Class to find eigenvalues and corresponding eigenvectors of a given matrix in a generalized eigenproblem, i.e. Find scalars l and non-null vectors v such that [K]{v} = l[M]{v} where [K] and [M] are symmetric matrices. The eigenproblem can be originated from a PDE. For this, we will refer to the matrices K and M as Stiffness and Mass matrices respectively. More...

#include <EigenProblemSolver.h>

Public Member Functions
	EigenProblemSolver ()
	Default constructor.

	EigenProblemSolver (DMatrix< real_t > &A, bool eigv=false)
	Constructor for a dense unsymmetric matrix that computes the eigenvalues.

	EigenProblemSolver (DSMatrix< real_t > &K, int n=0)
	Constructor for a dense symmetric matrix that computes the eigenvalues.

	EigenProblemSolver (SkSMatrix< real_t > &K, SkSMatrix< real_t > &M, int n=0)
	Constructor for Symmetric Skyline Matrices.

	EigenProblemSolver (SkSMatrix< real_t > &K, Vect< real_t > &M, int n=0)
	Constructor for Symmetric Skyline Matrices.

	EigenProblemSolver (DSMatrix< real_t > &A, Vect< real_t > &ev, int n=0)
	Constructor for a dense symmetric matrix that compute the eigenvalues.

	EigenProblemSolver (DMatrix< real_t > &A, Vect< real_t > &evr, Vect< real_t > &evi, bool eigv=false)
	Constructor for a dense matrix that compute the eigenvalues.

	EigenProblemSolver (Equa &eq, bool lumped=true)
	Consrtuctor using partial differential equation.

	~EigenProblemSolver ()
	Destructor.

void	set (EigenMethod m, bool sym)
	Set numerical method for eigenvalue computation.

void	setMatrix (Matrix< real_t > *K)
	Set pointer to matrix instance.

void	setMatrix (Matrix< real_t > K, Matrix< real_t > M)
	Set pointers to matrix instances.

void	setMatrix (SkSMatrix< real_t > &K, SkSMatrix< real_t > &M)
	Set matrix instances (Symmetric matrices).

void	setMatrix (SkSMatrix< real_t > &K, Vect< real_t > &M)
	Set matrix instances (Symmetric matrices).

void	setMatrix (DSMatrix< real_t > &K)
	Set matrix instance (Symmetric matrix).

void	setMatrix (DMatrix< real_t > &K)
	Set matrix instance.

void	setNbEigv (int n)
	Set number of extracted eigenvalues.

void	setEigenVectors ()
	Switch to compute (or not) eigenvectors as well.

void	setPDE (Equa &eq, bool lumped=true)
	Define partial differential equation to solve.

int	run (int nb=0, bool opt=false)
	Run the eigenproblem solver.

void	Assembly (const Element &el, real_t eK, real_t eM)
	Assemble element arrays into global matrices.

void	SAssembly (const Side &sd, real_t *sK)
	Assemble side arrays into global matrix and right-hand side.

int	runSubSpace (size_t nb_eigv, size_t ss_dim=0)
	Run the subspace iteration solver.

void	setSubspaceDimension (int dim)
	Define the subspace dimension.

void	setMaxIter (int max_it)
	set maximal number of iterations.

void	setTolerance (real_t eps)
	set tolerance value

int	checkSturm (int &nb_found, int &nb_lost)
	Check how many eigenvalues have been found using Sturm sequence method.

int	getNbIter () const
	Return actual number of performed iterations.

real_t	getEigenValue (int n, int i=1) const
	Return the n-th eigenvalue.

void	getEigenVector (int n, Vect< real_t > &v) const
	Return the n-th eigenvector.

void	getEigenVector (int n, Vect< real_t > &vr, Vect< real_t > &vi) const
	Return the n-th eigenvector in the case of complex eigenvectors.

