powerseries1D.h

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#ifndef POWERSERIES1D_H
#define POWERSERIES1D_H


typedef unsigned int uint;
typedef unsigned int const uintc;

template< typename T >
class powerseries1D
{
public:

  uint N;

  T * ai;

  void construct( T * ai_, uintc N_ )
    { N=N_; ai=ai_; }

  powerseries1D()
    : N(0), ai(0) {}

  powerseries1D( T * ai_, uintc N_ )
    { construct(ai_,N_); }

  void operator()(T & val, T const t) const;

  T const operator()(T const t) const;

  void differentiate();

  void taylorseries();

};

//--------------------------------------------------------
// Implementation


template< typename T >
void powerseries1D<T>::operator()(T & val, T const t) const
{
  // ai[0] + t(ai[1] + t(ai[2] + t(...
  val = 0.0;
  for (uint i=0; i<N; ++i)
  {
    val *= t;
    val += ai[N-1-i];
  }
}

template< typename T >
T const powerseries1D<T>::operator()(T const t) const
{
  // ai[0] + t(ai[1] + t(ai[2] + t(...
  T val = (T)0.0;
  for (uint i=0; i<N; ++i)
  {
    val *= t;
    val += ai[N-1-i];
  }

  return val;
}

template< typename T >
void powerseries1D<T>::differentiate()
{
  for (uint i=1; i<N; ++i)
  {
    ai[i]*=i;
    ai[i-1] = ai[i];
  }
  ai[N-1] = (T)0.0;
}

template< typename T >
void powerseries1D<T>::taylorseries()
{
  T s = (T)2.0;
  for (uint i=2; i<N; ++i)
  {
    ai[i] /= s;
    s *= (i+1);
  }
}


#endif