#include <gfit.h>

Public Member Functions
	GFit ()=default
	default ctor does nothing More...

	GFit (const GFit &other)=default
	copy constructor More...

	GFit (OperatorInfo info)

Tensor< T >	coeffs () const
	return the coefficients of the fit More...

Tensor< T >	exponents () const
	return the exponents of the fit More...

GFit &	operator= (const GFit &other)
	assignment operator More...

void	truncate_periodic_expansion (Tensor< double > &c, Tensor< double > &e, double L, bool discardG0) const

Static Public Member Functions
static GFit	BSHFit (double mu, double lo, double hi, double eps, bool prnt=false)
	return a fit for the bound-state Helmholtz function More...

static GFit	CoulombFit (double lo, double hi, double eps, bool prnt=false)
	return a fit for the Coulomb function More...

static GFit	F12Fit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a fit for the F12 correlation factor More...

static GFit	F12sqFit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a fit for the F12^2 correlation factor More...

static GFit	F2GFit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a fit for the F2G function More...

static GFit	FGFit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a fit for the FG function More...

static GFit	GaussFit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a (trivial) fit for a single Gauss function More...

static GFit	GeneralFit ()
	return a fit for a general isotropic function More...

static void	prune_small_coefficients (const double eps, const double lo, const double hi, Tensor< double > &coeff, Tensor< double > &expnt)

static GFit	SlaterFit (double gamma, double lo, double hi, double eps, bool prnt=false)
	return a fit for the Slater function More...

Private Member Functions
template<typename funcT >
	GFit (const funcT &f)
	ctor taking an isotropic function More...

template<typename opT >
void	print_accuracy (opT op, const double lo, const double hi) const
	print coefficients and exponents, and values and errors More...

Static Private Member Functions
static void	bsh_fit (double mu, double lo, double hi, double eps, Tensor< double > &pcoeff, Tensor< double > &pexpnt, bool prnt, bool fix_interval)
	fit the function exp(-mu r)/r More...

static void	bsh_fit_ndim (int ndim, double mu, double lo, double hi, double eps, Tensor< double > &pcoeff, Tensor< double > &pexpnt, bool prnt)

static void	bsh_spherical_moments (double mu, double R, Tensor< double > &q)

static void	f12_fit (double gamma, double lo, double hi, double eps, Tensor< double > &pcoeff, Tensor< double > &pexpnt, bool prnt)
	fit a correlation factor (1- exp(-mu r)) More...

static void	f12sq_fit (double gamma, double lo, double hi, double eps, Tensor< double > &pcoeff, Tensor< double > &pexpnt, bool prnt)
	fit a correlation factor f12^2 = (1- exp(-mu r))^2 = 1 - 2 exp(-mu r) + exp(-2 mu r) More...

static void	gaussian_spherical_moments (double alpha, double R, Tensor< double > &q)

static void	slater_fit (double gamma, double lo, double hi, double eps, Tensor< double > &pcoeff, Tensor< double > &pexpnt, bool prnt)
	fit a Slater function using a sum of Gaussians More...

Private Attributes
Tensor< T >	coeffs_
	the coefficients of the expansion f(x) = \sum_m coeffs[m] exp(-exponents[m] * x^2) More...

Tensor< T >	exponents_
	the exponents of the expansion f(x) = \sum_m coeffs[m] exp(-exponents[m] * x^2) More...

Constructor & Destructor Documentation

◆ GFit() [1/4]

template<typename T , std::size_t NDIM>

madness::GFit< T, NDIM >::GFit ( )

default

default ctor does nothing

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

◆ GFit() [2/4]

template<typename T , std::size_t NDIM>

madness::GFit< T, NDIM >::GFit ( OperatorInfo info )

inline

◆ GFit() [3/4]

template<typename T , std::size_t NDIM>

madness::GFit< T, NDIM >::GFit ( const GFit< T, NDIM > & other )

default

copy constructor

◆ GFit() [4/4]

template<typename T , std::size_t NDIM>

template<typename funcT >

madness::GFit< T, NDIM >::GFit ( const funcT & f )

inlineprivate

ctor taking an isotropic function

the function will be represented with a uniform error on a uniform grid

Parameters

[in] f a 1d-function that implements T operator()

Member Function Documentation

◆ bsh_fit()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::bsh_fit	(	double	mu,
		double	lo,
		double	hi,
		double	eps,
		Tensor< double > &	pcoeff,
		Tensor< double > &	pexpnt,
		bool	prnt,
		bool	fix_interval
	)

inlinestaticprivate

fit the function exp(-mu r)/r

formulas taken from G. Beylkin and L. Monzon, On approximation of functions by exponential sums, Appl Comput Harmon A, vol. 19, no. 1, pp. 17-48, Jul. 2005. and R. J. Harrison, G. I. Fann, T. Yanai, and G. Beylkin, Multiresolution Quantum Chemistry in Multiwavelet Bases, Lecture Notes in Computer Science, vol. 2660, p. 707, 2003.