Detailed Description

Class to find eigenvalues and corresponding eigenvectors of a given matrix in a generalized eigenproblem, i.e. Find scalars l and non-null vectors v such that [K]{v} = l[M]{v} where [K] and [M] are symmetric matrices. The eigenproblem can be originated from a PDE. For this, we will refer to the matrices K and M as Stiffness and Mass matrices respectively.

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ EigenProblemSolver() [1/7]

EigenProblemSolver	(	DMatrix< real_t > &	A,
		bool	eigv = `false`
	)

Constructor for a dense unsymmetric matrix that computes the eigenvalues.

This constructor solves in place the eigenvalues problem and stores them in a vector. The eigenvectors can be obtained by calling the member function getEigenVector. Eigenvalue extraction uses the reduction to Hessenberg form of the matrix.

Parameters

[in]	A	Matrix for which eigenmodes are sought.
[in]	eigv	Switch to compute or not eigenvectors [Default: `false`]

Remarks: All eigenvalues are extracted.

◆ EigenProblemSolver() [2/7]

EigenProblemSolver	(	DSMatrix< real_t > &	K,
		int	n = `0`
	)

Constructor for a dense symmetric matrix that computes the eigenvalues.

This constructor solves in place the eigenvalues problem and stores them in a vector. The eigenvectors can be obtained by calling the member function getEigenVector.

Parameters

[in]	K	Matrix for which eigenmodes are sought.
[in]	n	Number of eigenvalues to extract. By default all eigenvalues are computed.

◆ EigenProblemSolver() [3/7]

EigenProblemSolver	(	SkSMatrix< real_t > &	K,
		SkSMatrix< real_t > &	M,
		int	n = `0`
	)

Constructor for Symmetric Skyline Matrices.

Parameters

[in]	K	"Stiffness" matrix
[in]	M	"Mass" matrix
[in]	n	Number of eigenvalues to extract. By default all eigenvalues are computed.

Note: The generalized eigenvalue problem is defined by Kx = aMx, where K and M are referred to as stiffness and mass matrix.

◆ EigenProblemSolver() [4/7]

EigenProblemSolver	(	SkSMatrix< real_t > &	K,
		Vect< real_t > &	M,
		int	n = `0`
	)

Constructor for Symmetric Skyline Matrices.

Parameters

[in]	K	"Stiffness" matrix
[in]	M	Diagonal "Mass" matrix stored as a Vect instance
[in]	n	Number of eigenvalues to extract. By default all eigenvalues are computed.

Note: The generalized eigenvalue problem is defined by Kx = aMx, where K and M are referred to as stiffness and mass matrix.

◆ EigenProblemSolver() [5/7]

EigenProblemSolver	(	DSMatrix< real_t > &	A,
		Vect< real_t > &	ev,
		int	n = `0`
	)

Constructor for a dense symmetric matrix that compute the eigenvalues.

This constructor solves in place the eigenvalues problem and stores them in a vector. Extraction of eigenvalues and eigenvectors uses the subspace iteration method. The eigenvectors can be obtained by calling the member function getEigenVector.

Parameters

[in]	A	Matrix for which eigenmodes are sought.
[in]	ev	Vector containing all computed (real) eigenvalues.
[in]	n	Number of eigenvalues to extract. By default all eigenvalues are computed.

Remarks: The vector ev does not need to be sized before.

◆ EigenProblemSolver() [6/7]

EigenProblemSolver	(	DMatrix< real_t > &	A,
		Vect< real_t > &	evr,
		Vect< real_t > &	evi,
		bool	eigv = `false`
	)

Constructor for a dense matrix that compute the eigenvalues.

This constructor solves in place the eigenvalues problem and stores them separately in real and imaginary part vectors. Extraction of eigenvalues and eigenvectors uses the QR method after transforming the matrix in Hessenberg form. The eigenvectors can be obtained by calling the member function getEigenVector.

Parameters

[in]	A	Matrix for which eigenmodes are sought.
[in]	evr	Vector containing real parts of eigenvalues.
[in]	evi	Vector containing imaginary parts of eigenvalues.
[in]	eigv	Switch to say if eigenvectors are to be computed [Default: `false`].

