 Reference documentation for deal.II version Git d902c8c1aa 2019-12-15 00:36:45 -0500
PArpackSolver< VectorType > Class Template Reference

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

Inheritance diagram for PArpackSolver< VectorType >:
[legend]

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
}

using size_type = types::global_dof_index

## Public Member Functions

SolverControlcontrol () const

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 Public Member Functions inherited from Subscriptor
Subscriptor ()

Subscriptor (const Subscriptor &)

Subscriptor (Subscriptor &&) noexcept

virtual ~Subscriptor ()

Subscriptoroperator= (const Subscriptor &)

Subscriptoroperator= (Subscriptor &&) noexcept

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)

## Protected Attributes

SolverControlsolver_control

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_indexlocal_indices

double sigmar

double sigmai

## Private Member Functions

void internal_reinit (const IndexSet &locally_owned_dofs)

## Static Private Member Functions

static ::ExceptionBasePArpackExcConvergedEigenvectors (int arg1, int arg2)

static ::ExceptionBasePArpackExcInvalidNumberofEigenvalues (int arg1, int arg2)

static ::ExceptionBasePArpackExcInvalidEigenvectorSize (int arg1, int arg2)

static ::ExceptionBasePArpackExcInvalidEigenvectorSizeNonsymmetric (int arg1, int arg2)

static ::ExceptionBasePArpackExcInvalidEigenvalueSize (int arg1, int arg2)

static ::ExceptionBasePArpackExcInvalidNumberofArnoldiVectors (int arg1, int arg2)

static ::ExceptionBasePArpackExcSmallNumberofArnoldiVectors (int arg1, int arg2)

static ::ExceptionBasePArpackExcIdo (int arg1)

static ::ExceptionBasePArpackExcMode (int arg1)

static ::ExceptionBasePArpackExcInfoPdnaupd (int arg1)

static ::ExceptionBasePArpackExcInfoPdneupd (int arg1)

static ::ExceptionBasePArpackExcInfoMaxIt (int arg1)

static ::ExceptionBasePArpackExcNoShifts (int arg1) Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string 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:

const unsigned int num_arnoldi_vectors = 2*size_of_spectrum + 2;
true);
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 =

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 213 of file parpack_solver.h.

## ◆ size_type

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

Declare the type for container size.

Definition at line 219 of file parpack_solver.h.

## ◆ WhichEigenvalues

template<typename VectorType>

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 230 of file parpack_solver.h.

## ◆ PArpackSolver()

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

Constructor.

Definition at line 691 of file parpack_solver.h.

## ◆ control()

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

Definition at line 1210 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 777 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 805 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 791 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 723 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 713 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 821 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 839 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 640 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 737 of file parpack_solver.h.

## ◆ 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 432 of file parpack_solver.h.

template<typename VectorType>
protected

Store a copy of the flags for this particular solver.

Definition at line 437 of file parpack_solver.h.

## ◆ mpi_communicator

template<typename VectorType>
 MPI_Comm PArpackSolver< VectorType >::mpi_communicator
protected

C++ MPI communicator.

Definition at line 444 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 449 of file parpack_solver.h.

## ◆ lworkl

template<typename VectorType>
 int PArpackSolver< VectorType >::lworkl
protected

Length of the work array workl.

Definition at line 456 of file parpack_solver.h.

## ◆ workl

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::workl
protected

Double precision work array of length lworkl

Definition at line 461 of file parpack_solver.h.

## ◆ workd

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::workd
protected

Double precision work array of length 3*N

Definition at line 466 of file parpack_solver.h.

## ◆ nloc

template<typename VectorType>
 int PArpackSolver< VectorType >::nloc
protected

Number of local degrees of freedom.

Definition at line 471 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 476 of file parpack_solver.h.

## ◆ ldv

template<typename VectorType>
 int PArpackSolver< VectorType >::ldv
protected

The leading dimension of the array v

Definition at line 482 of file parpack_solver.h.

## ◆ v

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::v
protected

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

Definition at line 488 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 493 of file parpack_solver.h.

## ◆ resid

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::resid
protected

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

Definition at line 499 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 504 of file parpack_solver.h.

## ◆ z

template<typename VectorType>
 std::vector 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 511 of file parpack_solver.h.

## ◆ lworkev

template<typename VectorType>
 int PArpackSolver< VectorType >::lworkev
protected

The size of the workev array.

Definition at line 516 of file parpack_solver.h.

## ◆ workev

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::workev
protected

Double precision work array of dimension 3* NCV.

Definition at line 521 of file parpack_solver.h.

## ◆ select

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::select
protected

A vector of dimension NCV.

Definition at line 526 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 531 of file parpack_solver.h.

## ◆ local_indices

template<typename VectorType>
 std::vector PArpackSolver< VectorType >::local_indices
protected

Indices of local degrees of freedom.

Definition at line 536 of file parpack_solver.h.

## ◆ sigmar

template<typename VectorType>
 double PArpackSolver< VectorType >::sigmar
protected

Real part of the shift

Definition at line 541 of file parpack_solver.h.

## ◆ sigmai

template<typename VectorType>
 double PArpackSolver< VectorType >::sigmai
protected

Imaginary part of the shift

Definition at line 546 of file parpack_solver.h.

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