Inexact inverse iteration to solve a generalized Eigen value problem. More...

#include <inexactInv.hh>

Inheritance diagram for eigensolver::InexactInv< F >:

Public Member Functions
virtual uint	converged () const
	Returns the number of converged eigen pairs. More...

virtual const concepts::Array< concepts::Vector< F > * > &	getEF ()

virtual const concepts::Array< F > &	getEV ()
	Returns an array with the eigen values. More...

	InexactInv (concepts::Operator< F > &A, concepts::Operator< F > &B, const concepts::Vector< F > &EFguess, const Real innerTol=0.5, const uint innerMax=100, const Real outerTol=1e-6, const uint outerMax=100)
	Constructor. More...

virtual uint	iterations () const
	Returns the number of iterations. More...

virtual	~InexactInv ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Private Member Functions
void	compute_ ()
	Does the computations. More...

Private Attributes
concepts::Operator< F > &	A_

concepts::Operator< F > &	B_

bool	computed_

concepts::Vector< F >	eigenfunction_

F &	eigenvalue_

Real	epsilon_

uint	innerIter_

uint	innerMax_

Real	innerTol_

uint	iterations_

uint	outerMax_

Real	outerTol_

concepts::Array< F >	returnValue1_

concepts::Array< concepts::Vector< F > * >	returnValue2_

Detailed Description

template<typename F>
class eigensolver::InexactInv< F >

Inexact inverse iteration to solve a generalized Eigen value problem.

The problem to be solved is $Ax = \lambda Bx$ . This algorithm uses the inexact solution of a linear system to converge to the first Eigen pair of the Eigen problem.

The class is templated on the value type but only the real part works.

Author: Philipp Frauenfelder, 2003

Test:

test::GolubExample

test::GolubExampleSum

test::MaxwellTransmissionEVP

See also: Gene H. Golub and Qiang Ye, Inexact inverse iteration for generalized Eigenvalue problems, BIT Vol. 40, No. 4 (2000), 671-684.

Definition at line 36 of file inexactInv.hh.

Constructor & Destructor Documentation

◆ InexactInv()

template<typename F >

eigensolver::InexactInv< F >::InexactInv	(	concepts::Operator< F > &	A,
		concepts::Operator< F > &	B,
		const concepts::Vector< F > &	EFguess,
		const Real	innerTol = `0.5`,
		const uint	innerMax = `100`,
		const Real	outerTol = `1e-6`,
		const uint	outerMax = `100`
	)

Constructor.

The relative tolerance $\epsilon$ for the innner iteration can be kept fairly high. In fact, $\rho < \epsilon \leq 1$ where $\rho = |\lambda_1 / \lambda_2| < 1$ . Best results are achieved for $\epsilon$ only slightly larger than $\rho$ .

Parameters

A	A
B	B
EFguess	Initial value for the Eigen function
innerTol	Relative tolerance for the inner iteration (solution of the linear system)
innerMax	Maximal number of iterations for the inner iteration
outerTol	Tolerance for the outer iteration (residual of the Eigen function)
outerMax	Maximal number of outer iterations

◆ ~InexactInv()

template<typename F >

virtual eigensolver::InexactInv< F >::~InexactInv ( )

virtual

Member Function Documentation

◆ compute_()

template<typename F >

void eigensolver::InexactInv< F >::compute_ ( )

private

Does the computations.

◆ converged()

template<typename F >

virtual uint eigensolver::InexactInv< F >::converged ( ) const

inlinevirtual

Returns the number of converged eigen pairs.

Implements eigensolver::EigenSolver< F >.

Definition at line 67 of file inexactInv.hh.

◆ getEF()

template<typename F >

virtual const concepts::Array<concepts::Vector<F>*>& eigensolver::InexactInv< F >::getEF ( )

inlinevirtual

Implements eigensolver::EigenSolver< F >.

Definition at line 62 of file inexactInv.hh.

◆ getEV()

template<typename F >

virtual const concepts::Array<F>& eigensolver::InexactInv< F >::getEV ( )

inlinevirtual

Returns an array with the eigen values.

Deprecated:: : this interface requires that the returned array must be hold as a member variable of the class.

(use std::auto_pointer or similar)

Implements eigensolver::EigenSolver< F >.

Definition at line 59 of file inexactInv.hh.

◆ info()

template<typename F >

virtual std::ostream& eigensolver::InexactInv< F >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< F >.

◆ iterations()

template<typename F >

virtual uint eigensolver::InexactInv< F >::iterations ( ) const

inlinevirtual

Returns the number of iterations.

Implements eigensolver::EigenSolver< F >.

Definition at line 66 of file inexactInv.hh.

Member Data Documentation

◆ A_

template<typename F >

concepts::Operator<F>& eigensolver::InexactInv< F >::A_

private

Definition at line 73 of file inexactInv.hh.

◆ B_

template<typename F >

concepts::Operator<F> & eigensolver::InexactInv< F >::B_

private

Definition at line 73 of file inexactInv.hh.

◆ computed_

template<typename F >

bool eigensolver::InexactInv< F >::computed_

private

Definition at line 84 of file inexactInv.hh.

◆ eigenfunction_

template<typename F >

concepts::Vector<F> eigensolver::InexactInv< F >::eigenfunction_

private

Definition at line 76 of file inexactInv.hh.

◆ eigenvalue_

template<typename F >

F& eigensolver::InexactInv< F >::eigenvalue_

private

Definition at line 75 of file inexactInv.hh.

◆ epsilon_

template<typename F >

Real eigensolver::InexactInv< F >::epsilon_

private

Definition at line 82 of file inexactInv.hh.

◆ innerIter_

template<typename F >

uint eigensolver::InexactInv< F >::innerIter_

private

Definition at line 81 of file inexactInv.hh.

◆ innerMax_

template<typename F >

uint eigensolver::InexactInv< F >::innerMax_

private

Definition at line 79 of file inexactInv.hh.

◆ innerTol_

template<typename F >

Real eigensolver::InexactInv< F >::innerTol_

private

Definition at line 78 of file inexactInv.hh.

◆ iterations_

template<typename F >

uint eigensolver::InexactInv< F >::iterations_

private

Definition at line 81 of file inexactInv.hh.

◆ outerMax_

template<typename F >

uint eigensolver::InexactInv< F >::outerMax_

private

Definition at line 79 of file inexactInv.hh.

◆ outerTol_

template<typename F >

Real eigensolver::InexactInv< F >::outerTol_

private

Definition at line 78 of file inexactInv.hh.

◆ returnValue1_

template<typename F >

concepts::Array<F> eigensolver::InexactInv< F >::returnValue1_

private

Definition at line 74 of file inexactInv.hh.

◆ returnValue2_

template<typename F >

concepts::Array<concepts::Vector<F>*> eigensolver::InexactInv< F >::returnValue2_

private

Definition at line 77 of file inexactInv.hh.

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

eigensolver/inexactInv.hh

eigensolver::InexactInv< F > Class Template Reference

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename F> class eigensolver::InexactInv< F >

Constructor & Destructor Documentation

◆ InexactInv()

◆ ~InexactInv()

Member Function Documentation

◆ compute_()

◆ converged()

◆ getEF()

◆ getEV()

◆ info()

◆ iterations()

Member Data Documentation

◆ A_

◆ B_

◆ computed_

◆ eigenfunction_

◆ eigenvalue_

◆ epsilon_

◆ innerIter_

◆ innerMax_

◆ innerTol_

◆ iterations_

◆ outerMax_

◆ outerTol_

◆ returnValue1_

◆ returnValue2_

template<typename F>
class eigensolver::InexactInv< F >