Remarks: The vectors evr and evi do not need to be sized before.

◆ EigenProblemSolver() [7/7]

EigenProblemSolver	(	Equa &	eq,
		bool	lumped = `true`
	)

Consrtuctor using partial differential equation.

The used equation class must have been constructed using the Mesh instance

Parameters

[in]	eq	Reference to equation instance
[in]	lumped	Mass matrix is lumped (true) or not (false) [Default: `true`]

Member Function Documentation

◆ Assembly()

void Assembly	(	const Element &	el,
		real_t *	eK,
		real_t *	eM
	)

Assemble element arrays into global matrices.

This member function is to be called from finite element equation classes

Parameters

[in]	el	Reference to Element class
[in]	eK	Pointer to element stiffness (or assimilated) matrix
[in]	eM	Pointer to element mass (or assimilated) matrix

◆ checkSturm()

int checkSturm	(	int &	nb_found,
		int &	nb_lost
	)

Check how many eigenvalues have been found using Sturm sequence method.

Parameters

[out]	nb_found	number of eigenvalues actually found
[out]	nb_lost	number of eigenvalues missing

Returns

- 0, Successful completion of subroutine.

1, No convergent eigenvalues found.

◆ getEigenValue()

real_t getEigenValue	(	int	n,
		int	i = `1`
	)		const

Return the n-th eigenvalue.

Parameters

[in]	n	Index of eigenvalue (must be > 0)
[in]	i	i=1: Real part, i=2: Imaginary part. [Default: 1]

Returns: Eigenvalue

◆ getEigenVector() [1/2]

void getEigenVector	(	int	n,
		Vect< real_t > &	v
	)		const

Return the n-th eigenvector.

Parameters

[in]	n	Label of eigenvector (They are stored in ascending order of eigenvalues)
[out]	v	Vect instance where the eigenvector is stored.

◆ getEigenVector() [2/2]

void getEigenVector	(	int	n,
		Vect< real_t > &	vr,
		Vect< real_t > &	vi
	)		const

Return the n-th eigenvector in the case of complex eigenvectors.

Parameters

[in]	n	Label of eigenvector (They are stored in the order of eigenvalues)
[out]	vr	Vect instance where the real part of the eigenvector is stored.
[out]	vi	Vect instance where the imaginary part of the eigenvector is stored.

◆ run()

int run	(	int	nb = `0`,
		bool	opt = `false`
	)

Run the eigenproblem solver.

Parameters

[in]	nb	Number of eigenvalues to be computed. By default, all eigenvalues are computed.
[in]	opt	Toggle to compute or not corresponding eigenvectors. By default, no eigenvectors extracted.

◆ runSubSpace()

int runSubSpace	(	size_t	nb_eigv,
		size_t	ss_dim = `0`
	)

Run the subspace iteration solver.

This function rune the Bathe subspace iteration method.

Parameters

[in]	nb_eigv	Number of eigenvalues to be extracted
[in]	ss_dim	Subspace dimension. Must be at least equal to the number eigenvalues to seek. [Default: `nb_eigv`]

Returns: 1: Normal execution. Convergence has been achieved. 2: Convergence for eigenvalues has not been attained.

◆ SAssembly()

void SAssembly	(	const Side &	sd,
		real_t *	sK
	)

Assemble side arrays into global matrix and right-hand side.

This member function is to be called from finite element equation classes

Parameters

[in]	sd	Reference to Side class
[in]	sK	Pointer to side stiffness

◆ set()

void set	(	EigenMethod	m,
		bool	sym
	)

Set numerical method for eigenvalue computation.

Parameters

[in]	m	Numerical method to compute eigenvalues: SUBSPACE: Subspace iteration method (Valid for symmetric matrices only) QR: QR method (Reduction to Hessenberg form)
[in]	sym	Boolean variable to say if matrix is symmetric or not

◆ setEigenVectors()

void setEigenVectors ( )

Switch to compute (or not) eigenvectors as well.

