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

Inheritance diagram for PETScWrappers::MatrixFree:

Public Types
using	const_iterator = MatrixIterators::const_iterator

using	size_type = types::global_dof_index

using	value_type = PetscScalar

Public Member Functions
	MatrixFree ()

	MatrixFree (const MPI_Comm &communicator, const unsigned int m, const unsigned int n, const unsigned int local_rows, const unsigned int local_columns)

	MatrixFree (const MPI_Comm &communicator, const unsigned int m, const unsigned int n, const std::vector< unsigned int > &local_rows_per_process, const std::vector< unsigned int > &local_columns_per_process, const unsigned int this_process)

	MatrixFree (const unsigned int m, const unsigned int n, const unsigned int local_rows, const unsigned int local_columns)

	MatrixFree (const unsigned int m, const unsigned int n, const std::vector< unsigned int > &local_rows_per_process, const std::vector< unsigned int > &local_columns_per_process, const unsigned int this_process)

void	reinit (const MPI_Comm &communicator, const unsigned int m, const unsigned int n, const unsigned int local_rows, const unsigned int local_columns)

void	reinit (const MPI_Comm &communicator, const unsigned int m, const unsigned int n, const std::vector< unsigned int > &local_rows_per_process, const std::vector< unsigned int > &local_columns_per_process, const unsigned int this_process)

void	reinit (const unsigned int m, const unsigned int n, const unsigned int local_rows, const unsigned int local_columns)

void	reinit (const unsigned int m, const unsigned int n, const std::vector< unsigned int > &local_rows_per_process, const std::vector< unsigned int > &local_columns_per_process, const unsigned int this_process)

void	clear ()

const MPI_Comm &	get_mpi_communicator () const override

virtual void	vmult (VectorBase &dst, const VectorBase &src) const =0

virtual void	Tvmult (VectorBase &dst, const VectorBase &src) const =0

virtual void	vmult_add (VectorBase &dst, const VectorBase &src) const =0

virtual void	Tvmult_add (VectorBase &dst, const VectorBase &src) const =0

virtual void	vmult (Vec &dst, const Vec &src) const

void	set (const size_type i, const size_type j, const PetscScalar value)

void	set (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false)

void	set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false)

void	set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=false)

void	set (const size_type row, const size_type n_cols, const size_type col_indices, const PetscScalar values, const bool elide_zero_values=false)

void	add (const size_type i, const size_type j, const PetscScalar value)

void	add (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true)

void	add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true)

void	add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=true)

void	add (const size_type row, const size_type n_cols, const size_type col_indices, const PetscScalar values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false)

MatrixBase &	add (const PetscScalar factor, const MatrixBase &other)

void	clear_row (const size_type row, const PetscScalar new_diag_value=0)

void	clear_rows (const std::vector< size_type > &rows, const PetscScalar new_diag_value=0)

void	compress (const VectorOperation::values operation)

PetscScalar	operator() (const size_type i, const size_type j) const

PetscScalar	el (const size_type i, const size_type j) const

PetscScalar	diag_element (const size_type i) const

size_type	m () const

size_type	n () const

size_type	local_size () const

std::pair< size_type, size_type >	local_range () const

bool	in_local_range (const size_type index) const

std::uint64_t	n_nonzero_elements () const

size_type	row_length (const size_type row) const

PetscReal	l1_norm () const

PetscReal	linfty_norm () const

PetscReal	frobenius_norm () const

PetscScalar	matrix_norm_square (const VectorBase &v) const

PetscScalar	matrix_scalar_product (const VectorBase &u, const VectorBase &v) const

PetscScalar	trace () const

MatrixBase &	operator*= (const PetscScalar factor)

MatrixBase &	operator/= (const PetscScalar factor)

PetscScalar	residual (VectorBase &dst, const VectorBase &x, const VectorBase &b) const

const_iterator	begin () const

const_iterator	begin (const size_type r) const

const_iterator	end () const

const_iterator	end (const size_type r) const

	operator Mat () const

Mat &	petsc_matrix ()

void	transpose ()

PetscBool	is_symmetric (const double tolerance=1.e-12)

PetscBool	is_hermitian (const double tolerance=1.e-12)

void	write_ascii (const PetscViewerFormat format=PETSC_VIEWER_DEFAULT)

void	print (std::ostream &out, const bool alternative_output=false) const

std::size_t	memory_consumption () const

Static Public Member Functions
static ::ExceptionBase &	ExcSourceEqualsDestination ()

static ::ExceptionBase &	ExcWrongMode (int arg1, int arg2)

