math_sphbes.h

Go to the documentation of this file.

#ifndef MATH_SPHBES_H
#define MATH_SPHBES_H
 
#include <functional>
 
//========================================================
// Spherical Bessel functions, mohan 2021-05-06
//========================================================
namespace ModuleBase
{
 
class Sphbes 
{
    public:
 
    Sphbes();
    ~Sphbes();
 
    static void Spherical_Bessel
    (
        const int &msh,
        const double *r,
        const double &q,
        const int &l,
        double *jl
    );
 
    static void dSpherical_Bessel_dx
    (
        const int &msh,
        const double *r,
        const double &q,
        const int &l,
        double *jl
    );
 
    static void Spherical_Bessel
    (           
        const int &msh, 
        const double *r,
        const double &q, 
        const int &l,  
        double *sj,    
        double *sjp
    );
 
    static void Spherical_Bessel_Roots
    (
        const int &num,
        const int &l,
        const double &epsilon,
        double* eigenvalue,
        const double &rcut
    );
 
 
    static double sphbesj(const int l,   
                          const double x 
    );
 
    static double dsphbesj(const int l,   
                          const double x  
    );
 
    static void sphbesj(const int n,           
                        const double* const r, 
                        const double q,        
                        const int l,           
                        double* const jl       
    );
 
    static void dsphbesj(const int n,          
                        const double* const r, 
                        const double q,        
                        const int l,           
                        double* const djl      
    );
 
    static void sphbes_zeros(const int l,
                             const int n,
                             double* const zeros,
                             bool return_all = false
    );
 
private:
 
    static double Spherical_Bessel_7(const int n, const double &x);
 
    // Peize Lin change double to void 2019-05-01
    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);
 
    // utility functions for sphbesj
    static double _sphbesj_ascending_recurrence(int l, double x);
    static double _sphbesj_series(int l, double x);
 
    // Regula falsi with Illinois anti-stalling variation
    static double illinois(std::function<double(double)> func,
                           double x0,
                           double x1,
                           const double tol = 1e-12,
                           const int max_iter = 50);
};
 
}
 
#endif