lagrange.h

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/*
 *  Lagrange's interpolation.
 */
#ifndef AIMS_MATH_LAGRANGE_H
#define AIMS_MATH_LAGRANGE_H

#include <cstdlib>
#include <aims/config/aimsdata_config.h>
#include <aims/data/data.h>
#include <math.h>

namespace aims {


template <class REAL>
AIMSDATA_API REAL AimsLagrangeInterpolationOf( const AimsData<REAL> &xa,
                                               const AimsData<REAL> &ya,
                                               REAL x, REAL *dy )


{
  int  i,m,ns=0,n=std::min(xa.dimX(),ya.dimX());
  REAL den,dif,dift,ho,hp,w;
  REAL *c, *d, y;

  dif = fabs(x-xa(0));
  c = new float[n];
  d = new float[n];

  for (i=0;i<n;i++) { 
    if ((dift = fabs(x-xa(i))) < dif) { 
      ns  = i;
      dif = dift;
    }
    c[i] = ya(i);
    d[i] = ya(i);
  }
  
  y = ya(ns--);
  for (m=1;m<n;m++){ 
    for (i=0;i<n-m;i++){ 
      ho = xa(i)   - x;
      hp = xa(i+m) - x;
      w  = c[i+1]  - d[i];
      ASSERT( (den = ho - hp) != 0.0 );
      den = w / den;
      d[i] = hp * den;
      c[i] = ho * den;
    }
    y += (*dy=(2*ns+2 < (n-m) ? c[ns+1] : d[ns--]));
  }
  delete [] c;
  delete [] d;
  return y;
}

// for backward compatibility
inline  float AimsLagrangeInterpolation( const AimsData<float> &xa,
                                         const AimsData<float> &ya,
                                         float x, float *dy )
{
  return AimsLagrangeInterpolationOf<float>( xa, ya, x, dy );
}

} // namespace aims

#endif