alf.h

The Spectral Toolkit is a C++ spectral transform library written by Rodney James and Chuck Panaccion

//
// spectral toolkit 
// copyright (c) 2005 university corporation for atmospheric research
// licensed under the gnu general public license
//

#ifndef __alf__
#define __alf__

#include "spectral.h"

namespace spectral
{

  /// Associated Legendre function \f$ P_n^m(x)\f$. Constructs an associated 
  /// Legendre function for particular n,m with \f$ 0 \le m \le n \f$. 
  /// \f$ P_n^m(x)\f$ can then be evaluated for \f$ x \in [-1,1] \f$  with 
  /// the operator() member function.
  ///
  /// See Swartztrauber, P.N., The Vector Harmonic Transform 
  /// Method for Solving Partial Differential Equations in Spherical Geometry,
  /// <I>Monthly Weather Review</I>, <B>121</B> (1993), 3415-3437.
  ///
  /// The following example creates an associated Legendre polynomial and evaluates it at
  /// a series of points.
  /// \code
  /// #include <alf.h>
  /// #include <iostream>
  /// using namespace spectral;
  /// using namespace std;
  ///
  /// int main()
  /// {
  ///   int n=3;
  ///   int m=2;
  ///   alf P(n,m);
  ///   real x;
  ///   x=0.0;  cout <<  "P(" << n << "," << m << ")(" << x << ")=" << P(x) << endl;
  ///   x=1.0;  cout <<  "P(" << n << "," << m << ")(" << x << ")=" << P(x) << endl;
  ///   x=-1.0; cout <<  "P(" << n << "," << m << ")(" << x << ")=" << P(x) << endl;
  ///   x=-.12; cout <<  "P(" << n << "," << m << ")(" << x << ")=" << P(x) << endl;
  ///   x=.7;   cout <<  "P(" << n << "," << m << ")(" << x << ")=" << P(x) << endl;
  ///   return(0);
  /// }
  /// \endcode

  class alf
  {
  public:
    alf(int N,int M=0);
    ~alf();
    real operator()(real x);
  private:
    int m,n;
    real *cp;
  };
}

#endif

// Local Variables:
// mode:C++
// End: