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

Inheritance diagram for PArpackSolver< VectorType >:

Classes
struct	AdditionalData

Public Types
enum	WhichEigenvalues { algebraically_largest , algebraically_smallest , largest_magnitude , smallest_magnitude , largest_real_part , smallest_real_part , largest_imaginary_part , smallest_imaginary_part , both_ends }

using	size_type = types::global_dof_index

Public Member Functions
SolverControl &	control () const

	PArpackSolver (SolverControl &control, const MPI_Comm mpi_communicator, const AdditionalData &data=AdditionalData())

void	reinit (const IndexSet &locally_owned_dofs)

void	reinit (const IndexSet &locally_owned_dofs, const std::vector< IndexSet > &partitioning)

void	reinit (const VectorType &distributed_vector)

void	set_initial_vector (const VectorType &vec)

void	set_shift (const std::complex< double > sigma)

template<typename MatrixType1 , typename MatrixType2 , typename INVERSE >
void	solve (const MatrixType1 &A, const MatrixType2 &B, const INVERSE &inverse, std::vector< std::complex< double > > &eigenvalues, std::vector< VectorType > &eigenvectors, const unsigned int n_eigenvalues)

template<typename MatrixType1 , typename MatrixType2 , typename INVERSE >
void	solve (const MatrixType1 &A, const MatrixType2 &B, const INVERSE &inverse, std::vector< std::complex< double > > &eigenvalues, std::vector< VectorType * > &eigenvectors, const unsigned int n_eigenvalues)

std::size_t	memory_consumption () const

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

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
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

Static Public Member Functions
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

Protected Attributes
SolverControl &	solver_control

const AdditionalData	additional_data

MPI_Comm	mpi_communicator

MPI_Fint	mpi_communicator_fortran

int	lworkl

std::vector< double >	workl

std::vector< double >	workd

int	nloc

int	ncv

int	ldv

std::vector< double >	v

bool	initial_vector_provided

std::vector< double >	resid

int	ldz

std::vector< double >	z

int	lworkev

std::vector< double >	workev

std::vector< int >	select

VectorType	src

VectorType	dst

VectorType	tmp

std::vector< types::global_dof_index >	local_indices

double	sigmar

double	sigmai

Private Types
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	internal_reinit (const IndexSet &locally_owned_dofs)

void	check_no_subscribers () const noexcept

Static Private Member Functions
static ::ExceptionBase &	PArpackExcConvergedEigenvectors (int arg1, int arg2)

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

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

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

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

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

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

static ::ExceptionBase &	PArpackExcIdo (int arg1)

static ::ExceptionBase &	PArpackExcMode (int arg1)

static ::ExceptionBase &	PArpackExcInfoPdnaupd (int arg1)

static ::ExceptionBase &	PArpackExcInfoPdneupd (int arg1)

static ::ExceptionBase &	PArpackExcInfoMaxIt (int arg1)

static ::ExceptionBase &	PArpackExcNoShifts (int arg1)

Private Attributes
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

Static Private Attributes
static std::mutex	mutex

Detailed Description

template<typename VectorType>
class PArpackSolver< VectorType >

Interface for using PARPACK. PARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems. Here we interface to the routines pdneupd, pdseupd, pdnaupd, pdsaupd of PARPACK. The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse matrices A.

In this class we make use of the method applied to the generalized eigenspectrum problem \((A-\lambda B)x=0\), for \(x\neq0\); where \(A\) is a system matrix, \(B\) is a mass matrix, and \(\lambda, x\) are a set of eigenvalues and eigenvectors respectively.

The ArpackSolver can be used in application codes in the following way:

SolverControl solver_control (1000, 1e-9);
const unsigned int num_arnoldi_vectors = 2*size_of_spectrum + 2;
PArpackSolver<V>::AdditionalData
  additional_data(num_arnoldi_vectors,
                  ::PArpackSolver<V>::largest_magnitude,
                  true);
 
 PArpackSolver<V> eigensolver (solver_control,
                               mpi_communicator,
                               additional_data);
 eigensolver.set_shift(sigma);
 eigensolver.reinit(locally_owned_dofs);
 eigensolver.solve (A,
                    B,
                    OP,
                    lambda,
                    x,
                    size_of_spectrum);

for the generalized eigenvalue problem \(Ax=B\lambda x\), where the variable size_of_spectrum tells PARPACK the number of eigenvector/eigenvalue pairs to solve for. Here, lambda is a vector that will contain the eigenvalues computed, x a vector of objects of type V that will contain the eigenvectors computed.

