FFT1D.H

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#ifndef _FFT1D_H_
#define _FFT1D_H_
#include <cmath>
#include <complex>
#include <vector>
#include <cstdio>
#include <iostream>
#include "PowerItoI.H"
class FFT1D
{
 public:
  // Interface class for complex-to-complex power-of-two FFT on the
  // unit interval.
  FFT1D(){};
  // Constructor. argument a_M specifies number of points is N= 2^{a_M}
  FFT1D(unsigned int a_M){m_M = a_M; m_N = Power(2,m_M);}
  virtual ~FFT1D() { }
  // Forward FFT: a_fHat[k] = \sum_j=0^{N-1} a_f[j] z^{j k}, z = e^{-2
  // \pi \iota /m_N}
  virtual void
  forwardFFTCC(std::vector<std::complex<double> > & a_fHat, 
               const std::vector<std::complex<double> >& f) const = 0;
  // inverse FFT: a_f[j] = \sum_{k=0}^{N-1} a_fHat[k] z^{j k}, z =
  // e^{2 \pi \iota /m_N}
  virtual void
  inverseFFTCC(std::vector<std::complex<double> > & a_f, 
               const std::vector<std::complex<double> > & a_fHat) const = 0;
  // Access functions.
  const unsigned int& getN(){return m_N;} 
  const unsigned int& getM(){return m_M;}
 protected:
  unsigned int m_M, m_N;
};
#endif