Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType > Class Template Reference

#include <GenEigsBase.h>

Public Member Functions
Index	compute (Index maxit=1000, Scalar tol=1e-10, int sort_rule=LARGEST_MAGN)
ComplexVector	eigenvalues () const
ComplexMatrix	eigenvectors (Index nvec) const
ComplexMatrix	eigenvectors () const
int	info () const
void	init (const Scalar *init_resid)
void	init ()
Index	num_iterations () const
Index	num_operations () const

Protected Member Functions
virtual void	sort_ritzpair (int sort_rule)

Protected Attributes
ArnoldiFac	m_fac
const Index	m_n
const Index	m_ncv
const Index	m_nev
Index	m_niter
Index	m_nmatop
OpType *	m_op
ComplexVector	m_ritz_est
ComplexVector	m_ritz_val
ComplexMatrix	m_ritz_vec

Private Types
typedef Arnoldi< Scalar, ArnoldiOpType >	ArnoldiFac
typedef ArnoldiOp< Scalar, OpType, BOpType >	ArnoldiOpType
typedef Eigen::Array< Scalar, Eigen::Dynamic, 1 >	Array
typedef Eigen::Array< bool, Eigen::Dynamic, 1 >	BoolArray
typedef std::complex< Scalar >	Complex
typedef Eigen::Matrix< Complex, Eigen::Dynamic, Eigen::Dynamic >	ComplexMatrix
typedef Eigen::Matrix< Complex, Eigen::Dynamic, 1 >	ComplexVector
typedef Eigen::Index	Index
typedef Eigen::Map< const Vector >	MapConstVec
typedef Eigen::Map< Matrix >	MapMat
typedef Eigen::Map< Vector >	MapVec
typedef Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	Matrix
typedef Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	Vector

Private Member Functions
Index	nev_adjusted (Index nconv)
Index	num_converged (Scalar tol)
void	restart (Index k)
void	retrieve_ritzpair ()

Static Private Member Functions
static bool	is_complex (const Complex &v)
static bool	is_conj (const Complex &v1, const Complex &v2)

Private Attributes
const Scalar	m_eps
const Scalar	m_eps23
int	m_info
const Scalar	m_near_0
BoolArray	m_ritz_conv

Detailed Description

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>
class Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >

This is the base class for general eigen solvers, mainly for internal use. It is kept here to provide the documentation for member functions of concrete eigen solvers such as GenEigsSolver and GenEigsRealShiftSolver.

Definition at line 40 of file GenEigsBase.h.

Member Typedef Documentation

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Arnoldi<Scalar, ArnoldiOpType> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::ArnoldiFac

private

Definition at line 57 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef ArnoldiOp<Scalar, OpType, BOpType> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::ArnoldiOpType

private

Definition at line 56 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::Array

private

Definition at line 46 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Array<bool, Eigen::Dynamic, 1> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::BoolArray

private

Definition at line 47 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef std::complex<Scalar> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::Complex

private

Definition at line 52 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Matrix<Complex, Eigen::Dynamic, Eigen::Dynamic> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::ComplexMatrix

private

Definition at line 53 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::ComplexVector

private

Definition at line 54 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::Index

private

Definition at line 43 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Map<const Vector> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::MapConstVec

private

Definition at line 50 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Map<Matrix> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::MapMat

private

Definition at line 48 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Map<Vector> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::MapVec

private

Definition at line 49 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::Matrix

private

Definition at line 44 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::Vector

private

Definition at line 45 of file GenEigsBase.h.

Member Function Documentation

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::compute ( Index  maxit = 1000, Scalar  tol = 1e-10, int  sort_rule = LARGEST_MAGN  )

inline

Conducts the major computation procedure.

Parameters

maxit	Maximum number of iterations allowed in the algorithm.
tol	Precision parameter for the calculated eigenvalues.
sort_rule	Rule to sort the eigenvalues and eigenvectors. Supported values are Spectra::LARGEST_MAGN, Spectra::LARGEST_REAL, Spectra::LARGEST_IMAG, Spectra::SMALLEST_MAGN, Spectra::SMALLEST_REAL and Spectra::SMALLEST_IMAG, for example LARGEST_MAGN indicates that eigenvalues with largest magnitude 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 template parameter SelectionRule of GenEigsSolver.

Returns

Number of converged eigenvalues.

Definition at line 368 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexVector Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::eigenvalues ( ) const

inline

Returns the converged eigenvalues.

Returns

A complex-valued vector containing the eigenvalues. Returned vector type will be Eigen::Vector<std::complex<Scalar>, ...>, depending on the template parameter Scalar defined.

Definition at line 416 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexMatrix Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::eigenvectors ( Index  nvec ) const

inline

Returns the eigenvectors associated with the converged eigenvalues.

Parameters

nvec	The number of eigenvectors to return.

Returns

A complex-valued matrix containing the eigenvectors. Returned matrix type will be Eigen::Matrix<std::complex<Scalar>, ...>, depending on the template parameter Scalar defined.

Definition at line 446 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexMatrix Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::eigenvectors ( ) const

inline

Returns all converged eigenvectors.

Definition at line 474 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

int Spectra::GenEigsBase< Scalar, SelectionRule, 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 397 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

void Spectra::GenEigsBase< Scalar, SelectionRule, 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 313 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

void Spectra::GenEigsBase< Scalar, SelectionRule, 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 341 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

static bool Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::is_complex ( const Complex &  v )

inlinestaticprivate

Definition at line 88 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

static bool Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::is_conj ( const Complex &  v1, const Complex &  v2  )

inlinestaticprivate

Definition at line 89 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::nev_adjusted ( Index  nconv )

inlineprivate

Definition at line 159 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::num_converged ( Scalar  tol )

inlineprivate

Definition at line 147 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::num_iterations ( ) const

inline

Returns the number of iterations used in the computation.

Definition at line 402 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::num_operations ( ) const

inline

Returns the number of matrix operations used in the computation.

Definition at line 407 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

void Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::restart ( Index  k )

inlineprivate

Definition at line 92 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

void Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::retrieve_ritzpair ( )

inlineprivate

Definition at line 190 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

virtual void Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::sort_ritzpair ( int  sort_rule )

inlineprotectedvirtual

Reimplemented in Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >, and Spectra::GenEigsRealShiftSolver< Scalar, SelectionRule, OpType >.

Definition at line 214 of file GenEigsBase.h.

Member Data Documentation

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Scalar Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_eps

private

Definition at line 81 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Scalar Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_eps23

private

Definition at line 82 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ArnoldiFac Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_fac

protected

Definition at line 69 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

int Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_info

private

Definition at line 77 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_n

protected

Definition at line 63 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_ncv

protected

Definition at line 65 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Scalar Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_near_0

private

Definition at line 79 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

const Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_nev

protected

Definition at line 64 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_niter

protected

Definition at line 67 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

Index Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_nmatop

protected

Definition at line 66 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

OpType* Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_op

protected

Definition at line 61 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

BoolArray Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_ritz_conv

private

Definition at line 76 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexVector Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_ritz_est

protected

Definition at line 73 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexVector Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_ritz_val

protected

Definition at line 71 of file GenEigsBase.h.

template<typename Scalar, int SelectionRule, typename OpType, typename BOpType>

ComplexMatrix Spectra::GenEigsBase< Scalar, SelectionRule, OpType, BOpType >::m_ritz_vec

protected

Definition at line 72 of file GenEigsBase.h.

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

• GenEigsBase.h