Currently, only three modes of (P)Arpack are implemented. In mode 3 (default), OP is an inverse operation for the matrix A - sigma * B, where sigma is a shift value, set to zero by default. Whereas in mode 2, OP is an inverse of M. Finally, mode 1 corresponds to standard eigenvalue problem without spectral transformation \(Ax=\lambda x\). The mode can be specified via AdditionalData object. Note that for shift-and-invert (mode=3), the sought eigenpairs are those after the spectral transformation is applied.

The OP can be specified by using a LinearOperator:

const double shift = 5.0;
const auto op_A = linear_operator<vector_t>(A);
const auto op_B = linear_operator<vector_t>(B);
const auto op_shift = op_A - shift * op_B;
SolverControl solver_control_lin (1000, 1e-10,false,false);
 
SolverCG<vector_t> cg(solver_control_lin);
const auto op_shift_invert =
  inverse_operator(op_shift, cg, PreconditionIdentity ());

The class is intended to be used with MPI and can work on arbitrary vector and matrix distributed classes. Both symmetric and non-symmetric A are supported.

For further information on how the PARPACK routines pdneupd, pdseupd, pdnaupd, pdsaupd work and also how to set the parameters appropriately please take a look into the PARPACK manual.

Definition at line 210 of file parpack_solver.h.

Member Typedef Documentation

◆ size_type

template<typename VectorType >

using PArpackSolver< VectorType >::size_type = types::global_dof_index

Declare the type for container size.

Definition at line 216 of file parpack_solver.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Member Enumeration Documentation

◆ WhichEigenvalues

template<typename VectorType >

enum PArpackSolver::WhichEigenvalues

An enum that lists the possible choices for which eigenvalues to compute in the solve() function. Note, that this corresponds to the problem after shift-and-invert (the only currently supported spectral transformation) is applied.

A particular choice is limited based on symmetric or non-symmetric matrix A considered.

Enumerator
algebraically_largest	The algebraically largest eigenvalues.
algebraically_smallest	The algebraically smallest eigenvalues.
largest_magnitude	The eigenvalue with the largest magnitudes.
smallest_magnitude	The eigenvalue with the smallest magnitudes.
largest_real_part	The eigenvalues with the largest real parts.
smallest_real_part	The eigenvalues with the smallest real parts.
largest_imaginary_part	The eigenvalues with the largest imaginary parts.
smallest_imaginary_part	The eigenvalues with the smallest imaginary parts.
both_ends	Compute half of the eigenvalues from the high end of the spectrum and the other half from the low end. If the number of requested eigenvectors is odd, then the extra eigenvector comes from the high end of the spectrum.

Definition at line 227 of file parpack_solver.h.

Constructor & Destructor Documentation

◆ PArpackSolver()

template<typename VectorType >

PArpackSolver< VectorType >::PArpackSolver	(	SolverControl &	control,
		const MPI_Comm	mpi_communicator,
		const AdditionalData &	data = AdditionalData() )

Constructor.

Definition at line 639 of file parpack_solver.h.

Member Function Documentation

◆ control()

template<typename VectorType >

SolverControl & PArpackSolver< VectorType >::control ( ) const

Access to the object that controls convergence.

Definition at line 1159 of file parpack_solver.h.

◆ reinit() [1/3]

template<typename VectorType >

void PArpackSolver< VectorType >::reinit ( const IndexSet & locally_owned_dofs )

Initialize internal variables.

Definition at line 725 of file parpack_solver.h.

◆ reinit() [2/3]

template<typename VectorType >

void PArpackSolver< VectorType >::reinit	(	const IndexSet &	locally_owned_dofs,
		const std::vector< IndexSet > &	partitioning )

Initialize internal variables when working with BlockVectors. locally_owned_dofs is used to set the dimension of the problem, whereas partitioning is used for calling the reinit of the deal.II blockvectors used.

Definition at line 753 of file parpack_solver.h.

◆ reinit() [3/3]

template<typename VectorType >

void PArpackSolver< VectorType >::reinit ( const VectorType & distributed_vector )

Initialize internal variables from the input distributed_vector.

