gsLanczosMatrix< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsLanczosMatrix< T >

Class for representing a Lanczos matrix and calculating its eigenvalues.

The Lanczos matrix is a symmetric tridiagonal matrix with diagonal delta and offdiagonal gamma.

Public Member Functions
	gsLanczosMatrix (const std::vector< T > &gamma, const std::vector< T > &delta)
	Constructor for the Lanczos matrix The Lanczos matrix is a symmetric tridiagonal matrix with diagonal delta and offdiagonal gamma.
gsSparseMatrix< T >	matrix ()
	This function returns the Lanczos matrix as gsSparseMatrix.
T	maxEigenvalue (index_t maxIter=20, T tol=1.e-6)
	Calculates the largest eigenvalue.
T	minEigenvalue (index_t maxIter=20, T tol=1.e-6)
	Calculates the smallest eigenvalue.

Private Member Functions
std::pair< T, T >	eval (T lambda)
	Evalutates characteristic polynomial.
T	newtonIteration (T x0, index_t maxIter, T tol)
	Newton iteration for searching the zeros of the characteristic polynomial.

Constructor & Destructor Documentation

gsLanczosMatrix()

template<class T >

gsLanczosMatrix ( const std::vector< T > &  gamma, const std::vector< T > &  delta  )

inline

Constructor for the Lanczos matrix The Lanczos matrix is a symmetric tridiagonal matrix with diagonal delta and offdiagonal gamma.

Parameters

gamma	The off diagonal (the object stores a reference to this vector)
delta	The diagonal (the object stores a reference to this vector)

Member Function Documentation

eval()

template<class T >

std::pair< T, T > eval ( T  lambda )

inlineprivate

Evalutates characteristic polynomial.

Parameters

lambda

evaluation point

Returns

the value and the derivative at position lambda

maxEigenvalue()

template<class T >

T maxEigenvalue ( index_t  maxIter = 20, T  tol = 1.e-6  )

inline

Calculates the largest eigenvalue.

Parameters

maxIter	The number of maximal iterations of the Newton algorithm
tol	Tolerace for the Newton algorithm

Returns

The largest eigenvalue

minEigenvalue()

template<class T >

T minEigenvalue ( index_t  maxIter = 20, T  tol = 1.e-6  )

inline

Calculates the smallest eigenvalue.

Parameters

maxIter	The number of maximal iterations of the Newton algorithm
tol	Tolerace for the Newton algorithm

Returns

The smallest eigenvalue

newtonIteration()

template<class T >

T newtonIteration ( T  x0, index_t  maxIter, T  tol  )

inlineprivate

Newton iteration for searching the zeros of the characteristic polynomial.

Parameters

x0	the initial value
maxIter	The number of maximal iterations of the Newton algorithm
tol	Tolerace for the Newton algorithm

Returns

the root (= eigenvalue of the matrix)