Protected Member Functions
void	prepare_action (const VectorOperation::values new_action)

void	assert_is_compressed ()

void	prepare_add ()

void	prepare_set ()

void	mmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const

void	Tmmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const

Protected Attributes
Mat	matrix

VectorOperation::values	last_action

Private Member Functions
void	do_reinit (const unsigned int m, const unsigned int n, const unsigned int local_rows, const unsigned int local_columns)

Static Private Member Functions
static int	matrix_free_mult (Mat A, Vec src, Vec dst)

Private Attributes
MPI_Comm	communicator

std::vector< PetscInt >	column_indices

std::vector< PetscScalar >	column_values

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

void	check_no_subscribers () const noexcept

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

Detailed Description

Implementation of a parallel matrix class based on PETSc MatShell matrix-type. This base class implements only the interface to the PETSc matrix object, while all the functionality is contained in the matrix-vector multiplication which must be reimplemented in derived classes.

This interface is an addition to the MatrixFree class to realize user-defined matrix-classes together with PETSc solvers and functionalities. See also the documentation of MatrixFree class and step-37 and step-48.

Similar to other matrix classes in namespaces PETScWrappers and PETScWrappers::MPI, the MatrixFree class provides the usual matrix-vector multiplication vmult(VectorBase &dst, const VectorBase &src) which is pure virtual and must be reimplemented in derived classes. Besides the usual interface, this class has a matrix-vector multiplication vmult(Vec &dst, const Vec &src) taking PETSc Vec objects, which will be called by matrix_free_mult(Mat A, Vec src, Vec dst) registered as matrix-vector multiplication of this PETSc matrix object. The default implementation of the vmult function in the base class wraps the given PETSc vectors with the PETScWrappers::VectorBase class and then calls the usual vmult function with the usual interface.

Definition at line 59 of file petsc_matrix_free.h.

Member Typedef Documentation

◆ const_iterator

using PETScWrappers::MatrixBase::const_iterator = MatrixIterators::const_iterator

inherited

Declare an alias for the iterator class.

Definition at line 290 of file petsc_matrix_base.h.

◆ size_type

using PETScWrappers::MatrixBase::size_type = types::global_dof_index

inherited

Declare type for container size.

Definition at line 295 of file petsc_matrix_base.h.

◆ value_type

using PETScWrappers::MatrixBase::value_type = PetscScalar

inherited

Declare an alias in analogy to all the other container classes.

Definition at line 300 of file petsc_matrix_base.h.

Constructor & Destructor Documentation

◆ MatrixFree() [1/5]

MatrixFree< dim, Number, VectorizedArrayType >::MatrixFree ( )

Default constructor. Create an empty matrix object.

Definition at line 28 of file petsc_matrix_free.cc.

◆ MatrixFree() [2/5]

MatrixFree< dim, Number, VectorizedArrayType >::MatrixFree	(	const MPI_Comm &	communicator,
		const unsigned int	m,
		const unsigned int	n,
		const unsigned int	local_rows,
		const unsigned int	local_columns
	)

Create a matrix object of dimensions m times n with communication happening over the provided communicator.

For the meaning of the local_rows and local_columns parameters, see the PETScWrappers::MPI::SparseMatrix class documentation.

As other PETSc matrices, also the matrix-free object needs to have a size and to perform matrix vector multiplications efficiently in parallel also local_rows and local_columns. But in contrast to PETSc::SparseMatrix classes a PETSc matrix-free object does not need any estimation of non_zero entries and has no option is_symmetric.

Definition at line 37 of file petsc_matrix_free.cc.

◆ MatrixFree() [3/5]

MatrixFree< dim, Number, VectorizedArrayType >::MatrixFree	(	const MPI_Comm &	communicator,
		const unsigned int	m,
		const unsigned int	n,
		const std::vector< unsigned int > &	local_rows_per_process,
		const std::vector< unsigned int > &	local_columns_per_process,
		const unsigned int	this_process
	)

Create a matrix object of dimensions m times n with communication happening over the provided communicator.

As other PETSc matrices, also the matrix-free object needs to have a size and to perform matrix vector multiplications efficiently in parallel also local_rows and local_columns. But in contrast to PETSc::SparseMatrix classes a PETSc matrix-free object does not need any estimation of non_zero entries and has no option is_symmetric.

Definition at line 49 of file petsc_matrix_free.cc.

◆ MatrixFree() [4/5]

MatrixFree< dim, Number, VectorizedArrayType >::MatrixFree	(	const unsigned int	m,
		const unsigned int	n,
		const unsigned int	local_rows,
		const unsigned int	local_columns
	)

Constructor for the serial case: Same function as MatrixFree(), see above, with communicator = MPI_COMM_WORLD.

Definition at line 71 of file petsc_matrix_free.cc.

◆ MatrixFree() [5/5]

MatrixFree< dim, Number, VectorizedArrayType >::MatrixFree	(	const unsigned int	m,
		const unsigned int	n,
		const std::vector< unsigned int > &	local_rows_per_process,
		const std::vector< unsigned int > &	local_columns_per_process,
		const unsigned int	this_process
	)

Constructor for the serial case: Same function as MatrixFree(), see above, with communicator = MPI_COMM_WORLD.

Definition at line 82 of file petsc_matrix_free.cc.

Member Function Documentation

◆ reinit() [1/4]

void MatrixFree< dim, Number, VectorizedArrayType >::reinit	(	const MPI_Comm &	communicator,
		const unsigned int	m,
		const unsigned int	n,
		const unsigned int	local_rows,
		const unsigned int	local_columns
	)

Throw away the present matrix and generate one that has the same properties as if it were created by the constructor of this class with the same argument list as the present function.

Definition at line 104 of file petsc_matrix_free.cc.

◆ reinit() [2/4]

void MatrixFree< dim, Number, VectorizedArrayType >::reinit	(	const MPI_Comm &	communicator,
		const unsigned int	m,
		const unsigned int	n,
		const std::vector< unsigned int > &	local_rows_per_process,
		const std::vector< unsigned int > &	local_columns_per_process,
		const unsigned int	this_process
	)

Throw away the present matrix and generate one that has the same properties as if it were created by the constructor of this class with the same argument list as the present function.

Definition at line 122 of file petsc_matrix_free.cc.

◆ reinit() [3/4]

void MatrixFree< dim, Number, VectorizedArrayType >::reinit	(	const unsigned int	m,
		const unsigned int	n,
		const unsigned int	local_rows,
		const unsigned int	local_columns
	)

Call the reinit() function above with communicator = MPI_COMM_WORLD.

Definition at line 147 of file petsc_matrix_free.cc.

◆ reinit() [4/4]

void MatrixFree< dim, Number, VectorizedArrayType >::reinit	(	const unsigned int	m,
		const unsigned int	n,
		const std::vector< unsigned int > &	local_rows_per_process,
		const std::vector< unsigned int > &	local_columns_per_process,
		const unsigned int	this_process
	)

Call the reinit() function above with communicator = MPI_COMM_WORLD.

Definition at line 158 of file petsc_matrix_free.cc.

◆ clear()

void MatrixFree< dim, Number, VectorizedArrayType >::clear ( )

Release all memory and return to a state just like after having called the default constructor.

Definition at line 175 of file petsc_matrix_free.cc.

◆ get_mpi_communicator()

const MPI_Comm & MatrixFree< dim, Number, VectorizedArrayType >::get_mpi_communicator ( ) const

inlineoverridevirtual

Return a reference to the MPI communicator object in use with this matrix.

Implements PETScWrappers::MatrixBase.

Definition at line 293 of file petsc_matrix_free.h.

◆ vmult() [1/2]

virtual void PETScWrappers::MatrixFree::vmult	(	VectorBase &	dst,
		const VectorBase &	src
	)		const

pure virtual

Matrix-vector multiplication: let dst = M*src with M being this matrix.

Source and destination must not be the same vector.

Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

◆ Tvmult()

virtual void PETScWrappers::MatrixFree::Tvmult	(	VectorBase &	dst,
		const VectorBase &	src
	)		const

pure virtual

Matrix-vector multiplication: let dst = M^T*src with M being this matrix. This function does the same as vmult() but takes the transposed matrix.

Source and destination must not be the same vector.

Note that if the current object represents a parallel distributed matrix then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

◆ vmult_add()

virtual void PETScWrappers::MatrixFree::vmult_add	(	VectorBase &	dst,
		const VectorBase &	src
	)		const

pure virtual

Adding Matrix-vector multiplication. Add M*src on dst with M being this matrix.

Source and destination must not be the same vector.

Note that if the current object represents a parallel distributed matrix then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

◆ Tvmult_add()

virtual void PETScWrappers::MatrixFree::Tvmult_add	(	VectorBase &	dst,
		const VectorBase &	src
	)		const

pure virtual

Adding Matrix-vector multiplication. Add M^T*src to dst with M being this matrix. This function does the same as vmult_add() but takes the transposed matrix.

Source and destination must not be the same vector.

Note that if the current object represents a parallel distributed matrix then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

◆ vmult() [2/2]

void MatrixFree< dim, Number, VectorizedArrayType >::vmult	(	Vec &	dst,
		const Vec &	src
	)		const

virtual

The matrix-vector multiplication called by matrix_free_mult(). This function can be reimplemented in derived classes for efficiency. The default implementation copies the given vectors into PETScWrappers::*Vector and calls vmult(VectorBase &dst, const VectorBase &src) which is purely virtual and must be reimplemented in derived classes.

