Eigenvalue solver using the direct power iteration method. More...

#include <DirPowIt.hh>

Inheritance diagram for eigensolver::DirPowIt< F, G >:

Public Member Functions
virtual uint	converged () const
	Returns the number of converged eigenpairs (not implemented) More...

virtual uint	converged () const=0
	Returns the number of converged eigen pairs. More...

	DirPowIt (concepts::Operator< F > &A, const int nev=3, const int m=3, const int k=0, const int maxiter=300, concepts::Array< concepts::Vector< G > * > *start=0, const Real tol=0)
	Constructor. More...

virtual const concepts::Array< concepts::Vector< G > * > &	getEF ()
	Returns an array with the eigenfunctions. More...

virtual const concepts::Array< G > &	getEV ()
	Returns an array with the eigenvalues. More...

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

virtual uint	iterations () const=0
	Returns the number of iterations. More...

virtual	~DirPowIt ()
	Destructor. More...

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

Private Member Functions
void	compute_ ()
	Compute eigenpairs. More...

void	sort_ (concepts::Array< Real > &)
	Sorting an array using bubble sort and returning the permutation: More...

Private Attributes
concepts::Operator< F > &	A_
	Operator A. More...

bool	computed_
	Are the eigenpairs already computed ? More...

concepts::Array< G >	eigenvalues_
	Storage space for eigenvalues. More...

concepts::Array< concepts::Vector< G > * >	eigenvectors_
	Storage space for eigenvectors. More...

int	iter_
	Number of iterations. More...

int	k_
	Number of highest eigenvalues to be cut off: More...

int	m_
	Size of initial matrix V;. More...

int	maxiter_
	Maximum number of iterations allowed. More...

int	nev_
	Number of eigenpairs to be computed. More...

concepts::Array< uint >	permutation_

concepts::Array< concepts::Vector< G > * >	temp_eigenvectors_
	Temporary storage space for eigenvectors. More...

Real	tol_
	Convergence tolerance for the eigenpairs. More...

Detailed Description

template<typename F, typename G>
class eigensolver::DirPowIt< F, G >

Eigenvalue solver using the direct power iteration method.

Author: Peter Kauf, 2005

Definition at line 31 of file DirPowIt.hh.

Constructor & Destructor Documentation

◆ DirPowIt()

template<typename F , typename G >

eigensolver::DirPowIt< F, G >::DirPowIt	(	concepts::Operator< F > &	A,
		const int	nev = `3`,
		const int	m = `3`,
		const int	k = `0`,
		const int	maxiter = `300`,
		concepts::Array< concepts::Vector< G > * > *	start = `0`,
		const Real	tol = `0`
	)

Constructor.

Parameters

A	Operator A of which we want the eigenpairs
nev	Number of eigenpairs to be computed
m	Number of columns of the iteration matrix V (must be equal to the number of columns of start)
k	It is recommended to set k = 0; k was intended to cut out the largest k from the nev eigenvalues; but to really implement such a feature one would have to do it in a more sophisticated way. Presently if k != 0 sometimes the smallest and sometimes the largest k from the nev eigenvalues are cut out. Nevertehless it seems to work for k >= 0.5*nev.
maxiter	Maximum number of iterations allowed
start	Initial n x m array (estimate for the eigenvectors) for iteration (n is the dimension of A and m must be bigger than nev)
tol	Convergence tolerance for the eigenpairs. The default value is the machine precision for double numbers.

The routine implements the following algorithm:

n = size(A,1); V = zeros(n,m); / start
d = zeros(k,1);
for i = 1 : maxiter
  V = A*V;
  [Q,R] = qr(V,0);
  T = Q'*A*Q;
  [S,D] = eig(T);
  [l,perm] = sort(-abs(diag(D)));
  V_new = Q*S(:,perm);
  if (norm(d+l(1:k)) < tol), break; end;
  V = V_new; d = -l(1:k);
  iter = iter + 1;
end;
V = V_new(:,1:k); l = -l(1:k);

◆ ~DirPowIt()

template<typename F , typename G >

virtual eigensolver::DirPowIt< F, G >::~DirPowIt ( )

virtual

Destructor.

Member Function Documentation

◆ compute_()

template<typename F , typename G >

void eigensolver::DirPowIt< F, G >::compute_ ( )

private

Compute eigenpairs.

◆ converged() [1/2]

template<typename F , typename G >

virtual uint eigensolver::DirPowIt< F, G >::converged ( ) const

inlinevirtual

Returns the number of converged eigenpairs (not implemented)

Definition at line 85 of file DirPowIt.hh.

◆ converged() [2/2]

virtual uint eigensolver::EigenSolver< G >::converged

pure virtualinherited

Returns the number of converged eigen pairs.

