Computes the Boys function, $ F_m (T) = \int_0^1 u^{2m} \exp(-T u^2) \, {\rm d}u $, using Taylor interpolation of up to 8-th order. More...

#include <boys.h>

Public Member Functions
	FmEval_Taylor (unsigned int mmax, Real precision=std::numeric_limits< Real >::epsilon())
	Constructs the object to be able to compute Boys funcion for m in [0,mmax], with relative `precision`.

int	max_m () const

Real	precision () const

void	eval (Real *Fm, Real T, int mmax) const
	computes Boys function values with m index in range [0,mmax] More...

Static Public Member Functions
static std::shared_ptr< const FmEval_Taylor >	instance (unsigned int mmax, Real precision=std::numeric_limits< Real >::epsilon())
	Singleton interface allows to manage the lone instance; adjusts max m and precision values as needed in thread-safe fashion.

Static Public Attributes
static const int	max_interp_order = 8

static const bool	INTERPOLATION_AND_RECURSION = false

Detailed Description

Computes the Boys function, $ F_m (T) = \int_0^1 u^{2m} \exp(-T u^2) \, {\rm d}u $, using Taylor interpolation of up to 8-th order.

Template Parameters

Real	the type to use for all floating-point computations. Following expressions must be valid: exp(Real), pow(Real), fabs(Real), max(Real), and floor(Real).
INTERPOLATION_ORDER	the interpolation order. The higher the order the less memory this object will need, but the computational cost will increase (usually very slightly)

Member Function Documentation

template<typename Real = double, int INTERPOLATION_ORDER = 7>

void libint2::FmEval_Taylor< Real, INTERPOLATION_ORDER >::eval	(	Real *	Fm,
		Real	T,
		int	mmax
	)		const

inline

computes Boys function values with m index in range [0,mmax]

Parameters

[out]	Fm	array to be filled in with the Boys function values, must be at least mmax+1 elements long
[in]	x	the Boys function argument
[in]	mmax	the maximum value of m for which Boys function will be computed; it must be <= the value returned by max_m() (this is not checked)