Definition at line 187 of file petsc_matrix_free.cc.

◆ matrix_free_mult()

int MatrixFree< dim, Number, VectorizedArrayType >::matrix_free_mult	(	Mat	A,
		Vec	src,
		Vec	dst
	)

staticprivate

Callback-function registered as the matrix-vector multiplication of this matrix-free object called by PETSc routines. This function must be static and takes a PETSc matrix A, and vectors src and dst, where dst = A*src

Source and destination must not be the same vector.

This function calls vmult(Vec &dst, const Vec &src) which should be reimplemented in derived classes.

Definition at line 200 of file petsc_matrix_free.cc.

◆ do_reinit()

void MatrixFree< dim, Number, VectorizedArrayType >::do_reinit	(	const unsigned int	m,
		const unsigned int	n,
		const unsigned int	local_rows,
		const unsigned int	local_columns
	)

private

Do the actual work for the respective reinit() function and the matching constructor, i.e. create a matrix object. Getting rid of the previous matrix is left to the caller.

Definition at line 219 of file petsc_matrix_free.cc.

◆ set() [1/5]

void PETScWrappers::MatrixBase::set	(	const size_type	i,
		const size_type	j,
		const PetscScalar	value
	)

inherited

Set the element (i,j) to value.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value is not a finite number an exception is thrown.

◆ set() [2/5]

void PETScWrappers::MatrixBase::set	(	const std::vector< size_type > &	indices,
		const FullMatrix< PetscScalar > &	full_matrix,
		const bool	elide_zero_values = `false`
	)

inherited

Set all elements given in a FullMatrix<double> into the sparse matrix locations given by indices. In other words, this function writes the elements in full_matrix into the calling matrix, using the local-to-global indexing specified by indices for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false, i.e., even zero values are inserted/replaced.

◆ set() [3/5]

void PETScWrappers::MatrixBase::set	(	const std::vector< size_type > &	row_indices,
		const std::vector< size_type > &	col_indices,
		const FullMatrix< PetscScalar > &	full_matrix,
		const bool	elide_zero_values = `false`
	)

inherited

Same function as before, but now including the possibility to use rectangular full_matrices and different local-to-global indexing on rows and columns, respectively.

◆ set() [4/5]

void PETScWrappers::MatrixBase::set	(	const size_type	row,
		const std::vector< size_type > &	col_indices,
		const std::vector< PetscScalar > &	values,
		const bool	elide_zero_values = `false`
	)

inherited

Set several elements in the specified row of the matrix with column indices as given by col_indices to the respective value.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false, i.e., even zero values are inserted/replaced.

◆ set() [5/5]

void PETScWrappers::MatrixBase::set	(	const size_type	row,
		const size_type	n_cols,
		const size_type *	col_indices,
		const PetscScalar *	values,
		const bool	elide_zero_values = `false`
	)

inherited

Set several elements to values given by values in a given row in columns given by col_indices into the sparse matrix.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false, i.e., even zero values are inserted/replaced.

◆ add() [1/6]

void PETScWrappers::MatrixBase::add	(	const size_type	i,
		const size_type	j,
		const PetscScalar	value
	)

inherited

Add value to the element (i,j).

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value is not a finite number an exception is thrown.

◆ add() [2/6]

void PETScWrappers::MatrixBase::add	(	const std::vector< size_type > &	indices,
		const FullMatrix< PetscScalar > &	full_matrix,
		const bool	elide_zero_values = `true`
	)

inherited

Add all elements given in a FullMatrix<double> into sparse matrix locations given by indices. In other words, this function adds the elements in full_matrix to the respective entries in calling matrix, using the local-to-global indexing specified by indices for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be added anyway or these should be filtered away and only non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

◆ add() [3/6]

void PETScWrappers::MatrixBase::add	(	const std::vector< size_type > &	row_indices,
		const std::vector< size_type > &	col_indices,
		const FullMatrix< PetscScalar > &	full_matrix,
		const bool	elide_zero_values = `true`
	)

inherited

Same function as before, but now including the possibility to use rectangular full_matrices and different local-to-global indexing on rows and columns, respectively.

◆ add() [4/6]

void PETScWrappers::MatrixBase::add	(	const size_type	row,
		const std::vector< size_type > &	col_indices,
		const std::vector< PetscScalar > &	values,
		const bool	elide_zero_values = `true`
	)

inherited

Set several elements in the specified row of the matrix with column indices as given by col_indices to the respective value.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be added anyway or these should be filtered away and only non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

◆ add() [5/6]

void PETScWrappers::MatrixBase::add	(	const size_type	row,
		const size_type	n_cols,
		const size_type *	col_indices,
		const PetscScalar *	values,
		const bool	elide_zero_values = `true`,
		const bool	col_indices_are_sorted = `false`
	)

inherited

Add an array of values given by values in the given global matrix row at columns specified by col_indices in the sparse matrix.