◆ getEF()

template<typename F , typename G >

virtual const concepts::Array<concepts::Vector<G>*>& eigensolver::DirPowIt< F, G >::getEF ( )

virtual

Returns an array with the eigenfunctions.

Implements eigensolver::EigenSolver< G >.

◆ getEV()

template<typename F , typename G >

virtual const concepts::Array<G>& eigensolver::DirPowIt< F, G >::getEV ( )

virtual

Returns an array with the eigenvalues.

Implements eigensolver::EigenSolver< G >.

◆ info()

template<typename F , typename G >

virtual std::ostream& eigensolver::DirPowIt< F, G >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from eigensolver::EigenSolver< G >.

◆ iterations() [1/2]

template<typename F , typename G >

virtual uint eigensolver::DirPowIt< F, G >::iterations ( ) const

inlinevirtual

Returns the number of iterations.

Definition at line 83 of file DirPowIt.hh.

◆ iterations() [2/2]

virtual uint eigensolver::EigenSolver< G >::iterations

pure virtualinherited

Returns the number of iterations.

◆ sort_()

template<typename F , typename G >

void eigensolver::DirPowIt< F, G >::sort_ ( concepts::Array< Real > & )

private

Sorting an array using bubble sort and returning the permutation:

Member Data Documentation

◆ A_

template<typename F , typename G >

concepts::Operator<F>& eigensolver::DirPowIt< F, G >::A_

private

Operator A.

Definition at line 90 of file DirPowIt.hh.

◆ computed_

template<typename F , typename G >

bool eigensolver::DirPowIt< F, G >::computed_

private

Are the eigenpairs already computed ?

Definition at line 113 of file DirPowIt.hh.

◆ eigenvalues_

template<typename F , typename G >

concepts::Array<G> eigensolver::DirPowIt< F, G >::eigenvalues_

private

Storage space for eigenvalues.

Definition at line 104 of file DirPowIt.hh.

◆ eigenvectors_

template<typename F , typename G >

concepts::Array<concepts::Vector<G>*> eigensolver::DirPowIt< F, G >::eigenvectors_

private

Storage space for eigenvectors.

Definition at line 106 of file DirPowIt.hh.

◆ iter_

template<typename F , typename G >

int eigensolver::DirPowIt< F, G >::iter_

private

Number of iterations.

Definition at line 98 of file DirPowIt.hh.

◆ k_

template<typename F , typename G >

int eigensolver::DirPowIt< F, G >::k_

private

Number of highest eigenvalues to be cut off:

Definition at line 96 of file DirPowIt.hh.

◆ m_

template<typename F , typename G >

int eigensolver::DirPowIt< F, G >::m_

private

Size of initial matrix V;.

Definition at line 94 of file DirPowIt.hh.

◆ maxiter_

template<typename F , typename G >

int eigensolver::DirPowIt< F, G >::maxiter_

private

Maximum number of iterations allowed.

Definition at line 100 of file DirPowIt.hh.

◆ nev_

template<typename F , typename G >

int eigensolver::DirPowIt< F, G >::nev_

private

Number of eigenpairs to be computed.

Definition at line 92 of file DirPowIt.hh.

◆ permutation_

template<typename F , typename G >

concepts::Array<uint> eigensolver::DirPowIt< F, G >::permutation_

private

Definition at line 111 of file DirPowIt.hh.

◆ temp_eigenvectors_

template<typename F , typename G >

concepts::Array<concepts::Vector<G>*> eigensolver::DirPowIt< F, G >::temp_eigenvectors_

private

Temporary storage space for eigenvectors.

Definition at line 108 of file DirPowIt.hh.

◆ tol_

template<typename F , typename G >

Real eigensolver::DirPowIt< F, G >::tol_

private

Convergence tolerance for the eigenpairs.

Definition at line 102 of file DirPowIt.hh.

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

eigensolver/DirPowIt.hh

eigensolver::DirPowIt< F, G > Class Template Referenceabstract

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<typename F, typename G> class eigensolver::DirPowIt< F, G >

Constructor & Destructor Documentation

◆ DirPowIt()

◆ ~DirPowIt()

Member Function Documentation

◆ compute_()

◆ converged() [1/2]

◆ converged() [2/2]

◆ getEF()

◆ getEV()

◆ info()

◆ iterations() [1/2]

◆ iterations() [2/2]

◆ sort_()

Member Data Documentation

◆ A_

◆ computed_

◆ eigenvalues_

◆ eigenvectors_

◆ iter_

◆ k_

◆ m_

◆ maxiter_

◆ nev_

◆ permutation_

◆ temp_eigenvectors_

◆ tol_

template<typename F, typename G>
class eigensolver::DirPowIt< F, G >