep( const IndexType rowIdx, const double& value )`.
       * \tparam FetchValue is type returned by the Fetch lambda function.
       *
       * \param begin defines beginning of the range [begin,end) of rows to be processed.
       * \param end defines ending of the range [begin,end) of rows to be processed.
       * \param fetch is an instance of lambda function for data fetch.
       * \param reduce is an instance of lambda function for reduction.
       * \param keep in an instance of lambda function for storing results.
       * \param zero is zero of given reduction operation also known as idempotent element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_reduceRows.cpp
       * \par Output
       * \include SparseMatrixExample_reduceRows.out
       */
      template< typename Fetch, typename Reduce, typename Keep, typename FetchReal >
      void reduceRows( IndexType begin, IndexType end, Fetch& fetch, const Reduce& reduce, Keep& keep, const FetchReal& zero );

      /**
       * \brief Method for performing general reduction on matrix rows for constant instances.
       *
       * \tparam Fetch is a type of lambda function for data fetch declared as
       *          `fetch( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue`.
       *          The return type of this lambda can be any non void.
       * \tparam Reduce is a type of lambda function for reduction declared as
       *          `reduce( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue`.
       * \tparam Keep is a type of lambda function for storing results of reduction in each row.
       *          It is declared as `keep( const IndexType rowIdx, const double& value )`.
       * \tparam FetchValue is type returned by the Fetch lambda function.
       *
       * \param begin defines beginning of the range [begin,end) of rows to be processed.
       * \param end defines ending of the range [begin,end) of rows to be processed.
       * \param fetch is an instance of lambda function for data fetch.
       * \param reduce is an instance of lambda function for reduction.
       * \param keep in an instance of lambda function for storing results.
       * \param zero is zero of given reduction operation also known as idempotent element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_reduceRows.cpp
       * \par Output
       * \include SparseMatrixExample_reduceRows.out
       */
      template< typename Fetch, typename Reduce, typename Keep, typename FetchReal >
      void reduceRows( IndexType begin, IndexType end, Fetch& fetch, const Reduce& reduce, Keep& keep, const FetchReal& zero ) const;

      /**
       * \brief Method for performing general reduction on all matrix rows.
       *
       * \tparam Fetch is a type of lambda function for data fetch declared as
       *          `fetch( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue`.
       *          The return type of this lambda can be any non void.
       * \tparam Reduce is a type of lambda function for reduction declared as
       *          `reduce( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue`.
       * \tparam Keep is a type of lambda function for storing results of reduction in each row.
       *          It is declared as `keep( const IndexType rowIdx, const double& value )`.
       * \tparam FetchValue is type returned by the Fetch lambda function.
       *
       * \param fetch is an instance of lambda function for data fetch.
       * \param reduce is an instance of lambda function for reduction.
       * \param keep in an instance of lambda function for storing results.
       * \param zero is zero of given reduction operation also known as idempotent element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_reduceAllRows.cpp
       * \par Output
       * \include SparseMatrixExample_reduceAllRows.out
       */
      template< typename Fetch, typename Reduce, typename Keep, typename FetchReal >
      void reduceAllRows( Fetch& fetch, const Reduce& reduce, Keep& keep, const FetchReal& zero );

      /**
       * \brief Method for performing general reduction on all matrix rows for constant instances.
       *
       * \tparam Fetch is a type of lambda function for data fetch declared as
       *          `fetch( IndexType rowIdx, IndexType& columnIdx, RealType& elementValue ) -> FetchValue`.
       *          The return type of this lambda can be any non void.
       * \tparam Reduce is a type of lambda function for reduction declared as
       *          `reduce( const FetchValue& v1, const FetchValue& v2 ) -> FetchValue`.
       * \tparam Keep is a type of lambda function for storing results of reduction in each row.
       *          It is declared as `keep( const IndexType rowIdx, const double& value )`.
       * \tparam FetchValue is type returned by the Fetch lambda function.
       *
       * \param fetch is an instance of lambda function for data fetch.
       * \param reduce is an instance of lambda function for reduction.
       * \param keep in an instance of lambda function for storing results.
       * \param zero is zero of given reduction operation also known as idempotent element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_reduceAllRows.cpp
       * \par Output
       * \include SparseMatrixExample_reduceAllRows.out
       */
      template< typename Fetch, typename Reduce, typename Keep, typename FetchReal >
      void reduceAllRows( Fetch& fetch, const Reduce& reduce, Keep& keep, const FetchReal& zero ) const;

