#include <deal.II/lac/block_linear_operator.h>

Inheritance diagram for BlockLinearOperator< Range, Domain, BlockPayload >:

Public Types
using	BlockType = LinearOperator< typename Range::BlockType, typename Domain::BlockType, typename BlockPayload::BlockType >

Public Member Functions
	BlockLinearOperator (const BlockPayload &payload)

	BlockLinearOperator (const BlockLinearOperator< Range, Domain, BlockPayload > &)=default

template<typename Op >
	BlockLinearOperator (const Op &op)

template<std::size_t m, std::size_t n>
	BlockLinearOperator (const std::array< std::array< BlockType, n >, m > &ops)

template<std::size_t m>
	BlockLinearOperator (const std::array< BlockType, m > &ops)

BlockLinearOperator< Range, Domain, BlockPayload > &	operator= (const BlockLinearOperator< Range, Domain, BlockPayload > &)=default

template<typename Op >
BlockLinearOperator< Range, Domain, BlockPayload > &	operator= (const Op &op)

template<std::size_t m, std::size_t n>
BlockLinearOperator< Range, Domain, BlockPayload > &	operator= (const std::array< std::array< BlockType, n >, m > &ops)

template<std::size_t m>
BlockLinearOperator< Range, Domain, BlockPayload > &	operator= (const std::array< BlockType, m > &ops)

Public Member Functions inherited from LinearOperator< Range, Domain, BlockPayload::BlockType >
	LinearOperator (const BlockPayload::BlockType &payload=BlockPayload::BlockType())

	LinearOperator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &)=default

	LinearOperator (const Op &op)

LinearOperator< Range, Domain, BlockPayload::BlockType > &	operator= (const LinearOperator< Range, Domain, BlockPayload::BlockType > &)=default

LinearOperator< Range, Domain, BlockPayload::BlockType > &	operator= (const Op &op)

LinearOperator< Range, Domain, BlockPayload::BlockType > &	operator+= (const LinearOperator< Range, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Range, Domain, BlockPayload::BlockType > &	operator-= (const LinearOperator< Range, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Range, Domain, BlockPayload::BlockType > &	operator*= (const LinearOperator< Domain, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator*= (typename Domain::value_type number)

Public Attributes
std::function< unsigned int()>	n_block_rows

std::function< unsigned int()>	n_block_cols

std::function< BlockType(unsigned int, unsigned int)>	block

Public Attributes inherited from LinearOperator< Range, Domain, BlockPayload::BlockType >
std::function< void(Range &v, const Domain &u)>	vmult

std::function< void(Range &v, const Domain &u)>	vmult_add

std::function< void(Domain &v, const Range &u)>	Tvmult

std::function< void(Domain &v, const Range &u)>	Tvmult_add

std::function< void(Range &v, bool omit_zeroing_entries)>	reinit_range_vector

std::function< void(Domain &v, bool omit_zeroing_entries)>	reinit_domain_vector

bool	is_null_operator

Related Functions
(Note that these are not member functions.)
Creation of a BlockLinearOperator
template<typename Range , typename Domain , typename BlockPayload , typename BlockMatrixType >
BlockLinearOperator< Range, Domain, BlockPayload >	block_operator (const BlockMatrixType &block_matrix)

template<std::size_t m, std::size_t n, typename Range , typename Domain , typename BlockPayload >
BlockLinearOperator< Range, Domain, BlockPayload >	block_operator (const std::array< std::array< LinearOperator< typename Range::BlockType, typename Domain::BlockType, typename BlockPayload::BlockType >, n >, m > &ops)

template<typename Range , typename Domain , typename BlockPayload , typename BlockMatrixType >
BlockLinearOperator< Range, Domain, BlockPayload >	block_diagonal_operator (const BlockMatrixType &block_matrix)

template<std::size_t m, typename Range , typename Domain , typename BlockPayload >
BlockLinearOperator< Range, Domain, BlockPayload >	block_diagonal_operator (const std::array< LinearOperator< typename Range::BlockType, typename Domain::BlockType, typename BlockPayload::BlockType >, m > &ops)

template<std::size_t m, typename Range , typename Domain , typename BlockPayload >
BlockLinearOperator< Range, Domain, BlockPayload >	block_diagonal_operator (const LinearOperator< typename Range::BlockType, typename Domain::BlockType, typename BlockPayload::BlockType > &op)

Manipulation of a BlockLinearOperator
template<typename Range , typename Domain , typename BlockPayload >
LinearOperator< Domain, Range, typename BlockPayload::BlockType >	block_forward_substitution (const BlockLinearOperator< Range, Domain, BlockPayload > &block_operator, const BlockLinearOperator< Domain, Range, BlockPayload > &diagonal_inverse)

template<typename Range , typename Domain , typename BlockPayload >
LinearOperator< Domain, Range, typename BlockPayload::BlockType >	block_back_substitution (const BlockLinearOperator< Range, Domain, BlockPayload > &block_operator, const BlockLinearOperator< Domain, Range, BlockPayload > &diagonal_inverse)