This function is useful for the QR method. BY default eigenvectors are not extracted.

◆ setMatrix() [1/6]

void setMatrix ( DMatrix< real_t > & K )

Set matrix instance.

This function is to be used when the default constructor is applied. Case of a standard (not generalized) eigen problem is to be solved

Parameters

[in] K Matrix instance

◆ setMatrix() [2/6]

void setMatrix ( DSMatrix< real_t > & K )

Set matrix instance (Symmetric matrix).

This function is to be used when the default constructor is applied. Case of a standard (not generalized) eigen problem is to be solved

Parameters

[in] K Matrix instance

◆ setMatrix() [3/6]

void setMatrix ( Matrix< real_t > * K )

Set pointer to matrix instance.

This function is to be used when the default constructor is applied. Case where the mass matrix is consistent.

Parameters

[in] K Stiffness matrix pointer

◆ setMatrix() [4/6]

void setMatrix	(	Matrix< real_t > *	K,
		Matrix< real_t > *	M
	)

Set pointers to matrix instances.

This function is to be used when the default constructor is applied. Case where the mass matrix is consistent.

Parameters

[in]	K	Stiffness matrix instance pointer
[in]	M	Mass matrix instance pointer

◆ setMatrix() [5/6]

void setMatrix	(	SkSMatrix< real_t > &	K,
		SkSMatrix< real_t > &	M
	)

Set matrix instances (Symmetric matrices).

This function is to be used when the default constructor is applied. Case where the mass matrix is consistent.

Parameters

[in]	K	Stiffness matrix instance
[in]	M	Mass matrix instance

◆ setMatrix() [6/6]

void setMatrix	(	SkSMatrix< real_t > &	K,
		Vect< real_t > &	M
	)

Set matrix instances (Symmetric matrices).

This function is to be used when the default constructor is applied. Case where the mass matrix is (lumped) diagonal and stored in a vector.

Parameters

[in]	K	Stiffness matrix instance
[in]	M	Mass matrix instance where diagonal terms are stored as a vector.

◆ setNbEigv()

void setNbEigv ( int n )

Set number of extracted eigenvalues.

This function is useful for the subspace method only.

Parameters

[in] n Number of eigenvalues to compute. Must be at most equal to the matrix size

◆ setPDE()

void setPDE	(	Equa &	eq,
		bool	lumped = `true`
	)

Define partial differential equation to solve.

The used equation class must have been constructed using the Mesh instance

Parameters

[in]	eq	Reference to equation instance
[in]	lumped	Mass matrix is lumped (true) or not (false) [Default: `true`]

◆ setSubspaceDimension()

void setSubspaceDimension ( int dim )

Define the subspace dimension.

Parameters

[in] dim Subspace dimension. Must be larger or equal to the number of wanted eigenvalues. By default this value will be set to the number of wanted eigenvalues

◆ setTolerance()

void setTolerance ( real_t eps )

set tolerance value

Parameters

[in] eps Convergence tolerance for eigenvalues [Default: 1.e-8]

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ EigenProblemSolver() [1/7]

◆ EigenProblemSolver() [2/7]

◆ EigenProblemSolver() [3/7]

◆ EigenProblemSolver() [4/7]

◆ EigenProblemSolver() [5/7]

◆ EigenProblemSolver() [6/7]

◆ EigenProblemSolver() [7/7]

Member Function Documentation

◆ Assembly()

◆ checkSturm()

◆ getEigenValue()

◆ getEigenVector() [1/2]

◆ getEigenVector() [2/2]

◆ run()

◆ runSubSpace()

◆ SAssembly()

◆ set()

◆ setEigenVectors()

◆ setMatrix() [1/6]

◆ setMatrix() [2/6]

◆ setMatrix() [3/6]

◆ setMatrix() [4/6]

◆ setMatrix() [5/6]

◆ setMatrix() [6/6]

◆ setNbEigv()

◆ setPDE()

◆ setSubspaceDimension()

◆ setTolerance()