      /**
       * \brief Method for parallel iteration over matrix elements of given rows for constant instances.
       *
       * \tparam Function is type of lambda function that will operate on matrix elements.
       *
       * \param begin defines beginning of the range [ \e begin,\e end ) of rows to be processed.
       * \param end defines ending of the range [ \e begin, \e end ) of rows to be processed.
       * \param function is an instance of the lambda function to be called for element of given rows.
       *
       * The lambda function `function` should be declared like follows:
       *
       * ```
       * auto function = [] __cuda_callable__ ( IndexType rowIdx, IndexType localIdx, IndexType columnIdx, const RealType& value, bool& compute ) { ... };
       * ```
       *
       *  The \e localIdx parameter is a rank of the non-zero element in given row.
       *  If the 'compute' variable is set to false the iteration over the row can
       *  be interrupted.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forElements.cpp
       * \par Output
       * \include SparseMatrixExample_forElements.out
       */
      template< typename Function >
      void forElements( IndexType begin, IndexType end, Function&& function ) const;

      /**
       * \brief Method for parallel iteration over all matrix elements of given rows for non-constant instances.
       *
       * \tparam Function is type of lambda function that will operate on matrix elements.
       *
       * \param begin defines beginning of the range [ \e begin,\e end ) of rows to be processed.
       * \param end defines ending of the range [ \e begin, \e end ) of rows to be processed.
       * \param function is an instance of the lambda function to be called for each element of given rows.
       *
       * The lambda function `function` should be declared like follows:
       *
       * ```
       * auto function = [] __cuda_callable__ ( IndexType rowIdx, IndexType localIdx, IndexType columnIdx, const RealType& value, bool& compute ) mutable { ... }
       * ```
       *
       *  The \e localIdx parameter is a rank of the non-zero element in given row.
       *  If the 'compute' variable is set to false the iteration over the row can
       *  be interrupted.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forElements.cpp
       * \par Output
       * \include SparseMatrixExample_forElements.out
       */
      template< typename Function >
      void forElements( IndexType begin, IndexType end, Function&& function );

      /**
       * \brief Method for parallel iteration over all matrix elements for constant instances.
       *
       * See \ref SparseMatrix::forElements.
       *
       * \tparam Function is a type of lambda function that will operate on matrix elements.
       * \param function  is an instance of the lambda function to be called for each matrix element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forElements.cpp
       * \par Output
       * \include SparseMatrixExample_forElements.out
       */
      template< typename Function >
      void forAllElements( Function&& function ) const;

      /**
       * \brief Method for parallel iteration over all matrix elements for non-constant instances.
       *
       * See \ref SparseMatrix::forElements.
       *
       * \tparam Function is a type of lambda function that will operate on matrix elements.
       * \param function  is an instance of the lambda function to be called for each matrix element.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forElements.cpp
       * \par Output
       * \include SparseMatrixExample_forElements.out
       */
      template< typename Function >
      void forAllElements( Function&& function );

      /**
       * \brief Method for parallel iteration over matrix rows from interval [ \e begin, \e end).
       *
       * In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method
       * \ref SparseMatrix::forElements where more than one thread can be mapped to each row.
       *
       * \tparam Function is type of the lambda function.
       *
       * \param begin defines beginning of the range [ \e begin,\e end ) of rows to be processed.
       * \param end defines ending of the range [ \e begin, \e end ) of rows to be processed.
       * \param function is an instance of the lambda function to be called for each row.
       *
       * ```
       * auto function = [] __cuda_callable__ ( RowView& row ) mutable { ... };
       * ```
       *
       * \e RowView represents matrix row - see \ref TNL::Matrices::SparseMatrix::RowView.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forRows.cpp
       * \par Output
       * \include SparseMatrixExample_forRows.out
       */
      template< typename Function >
      void forRows( IndexType begin, IndexType end, Function&& function );

      /**
       * \brief Method for parallel iteration over matrix rows from interval [ \e begin, \e end) for constant instances.
       *
       * In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method
       * \ref SparseMatrix::forElements where more than one thread can be mapped to each row.
       *
       * \tparam Function is type of the lambda function.
       *
       * \param begin defines beginning of the range [ \e begin,\e end ) of rows to be processed.
       * \param end defines ending of the range [ \e begin, \e end ) of rows to be processed.
       * \param function is an instance of the lambda function to be called for each row.
       *
       * ```
       * auto function = [] __cuda_callable__ ( RowView& row ) { ... };
       * ```
       *
       * \e RowView represents matrix row - see \ref TNL::Matrices::SparseMatrix::RowView.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forRows.cpp
       * \par Output
       * \include SparseMatrixExample_forRows.out
       */
      template< typename Function >
      void forRows( IndexType begin, IndexType end, Function&& function ) const;