Creation of a BlockLinearOperator
template<typename Range , typename Domain = Range>
BlockLinearOperator< Range, Domain, TrilinosWrappers::internal::BlockLinearOperatorImplementation::TrilinosBlockPayload< TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload > >	block_operator (const TrilinosWrappers::BlockSparseMatrix &block_matrix)

template<std::size_t m, std::size_t n, typename Range , typename Domain = Range>
BlockLinearOperator< Range, Domain, TrilinosWrappers::internal::BlockLinearOperatorImplementation::TrilinosBlockPayload< TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload > >	block_operator (const std::array< std::array< LinearOperator< typename Range::BlockType, typename Domain::BlockType, TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload >, n >, m > &ops)

template<typename Range , typename Domain = Range>
BlockLinearOperator< Range, Domain, TrilinosWrappers::internal::BlockLinearOperatorImplementation::TrilinosBlockPayload< TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload > >	block_diagonal_operator (const TrilinosWrappers::BlockSparseMatrix &block_matrix)

template<std::size_t m, typename Range , typename Domain = Range>
BlockLinearOperator< Range, Domain, TrilinosWrappers::internal::BlockLinearOperatorImplementation::TrilinosBlockPayload< TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload > >	block_diagonal_operator (const std::array< LinearOperator< typename Range::BlockType, typename Domain::BlockType, TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload >, m > &ops)

Related Functions inherited from LinearOperator< Range, Domain, BlockPayload::BlockType >
LinearOperator< Range, Domain, BlockPayload::BlockType >	distribute_constraints_linear_operator (const AffineConstraints< typename Range::value_type > &constraints, const LinearOperator< Range, Domain, BlockPayload::BlockType > &exemplar)

LinearOperator< Range, Domain, BlockPayload::BlockType >	project_to_constrained_linear_operator (const AffineConstraints< typename Range::value_type > &constraints, const LinearOperator< Range, Domain, BlockPayload::BlockType > &exemplar)

LinearOperator< Range, Domain, BlockPayload::BlockType >	constrained_linear_operator (const AffineConstraints< typename Range::value_type > &constraints, const LinearOperator< Range, Domain, BlockPayload::BlockType > &linop)

PackagedOperation< Range >	constrained_right_hand_side (const AffineConstraints< typename Range::value_type > &constraints, const LinearOperator< Range, Domain, BlockPayload::BlockType > &linop, const Range &right_hand_side)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator+ (const LinearOperator< Range, Domain, BlockPayload::BlockType > &first_op, const LinearOperator< Range, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator- (const LinearOperator< Range, Domain, BlockPayload::BlockType > &first_op, const LinearOperator< Range, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator* (typename Range::value_type number, const LinearOperator< Range, Domain, BlockPayload::BlockType > &op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator* (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op, typename Domain::value_type number)

LinearOperator< Range, Domain, BlockPayload::BlockType >	operator* (const LinearOperator< Range, Intermediate, BlockPayload::BlockType > &first_op, const LinearOperator< Intermediate, Domain, BlockPayload::BlockType > &second_op)

LinearOperator< Domain, Range, BlockPayload::BlockType >	transpose_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op)

LinearOperator< Domain, Range, BlockPayload::BlockType >	inverse_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op, Solver &solver, const Preconditioner &preconditioner)

LinearOperator< Domain, Range, BlockPayload::BlockType >	inverse_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op, Solver &solver, const LinearOperator< Range, Domain, BlockPayload::BlockType > &preconditioner)

LinearOperator< Domain, Range, BlockPayload::BlockType >	inverse_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op, Solver &solver)

LinearOperator< Domain, Range, BlockPayload::BlockType >	inverse_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op, Solver &solver, const PreconditionIdentity &)

LinearOperator< Range, Range, BlockPayload::BlockType >	identity_operator (const std::function< void(Range &, bool)> &reinit_vector)

LinearOperator< Range, Domain, BlockPayload::BlockType >	identity_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	null_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op)

LinearOperator< Range, Range, BlockPayload::BlockType >	mean_value_filter (const std::function< void(Range &, bool)> &reinit_vector)

LinearOperator< Range, Domain, BlockPayload::BlockType >	mean_value_filter (const LinearOperator< Range, Domain, BlockPayload::BlockType > &op)

LinearOperator< Range, Domain, BlockPayload::BlockType >	linear_operator (const Matrix &matrix)

LinearOperator< Range, Domain, BlockPayload::BlockType >	linear_operator (const OperatorExemplar &operator_exemplar, const Matrix &matrix)