Definition at line 739 of file parpack_solver.h.

◆ set_initial_vector()

template<typename VectorType >

void PArpackSolver< VectorType >::set_initial_vector ( const VectorType & vec )

Set initial vector for building Krylov space.

Definition at line 671 of file parpack_solver.h.

◆ set_shift()

template<typename VectorType >

void PArpackSolver< VectorType >::set_shift ( const std::complex< double > sigma )

Set shift sigma for shift-and-invert spectral transformation.

If this function is not called, the shift is assumed to be zero.

Note: only relevant for mode=3 (see the general documentation of this class for a definition of what the different modes are).

Definition at line 661 of file parpack_solver.h.

◆ solve() [1/2]

template<typename VectorType >

template<typename MatrixType1 , typename MatrixType2 , typename INVERSE >

void PArpackSolver< VectorType >::solve	(	const MatrixType1 &	A,
		const MatrixType2 &	B,
		const INVERSE &	inverse,
		std::vector< std::complex< double > > &	eigenvalues,
		std::vector< VectorType > &	eigenvectors,
		const unsigned int	n_eigenvalues )

Solve the generalized eigensprectrum problem \(A x=\lambda B x\) by calling the pd(n/s)eupd and pd(n/s)aupd functions of PARPACK.

In mode=3, inverse should correspond to \([A-\sigma B]^{-1}\), whereas in mode=2 it should represent \(B^{-1}\). For mode=1 both B and inverse are ignored.

Definition at line 769 of file parpack_solver.h.

◆ solve() [2/2]

template<typename VectorType >

template<typename MatrixType1 , typename MatrixType2 , typename INVERSE >

void PArpackSolver< VectorType >::solve	(	const MatrixType1 &	A,
		const MatrixType2 &	B,
		const INVERSE &	inverse,
		std::vector< std::complex< double > > &	eigenvalues,
		std::vector< VectorType * > &	eigenvectors,
		const unsigned int	n_eigenvalues )

Same as above but takes eigenvectors as pointers.

Definition at line 787 of file parpack_solver.h.

◆ memory_consumption()

template<typename VectorType >

std::size_t PArpackSolver< VectorType >::memory_consumption ( ) const

Return the memory consumption of this class in bytes.

Definition at line 588 of file parpack_solver.h.

◆ internal_reinit()

template<typename VectorType >

void PArpackSolver< VectorType >::internal_reinit ( const IndexSet & locally_owned_dofs )

private

Initialize internal variables which depend on locally_owned_dofs.

This function is called inside the reinit() functions

Definition at line 685 of file parpack_solver.h.

◆ subscribe()

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

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 135 of file subscriptor.cc.

◆ unsubscribe()

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

inherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 155 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

◆ serialize()

template<class Archive >

void Subscriptor::serialize	(	Archive &	ar,
		const unsigned int	version )

inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

Member Data Documentation

◆ solver_control

template<typename VectorType >

SolverControl& PArpackSolver< VectorType >::solver_control

protected

Reference to the object that controls convergence of the iterative solver.

Definition at line 380 of file parpack_solver.h.

◆ additional_data

template<typename VectorType >

const AdditionalData PArpackSolver< VectorType >::additional_data

protected

Store a copy of the flags for this particular solver.

Definition at line 385 of file parpack_solver.h.

◆ mpi_communicator

template<typename VectorType >

MPI_Comm PArpackSolver< VectorType >::mpi_communicator

protected

C++ MPI communicator.

Definition at line 392 of file parpack_solver.h.

◆ mpi_communicator_fortran

template<typename VectorType >

MPI_Fint PArpackSolver< VectorType >::mpi_communicator_fortran

protected

Fortran MPI communicator.

Definition at line 397 of file parpack_solver.h.

◆ lworkl

template<typename VectorType >

int PArpackSolver< VectorType >::lworkl

protected

Length of the work array workl.

Definition at line 404 of file parpack_solver.h.

◆ workl

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::workl

protected

Double precision work array of length lworkl

Definition at line 409 of file parpack_solver.h.

◆ workd

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::workd

protected

Double precision work array of length 3*N

Definition at line 414 of file parpack_solver.h.