      /**
       * \brief Method for parallel iteration over all matrix rows.
       *
       * In each row, given lambda function is performed. Each row is processed by at most one thread unlike the method
       * \ref SparseMatrix::forAllElements where more than one thread can be mapped to each row.
       *
       * \tparam Function is type of the lambda function.
       *
       * \param function is an instance of the lambda function to be called for each row.
       *
       * ```
       * auto function = [] __cuda_callable__ ( RowView& row ) mutable { ... };
       * ```
       *
       * \e RowView represents matrix row - see \ref TNL::Matrices::SparseMatrix::RowView.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forRows.cpp
       * \par Output
       * \include SparseMatrixExample_forRows.out
       */
      template< typename Function >
      void forAllRows( Function&& function );

      /**
       * \brief 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
       * \ref SparseMatrix::forAllElements where more than one thread can be mapped to each row.
       *
       * \tparam Function is type of the lambda function.
       *
       * \param function is an instance of the lambda function to be called for each row.
       *
       * ```
       * auto function = [] __cuda_callable__ ( RowView& row ) { ... };
       * ```
       *
       * \e RowView represents matrix row - see \ref TNL::Matrices::SparseMatrix::RowView.
       *
       * \par Example
       * \include Matrices/SparseMatrix/SparseMatrixExample_forRows.cpp
       * \par Output
       * \include SparseMatrixExample_forRows.out
       */
      template< typename Function >
      void forAllRows( Function&& function ) const;

      /**
       * \brief Method for sequential iteration over all matrix rows for constant instances.
       *
       * \tparam Function is type of lambda function that will operate on matrix elements.
       *    It is should have form like
       *  `function( IndexType rowIdx, IndexType columnIdx, IndexType columnIdx_, const RealType& value, bool& compute )`.
       *  The column index repeats twice only for compatibility with sparse matrices.
       *  If the 'compute' variable is set to false the iteration over the row can
       *  be interrupted.
       *
       * \param begin defines beginning of the range [begin,end) of rows to be processed.
       * \param end defines ending of the range [begin,end) of rows to be processed.
       * \param function is an instance of the lambda function to be called in each row.
       */
      template< typename Function >
      void sequentialForRows( IndexType begin, IndexType end, Function& function ) const;

      /**
       * \brief Method for sequential iteration over all matrix rows for non-constant instances.
       *
       * \tparam Function is type of lambda function that will operate on matrix elements.
       *    It is should have form like
       *  `function( IndexType rowIdx, IndexType columnIdx, IndexType columnIdx_, RealType& value, bool& compute )`.
       *  The column index repeats twice only for compatibility with sparse matrices.
       *  If the 'compute' variable is set to false the iteration over the row can
       *  be interrupted.
       *
       * \param begin defines beginning of the range [begin,end) of rows to be processed.
       * \param end defines ending of the range [begin,end) of rows to be processed.
       * \param function is an instance of the lambda function to be called in each row.
       */
      template< typename Function >
      void sequentialForRows( IndexType begin, IndexType end, Function& function );

      /**
       * \brief This method calls \e sequentialForRows for all matrix rows (for constant instances).
       *
       * See \ref SparseMatrix::sequentialForRows.
       *
       * \tparam Function is a type of lambda function that will operate on matrix elements.
       * \param function  is an instance of the lambda function to be called in each row.
       */
      template< typename Function >
      void sequentialForAllRows( Function& function ) const;

      /**
       * \brief This method calls \e sequentialForRows for all matrix rows.
       *
       * See \ref SparseMatrix::sequentialForAllRows.
       *
       * \tparam Function is a type of lambda function that will operate on matrix elements.
       * \param function  is an instance of the lambda function to be called in each row.
       */
      template< typename Function >
      void sequentialForAllRows( Function& function );

      /**
       * \brief Computes product of matrix and vector.
       *
       * More precisely, it computes:
       *
       * `outVector = matrixMultiplicator * ( * this ) * inVector + outVectorMultiplicator * outVector`
       *
       * \tparam InVector is type of input vector.  It can be \ref Vector,
       *     \ref VectorView, \ref Array, \ref ArraView or similar container.
       * \tparam OutVector is type of output vector. It can be \ref Vector,
       *     \ref VectorView, \ref Array, \ref ArraView or similar container.
       *
       * \param inVector is input vector.
       * \param outVector is output vector.
       * \param matrixMultiplicator is a factor by which the matrix is multiplied. It is one by default.
       * \param outVectorMultiplicator is a factor by which the outVector is multiplied before added
       *    to the result of matrix-vector product. It is zero by default.
       * \param begin is the beginning of the rows range for which the vector product
       *    is computed. It is zero by default.
       * \param end is the end of the rows range for which the vector product
       *    is computed. It is number if the matrix rows by default.
       */
      template< typename InVector,
                typename OutVector >
      void vectorProduct( const InVector& inVector,
                          OutVector& outVector,
                          const ComputeRealType& matrixMultiplicator = 1.0,
                          const ComputeRealType& outVectorMultiplicator = 0.0,
                          const IndexType firstRow = 0,
                          const IndexType lastRow = 0 ) const;