LinearOperator< Range, Domain, BlockPayload::BlockType >	linear_operator (const LinearOperator< Range, Domain, BlockPayload::BlockType > &operator_exemplar, const Matrix &matrix)

LinearOperator< Range, Domain, TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload >	linear_operator (const TrilinosWrappers::SparseMatrix &operator_exemplar, const Matrix &matrix)

LinearOperator< Range, Domain, TrilinosWrappers::internal::LinearOperatorImplementation::TrilinosPayload >	linear_operator (const TrilinosWrappers::SparseMatrix &matrix)

LinearOperator< Range_2, Domain_2, BlockPayload::BlockType >	schur_complement (const LinearOperator< Domain_1, Range_1, BlockPayload::BlockType > &A_inv, const LinearOperator< Range_1, Domain_2, BlockPayload::BlockType > &B, const LinearOperator< Range_2, Domain_1, BlockPayload::BlockType > &C, const LinearOperator< Range_2, Domain_2, BlockPayload::BlockType > &D)

Detailed Description

template<typename Range, typename Domain, typename BlockPayload>
class BlockLinearOperator< Range, Domain, BlockPayload >

A class to store the concept of a block linear operator.

This class increases the interface of LinearOperator (which encapsulates the Matrix interface) by three additional functions:

std::function<unsigned int()> n_block_rows;
std::function<unsigned int()> n_block_cols;
std::function<BlockType(unsigned int, unsigned int)> block;

that describe the underlying block structure (of an otherwise opaque) linear operator.

Objects of type BlockLinearOperator can be created similarly to LinearOperator with a wrapper function:

::BlockSparseMatrix<double> A;

const auto block_op_a = block_operator(A);

Alternatively, there are several helper functions available for creating instances from multiple independent matrices of possibly different types. Here is an example of a block diagonal matrix created from a FullMatrix and a SparseMatrixEZ:

FullMatrix<double> top_left(2, 2);
top_left(0, 0) = 2.0;
top_left(0, 1) = -1.0;
top_left(1, 0) = -1.0;
top_left(1, 1) = 2.0;
 
SparseMatrixEZ<double> bottom_right(4, 4, 4);
for (std::size_t row_n = 0; row_n < 4; ++row_n)
  {
    bottom_right.add(row_n, row_n, 1.0);
    if (row_n < 3)
      bottom_right.add(row_n, row_n + 1, -1.0);
  }
 
auto top_left_op = linear_operator(top_left);
auto bottom_right_op = linear_operator(bottom_right);
std::array<decltype(top_left_op), 2> operators {{top_left_op,
                                                 bottom_right_op}};
auto block_op = block_diagonal_operator (operators);
 
std::vector<BlockVector<double>::size_type> block_sizes {2, 4};
BlockVector<double> src(block_sizes);
src = 2.0;
BlockVector<double> dst(block_sizes);
block_op.vmult(dst, src); // now equal to 2, 2, 0, 0, 0, 2

A BlockLinearOperator can be sliced to a LinearOperator at any time. This removes all information about the underlying block structure (because above std::function objects are no longer available) - the linear operator interface, however, remains intact.

Note: This class makes heavy use of std::function objects and lambda functions. This flexibility comes with a run-time penalty. Only use this object to encapsulate object with medium to large individual block sizes, and small block structure (as a rule of thumb, matrix blocks greater than \(1000\times1000\)).

Author: Matthias Maier, 2015

Definition at line 202 of file block_linear_operator.h.

Member Typedef Documentation

◆ BlockType

template<typename Range , typename Domain , typename BlockPayload >

using BlockLinearOperator< Range, Domain, BlockPayload >::BlockType = LinearOperator<typename Range::BlockType, typename Domain::BlockType, typename BlockPayload::BlockType>

Definition at line 208 of file block_linear_operator.h.

Constructor & Destructor Documentation

◆ BlockLinearOperator() [1/5]

template<typename Range , typename Domain , typename BlockPayload >

BlockLinearOperator< Range, Domain, BlockPayload >::BlockLinearOperator ( const BlockPayload & payload )

inline

Create an empty BlockLinearOperator object.

Allstd::function member objects of this class and its base class LinearOperator are initialized with default variants that throw an exception upon invocation.

Definition at line 217 of file block_linear_operator.h.

◆ BlockLinearOperator() [2/5]

template<typename Range , typename Domain , typename BlockPayload >

BlockLinearOperator< Range, Domain, BlockPayload >::BlockLinearOperator ( const BlockLinearOperator< Range, Domain, BlockPayload > & )

default

Default copy constructor.

◆ BlockLinearOperator() [3/5]

template<typename Range , typename Domain , typename BlockPayload >

template<typename Op >

BlockLinearOperator< Range, Domain, BlockPayload >::BlockLinearOperator ( const Op & op )

inline

Templated copy constructor that creates a BlockLinearOperator object from an object op for which the conversion function block_operator is defined.