If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.

The optional parameter elide_zero_values can be used to specify whether zero values should be added anyway or these should be filtered away and only non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

◆ add() [6/6]

MatrixBase & PETScWrappers::MatrixBase::add	(	const PetscScalar	factor,
		const MatrixBase &	other
	)

inherited

Add the matrix other scaled by the factor factor to the current matrix.

Definition at line 432 of file petsc_matrix_base.cc.

◆ clear_row()

void PETScWrappers::MatrixBase::clear_row	(	const size_type	row,
		const PetscScalar	new_diag_value = `0`
	)

inherited

Remove all elements from this row by setting them to zero. The function does not modify the number of allocated nonzero entries, it only sets some entries to zero. It may drop them from the sparsity pattern, though (but retains the allocated memory in case new entries are again added later).

This operation is used in eliminating constraints (e.g. due to hanging nodes) and makes sure that we can write this modification to the matrix without having to read entries (such as the locations of non-zero elements) from it – without this operation, removing constraints on parallel matrices is a rather complicated procedure.

The second parameter can be used to set the diagonal entry of this row to a value different from zero. The default is to set it to zero.

Definition at line 127 of file petsc_matrix_base.cc.

◆ clear_rows()

void PETScWrappers::MatrixBase::clear_rows	(	const std::vector< size_type > &	rows,
		const PetscScalar	new_diag_value = `0`
	)

inherited

Same as clear_row(), except that it works on a number of rows at once.

The second parameter can be used to set the diagonal entries of all cleared rows to something different from zero. Note that all of these diagonal entries get the same value – if you want different values for the diagonal entries, you have to set them by hand.

Definition at line 136 of file petsc_matrix_base.cc.

◆ compress()

void PETScWrappers::MatrixBase::compress ( const VectorOperation::values operation )

inherited

PETSc matrices store their own sparsity patterns. So, in analogy to our own SparsityPattern class, this function compresses the sparsity pattern and allows the resulting matrix to be used in all other operations where before only assembly functions were allowed. This function must therefore be called once you have assembled the matrix.

See Compressing distributed objects for more information.

Definition at line 193 of file petsc_matrix_base.cc.

◆ operator()()

PetscScalar PETScWrappers::MatrixBase::operator()	(	const size_type	i,
		const size_type	j
	)		const

inherited

Return the value of the entry (i,j). This may be an expensive operation and you should always take care where to call this function. In contrast to the respective function in the MatrixBase class, we don't throw an exception if the respective entry doesn't exist in the sparsity pattern of this class, since PETSc does not transmit this information.

This function is therefore exactly equivalent to the el() function.

◆ el()

PetscScalar PETScWrappers::MatrixBase::el	(	const size_type	i,
		const size_type	j
	)		const

inherited

Return the value of the matrix entry (i,j). If this entry does not exist in the sparsity pattern, then zero is returned. While this may be convenient in some cases, note that it is simple to write algorithms that are slow compared to an optimal solution, since the sparsity of the matrix is not used.

Definition at line 165 of file petsc_matrix_base.cc.

◆ diag_element()

PetscScalar PETScWrappers::MatrixBase::diag_element ( const size_type i ) const

inherited

Return the main diagonal element in the ith row. This function throws an error if the matrix is not quadratic.

Since we do not have direct access to the underlying data structure, this function is no faster than the elementwise access using the el() function. However, we provide this function for compatibility with the SparseMatrix class.

Definition at line 181 of file petsc_matrix_base.cc.

◆ m()

MatrixBase::size_type PETScWrappers::MatrixBase::m ( ) const

inherited

Return the number of rows in this matrix.

Definition at line 237 of file petsc_matrix_base.cc.

◆ n()

MatrixBase::size_type PETScWrappers::MatrixBase::n ( ) const

inherited

Return the number of columns in this matrix.

Definition at line 250 of file petsc_matrix_base.cc.

◆ local_size()

MatrixBase::size_type PETScWrappers::MatrixBase::local_size ( ) const

inherited

Return the local dimension of the matrix, i.e. the number of rows stored on the present MPI process. For sequential matrices, this number is the same as m(), but for parallel matrices it may be smaller.

To figure out which elements exactly are stored locally, use local_range().

Definition at line 263 of file petsc_matrix_base.cc.