      /*template< typename Real2, typename Index2 >
      void addMatrix( const SparseMatrix< Real2, Segments, Device, Index2 >& matrix,
                      const RealType& matrixMultiplicator = 1.0,
                      const RealType& thisMatrixMultiplicator = 1.0 );

      template< typename Real2, typename Index2 >
      void getTransposition( const SparseMatrix< Real2, Segments, Device, Index2 >& matrix,
                             const RealType& matrixMultiplicator = 1.0 );
       */

      template< typename Vector1, typename Vector2 >
      bool performSORIteration( const Vector1& b,
                                const IndexType row,
                                Vector2& x,
                                const RealType& omega = 1.0 ) const;

      /**
       * \brief Assignment of exactly the same matrix type.
       *
       * \param matrix is input matrix for the assignment.
       * \return reference to this matrix.
       */
      SparseMatrix& operator=( const SparseMatrix& matrix );

      /**
       * \brief Assignment of dense matrix
       *
       * \param matrix is input matrix for the assignment.
       * \return reference to this matrix.
       */
      template< typename Real_, typename Device_, typename Index_, ElementsOrganization Organization, typename RealAllocator_ >
      SparseMatrix& operator=( const DenseMatrix< Real_, Device_, Index_, Organization, RealAllocator_ >& matrix );


      /**
       * \brief Assignment of any matrix type other then this and dense.
       *
       * **Warning: Assignment of symmetric sparse matrix to general sparse matrix does not give correct result, currently. Only the diagonal and the lower part of the matrix is assigned.**
       *
       * \param matrix is input matrix for the assignment.
       * \return reference to this matrix.
       */
      template< typename RHSMatrix >
      SparseMatrix& operator=( const RHSMatrix& matrix );

      /**
       * \brief Comparison operator with another arbitrary matrix type.
       *
       * \param matrix is the right-hand side matrix.
       * \return \e true if the RHS matrix is equal, \e false otherwise.
       */
      template< typename Matrix >
      bool operator==( const Matrix& m ) const;

      /**
       * \brief Comparison operator with another arbitrary matrix type.
       *
       * \param matrix is the right-hand side matrix.
       * \return \e true if the RHS matrix is equal, \e false otherwise.
       */
      template< typename Matrix >
      bool operator!=( const Matrix& m ) const;

      /**
       * \brief Method for saving the matrix to the file with given filename.
       *
       * \param fileName is name of the file.
       */
      void save( const String& fileName ) const;

      /**
       * \brief Method for loading the matrix from the file with given filename.
       *
       * \param fileName is name of the file.
       */
      void load( const String& fileName );

      /**
       * \brief Method for saving the matrix to a file.
       *
       * \param file is the output file.
       */
      virtual void save( File& file ) const override;

      /**
       * \brief Method for loading the matrix from a file.
       *
       * \param file is the input file.
       */
      virtual void load( File& file ) override;

      /**
       * \brief Method for printing the matrix to output stream.
       *
       * \param str is the output stream.
       */
      virtual void print( std::ostream& str ) const override;

      /**
       * \brief Returns a padding index value.
       *
       * Padding index is used for column indexes of padding zeros. Padding zeros
       * are used in some sparse matrix formats for better data alignment in memory.
       *
       * \return value of the padding index.
       */
      __cuda_callable__
      IndexType getPaddingIndex() const;

      /**
       * \brief Getter of segments for non-constant instances.
       *
       * \e Segments are a structure for addressing the matrix elements columns and values.
       * In fact, \e Segments represent the sparse matrix format.
       *
       * \return Non-constant reference to segments.
       */
      SegmentsType& getSegments();

      /**
       * \brief Getter of segments for constant instances.
       *
       * \e Segments are a structure for addressing the matrix elements columns and values.
       * In fact, \e Segments represent the sparse matrix format.
       *
       * \return Constant reference to segments.
       */
      const SegmentsType& getSegments() const;

      /**
       * \brief Getter of column indexes for constant instances.
       *
       * \return Constant reference to a vector with matrix elements column indexes.
       */
      const ColumnsIndexesVectorType& getColumnIndexes() const;

      /**
       * \brief Getter of column indexes for nonconstant instances.
       *
       * \return Reference to a vector with matrix elements column indexes.
       */
      ColumnsIndexesVectorType& getColumnIndexes();

   protected:

      ColumnsIndexesVectorType columnIndexes;

      SegmentsType segments;

      IndexAllocator indexAllocator;

      ViewType view;
};

   } // namespace Matrices
} // namespace TNL

#include <TNL/Matrices/SparseMatrix.hpp>
