Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT > Struct Template Reference

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 the full spectrum of eigenvalues. 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>>)
	GeneralizedSymEigenSolver (MATA &&A, MATB &&B)
	Construct a new GeneralizedSymEigenSolver object. More...
template<Concepts::FlatAssembler AssemblerA, Concepts::FlatAssembler AssemblerB>
	GeneralizedSymEigenSolver (std::shared_ptr< AssemblerA > assemblerA, const std::shared_ptr< AssemblerB > &assemblerB)
	Construct a new GeneralSymEigenSolver object. More...
bool	compute (Eigen::Index maxit=1000, ScalarType tolerance=1e-10)
	Starts the computation of the eigenvalue solver. More...
auto &	eigenvalues () const
	Returns the eigenvalues of the generalized eigenvalue problem. More...
auto &	eigenvectors () const
	Returns the eigenvectors of the generalized eigenvalue problem. More...
Eigen::Index	nev () const
	Returns the number of eigenvalues of the problem. More...

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

Detailed Description

template<Concepts::DenseOrSparseEigenMatrix MT>
struct Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >

Under the hood it uses the Spectra::SymGEigsSolver with Cholesky decomposition for B. As this class can only compute up to \( n-1 \) smallest or greatest eigenvalues, we use two different solvers for the n/2 smallest and n/2 greatest eigenvalues. The matrices are shared throughout the solvers so no extra copy is being made.

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::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::CholeskyType = std::conditional_t<isDense, Spectra::DenseCholesky<ScalarType>, Spectra::SparseCholesky<ScalarType> >

MatrixType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::MatrixType = MT

ProductType

template<Concepts::DenseOrSparseEigenMatrix MT>

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

ScalarType

template<Concepts::DenseOrSparseEigenMatrix MT>

using Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::ScalarType = typename MT::Scalar

SolverType

template<Concepts::DenseOrSparseEigenMatrix MT>

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

Constructor & Destructor Documentation

GeneralizedSymEigenSolver() [1/2]

template<Concepts::DenseOrSparseEigenMatrix MT>

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

Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::GeneralizedSymEigenSolver ( MATA &&  A, MATB &&  B  )

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

GeneralizedSymEigenSolver() [2/2]

template<Concepts::DenseOrSparseEigenMatrix MT>

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

Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::GeneralizedSymEigenSolver ( std::shared_ptr< AssemblerA >  assemblerA, const std::shared_ptr< AssemblerB > &  assemblerB  )

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::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::compute ( Eigen::Index  maxit = 1000, ScalarType  tolerance = 1e-10  )

inline

Parameters

tolerance	given tolerance for iterative eigenvalue solving (default: 1e-10)
maxit	given maximum iterations for eigenvalue solving (default: 1000)

Returns

true solving was successful

false solving was not successful

eigenvalues()

template<Concepts::DenseOrSparseEigenMatrix MT>

auto & Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::eigenvalues ( ) const

inline

Returns

Eigen::VectorXd vector of eigenvalues

eigenvectors()

template<Concepts::DenseOrSparseEigenMatrix MT>

auto & Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::eigenvectors ( ) const

inline

Returns

auto matrix with the eigevectors as columns

nev()

template<Concepts::DenseOrSparseEigenMatrix MT>

Eigen::Index Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::nev ( ) const

inline

Member Data Documentation

isDense

template<Concepts::DenseOrSparseEigenMatrix MT>

constexpr bool Ikarus::GeneralizedSymEigenSolver< EigenValueSolverType::Spectra, MT >::isDense = Concepts::EigenMatrix<MT>

staticconstexpr

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

• generalizedeigensolver.hh