◆ local_range()

std::pair< MatrixBase::size_type, MatrixBase::size_type > PETScWrappers::MatrixBase::local_range ( ) const

inherited

Return a pair of indices indicating which rows of this matrix are stored locally. The first number is the index of the first row stored, the second the index of the one past the last one that is stored locally. If this is a sequential matrix, then the result will be the pair (0,m()), otherwise it will be a pair (i,i+n), where n=local_size().

Definition at line 276 of file petsc_matrix_base.cc.

◆ in_local_range()

bool PETScWrappers::MatrixBase::in_local_range ( const size_type index ) const

inherited

Return whether index is in the local range or not, see also local_range().

◆ n_nonzero_elements()

std::uint64_t PETScWrappers::MatrixBase::n_nonzero_elements ( ) const

inherited

Return the number of nonzero elements of this matrix. Actually, it returns the number of entries in the sparsity pattern; if any of the entries should happen to be zero, it is counted anyway.

Definition at line 290 of file petsc_matrix_base.cc.

◆ row_length()

MatrixBase::size_type PETScWrappers::MatrixBase::row_length ( const size_type row ) const

inherited

Number of entries in a specific row.

Definition at line 304 of file petsc_matrix_base.cc.

◆ l1_norm()

PetscReal PETScWrappers::MatrixBase::l1_norm ( ) const

inherited

Return the l1-norm of the matrix, that is \(|M|_1=max_{all columns j}\sum_{all rows i} |M_ij|\), (max. sum of columns). This is the natural matrix norm that is compatible to the l1-norm for vectors, i.e. \(|Mv|_1\leq |M|_1 |v|_1\). (cf. Haemmerlin-Hoffmann: Numerische Mathematik)

Definition at line 340 of file petsc_matrix_base.cc.

◆ linfty_norm()

PetscReal PETScWrappers::MatrixBase::linfty_norm ( ) const

inherited

Return the linfty-norm of the matrix, that is \(|M|_infty=max_{all rows i}\sum_{all columns j} |M_ij|\), (max. sum of rows). This is the natural matrix norm that is compatible to the linfty-norm of vectors, i.e. \(|Mv|_infty \leq |M|_infty |v|_infty\). (cf. Haemmerlin-Hoffmann: Numerische Mathematik)

Definition at line 353 of file petsc_matrix_base.cc.

◆ frobenius_norm()

PetscReal PETScWrappers::MatrixBase::frobenius_norm ( ) const

inherited

Return the frobenius norm of the matrix, i.e. the square root of the sum of squares of all entries in the matrix.

Definition at line 366 of file petsc_matrix_base.cc.

◆ matrix_norm_square()

PetscScalar PETScWrappers::MatrixBase::matrix_norm_square ( const VectorBase & v ) const

inherited

Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e. \(\left(v,Mv\right)\). This is useful, e.g. in the finite element context, where the \(L_2\) norm of a function equals the matrix norm with respect to the mass matrix of the vector representing the nodal values of the finite element function.

Obviously, the matrix needs to be quadratic for this operation.

The implementation of this function is not as efficient as the one in the MatrixBase class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.

Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then the given vector has to be a distributed vector as well. Conversely, if the matrix is not distributed, then neither may the vector be.

Definition at line 378 of file petsc_matrix_base.cc.

◆ matrix_scalar_product()

PetscScalar PETScWrappers::MatrixBase::matrix_scalar_product	(	const VectorBase &	u,
		const VectorBase &	v
	)		const

inherited

Compute the matrix scalar product \(\left(u,Mv\right)\).

The implementation of this function is not as efficient as the one in the MatrixBase class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.

Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

Definition at line 387 of file petsc_matrix_base.cc.

◆ trace()

PetscScalar PETScWrappers::MatrixBase::trace ( ) const

inherited

Return the trace of the matrix, i.e. the sum of all diagonal entries in the matrix.

Definition at line 397 of file petsc_matrix_base.cc.

◆ operator*=()

MatrixBase & PETScWrappers::MatrixBase::operator*= ( const PetscScalar factor )

inherited

Multiply the entire matrix by a fixed factor.

Definition at line 410 of file petsc_matrix_base.cc.

◆ operator/=()

MatrixBase & PETScWrappers::MatrixBase::operator/= ( const PetscScalar factor )

inherited

Divide the entire matrix by a fixed factor.

Definition at line 421 of file petsc_matrix_base.cc.

◆ residual()

PetscScalar PETScWrappers::MatrixBase::residual	(	VectorBase &	dst,
		const VectorBase &	x,
		const VectorBase &	b
	)		const

inherited

Compute the residual of an equation Mx=b, where the residual is defined to be r=b-Mx. Write the residual into dst. The l₂ norm of the residual vector is returned.

