This class implements a wrapper to the Spectra generalized eigen solver for square real symmetric matrices, i.e. to solve \( Ax = \lambda Bx\), where A is symmetric and B is positive definite. It calculates a selection of eigenvalues. At most \( n - 1 \), where \( n \) is the number of rows/cols of the matrices. More...

#include <ikarus/solver/eigenvaluesolver/generalizedeigensolver.hh>

Public Types
using	ScalarType = typename MT::Scalar

using	MatrixType = MT

using	ProductType = std::conditional_t< isDense, Spectra::DenseSymMatProd< ScalarType >, Spectra::SparseSymMatProd< ScalarType > >

using	CholeskyType = std::conditional_t< isDense, Spectra::DenseCholesky< ScalarType >, Spectra::SparseCholesky< ScalarType > >

using	SolverType = Spectra::SymGEigsSolver< ProductType, CholeskyType, Spectra::GEigsMode::Cholesky >

Public Member Functions
template<typename MATA , typename MATB > requires (Concepts::DenseOrSparseEigenMatrix<std::remove_cvref_t<MATA>>)
	PartialGeneralizedSymEigenSolver (MATA &&A, MATB &&B, Eigen::Index nev)
	Construct a new PartialGeneralizedSymEigenSolver object. More...

template<Concepts::FlatAssembler AssemblerA, Concepts::FlatAssembler AssemblerB>
	PartialGeneralizedSymEigenSolver (std::shared_ptr< AssemblerA > assemblerA, std::shared_ptr< AssemblerB > assemblerB, Eigen::Index nev)
	Construct a new PartialGeneralizedSymEigenSolver object. More...

bool	compute (Spectra::SortRule selection=Spectra::SortRule::SmallestAlge, Spectra::SortRule sortRule=Spectra::SortRule::SmallestAlge, Eigen::Index maxit=1000, ScalarType tolerance=1e-10)
	Starts the computation of the eigenvalue solver. More...

Eigen::VectorXd	eigenvalues () const
	Returns the eigenvalues of the generalized eigenvalue problem. More...

auto	eigenvectors (std::optional< Eigen::Index > _nev=std::nullopt) const
	Returns the eigenvectors of the generalized eigenvalue problem. More...

Eigen::Index	nev () const

Static Public Attributes
static constexpr bool	isDense = Concepts::EigenMatrix<MT>

Detailed Description

template<Concepts::DenseOrSparseEigenMatrix MT>
struct Ikarus::PartialGeneralizedSymEigenSolver< MT >

Under the hood it uses the Spectra::SymGEigsSolver with Cholesky decomposition for B

Template Parameters

MT	the used Matrix Type, can be a sparse or dense Eigen::Matrix

Member Typedef Documentation

◆ CholeskyType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::PartialGeneralizedSymEigenSolver< MT >::CholeskyType = std::conditional_t<isDense, Spectra::DenseCholesky<ScalarType>, Spectra::SparseCholesky<ScalarType> >

◆ MatrixType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::PartialGeneralizedSymEigenSolver< MT >::MatrixType = MT

◆ ProductType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::PartialGeneralizedSymEigenSolver< MT >::ProductType = std::conditional_t<isDense, Spectra::DenseSymMatProd<ScalarType>, Spectra::SparseSymMatProd<ScalarType> >

◆ ScalarType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::PartialGeneralizedSymEigenSolver< MT >::ScalarType = typename MT::Scalar

◆ SolverType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::PartialGeneralizedSymEigenSolver< MT >::SolverType = Spectra::SymGEigsSolver<ProductType, CholeskyType, Spectra::GEigsMode::Cholesky>

Constructor & Destructor Documentation

◆ PartialGeneralizedSymEigenSolver() [1/2]

template<Concepts::DenseOrSparseEigenMatrix MT>

template<typename MATA , typename MATB >
requires (Concepts::DenseOrSparseEigenMatrix<std::remove_cvref_t<MATA>>)

Ikarus::PartialGeneralizedSymEigenSolver< MT >::PartialGeneralizedSymEigenSolver	(	MATA &&	A,
		MATB &&	B,
		Eigen::Index	nev
	)

inline

Template Parameters

MATA	the deduced type of the matrix A
MATB	the deduced type of the matrix B

Parameters

A	the matrix A
B	the matrix B

◆ PartialGeneralizedSymEigenSolver() [2/2]

template<Concepts::DenseOrSparseEigenMatrix MT>

template<Concepts::FlatAssembler AssemblerA, Concepts::FlatAssembler AssemblerB>

Ikarus::PartialGeneralizedSymEigenSolver< MT >::PartialGeneralizedSymEigenSolver	(	std::shared_ptr< AssemblerA >	assemblerA,
		std::shared_ptr< AssemblerB >	assemblerB,
		Eigen::Index	nev
	)

inline

Template Parameters

AssemblerA	the type of the assembler for matrix A.
AssemblerB	the type of the assembler for matrix B.

Parameters

assemblerA	assembler for matrix A.
assemblerB	assembler for matrix B.

Member Function Documentation

◆ compute()

template<Concepts::DenseOrSparseEigenMatrix MT>

bool Ikarus::PartialGeneralizedSymEigenSolver< MT >::compute	(	Spectra::SortRule	selection = `Spectra::SortRule::SmallestAlge`,
		Spectra::SortRule	sortRule = `Spectra::SortRule::SmallestAlge`,
		Eigen::Index	maxit = `1000`,
		ScalarType	tolerance = `1e-10`
	)

inline

Parameters

selection	defines which n eigenvalues should be returned (i.e. smallest or greatesst).
sortRule	defines how these eigenvalues should be sorted.
tolerance	given tolerance for iterative eigenvalue solving (default: 1e-10).
maxit	givenn maximum iterations for eigenvalue solving (default: 1000).

Returns: true solving was successful.; false solving was not successful.

◆ eigenvalues()

template<Concepts::DenseOrSparseEigenMatrix MT>

Eigen::VectorXd Ikarus::PartialGeneralizedSymEigenSolver< MT >::eigenvalues ( ) const

inline

Returns: Eigen::VectorXd vector of eigenvalues

◆ eigenvectors()

template<Concepts::DenseOrSparseEigenMatrix MT>

auto Ikarus::PartialGeneralizedSymEigenSolver< MT >::eigenvectors ( std::optional< Eigen::Index > _nev = std::nullopt ) const

inline

Parameters

_nev	optionally specify how many eigenvectors are requested

Returns: auto matrix with the eigevectors as columns

◆ nev()

template<Concepts::DenseOrSparseEigenMatrix MT>

Eigen::Index Ikarus::PartialGeneralizedSymEigenSolver< MT >::nev ( ) const

inline

Member Data Documentation

◆ isDense

template<Concepts::DenseOrSparseEigenMatrix MT>

constexpr bool Ikarus::PartialGeneralizedSymEigenSolver< MT >::isDense = Concepts::EigenMatrix<MT>

staticconstexpr

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

generalizedeigensolver.hh

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ CholeskyType

◆ MatrixType

◆ ProductType

◆ ScalarType

◆ SolverType

Constructor & Destructor Documentation

◆ PartialGeneralizedSymEigenSolver() [1/2]

◆ PartialGeneralizedSymEigenSolver() [2/2]

Member Function Documentation

◆ compute()

◆ eigenvalues()

◆ eigenvectors()

◆ nev()

Member Data Documentation

◆ isDense