Definition at line 258 of file block_linear_operator.h.

◆ BlockLinearOperator() [4/5]

template<typename Range , typename Domain , typename BlockPayload >

template<std::size_t m, std::size_t n>

BlockLinearOperator< Range, Domain, BlockPayload >::BlockLinearOperator ( const std::array< std::array< BlockType, n >, m > & ops )

inline

Create a BlockLinearOperator from a two-dimensional array ops of LinearOperator. This constructor calls the corresponding block_operator() specialization.

Definition at line 269 of file block_linear_operator.h.

◆ BlockLinearOperator() [5/5]

template<typename Range , typename Domain , typename BlockPayload >

template<std::size_t m>

BlockLinearOperator< Range, Domain, BlockPayload >::BlockLinearOperator ( const std::array< BlockType, m > & ops )

inline

Create a block-diagonal BlockLinearOperator from a one-dimensional array ops of LinearOperator. This constructor calls the corresponding block_operator() specialization.

Definition at line 280 of file block_linear_operator.h.

Member Function Documentation

◆ operator=() [1/4]

template<typename Range , typename Domain , typename BlockPayload >

BlockLinearOperator<Range, Domain, BlockPayload>& BlockLinearOperator< Range, Domain, BlockPayload >::operator= ( const BlockLinearOperator< Range, Domain, BlockPayload > & )

default

Default copy assignment operator.

◆ operator=() [2/4]

template<typename Range , typename Domain , typename BlockPayload >

template<typename Op >

BlockLinearOperator<Range, Domain, BlockPayload>& BlockLinearOperator< Range, Domain, BlockPayload >::operator= ( const Op & op )

inline

Templated copy assignment operator for an object op for which the conversion function block_operator is defined.

Definition at line 297 of file block_linear_operator.h.

◆ operator=() [3/4]

template<typename Range , typename Domain , typename BlockPayload >

template<std::size_t m, std::size_t n>

BlockLinearOperator<Range, Domain, BlockPayload>& BlockLinearOperator< Range, Domain, BlockPayload >::operator= ( const std::array< std::array< BlockType, n >, m > & ops )

inline

Copy assignment from a two-dimensional array ops of LinearOperator. This assignment operator calls the corresponding block_operator() specialization.

Definition at line 310 of file block_linear_operator.h.

◆ operator=() [4/4]

template<typename Range , typename Domain , typename BlockPayload >

template<std::size_t m>

BlockLinearOperator<Range, Domain, BlockPayload>& BlockLinearOperator< Range, Domain, BlockPayload >::operator= ( const std::array< BlockType, m > & ops )

inline

Copy assignment from a one-dimensional array ops of LinearOperator that creates a block-diagonal BlockLinearOperator. This assignment operator calls the corresponding block_operator() specialization.

Definition at line 323 of file block_linear_operator.h.

Member Data Documentation

◆ n_block_rows

template<typename Range , typename Domain , typename BlockPayload >

std::function<unsigned int()> BlockLinearOperator< Range, Domain, BlockPayload >::n_block_rows

Return the number of blocks in a column (i.e, the number of "block rows", or the number \(m\), if interpreted as a \(m\times n\) block system).

Definition at line 333 of file block_linear_operator.h.

◆ n_block_cols

template<typename Range , typename Domain , typename BlockPayload >

std::function<unsigned int()> BlockLinearOperator< Range, Domain, BlockPayload >::n_block_cols

Return the number of blocks in a row (i.e, the number of "block columns", or the number \(n\), if interpreted as a \(m\times n\) block system).

Definition at line 339 of file block_linear_operator.h.

◆ block

template<typename Range , typename Domain , typename BlockPayload >

std::function<BlockType(unsigned int, unsigned int)> BlockLinearOperator< Range, Domain, BlockPayload >::block

Access the block with the given coordinates. This std::function object returns a LinearOperator representing the \((i,j)\)-th block of the BlockLinearOperator.

Definition at line 346 of file block_linear_operator.h.

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

include/deal.II/lac/block_linear_operator.h
include/deal.II/lac/trilinos_linear_operator.h

Public Types

Public Member Functions

Public Attributes

Related Functions

Detailed Description

template<typename Range, typename Domain, typename BlockPayload> class BlockLinearOperator< Range, Domain, BlockPayload >

Member Typedef Documentation

◆ BlockType

Constructor & Destructor Documentation

◆ BlockLinearOperator() [1/5]

◆ BlockLinearOperator() [2/5]

◆ BlockLinearOperator() [3/5]

◆ BlockLinearOperator() [4/5]

◆ BlockLinearOperator() [5/5]

Member Function Documentation

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

Member Data Documentation

◆ n_block_rows

◆ n_block_cols

◆ block

template<typename Range, typename Domain, typename BlockPayload>
class BlockLinearOperator< Range, Domain, BlockPayload >