References madness::GFit< T, NDIM >::bsh_spherical_moments(), e(), madness::GFit< T, NDIM >::gaussian_spherical_moments(), madness::gesv(), h(), lo, mu, madness::constants::pi, madness::print(), madness::GFit< T, NDIM >::prune_small_coefficients(), and q().

Referenced by madness::GFit< T, NDIM >::BSHFit(), madness::GFit< T, NDIM >::F2GFit(), and madness::GFit< T, NDIM >::FGFit().

◆ bsh_fit_ndim()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::bsh_fit_ndim	(	int	ndim,
		double	mu,
		double	lo,
		double	hi,
		double	eps,
		Tensor< double > &	pcoeff,
		Tensor< double > &	pexpnt,
		bool	prnt
	)

inlinestaticprivate

References std::abs(), c, h(), lo, max, mu, p(), madness::constants::pi, pow(), madness::print(), and test().

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

◆ bsh_spherical_moments()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::bsh_spherical_moments	(	double	mu,
		double	R,
		Tensor< double > &	q
	)

inlinestaticprivate

References mu, madness::constants::pi, pow(), q(), and R.

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

◆ BSHFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::BSHFit	(	double	mu,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the bound-state Helmholtz function

the BSH function is defined by f(r) = 1/ (4 pi) exp(-\mu r)/r

Parameters

[in]	mu	the exponent of the BSH
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References madness::GFit< T, NDIM >::bsh_fit(), madness::GFit< T, NDIM >::bsh_fit_ndim(), exact, fit(), lo, mu, NDIM, madness::constants::pi, and madness::print().

Referenced by madness::GFit< T, NDIM >::GFit(), madness::BSHOperatorPtr3D(), madness::GFit< T, NDIM >::CoulombFit(), madness::BSHFunctionInterface::fit(), madness::GradBSHOperator(), GradBSHOperator_Joel(), madness::PeriodicBSHOperator3D(), and madness::PeriodicBSHOperatorPtr3D().

◆ coeffs()

template<typename T , std::size_t NDIM>

Tensor<T> madness::GFit< T, NDIM >::coeffs ( ) const

inline

return the coefficients of the fit

References madness::GFit< T, NDIM >::coeffs_.

Referenced by madness::GFit< T, NDIM >::F2GFit(), and madness::GFit< T, NDIM >::FGFit().

◆ CoulombFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::CoulombFit	(	double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the Coulomb function

f(r) = 1/r

References madness::GFit< T, NDIM >::BSHFit(), fit(), lo, and madness::constants::pi.

Referenced by madness::GFit< T, NDIM >::GFit(), madness::ElectronRepulsionInterface< T, NDIM >::fit(), madness::GradCoulombOperator(), and madness::PeriodicHFExchangeOperator().

◆ exponents()

template<typename T , std::size_t NDIM>

Tensor<T> madness::GFit< T, NDIM >::exponents ( ) const

inline

return the exponents of the fit

References madness::GFit< T, NDIM >::exponents_.

Referenced by madness::GFit< T, NDIM >::F2GFit(), and madness::GFit< T, NDIM >::FGFit().

◆ f12_fit()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::f12_fit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		Tensor< double > &	pcoeff,
		Tensor< double > &	pexpnt,
		bool	prnt
	)

inlinestaticprivate

fit a correlation factor (1- exp(-mu r))

use the Slater fit with an additional term: 1*exp(-0 r^2)

References madness::_(), lo, madness::BaseTensor::size(), and madness::GFit< T, NDIM >::slater_fit().

Referenced by madness::GFit< T, NDIM >::F12Fit().

◆ F12Fit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::F12Fit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the F12 correlation factor

the Slater function is defined by f(r) = 1/(2 gamma) * (1 - exp(-\gamma r))

Parameters

[in]	gamma	the exponent of the Slater function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References exact, madness::GFit< T, NDIM >::f12_fit(), fit(), lo, and madness::print().

Referenced by madness::GFit< T, NDIM >::GFit(), and madness::SlaterF12Interface::fit().

