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

Inheritance diagram for PArpackSolver< VectorType >:

Classes
struct	AdditionalData

class	Shift

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 }

typedef types::global_dof_index	size_type

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)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

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

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

std::vector< types::global_dof_index >	local_indices

double	sigmar

double	sigmai

Private Member Functions
void	internal_reinit (const IndexSet &locally_owned_dofs)

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)

Additional Inherited Members
Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, char *arg2, std::string &arg3)

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char arg2)

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. OP is an inverse operation for the matrix A - sigma * B, where sigma is a shift value, set to zero by default. Note that (P)Arpack supports other transformations, but currently this class implements only shift-and-invert mode.

The OP can be specified either using auxiliary Shift class together with IterativeInverse or by using 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 ());

Through the AdditionalData the user can specify some of the parameters to be set.

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.

Author: Denis Davydov, 2015.

Definition at line 144 of file parpack_solver.h.

Member Typedef Documentation

◆ size_type

template<typename VectorType>

typedef types::global_dof_index PArpackSolver< VectorType >::size_type

Declare the type for container size.

Definition at line 150 of file parpack_solver.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 161 of file parpack_solver.h.