ModuleBase::Sphbes Class Reference

#include <math_sphbes.h>

Collaboration diagram for ModuleBase::Sphbes:

Public Member Functions
	Sphbes ()
	~Sphbes ()

Static Public Member Functions
static void	Spherical_Bessel (const int &msh, const double *r, const double &q, const int &l, double *jl)
	spherical bessel jl(qr)
static void	dSpherical_Bessel_dx (const int &msh, const double *r, const double &q, const int &l, double *jl)
	derivative of spherical bessel djl(qr)/d(qr)
static void	Spherical_Bessel (const int &msh, const double *r, const double &q, const int &l, double *sj, double *sjp)
	spherical bessel
static void	Spherical_Bessel_Roots (const int &num, const int &l, const double &epsilon, double *eigenvalue, const double &rcut)
	return num eigenvalues of spherical bessel function
static double	sphbesj (const int l, const double x)
	spherical Bessel function of the first kind
static double	dsphbesj (const int l, const double x)
	derivative of spherical Bessel function
static void	sphbesj (const int n, const double *const r, const double q, const int l, double *const jl)
	computes the values of l-th order spherical Bessel function at q*r[ir]
static void	dsphbesj (const int n, const double *const r, const double q, const int l, double *const djl)
	computes the derivative of l-th order spherical Bessel function at q*r[ir]
static void	sphbes_zeros (const int l, const int n, double *const zeros, bool return_all=false)
	Zeros of spherical Bessel functions.

Static Private Member Functions
static double	Spherical_Bessel_7 (const int n, const double &x)
static void	BESSJY (double x, double xnu, double *rj, double *ry, double *rjp, double *ryp)
static void	BESCHB (double x, double *gam1, double *gam2, double *gampl, double *gammi)
static double	CHEBEV (double a, double b, double c[], int m, double x)
static int	IMAX (int a, int b)
static double	_sphbesj_ascending_recurrence (int l, double x)
static double	_sphbesj_series (int l, double x)
static double	illinois (std::function< double(double)> func, double x0, double x1, const double tol=1e-12, const int max_iter=50)

Constructor & Destructor Documentation

Sphbes()

Sphbes::Sphbes

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~Sphbes()

Sphbes::~Sphbes

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Member Function Documentation

_sphbesj_ascending_recurrence()

double Sphbes::_sphbesj_ascending_recurrence ( int  l, double  x  )

staticprivate

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_sphbesj_series()

double Sphbes::_sphbesj_series ( int  l, double  x  )

staticprivate

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BESCHB()

void Sphbes::BESCHB ( double  x, double *  gam1, double *  gam2, double *  gampl, double *  gammi  )

staticprivate

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BESSJY()

void Sphbes::BESSJY ( double  x, double  xnu, double *  rj, double *  ry, double *  rjp, double *  ryp  )

staticprivate

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CHEBEV()

double Sphbes::CHEBEV ( double  a, double  b, double  c[], int  m, double  x  )

staticprivate

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dsphbesj() [1/2]

double Sphbes::dsphbesj ( const int  l, const double  x  )

static

derivative of spherical Bessel function

Parameters

[in]	l	order
[in]	x	argument

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dsphbesj() [2/2]

void Sphbes::dsphbesj ( const int  n, const double *const  r, const double  q, const int  l, double *const  djl  )

static

computes the derivative of l-th order spherical Bessel function at q*r[ir]

Parameters

[in]	n	number of r grid points
[in]	r	r grid
[in]	q	wave vector
[in]	l	order of the spherical Bessel function
[out]	djl	results

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dSpherical_Bessel_dx()

void Sphbes::dSpherical_Bessel_dx ( const int &  msh, const double *  r, const double &  q, const int &  l, double *  jl  )

static

derivative of spherical bessel djl(qr)/d(qr)

Parameters

msh	[in] number of grid points
r	[in] radial grid
q	[in] k_radial
l	[in] angular momentum
jl	[out] jl spherical bessel function

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illinois()

double Sphbes::illinois ( std::function< double(double)>  func, double  x0, double  x1, const double  tol = 1e-12, const int  max_iter = 50  )

staticprivate

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IMAX()

int Sphbes::IMAX ( int  a, int  b  )

staticprivate

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sphbes_zeros()

void Sphbes::sphbes_zeros ( const int  l, const int  n, double *const  zeros, bool  return_all = false  )

static

Zeros of spherical Bessel functions.

This function computes the first n positive zeros of the l-th order spherical Bessel function of the first kind.

Parameters

[in]	l	(maximum) order of the spherical Bessel function
[in]	n	number of zeros to be computed (for each j_l if return_all is true)
[out]	zeros	on exit, contains the positive zeros.
[in]	return_all	if true, return all zeros from j_0 to j_l such that zeros[l*n+i] is the i-th zero of j_l. If false, return only the first n zeros of j_l.

Note

The size of array "zeros" must be at least (l+1)*n if return_all is true, and n otherwise.

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sphbesj() [1/2]

double Sphbes::sphbesj ( const int  l, const double  x  )

static

spherical Bessel function of the first kind

This function computes j_l(x) by series expansion for x < l and by ascending recurrence for x >= l.

Parameters

[in]	l	order
[in]	x	argument

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sphbesj() [2/2]

void Sphbes::sphbesj ( const int  n, const double *const  r, const double  q, const int  l, double *const  jl  )

static

computes the values of l-th order spherical Bessel function at q*r[ir]

Parameters

[in]	n	number of r grid points
[in]	r	r grid
[in]	q	wave vector
[in]	l	order of the spherical Bessel function
[out]	jl	results

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Spherical_Bessel() [1/2]

void Sphbes::Spherical_Bessel ( const int &  msh, const double *  r, const double &  q, const int &  l, double *  jl  )

static

spherical bessel jl(qr)

Parameters

msh	[in] number of grid points
r	[in] radial grid
q	[in] k_radial
l	[in] angular momentum
jl	[out] jl spherical bessel function

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Spherical_Bessel() [2/2]

void Sphbes::Spherical_Bessel ( const int &  msh, const double *  r, const double &  q, const int &  l, double *  sj, double *  sjp  )

static

spherical bessel

Parameters

msh	[in] number of grid points
r	[in] radial grid
q	[in] k_radial
l	[in] angular momentum
jl	[out] jl spherical bessel function
sjp	[out] sjp[i] is assigned to be 1.0. i < msh.

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Spherical_Bessel_7()

double Sphbes::Spherical_Bessel_7 ( const int  n, const double &  x  )

staticprivate

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Spherical_Bessel_Roots()

void Sphbes::Spherical_Bessel_Roots ( const int &  num, const int &  l, const double &  epsilon, double *  eigenvalue, const double &  rcut  )

static

return num eigenvalues of spherical bessel function

Parameters

num	[in] the number of eigenvalues
l	[in] angular number
epsilon	[in] the accuracy
eigenvalue	[out] the calculated eigenvalues
rcut	[in] the cutoff the radial function

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

• /home/runner/work/abacus-develop/abacus-develop/source/source_base/math_sphbes.h
• /home/runner/work/abacus-develop/abacus-develop/source/source_base/math_sphbes.cpp