SphericalHarmonicExpansion.icc

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// -*- C++ -*-
// $Id: 
#include <sstream>
#include <cmath>
#include <gsl/gsl_sf_legendre.h>
#include <complex>
#include <cstdlib>
#include <sstream>
#include <stdexcept>
namespace Genfun {
  
  FUNCTION_OBJECT_IMP(SphericalHarmonicExpansion)
  
  class SphericalHarmonicExpansion::Clockwork {
    
  public:
    
    Clockwork(SphericalHarmonicExpansion::Type type, const SphericalHarmonicCoefficientSet & coefficients):type(type),coefficients(coefficients){}

    SphericalHarmonicExpansion::Type type;
    SphericalHarmonicCoefficientSet coefficients;
    
  };
  
  
  inline
  SphericalHarmonicExpansion::SphericalHarmonicExpansion(Type type, const SphericalHarmonicCoefficientSet & coefficients):
    c(new Clockwork(type,coefficients))
  {
    
  }
  
  
  inline
  SphericalHarmonicExpansion::~SphericalHarmonicExpansion() {
    delete c;
  }
  
  inline
  SphericalHarmonicExpansion::SphericalHarmonicExpansion(const SphericalHarmonicExpansion & right):
    AbsFunction(),
    c(new Clockwork(right.c->type,right.c->coefficients))
  {
  }
  
  inline
  double SphericalHarmonicExpansion::operator() (double ) const {
    throw std::runtime_error("Dimensionality error in SphericalHarmonicExpansion");
    return 0;
  }
  
  inline
  double SphericalHarmonicExpansion::operator() (const Argument & a ) const {
    const unsigned int LMAX=c->coefficients.getLMax();
    double x = a[0];
    double phi=a[1];

    // Note, the calling sequence of the GSL Special Function forces us to 
    // transpose Plm from its "natural" order.. It is addressed as P[m][l].

    //double Plm[LMAX+1][LMAX+1];
    std::vector< std::vector<double> > Plm(LMAX+1);
    for (int m=0;m<=int(LMAX);m++) {
      Plm[m].resize(LMAX+1);
      gsl_sf_legendre_sphPlm_array (LMAX, m, x, &*Plm[m].begin());
      //gsl_sf_legendre_sphPlm_array (LMAX, m, x, Plm[m]);
    }

    std::complex<double> P=0.0;
    std::complex<double> I(0,1.0);
    for (unsigned int l=0;l<=LMAX;l++) {
      for (int m=0;m<=int(l);m++) {
        {
          int LP=l-abs(m);
          double Pn= Plm[abs(m)][LP];
        
          if (!finite(Pn)) {
            std::ostringstream stream;
            stream << "Non-finite Pn(x=" << x << ")"; 
            throw std::runtime_error(stream.str());
          }
          // Once for positive m (in all cases):
          P+=(c->coefficients(l,m)*Pn*exp(I*(m*phi)));
          // Once for negative m (skip if m==0);
          if (m!=0) P+= ( (m%2 ?-1.0:1.0)*c->coefficients(l,-m)*Pn*exp(-I*(m*phi)));
        }
      }
    }
    double retVal=0;
    if (c->type==MAGSQ) return norm(P);
    if (c->type==MAG)   return abs(P);
    if (c->type==REAL)  return real(P);
    if (c->type==IMAG)  return imag(P);
    if (!finite(retVal)) {
      throw std::runtime_error("Non-finite return value in SphericalHarmonicExpansion");
    }
    return retVal;
  }

  inline
  const SphericalHarmonicCoefficientSet & SphericalHarmonicExpansion::coefficientSet() const {
    return c->coefficients;
  }

  inline
  SphericalHarmonicCoefficientSet & SphericalHarmonicExpansion::coefficientSet() {
    return c->coefficients;
  }
  
} // end namespace Genfun