Source x and destination dst must not be the same vector.

Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then all vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.

Definition at line 576 of file petsc_matrix_base.cc.

◆ begin() [1/2]

const_iterator PETScWrappers::MatrixBase::begin ( ) const

inherited

Iterator starting at the first entry. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of begin() taking a row number as an argument.

◆ begin() [2/2]

const_iterator PETScWrappers::MatrixBase::begin ( const size_type r ) const

inherited

Iterator starting at the first entry of row r.

Note that if the given row is empty, i.e. does not contain any nonzero entries, then the iterator returned by this function equals end(r). Note also that the iterator may not be dereferenceable in that case.

◆ end() [1/2]

const_iterator PETScWrappers::MatrixBase::end ( ) const

inherited

Final iterator. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of end() taking a row number as an argument.

◆ end() [2/2]

const_iterator PETScWrappers::MatrixBase::end ( const size_type r ) const

inherited

Final iterator of row r. It points to the first element past the end of line r, or past the end of the entire sparsity pattern.

Note that the end iterator is not necessarily dereferenceable. This is in particular the case if it is the end iterator for the last row of a matrix.

◆ operator Mat()

PETScWrappers::MatrixBase::operator Mat ( ) const

inherited

Conversion operator to gain access to the underlying PETSc type. If you do this, you cut this class off some information it may need, so this conversion operator should only be used if you know what you do. In particular, it should only be used for read-only operations into the matrix.

Definition at line 592 of file petsc_matrix_base.cc.

◆ petsc_matrix()

Mat & PETScWrappers::MatrixBase::petsc_matrix ( )

inherited

Return a reference to the underlying PETSc type. It can be used to modify the underlying data, so use it only when you know what you are doing.

Definition at line 598 of file petsc_matrix_base.cc.

◆ transpose()

void PETScWrappers::MatrixBase::transpose ( )

inherited

Make an in-place transpose of a matrix.

Definition at line 604 of file petsc_matrix_base.cc.

◆ is_symmetric()

PetscBool PETScWrappers::MatrixBase::is_symmetric ( const double tolerance = 1.e-12 )

inherited

Test whether a matrix is symmetric. Default tolerance is \(1000\times32\)-bit machine precision.

Definition at line 616 of file petsc_matrix_base.cc.

◆ is_hermitian()

PetscBool PETScWrappers::MatrixBase::is_hermitian ( const double tolerance = 1.e-12 )

inherited

Test whether a matrix is Hermitian, i.e. it is the complex conjugate of its transpose. Default tolerance is \(1000\times32\)-bit machine precision.

Definition at line 626 of file petsc_matrix_base.cc.

◆ write_ascii()

void PETScWrappers::MatrixBase::write_ascii ( const PetscViewerFormat format = PETSC_VIEWER_DEFAULT )

inherited

Print the PETSc matrix object values using PETSc internal matrix viewer function MatView. The default format prints the non- zero matrix elements. For other valid view formats, consult http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatView.html

Definition at line 638 of file petsc_matrix_base.cc.

◆ print()

void PETScWrappers::MatrixBase::print	(	std::ostream &	out,
		const bool	alternative_output = `false`
	)		const

inherited

Print the elements of a matrix to the given output stream.

Parameters

[in,out]	out	The output stream to which to write.
[in]	alternative_output	This argument is ignored. It exists for compatibility with similar functions in other matrix classes.

Definition at line 653 of file petsc_matrix_base.cc.

◆ memory_consumption()

std::size_t PETScWrappers::MatrixBase::memory_consumption ( ) const

inherited

Return the number bytes consumed by this matrix on this CPU.

Definition at line 684 of file petsc_matrix_base.cc.

◆ prepare_action()

void PETScWrappers::MatrixBase::prepare_action ( const VectorOperation::values new_action )

protectedinherited

Ensure that the add/set mode that is required for actions following this call is compatible with the current mode. Should be called from all internal functions accessing matrix elements.

◆ assert_is_compressed()

void PETScWrappers::MatrixBase::assert_is_compressed ( )

protectedinherited

Internal function that checks that there are no pending insert/add operations. Throws an exception otherwise. Useful before calling any PETSc internal functions modifying the matrix.

◆ prepare_add()

void PETScWrappers::MatrixBase::prepare_add ( )

protectedinherited

For some matrix storage formats, in particular for the PETSc distributed blockmatrices, set and add operations on individual elements can not be freely mixed. Rather, one has to synchronize operations when one wants to switch from setting elements to adding to elements. BlockMatrixBase automatically synchronizes the access by calling this helper function for each block. This function ensures that the matrix is in a state that allows adding elements; if it previously already was in this state, the function does nothing.

