mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray > Class Template Reference

The Lanczos state: the v/v_prev/z/Az vectors, the tridiagonal T as its diagonal alpha and off-diagonal beta, and the iteration scalars. More...

#include <eigenvalues.hpp>

Public Types
using	value_type = Scalar

Public Member Functions
	LanczosState (VVector &&v, VPrevVector &&v_prev, ZVector &&z, AzVector &&Az, AlphaArray &&alpha, BetaArray &&beta)
auto &	v ()
const auto &	v () const
auto &	v_prev ()
const auto &	v_prev () const
auto &	z ()
const auto &	z () const
auto &	Az ()
const auto &	Az () const
auto &	alpha ()
const auto &	alpha () const
auto &	beta ()
const auto &	beta () const
unsigned &	iter ()
unsigned	iter () const
bool &	converged ()
bool	converged () const
value_type &	residual ()
value_type	residual () const
value_type &	smallest_eigenvalue ()
value_type	smallest_eigenvalue () const
value_type &	largest_eigenvalue ()
value_type	largest_eigenvalue () const
value_type &	smallest_ritz_residual ()
value_type	smallest_ritz_residual () const
value_type &	largest_ritz_residual ()
value_type	largest_ritz_residual () const

Detailed Description

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>
class mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >

v is the start vector on entry. smallest_eigenvalue() and largest_eigenvalue() are T's extreme eigenvalues, and smallest_ritz_residual() and largest_ritz_residual() the least Ritz residual of each so far.

Member Typedef Documentation

value_type

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

using mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::value_type = Scalar

Constructor & Destructor Documentation

LanczosState()

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::LanczosState ( VVector && v, VPrevVector && v_prev, ZVector && z, AzVector && Az, AlphaArray && alpha, BetaArray && beta )

inline

Member Function Documentation

v() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::v ( )

inline

v() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::v ( ) const

inline

v_prev() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::v_prev ( )

inline

v_prev() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::v_prev ( ) const

inline

z() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::z ( )

inline

z() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::z ( ) const

inline

Az() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::Az ( )

inline

Az() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::Az ( ) const

inline

alpha() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::alpha ( )

inline

alpha() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::alpha ( ) const

inline

beta() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::beta ( )

inline

beta() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

const auto & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::beta ( ) const

inline

iter() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

unsigned & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::iter ( )

inline

iter() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

unsigned mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::iter ( ) const

inline

converged() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

bool & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::converged ( )

inline

converged() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

bool mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::converged ( ) const

inline

residual() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::residual ( )

inline

residual() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::residual ( ) const

inline

smallest_eigenvalue() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::smallest_eigenvalue ( )

inline

smallest_eigenvalue() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::smallest_eigenvalue ( ) const

inline

largest_eigenvalue() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::largest_eigenvalue ( )

inline

largest_eigenvalue() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::largest_eigenvalue ( ) const

inline

smallest_ritz_residual() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::smallest_ritz_residual ( )

inline

smallest_ritz_residual() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::smallest_ritz_residual ( ) const

inline

largest_ritz_residual() [1/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type & mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::largest_ritz_residual ( )

inline

largest_ritz_residual() [2/2]

template<class Scalar, class VVector, class VPrevVector, class ZVector, class AzVector, class AlphaArray, class BetaArray>

value_type mundy::LanczosState< Scalar, VVector, VPrevVector, ZVector, AzVector, AlphaArray, BetaArray >::largest_ritz_residual ( ) const

inline