Evaluates a wavepacket slice by slice. More...

#include <hawp_evaluator.hpp>

Public Types
typedef Eigen::Matrix< complex_t, D, D >	CMatrixDD

typedef Eigen::Array< complex_t, 1, N >	CArray1N

typedef Eigen::Matrix< complex_t, D, N >	CMatrixDN

typedef Eigen::Matrix< real_t, D, N >	RMatrixDN

Public Member Functions
	HaWpEvaluator (real_t eps, const HaWpParamSet< D > parameters, const ShapeEnum< D, MultiIndex > enumeration, const CMatrixDN &x)

CArray1N	seed () const
	Evaluates basis function on node \( \underline{0} \) (ground-state). More...

HaWpBasisVector< N >	step (std::size_t islice, const HaWpBasisVector< N > &prev_basis, const HaWpBasisVector< N > &curr_basis) const
	Having basis function values on previous and current slice, this member function computes basis function values on the next slice (using recursive evaluation formula). More...

HaWpBasisVector< N >	all () const
	Evaluates all basis functions. More...

CArray< 1, N >	reduce (const Coefficients &coefficients) const
	Evaluates wavepacket in a memory efficient manner. More...

CArray< Eigen::Dynamic, N >	vector_reduce (ShapeEnum< D, MultiIndex > subset_enums, complex_t const subset_coeffs, std::size_t n_components) const
	Efficiently evaluates a vectorial wavepacket with shared Hagedorn parameter set, but different basis shapes. More...

CArray< Eigen::Dynamic, N >	vector_reduce (complex_t const **coefficients, std::size_t n_components) const
	Efficiently evaluates a vectorial wavepacket with shared Hagedorn parameter set and shared basis shapes. More...

Private Attributes
real_t	eps_

const HaWpParamSet< D > *	parameters_

const ShapeEnum< D, MultiIndex > *	enumeration_

int	npts_

CMatrixDN	dx_

CMatrixDD	Qinv_

CMatrixDD	Qh_Qinvt_

CMatrixDN	Qinv_dx_

std::vector< real_t >	sqrt_

Detailed Description

template<dim_t D, class MultiIndex, int N>
class waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >

Evaluates a wavepacket slice by slice.

This class is low-level. You should not use it directly. You should use the high-level member functions AbstractScalarHaWp::evaluate() and AbstractScalarHaWpBasis::evaluate_basis().

The only reason you may want to use HaWpEvaluator directly is when you gain an advantage by evaluating a wavepacket slice-by-slice. The slice-by-slice evaluation reduces memory since you don't have to store all basis function values, but only the 'active' ones. Take a look at the implementation of the member functions all() or reduce() to learn, how to evaluate a wave packet slice-by-slice.

Template Parameters

D	dimensionality of wavepacket
MulitIndex	The type used to represent multi-indices.
N	Number of quadrature points. Don't use Eigen::Dynamic. It works, but performance is bad.

Member Typedef Documentation

template<dim_t D, class MultiIndex , int N>

typedef Eigen::Array<complex_t,1,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::CArray1N

template<dim_t D, class MultiIndex , int N>

typedef Eigen::Matrix<complex_t,D,D> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::CMatrixDD

template<dim_t D, class MultiIndex , int N>

typedef Eigen::Matrix<complex_t,D,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::CMatrixDN

template<dim_t D, class MultiIndex , int N>

typedef Eigen::Matrix<real_t,D,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::RMatrixDN

Constructor & Destructor Documentation

template<dim_t D, class MultiIndex , int N>

waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::HaWpEvaluator	(	real_t	eps,
		const HaWpParamSet< D > *	parameters,
		const ShapeEnum< D, MultiIndex > *	enumeration,
		const CMatrixDN &	x
	)

inline

Parameters

[in]	eps	The semi-classical scaling parameter \( \varepsilon \) of the wavepacket.
[in]	parameters	The Hagedorn parameter set \( \Pi \) of the wavepacket.
[in]	enumeration	The basis shape \( \mathfrak{K} \) of the wavepacket. Or the union of all component's basis shapes, if you want to evaluate a vectorial wavepacket.
[in]	x	Quadrature points: Complex matrix of shape \( (D \times N) \), where \( N \) number of quadrature points).

Member Function Documentation

template<dim_t D, class MultiIndex , int N>

HaWpBasisVector<N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::all ( ) const

inline

Evaluates all basis functions.

Returns: Complex 2D-Array of shape \( (|\mathfrak{K}| \times N) \), where \( N \) is the number of quadrature points.

template<dim_t D, class MultiIndex , int N>

CArray<1,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::reduce ( const Coefficients & coefficients ) const

inline

Evaluates wavepacket in a memory efficient manner.

This function computes the dot product (thus the name 'reduce') of the wavepacket coefficients with the wavepacket basis. This is done by evaluating the wavepacket basis slice by slice and multiplying the basis values with the coefficients on the fly. Computed basis values are discarded, once they are not needed any more.

Parameters

[in] coefficients Vector of wavepacket coefficients, length is \( |\mathfrak{K}| \).

Returns: Complex 2D-Array of shape \( (1 \times N) \), where \( N \) is the number of quadrature points.

template<dim_t D, class MultiIndex , int N>

CArray1N waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::seed ( ) const

inline

Evaluates basis function on node \( \underline{0} \) (ground-state).

Returns: Complex 2D-Array of shape \( (D \times N) \), where \( N \) is the number of quadrature points.

template<dim_t D, class MultiIndex , int N>

HaWpBasisVector<N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::step	(	std::size_t	islice,
		const HaWpBasisVector< N > &	prev_basis,
		const HaWpBasisVector< N > &	curr_basis
	)		const

inline

Having basis function values on previous and current slice, this member function computes basis function values on the next slice (using recursive evaluation formula).

Hint: Use function seed() to bootstrap recursion.

Parameters

[in]	islice	Ordinal of current slice.
[in]	prev_basis	Basis values on previous slice. Type: Complex 2D-array of shape \( (S \times N) \), where \( S \) is the number of nodes in the current slice and \( N \) is the number of quadrature points.
[in]	curr_basis	B Basis values on current slice. Type: Complex 2D-array of shape \( (S \times N) \)

Returns: Computed basis values on next slice. Type: Complex 2D-Array of shape \( (S^+ \times N) \), where \( S^+ \) is the number of nodes in the next slice.

template<dim_t D, class MultiIndex , int N>

CArray<Eigen::Dynamic,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::vector_reduce	(	ShapeEnum< D, MultiIndex > **	subset_enums,
		complex_t const **	subset_coeffs,
		std::size_t	n_components
	)		const

inline

Efficiently evaluates a vectorial wavepacket with shared Hagedorn parameter set, but different basis shapes.

The union of all component's basis shapes is passed to the constructor.

This function is used to evaluate a homogeneous wavepacket (see HomogeneousHaWp::evaluate())

Parameters

[in]	subset_enums	The shape enumerations of each wavepacket component.
[in]	subset_coeffs	The coefficients of each wavepacket component.
[in]	n_components	The number of wavepacket components \( C \).

Returns: Complex 2D-Array of shape \( (C \times N) \), where \( N \) is the number of quadrature points.

template<dim_t D, class MultiIndex , int N>

CArray<Eigen::Dynamic,N> waveblocks::wavepackets::HaWpEvaluator< D, MultiIndex, N >::vector_reduce	(	complex_t const **	coefficients,
		std::size_t	n_components
	)		const

inline

Efficiently evaluates a vectorial wavepacket with shared Hagedorn parameter set and shared basis shapes.

This function is used to evaluate a wavepacket gradient (see HaWpGradient::evaluate()).

Parameters

[in]	coefficients	The coefficients of each wavepacket component.
[in]	n_components	The number of wavepacket components.
[in]	n_components	The number of wavepacket components \( C \).