#include <HermEigsBase.h>

Public Member Functions
Index	compute (SortRule selection=SortRule::LargestMagn, Index maxit=1000, RealScalar tol=1e-10, SortRule sorting=SortRule::LargestAlge)

RealVector	eigenvalues () const

virtual Matrix	eigenvectors () const

virtual Matrix	eigenvectors (Index nvec) const

CompInfo	info () const

void	init ()

void	init (const Scalar *init_resid)

Index	num_iterations () const

Index	num_operations () const

Protected Member Functions
virtual void	sort_ritzpair (SortRule sort_rule)

Protected Attributes
LanczosFac	m_fac

const Index	m_n

const Index	m_ncv

const Index	m_nev

Index	m_niter

Index	m_nmatop

const OpType &	m_op

std::vector< OpType >	m_op_container

RealVector	m_ritz_val

Private Types
using	ArnoldiOpType = ArnoldiOp< Scalar, OpType, BOpType >

using	BoolArray = Eigen::Array< bool, Eigen::Dynamic, 1 >

using	Index = Eigen::Index

using	LanczosFac = Lanczos< Scalar, ArnoldiOpType >

using	MapConstVec = Eigen::Map< const Vector >

using	MapMat = Eigen::Map< Matrix >

using	MapVec = Eigen::Map< Vector >

using	Matrix = Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >

using	RealArray = Eigen::Array< RealScalar, Eigen::Dynamic, 1 >

using	RealMatrix = Eigen::Matrix< RealScalar, Eigen::Dynamic, Eigen::Dynamic >

using	RealScalar = typename Eigen::NumTraits< Scalar >::Real

using	RealVector = Eigen::Matrix< RealScalar, Eigen::Dynamic, 1 >

using	Scalar = typename OpType::Scalar

using	Vector = Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >

Private Member Functions
Index	nev_adjusted (Index nconv)

Index	num_converged (const RealScalar &tol)

void	restart (Index k, SortRule selection)

void	retrieve_ritzpair (SortRule selection)

Static Private Member Functions
static std::vector< OpType >	create_op_container (OpType &&rval)

Private Attributes
CompInfo	m_info

BoolArray	m_ritz_conv

RealVector	m_ritz_est

RealMatrix	m_ritz_vec

Detailed Description

template<typename OpType, typename BOpType>
class Spectra::HermEigsBase< OpType, BOpType >

This is the base class for Hermitian (and real symmetric) eigen solvers, mainly for internal use. It is kept here to provide the documentation for member functions of concrete eigen solvers such as SymEigsSolver, HermEigsSolver, SymEigsShiftSolver, etc.

Definition at line 44 of file HermEigsBase.h.

Member Typedef Documentation

◆ ArnoldiOpType

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::ArnoldiOpType = ArnoldiOp<Scalar, OpType, BOpType>

private

Definition at line 63 of file HermEigsBase.h.

◆ BoolArray

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::BoolArray = Eigen::Array<bool, Eigen::Dynamic, 1>

private

Definition at line 58 of file HermEigsBase.h.

◆ Index

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::Index = Eigen::Index

private

Definition at line 52 of file HermEigsBase.h.

◆ LanczosFac

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::LanczosFac = Lanczos<Scalar, ArnoldiOpType>

private

Definition at line 64 of file HermEigsBase.h.

◆ MapConstVec

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::MapConstVec = Eigen::Map<const Vector>

private

Definition at line 61 of file HermEigsBase.h.

◆ MapMat

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::MapMat = Eigen::Map<Matrix>

private

Definition at line 59 of file HermEigsBase.h.

◆ MapVec

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::MapVec = Eigen::Map<Vector>

private

Definition at line 60 of file HermEigsBase.h.

◆ Matrix

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::Matrix = Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

private

Definition at line 53 of file HermEigsBase.h.

◆ RealArray

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::RealArray = Eigen::Array<RealScalar, Eigen::Dynamic, 1>

private

Definition at line 57 of file HermEigsBase.h.

◆ RealMatrix

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::RealMatrix = Eigen::Matrix<RealScalar, Eigen::Dynamic, Eigen::Dynamic>

private

Definition at line 55 of file HermEigsBase.h.

◆ RealScalar

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::RealScalar = typename Eigen::NumTraits<Scalar>::Real

private

Definition at line 51 of file HermEigsBase.h.

◆ RealVector

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::RealVector = Eigen::Matrix<RealScalar, Eigen::Dynamic, 1>

private

Definition at line 56 of file HermEigsBase.h.

◆ Scalar

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::Scalar = typename OpType::Scalar

private

Definition at line 47 of file HermEigsBase.h.

◆ Vector

template<typename OpType , typename BOpType >

using Spectra::HermEigsBase< OpType, BOpType >::Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>

private

Definition at line 54 of file HermEigsBase.h.

