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

#include <DirPowIt.hh>

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

Public Member Functions
	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)
virtual	~DirPowIt ()
	Destructor.
virtual const concepts::Array< G > &	getEV ()
	Returns an array with the eigenvalues.
virtual const concepts::Array< concepts::Vector< G > * > &	getEF ()
	Returns an array with the eigenfunctions.
virtual uint	iterations () const
	Returns the number of iterations.
virtual uint	converged () const
	Returns the number of converged eigenpairs (not implemented)

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

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);

Member Function Documentation

converged()

template<typename F , typename G >

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

inlinevirtual

Returns the number of converged eigenpairs (not implemented)

Implements eigensolver::EigenSolver< G >.

Definition at line 85 of file DirPowIt.hh.

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()

template<typename F , typename G >

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

inlinevirtual

Returns the number of iterations.

Implements eigensolver::EigenSolver< G >.

Definition at line 83 of file DirPowIt.hh.

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

• eigensolver/DirPowIt.hh