◆ prepare_set()

void PETScWrappers::MatrixBase::prepare_set ( )

protectedinherited

Same as prepare_add() but prepare the matrix for setting elements if the representation of elements in this class requires such an operation.

◆ mmult()

void PETScWrappers::MatrixBase::mmult	(	MatrixBase &	C,
		const MatrixBase &	B,
		const VectorBase &	V
	)		const

protectedinherited

Base function to perform the matrix-matrix multiplication \(C = AB\), or, if a vector \(V\) whose size is compatible with B is given, \(C = A \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.

This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.

The content as well as the sparsity pattern of the matrix \(C\) will be reset by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.

Definition at line 560 of file petsc_matrix_base.cc.

◆ Tmmult()

void PETScWrappers::MatrixBase::Tmmult	(	MatrixBase &	C,
		const MatrixBase &	B,
		const VectorBase &	V
	)		const

protectedinherited

Base function to perform the matrix-matrix multiplication with the transpose of this, i.e., \(C = A^T B\), or, if an optional vector \(V\) whose size is compatible with \(B\) is given, \(C = A^T \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.

This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.

The content as well as the sparsity pattern of the matrix \(C\) will be changed by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.

Definition at line 568 of file petsc_matrix_base.cc.

Member Data Documentation

◆ communicator

MPI_Comm PETScWrappers::MatrixFree::communicator

private

Copy of the communicator object to be used for this parallel matrix- free object.

Definition at line 260 of file petsc_matrix_free.h.

◆ matrix

Mat PETScWrappers::MatrixBase::matrix

protectedinherited

A generic matrix object in PETSc. The actual type, a sparse matrix, is set in the constructor.

Definition at line 958 of file petsc_matrix_base.h.

◆ last_action

VectorOperation::values PETScWrappers::MatrixBase::last_action

protectedinherited

Store whether the last action was a write or add operation.

Definition at line 963 of file petsc_matrix_base.h.

◆ column_indices

std::vector<PetscInt> PETScWrappers::MatrixBase::column_indices

mutableprivateinherited

An internal array of integer values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.

This variable does not store any "state" of the matrix object. Rather, it is only used as a temporary buffer by some of the member functions of this class. As with all mutable member variables, the use of this variable is not thread-safe unless guarded by a mutex. However, since PETSc matrix operations are not thread-safe anyway, there is no need to attempt to make things thread-safe, and so there is no mutex associated with this variable.

Definition at line 1053 of file petsc_matrix_base.h.

◆ column_values

std::vector<PetscScalar> PETScWrappers::MatrixBase::column_values

mutableprivateinherited

An internal array of double values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.

The same comment as for the column_indices variable above applies.

Definition at line 1063 of file petsc_matrix_base.h.

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

include/deal.II/lac/petsc_matrix_free.h
source/lac/petsc_matrix_free.cc

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Static Private Member Functions

Private Attributes

Subscriptor functionality

Detailed Description

Member Typedef Documentation

◆ const_iterator

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ MatrixFree() [1/5]

◆ MatrixFree() [2/5]

◆ MatrixFree() [3/5]

◆ MatrixFree() [4/5]

◆ MatrixFree() [5/5]

Member Function Documentation

◆ reinit() [1/4]

◆ reinit() [2/4]

◆ reinit() [3/4]

◆ reinit() [4/4]

◆ clear()

◆ get_mpi_communicator()

◆ vmult() [1/2]

◆ Tvmult()

◆ vmult_add()

◆ Tvmult_add()

◆ vmult() [2/2]

◆ matrix_free_mult()

◆ do_reinit()

◆ set() [1/5]

◆ set() [2/5]

◆ set() [3/5]

◆ set() [4/5]

◆ set() [5/5]

◆ add() [1/6]

◆ add() [2/6]

◆ add() [3/6]

◆ add() [4/6]

◆ add() [5/6]

◆ add() [6/6]

◆ clear_row()

◆ clear_rows()

◆ compress()

◆ operator()()

◆ el()

◆ diag_element()

◆ m()

◆ n()

◆ local_size()

◆ local_range()

◆ in_local_range()

◆ n_nonzero_elements()

◆ row_length()

◆ l1_norm()

◆ linfty_norm()

◆ frobenius_norm()

◆ matrix_norm_square()

◆ matrix_scalar_product()

◆ trace()

◆ operator*=()

◆ operator/=()

◆ residual()

◆ begin() [1/2]

◆ begin() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ operator Mat()

◆ petsc_matrix()

◆ transpose()

◆ is_symmetric()

◆ is_hermitian()

◆ write_ascii()

◆ print()

◆ memory_consumption()

◆ prepare_action()