autocorrelation.hpp

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#ifndef STAN__PROB__AUTOCORRELATION_HPP
#define STAN__PROB__AUTOCORRELATION_HPP

#include <stan/math/matrix.hpp>
#include <stan/math/matrix/mean.hpp>

#include <vector>
#include <complex>
#include <unsupported/Eigen/FFT>


namespace stan {
  
  namespace prob {

    namespace {
      size_t fft_next_good_size(size_t N) { 
        if (N <= 2) return 2;
        while (true) {
          size_t m = N;
          while((m % 2) == 0) m /= 2;
          while((m % 3) == 0) m /= 3;
          while((m % 5) == 0) m /= 5;
          if (m <= 1)
            return N; 
          N++;
        }
      }
    } 
    
    template <typename T>
    void autocorrelation(const std::vector<T>& y,
                         std::vector<T>& ac,
                         Eigen::FFT<T>& fft) {

      using std::vector;
      using std::complex;

      size_t N = y.size();
      size_t M = fft_next_good_size(N); 
      size_t Mt2 = 2 * M;


      vector<complex<T> > freqvec;
      
      // centered_signal = y-mean(y) followed by N zeroes
      vector<T> centered_signal(y);
      centered_signal.insert(centered_signal.end(),Mt2-N,0.0);
      T mean = stan::math::mean(y);
      for (size_t i = 0; i < N; i++)
        centered_signal[i] -= mean;
      
      fft.fwd(freqvec,centered_signal);
      for (size_t i = 0; i < Mt2; ++i)
        freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
      
      fft.inv(ac,freqvec);
      ac.resize(N);

      /*
      vector<T> mask_correction_factors;      
      vector<T> mask;
      mask.insert(mask.end(),N,1.0);
      mask.insert(mask.end(),N,0.0);
      
      freqvec.resize(0);
      fft.fwd(freqvec,mask);
      for (size_t i = 0; i < Nt2; ++i)
        freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
      
      fft.inv(mask_correction_factors, freqvec);

      for (size_t i = 0; i < N; ++i) {
        ac[i] /= mask_correction_factors[i];
      }
      */
      for (size_t i = 0; i < N; ++i) {
        ac[i] /= (N - i); 
      } 
      T var = ac[0];      
      for (size_t i = 0; i < N; ++i)
        ac[i] /= var;
    }

    template <typename T>
    void autocorrelation(const std::vector<T>& y,
                         std::vector<T>& ac) {
      Eigen::FFT<T> fft;
      return autocorrelation(y,ac,fft);
    }


  }
}

#endif