madness::Laplacian< T, NDIM > Class Template Reference

the Laplacian operator: \sum_i \nabla^2_i More...

#include <SCFOperators.h>

Inheritance diagram for madness::Laplacian< T, NDIM >:

Collaboration diagram for madness::Laplacian< T, NDIM >:

Public Member Functions
	Laplacian (World &world, const double e=0.0)
std::string	info () const
	print some information about this operator
T	operator() (const functionT &bra, const functionT &ket) const
	compute the matrix element <bra | op | ket>
functionT	operator() (const functionT &ket) const
tensorT	operator() (const vecfuncT &vbra, const vecfuncT &vket) const
	compute the matrix <vbra | op | vket>
vecfuncT	operator() (const vecfuncT &vket) const
	apply this operator on the argument vector of functions
Public Member Functions inherited from madness::SCFOperatorBase< T, NDIM >
	SCFOperatorBase ()=default
	SCFOperatorBase (std::shared_ptr< MacroTaskQ > taskq)
virtual	~SCFOperatorBase ()

Private Types
typedef Function< T, NDIM >	functionT
typedef Tensor< T >	tensorT
typedef std::vector< functionT >	vecfuncT

Private Attributes
double	eps
std::vector< std::shared_ptr< Derivative< T, NDIM > > >	gradop
World &	world

Additional Inherited Members
Public Types inherited from madness::SCFOperatorBase< T, NDIM >
typedef Function< T, NDIM >	functionT
typedef Tensor< T >	tensorT
typedef std::vector< functionT >	vecfuncT
Public Attributes inherited from madness::SCFOperatorBase< T, NDIM >
std::shared_ptr< MacroTaskQ >	taskq =0

Detailed Description

template<typename T, std::size_t NDIM>
class madness::Laplacian< T, NDIM >

the Laplacian operator: \sum_i \nabla^2_i

note that the application of the Laplacian operator is in general unstable and very sensitive to noise and cusps in the argument.

!!! BE SURE YOU KNOW WHAT YOU ARE DOING !!!

For computing matrix elements, which is reasonably stable, we refer

Member Typedef Documentation

functionT

template<typename T , std::size_t NDIM>

typedef Function<T,NDIM> madness::Laplacian< T, NDIM >::functionT

private

tensorT

template<typename T , std::size_t NDIM>

typedef Tensor<T> madness::Laplacian< T, NDIM >::tensorT

private

vecfuncT

template<typename T , std::size_t NDIM>

typedef std::vector<functionT> madness::Laplacian< T, NDIM >::vecfuncT

private

Constructor & Destructor Documentation

Laplacian()

template<typename T , std::size_t NDIM>

madness::Laplacian< T, NDIM >::Laplacian ( World &  world, const double  e = 0.0  )

inline

References madness::Laplacian< T, NDIM >::gradop, and madness::Laplacian< T, NDIM >::world.

Member Function Documentation

info()

template<typename T , std::size_t NDIM>

std::string madness::Laplacian< T, NDIM >::info ( ) const

inlinevirtual

print some information about this operator

Implements madness::SCFOperatorBase< T, NDIM >.

operator()() [1/4]

template<typename T , std::size_t NDIM>

T madness::Laplacian< T, NDIM >::operator() ( const functionT &  bra, const functionT &  ket  ) const

inlinevirtual

compute the matrix element <bra | op | ket>

Parameters

bra	bra state
ket	ket state

Returns

the matrix element <bra | op | ket>

Implements madness::SCFOperatorBase< T, NDIM >.

References madness::Laplacian< T, NDIM >::operator()().

operator()() [2/4]

template<typename T , std::size_t NDIM>

functionT madness::Laplacian< T, NDIM >::operator() ( const functionT &  ket ) const

inlinevirtual

apply this operator on the argument function

Parameters

ket	the argument function

Returns

op(ket)

Implements madness::SCFOperatorBase< T, NDIM >.

References madness::Laplacian< T, NDIM >::operator()().

Referenced by madness::Laplacian< T, NDIM >::operator()(), and madness::Laplacian< T, NDIM >::operator()().

operator()() [3/4]

template<typename T , std::size_t NDIM>

tensorT madness::Laplacian< T, NDIM >::operator() ( const vecfuncT &  vbra, const vecfuncT &  vket  ) const

inlinevirtual

compute the matrix <vbra | op | vket>

Parameters

vbra	vector of bra states
vket	vector of ket states

Returns

the matrix <vbra | op | vket>

Implements madness::SCFOperatorBase< T, NDIM >.

References madness::Laplacian< T, NDIM >::world.

operator()() [4/4]

template<typename T , std::size_t NDIM>

vecfuncT madness::Laplacian< T, NDIM >::operator() ( const vecfuncT &  vket ) const

virtual

apply this operator on the argument vector of functions

Parameters

vket	argument vector

Returns

op(vket)

Implements madness::SCFOperatorBase< T, NDIM >.

Member Data Documentation

eps

template<typename T , std::size_t NDIM>

double madness::Laplacian< T, NDIM >::eps

private

gradop

template<typename T , std::size_t NDIM>

std::vector< std::shared_ptr< Derivative<T,NDIM> > > madness::Laplacian< T, NDIM >::gradop

private

Referenced by madness::Laplacian< T, NDIM >::Laplacian().

world

template<typename T , std::size_t NDIM>

World& madness::Laplacian< T, NDIM >::world

private

Referenced by madness::Laplacian< T, NDIM >::Laplacian(), and madness::Laplacian< T, NDIM >::operator()().

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

• SCFOperators.h