◆ f12sq_fit()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::f12sq_fit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		Tensor< double > &	pcoeff,
		Tensor< double > &	pexpnt,
		bool	prnt
	)

inlinestaticprivate

fit a correlation factor f12^2 = (1- exp(-mu r))^2 = 1 - 2 exp(-mu r) + exp(-2 mu r)

no factor 1/(2 mu) or square of it included! use the Slater fit with an additional term: 1*exp(-0 r^2)

References madness::_(), lo, MADNESS_CHECK, madness::BaseTensor::size(), and madness::GFit< T, NDIM >::slater_fit().

Referenced by madness::GFit< T, NDIM >::F12sqFit().

◆ F12sqFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::F12sqFit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the F12^2 correlation factor

the Slater function square is defined by f(r) = [ 1/(2 gamma) * (1 - exp(-\gamma r)) ] ^2

Parameters

[in]	gamma	the exponent of the Slater function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References exact, madness::GFit< T, NDIM >::f12sq_fit(), fit(), lo, pow(), and madness::print().

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

◆ F2GFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::F2GFit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the F2G function

f2g = (1/(2 mu) * (1 - exp(-gamma r12)))^2 / r12 = 1/(4 mu^2) * [ 1/r12 - 2 exp(-gamma r12)/r12) + exp(-2 gamma r12)/r12 ]

Parameters

[in]	gamma	the exponent of the Slater function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References madness::GFit< T, NDIM >::bsh_fit(), madness::GFit< T, NDIM >::coeffs(), madness::GFit< T, NDIM >::coeffs_, exact, madness::GFit< T, NDIM >::exponents(), madness::GFit< T, NDIM >::exponents_, lo, MADNESS_CHECK, madness::constants::pi, madness::print(), madness::GFit< T, NDIM >::print_accuracy(), and madness::GFit< T, NDIM >::prune_small_coefficients().

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

◆ FGFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::FGFit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the FG function

fg = 1/(2 mu) * (1 - exp(-gamma r12)) / r12 = 1/(2 mu) *( 1/r12 - exp(-gamma r12)/r12) = 1/(2 mu) * (coulomb - bsh)

Parameters

[in]	gamma	the exponent of the Slater function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References madness::GFit< T, NDIM >::bsh_fit(), madness::GFit< T, NDIM >::coeffs(), madness::GFit< T, NDIM >::coeffs_, exact, madness::GFit< T, NDIM >::exponents(), madness::GFit< T, NDIM >::exponents_, lo, MADNESS_CHECK, madness::constants::pi, madness::print(), madness::GFit< T, NDIM >::print_accuracy(), and madness::GFit< T, NDIM >::prune_small_coefficients().

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

◆ GaussFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::GaussFit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a (trivial) fit for a single Gauss function

the Gauss function is defined by f(r) = exp(-\gamma r^2)

Parameters

[in]	gamma	the exponent of the Gauss function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References exact, fit(), lo, and madness::print().

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

◆ gaussian_spherical_moments()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::gaussian_spherical_moments	(	double	alpha,
		double	R,
		Tensor< double > &	q
	)

inlinestaticprivate

References alpha, madness::constants::pi, pow(), q(), and R.

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

◆ GeneralFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::GeneralFit ( )

inlinestatic

return a fit for a general isotropic function

note that the error is controlled over a uniform grid, the boundaries will be poorly represented in general. Following Beylkin 2005

References madness::GFit< T, NDIM >::GFit(), and MADNESS_EXCEPTION.

◆ operator=()

template<typename T , std::size_t NDIM>

GFit& madness::GFit< T, NDIM >::operator= ( const GFit< T, NDIM > & other )

inline

assignment operator

References madness::GFit< T, NDIM >::coeffs_, and madness::GFit< T, NDIM >::exponents_.

◆ print_accuracy()

template<typename T , std::size_t NDIM>

template<typename opT >

void madness::GFit< T, NDIM >::print_accuracy	(	opT	op,
		const double	lo,
		const double	hi
	)		const

inlineprivate

print coefficients and exponents, and values and errors

Parameters

[in]	op	the exact function, e.g. 1/r, exp(-mu r), etc
[in]	lo	lower bound for the range r
[in]	hi	higher bound for the range r

References madness::GFit< T, NDIM >::coeffs_, exact, madness::GFit< T, NDIM >::exponents_, lo, op(), pow(), and test().

Referenced by madness::GFit< T, NDIM >::F2GFit(), and madness::GFit< T, NDIM >::FGFit().

