MuonCalib::Legendre Namespace Reference

Functions
constexpr double	coeff (unsigned int l, unsigned int k)
	Calculates the n-th coefficient of the legendre polynomial series. More...
template<unsigned int l, unsigned int k>
constexpr double	polySum (const double x)
	Assembles the sum of the legendre monomials. More...
template<unsigned int l, unsigned int k, unsigned int d>
constexpr double	derivativeSum (const double x)
	Assembles the n-th derivative of the legendre polynomial. More...
template<unsigned int l>
constexpr double	poly (const double x)
template<unsigned int l, unsigned d>
constexpr double	derivative (const double x)

Function Documentation

coeff()

constexpr double MuonCalib::Legendre::coeff ( unsigned int  l, unsigned int  k  )

constexpr

Calculates the n-th coefficient of the legendre polynomial series.

Parameters

l	Order of the legendre polynomial
k	Coefficient of the polynomial representation

Definition at line 73 of file LegendrePoly.h.

                                                               {
            if (k %2 != l %2) {
                return 0.;
            } else if (k > 1) {
                const double a_k = -(1.*(l- k +2)*(l+ k-1)) / (1.*(k * (k-1))) * coeff(l, k-2);
                return a_k;
            } else {
                unsigned fl =  (l - l %2) /2;
                unsigned long binom = binomial(l,fl) * binomial(2*l - 2*fl,l);
                return (fl % 2 ? -1. : 1.) * std::pow(0.5, l) * (1.*binom);
            }
        }

derivative()

template<unsigned int l, unsigned d>

constexpr double MuonCalib::Legendre::derivative ( const double  x )

constexpr

Definition at line 120 of file LegendrePoly.h.

                                                        {
                return derivativeSum<l,l,d>(x);
            }

derivativeSum()

template<unsigned int l, unsigned int k, unsigned int d>

constexpr double MuonCalib::Legendre::derivativeSum ( const double  x )

constexpr

Assembles the n-th derivative of the legendre polynomial.

Parameters

l	Order of the legendre polynomial
k	Term in the polynomial to add to the sum
k	Order of the derivative
x	Dependency of the polynomial

Definition at line 104 of file LegendrePoly.h.

                                                           {
                static_assert(d> 0);
                if constexpr(k <= l && k>=d) {
                    constexpr unsigned long powFac = factorial(k) / factorial(k-d);
                    const double a_n = coeff(l,k) * powFac;
                    return a_n *std::pow(x,k-d) + derivativeSum<l, k-2, d>(x);
                } else {
                     return 0.;
                }
            }        

poly()

template<unsigned int l>

constexpr double MuonCalib::Legendre::poly ( const double  x )

constexpr

Definition at line 116 of file LegendrePoly.h.

                                                  {
                return polySum<l,l>(x);
        }

polySum()

template<unsigned int l, unsigned int k>

constexpr double MuonCalib::Legendre::polySum ( const double  x )

constexpr

Assembles the sum of the legendre monomials.

Parameters

l	Order of the legendre polynomial
k	Term in the polynomial to add to the sum
x	Dependency of the polynomial

Definition at line 90 of file LegendrePoly.h.

                                                     {
                const double a_n = coeff(l,k);
                if constexpr (k > 1) {                    
                    return a_n* std::pow(x,k) + polySum<l, k-2>(x);
                } else{
                    return a_n*std::pow(x,k);
                }
            }