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autocorrelation.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUN_AUTOCORRELATION_HPP
2 #define STAN_MATH_PRIM_MAT_FUN_AUTOCORRELATION_HPP
3
4 #include <stan/math/prim/mat/fun/mean.hpp>
5 #include <unsupported/Eigen/FFT>
6 #include <complex>
7 #include <vector>
8
9 namespace stan {
10 namespace math {
11
12 namespace {
17 size_t fft_next_good_size(size_t N) {
18 if (N <= 2) return 2;
19 while (true) {
20 size_t m = N;
21 while ((m % 2) == 0) m /= 2;
22 while ((m % 3) == 0) m /= 3;
23 while ((m % 5) == 0) m /= 5;
24 if (m <= 1)
25 return N;
26 N++;
27 }
28 }
29 }
30
51 template <typename T>
52 void autocorrelation(const std::vector<T>& y,
53 std::vector<T>& ac,
54 Eigen::FFT<T>& fft) {
55 using std::vector;
56 using std::complex;
57
58 size_t N = y.size();
59 size_t M = fft_next_good_size(N);
60 size_t Mt2 = 2 * M;
61
62 vector<complex<T> > freqvec;
63
64 // centered_signal = y-mean(y) followed by N zeroes
65 vector<T> centered_signal(y);
66 centered_signal.insert(centered_signal.end(), Mt2-N, 0.0);
67 T mean = stan::math::mean(y);
68 for (size_t i = 0; i < N; i++)
69 centered_signal[i] -= mean;
70
71 fft.fwd(freqvec, centered_signal);
72 for (size_t i = 0; i < Mt2; ++i)
73 freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
74
75 fft.inv(ac, freqvec);
76 ac.resize(N);
77
78 /*
79 vector<T> mask_correction_factors;
80 vector<T> mask;
81 mask.insert(mask.end(), N, 1.0);
82 mask.insert(mask.end(), N, 0.0);
83
84 freqvec.resize(0);
85 fft.fwd(freqvec, mask);
86 for (size_t i = 0; i < Nt2; ++i)
87 freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
88
89 fft.inv(mask_correction_factors, freqvec);
90
91 for (size_t i = 0; i < N; ++i) {
92 ac[i] /= mask_correction_factors[i];
93 }
94 */
95 for (size_t i = 0; i < N; ++i) {
96 ac[i] /= (N - i);
97 }
98 T var = ac[0];
99 for (size_t i = 0; i < N; ++i)
100 ac[i] /= var;
101 }
102
119 template <typename T>
120 void autocorrelation(const std::vector<T>& y,
121 std::vector<T>& ac) {
122 Eigen::FFT<T> fft;
123 return autocorrelation(y, ac, fft);
124 }
125
126 }
127 }
128 #endif
stan
Definition: log_sum_exp.hpp:8
stan::math::var
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:30
mean.hpp
stan::math::mean
boost::math::tools::promote_args< T >::type mean(const std::vector< T > &v)
Returns the sample mean (i.e., average) of the coefficients in the specified standard vector...
Definition: mean.hpp:23
stan::math::autocorrelation
void autocorrelation(const std::vector< T > &y, std::vector< T > &ac, Eigen::FFT< T > &fft)
Write autocorrelation estimates for every lag for the specified input sequence into the specified res...
Definition: autocorrelation.hpp:52

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