rombergitg.h

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/*
 *  Romberg's numerical integration.
 */
#ifndef AIMS_MATH_ROMBERGITG_H
#define AIMS_MATH_ROMBERGITG_H


#include <cstdlib>
#include <aims/math/trapezeitg.h>
#include <aims/data/data.h>
#include <aims/math/lagrange.h>
#include <math.h>


namespace aims
{

template <class REAL>
class RombergIntegratorOf
{
  public:

    RombergIntegratorOf( const REAL &eps, int jmax, int k ) : _eps( eps ),
                                                        _jmax( jmax ),
                                                        _k( k ) { }
    virtual ~RombergIntegratorOf() { }

    virtual REAL eval( const Integrable& func, REAL a, REAL b ) const;

  private:

    REAL _eps;
    int _jmax;
    int _k;
};

template <class REAL>
REAL RombergIntegratorOf<REAL>::eval( const Integrable& func, 
                                       REAL a, REAL b ) const
{
  REAL ss, dss;
  AimsData< REAL > s( _jmax ), h( _jmax + 1 );

  if ( a == b )
    return 0.0;
  
  h( 0 ) = 1.0;
  for ( int j = 0; j < _jmax; j++ )
  {
    TrapezeIntegratorOf<REAL> integrator;
    s( j ) = integrator.stage( func, a, b, j + 1 );
    if ( j + 1 >= _k )
    {
      AimsData< REAL > tmph( _k ), tmps( _k );
      for ( int kk = 0; kk < _k; kk++ )
      {
        tmph( kk ) = h( j - _k + kk + 1 );
        tmps( kk ) = s( j - _k + kk + 1 );
      }
      ss = AimsLagrangeInterpolationOf<REAL>( tmph, tmps, 0.0, &dss );
      if ( fabs( dss ) <= _eps * fabs( ss ) )
        return ss;
    }
    h( j + 1 ) = 0.25 * h( j );
  }
  return 0.0;
}


// For backward compatibility
typedef RombergIntegratorOf<float> RombergIntegrator;

} // namespace aims

#endif