◆ prune_small_coefficients()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::prune_small_coefficients	(	const double	eps,
		const double	lo,
		const double	hi,
		Tensor< double > &	coeff,
		Tensor< double > &	expnt
	)

inlinestatic

References std::abs(), lo, max, and madness::BaseTensor::size().

Referenced by madness::GFit< T, NDIM >::bsh_fit(), madness::GFit< T, NDIM >::F2GFit(), and madness::GFit< T, NDIM >::FGFit().

◆ slater_fit()

template<typename T , std::size_t NDIM>

static void madness::GFit< T, NDIM >::slater_fit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		Tensor< double > &	pcoeff,
		Tensor< double > &	pexpnt,
		bool	prnt
	)

inlinestaticprivate

fit a Slater function using a sum of Gaussians

formula inspired by the BSH fit, with the roles of r and mu exchanged see also Eq. (A3) in S. Ten-no, Initiation of explicitly correlated Slater-type geminal theory, Chem. Phys. Lett., vol. 398, no. 1, pp. 56-61, 2004.

References e(), exact, h(), lo, MADNESS_CHECK, madness::constants::pi, pow(), and test().

Referenced by madness::GFit< T, NDIM >::f12_fit(), madness::GFit< T, NDIM >::f12sq_fit(), and madness::GFit< T, NDIM >::SlaterFit().

◆ SlaterFit()

template<typename T , std::size_t NDIM>

static GFit madness::GFit< T, NDIM >::SlaterFit	(	double	gamma,
		double	lo,
		double	hi,
		double	eps,
		bool	prnt = `false`
	)

inlinestatic

return a fit for the Slater function

the Slater function is defined by f(r) = exp(-\gamma r)

Parameters

[in]	gamma	the exponent of the Slater function
[in]	lo	the smallest length scale that needs to be precisely represented
[in]	hi	the largest length scale that needs to be precisely represented
[in]	eps	the precision threshold @parma[in] prnt print level

References exact, fit(), lo, madness::print(), and madness::GFit< T, NDIM >::slater_fit().

Referenced by madness::GFit< T, NDIM >::GFit(), madness::SlaterFunctionInterface::fit(), and madness::GradSlaterOperator().

◆ truncate_periodic_expansion()

template<typename T , std::size_t NDIM>

void madness::GFit< T, NDIM >::truncate_periodic_expansion	(	Tensor< double > &	c,
		Tensor< double > &	e,
		double	L,
		bool	discardG0
	)		const

inline

References c, e(), and L.

Member Data Documentation

◆ coeffs_

template<typename T , std::size_t NDIM>

Tensor<T> madness::GFit< T, NDIM >::coeffs_

private

the coefficients of the expansion f(x) = \sum_m coeffs[m] exp(-exponents[m] * x^2)

Referenced by madness::GFit< T, NDIM >::coeffs(), madness::GFit< T, NDIM >::F2GFit(), madness::GFit< T, NDIM >::FGFit(), madness::GFit< T, NDIM >::operator=(), and madness::GFit< T, NDIM >::print_accuracy().

◆ exponents_

template<typename T , std::size_t NDIM>

Tensor<T> madness::GFit< T, NDIM >::exponents_

private

the exponents of the expansion f(x) = \sum_m coeffs[m] exp(-exponents[m] * x^2)

Referenced by madness::GFit< T, NDIM >::exponents(), madness::GFit< T, NDIM >::F2GFit(), madness::GFit< T, NDIM >::FGFit(), madness::GFit< T, NDIM >::operator=(), and madness::GFit< T, NDIM >::print_accuracy().

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

gfit.h

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ GFit() [1/4]

◆ GFit() [2/4]

◆ GFit() [3/4]

◆ GFit() [4/4]

Member Function Documentation

◆ bsh_fit()

◆ bsh_fit_ndim()

◆ bsh_spherical_moments()

◆ BSHFit()

◆ coeffs()

◆ CoulombFit()

◆ exponents()

◆ f12_fit()

◆ F12Fit()

◆ f12sq_fit()

◆ F12sqFit()

◆ F2GFit()

◆ FGFit()

◆ GaussFit()

◆ gaussian_spherical_moments()

◆ GeneralFit()

◆ operator=()

◆ print_accuracy()

◆ prune_small_coefficients()

◆ slater_fit()

◆ SlaterFit()

◆ truncate_periodic_expansion()

Member Data Documentation

◆ coeffs_

◆ exponents_