splinterpolator.h

}

/////////////////////////////////////////////////////////////////////
//
// Performs deconvolution, converting signal to spline coefficients.
//
/////////////////////////////////////////////////////////////////////

template<class T>
bool Splinterpolator<T>::calc_coef(const T *data, bool copy)
{
  if (_order < 2 && !copy) { _cptr = data; return(false); }

  // Allocate memory and put the original data into _coef
  //
  unsigned int ts=1;
  for (unsigned int i=0; i<_dim.size(); i++) ts *= _dim[i];
  _coef = new T[ts];
  memcpy(_coef,data,ts*sizeof(T));

  if (_order < 2) return(true);  // If nearest neighbour or linear, that's all we need 

  // Loop over all non-singleton dimensions and deconvolve along them
  //
  std::vector<unsigned int>  tdim(_dim.size()-1,0); 
  for (unsigned int cdir=0; cdir<_dim.size(); cdir++) {
    if (_dim[cdir] > 1) deconv_along(cdir);
  }

  return(true);
}

/////////////////////////////////////////////////////////////////////
//
// Performs deconvolution along one of the dimensions, visiting
// all points along the other dimensions.
//
/////////////////////////////////////////////////////////////////////

template<class T>
void Splinterpolator<T>::deconv_along(unsigned int dim)
{
  // Set up to reflect "missing" dimension
  //
  std::vector<unsigned int>   rdim(4,1);     // Sizes along remaining dimensions
  std::vector<unsigned int>   rstep(4,1);    // Step-sizes (in "volume") of remaining dimensions
  unsigned int                mdim = 1;      // Size along "missing" dimension
  unsigned int                mstep = 1;     // Step-size along "missing" dimension
  for (unsigned int i=0, j=0, ss=1; i<5; i++) {
    if (i == dim) {  // If it is our "missing" dimension
      mdim = _dim[i];
      mstep = ss;
    }
    else {
      rdim[j] = _dim[i];
      rstep[j++] = ss;
    }
    ss *= _dim[i];
  }

  SplineColumn  col(mdim,mstep);          // Column helps us do the job
  
  for (unsigned int l=0; l<rdim[3]; l++) {
    for (unsigned int k=0; k<rdim[2]; k++) {
      for (unsigned int j=0; j<rdim[1]; j++) {
        T *dp = _coef + l*rstep[3] + k*rstep[2] + j*rstep[1];
	for (unsigned int i=0; i<rdim[0]; i++, dp+=rstep[0]) {
	  col.Get(dp);                          // Extract a column from the volume
          col.Deconv(_order,_et[dim],_prec);    // Deconvolve it
          col.Set(dp);                          // Put back the deconvolved column
	}
      }
    }
  }
  return;
}

/////////////////////////////////////////////////////////////////////
//
// Here starts private member functions for SplineColumn
//
/////////////////////////////////////////////////////////////////////

/////////////////////////////////////////////////////////////////////
//
// This function returns the poles and scale-factors for splines
// of order 2--7. The values correspond to those found in
// table 1 in Unsers 1993 paper: 
// B-spline signal processing. II. Efficiency design and applications
// 
// The actual values have been taken from
// http://bigwww.epfl.ch/thevenaz/interpolation/coeff.c
//
/////////////////////////////////////////////////////////////////////

template<class T>
unsigned int Splinterpolator<T>::SplineColumn::get_poles(unsigned int order, double *z, unsigned int *sf) const
{
  unsigned int   np = 0;                     // # of poles

  switch (order) {
  case 2:
    np = 1;
    z[0] = 2.0*sqrt(2.0) - 3.0;
    *sf = 8;
    break;
  case 3:
    np = 1;
    z[0] = sqrt(3.0) - 2.0;
    *sf = 6;
    break;
  case 4:
    np = 2;
    z[0] = sqrt(664.0 - sqrt(438976.0)) + sqrt(304.0) - 19.0;
    z[1] = sqrt(664.0 + sqrt(438976.0)) - sqrt(304.0) - 19.0;
    *sf = 384;
    break;
  case 5:
    np = 2;
    z[0] = sqrt(135.0 / 2.0 - sqrt(17745.0 / 4.0)) + sqrt(105.0 / 4.0) - 13.0 / 2.0;
    z[1] = sqrt(135.0 / 2.0 + sqrt(17745.0 / 4.0)) - sqrt(105.0 / 4.0) - 13.0 / 2.0;
    *sf = 120;
    break;
  case 6:
    np = 3;
    z[0] = -0.48829458930304475513011803888378906211227916123938;
    z[1] = -0.081679271076237512597937765737059080653379610398148;
    z[2] = -0.0014141518083258177510872439765585925278641690553467;
    *sf = 46080;
    break;
  case 7:
    np = 3;
    z[0] = -0.53528043079643816554240378168164607183392315234269;
    z[1] = -0.12255461519232669051527226435935734360548654942730;
    z[2] = -0.0091486948096082769285930216516478534156925639545994;
    *sf = 5040;
    break;
  default:
    throw SplinterpolatorException("SplineColumn::get_poles: invalid order of spline");
    break;
  }
  return(np);
}

/////////////////////////////////////////////////////////////////////
//
// Initialises the first value for the forward sweep. The initialisation
// will always be an approximation (this is where the "infinite" in IIR
// breaks down) so the value will be calculated to a predefined precision.
//
/////////////////////////////////////////////////////////////////////

template<class T>
double Splinterpolator<T>::SplineColumn::init_fwd_sweep(double z, ExtrapolationType et, double prec) const
{
  //
  // Move logs away from here after debugging
  //
  unsigned int n = static_cast<unsigned int>((log(prec)/log(abs(z))) + 1.5);
  n = (n > _sz) ? _sz : n;

  double iv = _col[0];
  if (et == Periodic) {
    double *ptr=&_col[_sz-1];
    double z2i=z;
    for (unsigned int i=1; i<n; i++, ptr--, z2i*=z) iv += z2i * *ptr;
  }
  else {
    double *ptr=&_col[1];
    double z2i=z;
    for (unsigned int i=1; i<n; i++, ptr++, z2i*=z) iv += z2i * *ptr;
  }
  return(iv); 
}

/////////////////////////////////////////////////////////////////////
//
// Initialises the first value for the backward sweep. The initialisation
// will always be an approximation (this is where the "infinite" in IIR
// breaks down) so the value will be calculated to a predefined precision.
//
/////////////////////////////////////////////////////////////////////

template<class T>
double Splinterpolator<T>::SplineColumn::init_bwd_sweep(double z, double lv, ExtrapolationType et, double prec) const
{
  double iv = 0.0;
  if (et == Periodic) {
    unsigned int n = static_cast<unsigned int>((log(prec)/log(abs(z))) + 1.5);
    n = (n > _sz) ? _sz : n;
    iv = z * _col[_sz-1];
    double z2i = z*z;
    double *ptr=_col;
    for (unsigned int i=1; i<n; i++, ptr++, z2i*=z) {
      iv += z2i * *ptr;
    }
    iv /= (z2i-1.0);
  }
  else {
    iv = -z/(1.0-z*z) * (2.0*_col[_sz-1] - lv);
  }
  return(iv);
}

} // End namespace SPLINTERPOLATOR

#endif // End #ifndef splinterpolator.h