Member Function Documentation

◆ compute()

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::compute	(	SortRule	selection = `SortRule::LargestMagn`,
		Index	maxit = `1000`,
		RealScalar	tol = `1e-10`,
		SortRule	sorting = `SortRule::LargestAlge`
	)

inline

Conducts the major computation procedure.

Parameters

selection	An enumeration value indicating the selection rule of the requested eigenvalues, for example `SortRule::LargestMagn` to retrieve eigenvalues with the largest magnitude. The full list of enumeration values can be found in Enumerations.
maxit	Maximum number of iterations allowed in the algorithm.
tol	Precision parameter for the calculated eigenvalues.
sorting	Rule to sort the eigenvalues and eigenvectors. Supported values are `SortRule::LargestAlge`, `SortRule::LargestMagn`, `SortRule::SmallestAlge`, and `SortRule::SmallestMagn`. For example, `SortRule::LargestAlge` indicates that largest eigenvalues come first. Note that this argument is only used to sort the final result, and the selection rule (e.g. selecting the largest or smallest eigenvalues in the full spectrum) is specified by the parameter `selection`.

Returns: Number of converged eigenvalues.

Definition at line 360 of file HermEigsBase.h.

◆ create_op_container()

template<typename OpType , typename BOpType >

static std::vector<OpType> Spectra::HermEigsBase< OpType, BOpType >::create_op_container ( OpType && rval )

inlinestaticprivate

Definition at line 94 of file HermEigsBase.h.

◆ eigenvalues()

template<typename OpType , typename BOpType >

RealVector Spectra::HermEigsBase< OpType, BOpType >::eigenvalues ( ) const

inline

Returns the converged eigenvalues.

Returns: A vector containing the real-valued eigenvalues. Returned vector type will be Eigen::Vector<RealScalar, ...>, depending on the Scalar type defined in the matrix operation class. For example, if Scalar is double or std::complex<double>, then RealScalar would be double.

Definition at line 411 of file HermEigsBase.h.

◆ eigenvectors() [1/2]

template<typename OpType , typename BOpType >

virtual Matrix Spectra::HermEigsBase< OpType, BOpType >::eigenvectors ( ) const

inlinevirtual

Returns all converged eigenvectors.

Definition at line 469 of file HermEigsBase.h.

◆ eigenvectors() [2/2]

template<typename OpType , typename BOpType >

virtual Matrix Spectra::HermEigsBase< OpType, BOpType >::eigenvectors ( Index nvec ) const

inlinevirtual

Returns the eigenvectors associated with the converged eigenvalues.

Parameters

nvec	The number of eigenvectors to return.

Returns: A matrix containing the eigenvectors. Returned matrix type will be Eigen::Matrix<Scalar, ...>, depending on the Scalar type defined in the matrix operation class.

Definition at line 441 of file HermEigsBase.h.

◆ info()

template<typename OpType , typename BOpType >

CompInfo Spectra::HermEigsBase< OpType, BOpType >::info ( ) const

inline

Returns the status of the computation. The full list of enumeration values can be found in Enumerations.

Definition at line 390 of file HermEigsBase.h.

◆ init() [1/2]

template<typename OpType , typename BOpType >

void Spectra::HermEigsBase< OpType, BOpType >::init ( )

inline

Initializes the solver by providing a random initial residual vector.

This overloaded function generates a random initial residual vector (with a fixed random seed) for the algorithm. Elements in the vector follow independent Uniform(-0.5, 0.5) distribution.

Definition at line 331 of file HermEigsBase.h.

◆ init() [2/2]

template<typename OpType , typename BOpType >

void Spectra::HermEigsBase< OpType, BOpType >::init ( const Scalar * init_resid )

inline

Initializes the solver by providing an initial residual vector.

Parameters

init_resid Pointer to the initial residual vector.

Spectra (and also ARPACK) uses an iterative algorithm to find eigenvalues. This function allows the user to provide the initial residual vector.

Definition at line 303 of file HermEigsBase.h.

◆ nev_adjusted()

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::nev_adjusted ( Index nconv )

inlineprivate

Definition at line 172 of file HermEigsBase.h.

◆ num_converged()

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::num_converged ( const RealScalar & tol )

inlineprivate

Definition at line 152 of file HermEigsBase.h.

◆ num_iterations()

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::num_iterations ( ) const

inline

Returns the number of iterations used in the computation.

Definition at line 395 of file HermEigsBase.h.

◆ num_operations()

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::num_operations ( ) const

inline

Returns the number of matrix operations used in the computation.

Definition at line 400 of file HermEigsBase.h.

◆ restart()

template<typename OpType , typename BOpType >

void Spectra::HermEigsBase< OpType, BOpType >::restart	(	Index	k,
		SortRule	selection
	)

inlineprivate

Definition at line 102 of file HermEigsBase.h.

◆ retrieve_ritzpair()

template<typename OpType , typename BOpType >

void Spectra::HermEigsBase< OpType, BOpType >::retrieve_ritzpair ( SortRule selection )

inlineprivate

Definition at line 199 of file HermEigsBase.h.

◆ sort_ritzpair()

template<typename OpType , typename BOpType >

virtual void Spectra::HermEigsBase< OpType, BOpType >::sort_ritzpair ( SortRule sort_rule )

inlineprotectedvirtual

Reimplemented in Spectra::SymGEigsShiftSolver< OpType, BOpType, GEigsMode::Cayley >, Spectra::SymGEigsShiftSolver< OpType, BOpType, GEigsMode::Buckling >, Spectra::SymGEigsShiftSolver< OpType, BOpType, GEigsMode::ShiftInvert >, and Spectra::SymEigsShiftSolver< OpType >.

Definition at line 223 of file HermEigsBase.h.

Member Data Documentation

◆ m_fac

template<typename OpType , typename BOpType >

LanczosFac Spectra::HermEigsBase< OpType, BOpType >::m_fac

protected

Definition at line 83 of file HermEigsBase.h.

◆ m_info

template<typename OpType , typename BOpType >

CompInfo Spectra::HermEigsBase< OpType, BOpType >::m_info

private

Definition at line 90 of file HermEigsBase.h.

◆ m_n

template<typename OpType , typename BOpType >

const Index Spectra::HermEigsBase< OpType, BOpType >::m_n

protected

Definition at line 77 of file HermEigsBase.h.

◆ m_ncv

template<typename OpType , typename BOpType >

const Index Spectra::HermEigsBase< OpType, BOpType >::m_ncv

protected

Definition at line 79 of file HermEigsBase.h.

◆ m_nev

template<typename OpType , typename BOpType >

const Index Spectra::HermEigsBase< OpType, BOpType >::m_nev

protected

Definition at line 78 of file HermEigsBase.h.

◆ m_niter

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::m_niter

protected

Definition at line 81 of file HermEigsBase.h.

◆ m_nmatop

template<typename OpType , typename BOpType >

Index Spectra::HermEigsBase< OpType, BOpType >::m_nmatop

protected

Definition at line 80 of file HermEigsBase.h.

◆ m_op

template<typename OpType , typename BOpType >

const OpType& Spectra::HermEigsBase< OpType, BOpType >::m_op

protected

Definition at line 76 of file HermEigsBase.h.

◆ m_op_container

template<typename OpType , typename BOpType >

std::vector<OpType> Spectra::HermEigsBase< OpType, BOpType >::m_op_container

protected

Definition at line 75 of file HermEigsBase.h.

◆ m_ritz_conv

template<typename OpType , typename BOpType >

BoolArray Spectra::HermEigsBase< OpType, BOpType >::m_ritz_conv

private

Definition at line 89 of file HermEigsBase.h.

◆ m_ritz_est

template<typename OpType , typename BOpType >

RealVector Spectra::HermEigsBase< OpType, BOpType >::m_ritz_est

private

Definition at line 88 of file HermEigsBase.h.

◆ m_ritz_val

template<typename OpType , typename BOpType >

RealVector Spectra::HermEigsBase< OpType, BOpType >::m_ritz_val

protected

Definition at line 84 of file HermEigsBase.h.

◆ m_ritz_vec

template<typename OpType , typename BOpType >

RealMatrix Spectra::HermEigsBase< OpType, BOpType >::m_ritz_vec

private

Definition at line 87 of file HermEigsBase.h.

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

HermEigsBase.h

Public Member Functions

Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

template<typename OpType, typename BOpType> class Spectra::HermEigsBase< OpType, BOpType >

Member Typedef Documentation

◆ ArnoldiOpType

◆ BoolArray

◆ Index

◆ LanczosFac

◆ MapConstVec

◆ MapMat

◆ MapVec

◆ Matrix

◆ RealArray

◆ RealMatrix

◆ RealScalar

◆ RealVector

◆ Scalar

◆ Vector

Member Function Documentation

◆ compute()

◆ create_op_container()

◆ eigenvalues()

◆ eigenvectors() [1/2]

◆ eigenvectors() [2/2]

◆ info()

◆ init() [1/2]

◆ init() [2/2]

◆ nev_adjusted()

◆ num_converged()

◆ num_iterations()

◆ num_operations()

◆ restart()

◆ retrieve_ritzpair()

◆ sort_ritzpair()

Member Data Documentation

◆ m_fac

◆ m_info

◆ m_n

◆ m_ncv

◆ m_nev

◆ m_niter

◆ m_nmatop

◆ m_op

◆ m_op_container

◆ m_ritz_conv

◆ m_ritz_est

◆ m_ritz_val

◆ m_ritz_vec

template<typename OpType, typename BOpType>
class Spectra::HermEigsBase< OpType, BOpType >