◆ nloc

template<typename VectorType >

int PArpackSolver< VectorType >::nloc

protected

Number of local degrees of freedom.

Definition at line 419 of file parpack_solver.h.

◆ ncv

template<typename VectorType >

int PArpackSolver< VectorType >::ncv

protected

Number of Arnoldi basis vectors specified in additional_data

Definition at line 424 of file parpack_solver.h.

◆ ldv

template<typename VectorType >

int PArpackSolver< VectorType >::ldv

protected

The leading dimension of the array v

Definition at line 430 of file parpack_solver.h.

◆ v

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::v

protected

Double precision vector of size ldv by NCV. Will contains the final set of Arnoldi basis vectors.

Definition at line 436 of file parpack_solver.h.

◆ initial_vector_provided

template<typename VectorType >

bool PArpackSolver< VectorType >::initial_vector_provided

protected

An auxiliary flag which is set to true when initial vector is provided.

Definition at line 441 of file parpack_solver.h.

◆ resid

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::resid

protected

The initial residual vector, possibly from a previous run. On output, it contains the final residual vector.

Definition at line 447 of file parpack_solver.h.

◆ ldz

template<typename VectorType >

int PArpackSolver< VectorType >::ldz

protected

The leading dimension of the array Z equal to nloc.

Definition at line 452 of file parpack_solver.h.

◆ z

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::z

protected

A vector of minimum size of nloc by NEV+1. Z contains the B-orthonormal Ritz vectors of the eigensystem A*z = lambda*B*z corresponding to the Ritz value approximations.

Definition at line 459 of file parpack_solver.h.

◆ lworkev

template<typename VectorType >

int PArpackSolver< VectorType >::lworkev

protected

The size of the workev array.

Definition at line 464 of file parpack_solver.h.

◆ workev

template<typename VectorType >

std::vector<double> PArpackSolver< VectorType >::workev

protected

Double precision work array of dimension 3* NCV.

Definition at line 469 of file parpack_solver.h.

◆ select

template<typename VectorType >

std::vector<int> PArpackSolver< VectorType >::select

protected

A vector of dimension NCV.

Definition at line 474 of file parpack_solver.h.

◆ src

template<typename VectorType >

VectorType PArpackSolver< VectorType >::src

protected

Temporary vectors used between Arpack and deal.II

Definition at line 479 of file parpack_solver.h.

◆ dst

template<typename VectorType >

VectorType PArpackSolver< VectorType >::dst

protected

Definition at line 479 of file parpack_solver.h.

◆ tmp

template<typename VectorType >

VectorType PArpackSolver< VectorType >::tmp

protected

Definition at line 479 of file parpack_solver.h.

◆ local_indices

template<typename VectorType >

std::vector<types::global_dof_index> PArpackSolver< VectorType >::local_indices

protected

Indices of local degrees of freedom.

Definition at line 484 of file parpack_solver.h.

◆ sigmar

template<typename VectorType >

double PArpackSolver< VectorType >::sigmar

protected

Real part of the shift

Definition at line 489 of file parpack_solver.h.

◆ sigmai

template<typename VectorType >

double PArpackSolver< VectorType >::sigmai

protected

Imaginary part of the shift

Definition at line 494 of file parpack_solver.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

◆ counter_map

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

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

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

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

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

include/deal.II/lac/parpack_solver.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ size_type

◆ map_value_type

◆ map_iterator

Member Enumeration Documentation

◆ WhichEigenvalues

Constructor & Destructor Documentation

◆ PArpackSolver()

Member Function Documentation

◆ control()

◆ reinit() [1/3]

◆ reinit() [2/3]

◆ reinit() [3/3]

◆ set_initial_vector()

◆ set_shift()

◆ solve() [1/2]

◆ solve() [2/2]

◆ memory_consumption()

◆ internal_reinit()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ check_no_subscribers()

Member Data Documentation

◆ solver_control

◆ additional_data

◆ mpi_communicator

◆ mpi_communicator_fortran

◆ lworkl

◆ workl

◆ workd

◆ nloc

◆ ncv

◆ ldv

◆ v

◆ initial_vector_provided

◆ resid

◆ ldz

◆ z

◆ lworkev

◆ workev

◆ select

◆ src

◆ dst

◆ tmp

◆ local_indices

◆ sigmar

◆ sigmai

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex