LegendrePolynomial.cxx

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/*
  Copyright (C) 2002-2017 CERN for the benefit of the ATLAS collaboration
*/
 
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// 29.06.2006, AUTHOR: OLIVER KORTNER
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
//::::::::::::::::::
//:: HEADER FILES ::
//::::::::::::::::::
 
#include "MuonCalibMath/LegendrePolynomial.h"
#include "cmath"
 
//::::::::::::::::::::::::
//:: NAMESPACE SETTINGS ::
//::::::::::::::::::::::::
 
using namespace MuonCalib;
 
//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
//:: IMPLEMENTATION OF METHODS DEFINED IN THE CLASS LegendrePolynomial ::
//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
//*****************************************************************************
 
//::::::::::::::::::
//:: METHOD value ::
//::::::::::::::::::
 
double LegendrePolynomial::value(const int & k, const double & x) const {
 
 
// LOWER ORDER LEGENDRE POLYNOMIALS ARE GIVEN EXPLICITLY, HIGHER ORDERS ARE //
// CALCULATE RECURSIVELY.                                                   //
 
    switch(k) {
        case 0:
            return 1;
            break;
        case 1:
            return x;
            break;
        case 2:
            return 0.5*(3.0*x*x-1.0);
            break;
        case 3:
            return 0.5*(5.0*x*x*x-3.0*x);
            break;
        case 4:
            return (35.0*std::pow(x, 4)-30.0*x*x+3.0)/8.0;
            break;
        case 5:
            return (63.0*std::pow(x, 5)-70.0*x*x*x+15.0*x)/8.0;
            break;
        case 6:
            return (231.0*std::pow(x, 6)-315.0*std::pow(x, 4)+105.0*x*x-5.0)
                                    /16.0;
            break;
        case 7:
            return (429.0*std::pow(x, 7)-693*std::pow(x, 5)+315.0*x*x*x
                -35.0*x)/16.0;
            break;
        default:
            return (2.0*k-1)*x*value(k-1, x)/
                    static_cast<double>(k)
                - (k-1)*value(k-2, x)/
                    static_cast<double>(k);
            break;
    }
 
}