math_integral.h

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#ifndef MATH_INTEGRAL_H
#define MATH_INTEGRAL_H
 
// mohan add 2021-04-03
namespace ModuleBase
{
 
class Integral
{
 
    public:
 
    Integral();
    ~Integral();
 
    static void Simpson_Integral 
    (    
        const int mesh,
        const double * const func,
        const double * const rab,
        double &asum
    );
 
    static void Simpson_Integral 
    (
        const int mesh,
        const double * const func,
        const double dr,
        double &asum
    );
 
    static void Simpson_Integral_0toall 
    (
        const int mesh,
        const double * const func,
        const double * const rab,
        double * const asum
    );
 
    static void Simpson_Integral_alltoinf 
    (
        const int mesh,
        const double * const func,
        const double * const rab,
        double * const asum
    );     
 
    static double simpson(const int n,           
                          const double* const f, 
                          const double dx        
    );
 
    static double simpson(const int n,           
                          const double* const f, 
                          const double* const h  
    );
 
    // Grid points and weights used to generate Gauss_Legendre integrals. Returns x in [-1, 1], the integration area is -1, 1.
    // https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature
    // \int_{-1}^{1} f(x) dx \approx \sum_{i = 1}^{n} w_{i} f(x_{i})
    // n is the number of sample points used,
    // w_{i} are quadrature weights
    // x_{i} are the roots of the n-th Legendre polynomial.
    static void Gauss_Legendre_grid_and_weight(const int n, double *x, double *weights);
 
    // Grid points and weights used to generate Gauss_Legendre integrals. Returns x in [xmin, xmax], the integration area is at xmin, xmax.
    // \int_{-1}^{1} f(x) dx \approx \sum_{i = 1}^{n} w_{i} f(x_{i})
    // xl = (xmax - xmin) / 2
    // xmean = (xmax + xmin) / 2
    // \int_{xmin}^{xmax} f(x) dx = xl \int_{-1}^{1} f(xl * t + xmean) dt
    static void Gauss_Legendre_grid_and_weight(const double xmin, const double xmax, const int n, double *x, double *weights);
 
    // Grid points and weights used to generate Gauss_Legendre integrals. can be generated with function Lebedev_laikov_grid in math_lebedev_laikov.cpp
    static const double Lebedev_Laikov_grid110_x[110];
    static const double Lebedev_Laikov_grid110_y[110];
    static const double Lebedev_Laikov_grid110_z[110];
    static const double Lebedev_Laikov_grid110_w[110];
};
 
}
#endif