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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
10 namespace stan {
11
12 namespace math {
13
14 namespace {
19 size_t fft_next_good_size(size_t N) {
20 if (N <= 2) return 2;
21 while (true) {
22 size_t m = N;
23 while ((m % 2) == 0) m /= 2;
24 while ((m % 3) == 0) m /= 3;
25 while ((m % 5) == 0) m /= 5;
26 if (m <= 1)
27 return N;
28 N++;
29 }
30 }
31 }
32
53 template <typename T>
54 void autocorrelation(const std::vector<T>& y,
55 std::vector<T>& ac,
56 Eigen::FFT<T>& fft) {
57 using std::vector;
58 using std::complex;
59
60 size_t N = y.size();
61 size_t M = fft_next_good_size(N);
62 size_t Mt2 = 2 * M;
63
64
65 vector<complex<T> > freqvec;
66
67 // centered_signal = y-mean(y) followed by N zeroes
68 vector<T> centered_signal(y);
69 centered_signal.insert(centered_signal.end(), Mt2-N, 0.0);
70 T mean = stan::math::mean(y);
71 for (size_t i = 0; i < N; i++)
72 centered_signal[i] -= mean;
73
74 fft.fwd(freqvec, centered_signal);
75 for (size_t i = 0; i < Mt2; ++i)
76 freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
77
78 fft.inv(ac, freqvec);
79 ac.resize(N);
80
81 /*
82 vector<T> mask_correction_factors;
83 vector<T> mask;
84 mask.insert(mask.end(), N, 1.0);
85 mask.insert(mask.end(), N, 0.0);
86
87 freqvec.resize(0);
88 fft.fwd(freqvec, mask);
89 for (size_t i = 0; i < Nt2; ++i)
90 freqvec[i] = complex<T>(norm(freqvec[i]), 0.0);
91
92 fft.inv(mask_correction_factors, freqvec);
93
94 for (size_t i = 0; i < N; ++i) {
95 ac[i] /= mask_correction_factors[i];
96 }
97 */
98 for (size_t i = 0; i < N; ++i) {
99 ac[i] /= (N - i);
100 }
101 T var = ac[0];
102 for (size_t i = 0; i < N; ++i)
103 ac[i] /= var;
104 }
105
122 template <typename T>
123 void autocorrelation(const std::vector<T>& y,
124 std::vector<T>& ac) {
125 Eigen::FFT<T> fft;
126 return autocorrelation(y, ac, fft);
127 }
128
129
130 }
131 }
132
133 #endif
stan::math::var
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:32
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:54

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