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Submodule stan_math
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| Original file line number | Diff line number | Diff line change |
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| #ifndef STAN_ANALYZE_MCMC_AUTOCOVARIANCE_HPP | ||
| #define STAN_ANALYZE_MCMC_AUTOCOVARIANCE_HPP | ||
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| #include <stan/math/prim/mat/fun/Eigen.hpp> | ||
| #include <stan/math/prim/mat.hpp> | ||
| #include <unsupported/Eigen/FFT> | ||
| #include <complex> | ||
| #include <vector> | ||
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| namespace stan { | ||
| namespace analyze { | ||
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| /** | ||
| * Write autocorrelation estimates for every lag for the specified | ||
| * input sequence into the specified result using the specified FFT | ||
| * engine. Normalizes lag-k autocorrelation estimators by N instead | ||
| * of (N - k), yielding biased but more stable estimators as | ||
| * discussed in Geyer (1992); see | ||
| * https://projecteuclid.org/euclid.ss/1177011137. The return vector | ||
| * will be resized to the same length as the input sequence with | ||
| * lags given by array index. | ||
| * | ||
| * <p>The implementation involves a fast Fourier transform, | ||
| * followed by a normalization, followed by an inverse transform. | ||
| * | ||
| * <p>An FFT engine can be created for reuse for type double with: | ||
| * | ||
| * <pre> | ||
| * Eigen::FFT<double> fft; | ||
| * </pre> | ||
| * | ||
| * @tparam T Scalar type. | ||
| * @param y Input sequence. | ||
| * @param ac Autocorrelations. | ||
| * @param fft FFT engine instance. | ||
| */ | ||
| template <typename T, typename DerivedA, typename DerivedB> | ||
| void autocorrelation(const Eigen::MatrixBase<DerivedA>& y, | ||
| Eigen::MatrixBase<DerivedB>& ac, Eigen::FFT<T>& fft) { | ||
| size_t N = y.size(); | ||
| size_t M = math::internal::fft_next_good_size(N); | ||
| size_t Mt2 = 2 * M; | ||
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| // centered_signal = y-mean(y) followed by N zeros | ||
| Eigen::Matrix<T, Eigen::Dynamic, 1> centered_signal(Mt2); | ||
| centered_signal.setZero(); | ||
| centered_signal.head(N) = y.array() - y.mean(); | ||
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| Eigen::Matrix<std::complex<T>, Eigen::Dynamic, 1> freqvec(Mt2); | ||
| fft.fwd(freqvec, centered_signal); | ||
| // cwiseAbs2 == norm | ||
| freqvec = freqvec.cwiseAbs2(); | ||
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| Eigen::Matrix<std::complex<T>, Eigen::Dynamic, 1> ac_tmp(Mt2); | ||
| fft.inv(ac_tmp, freqvec); | ||
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| // use "biased" estimate as recommended by Geyer (1992) | ||
| ac = ac_tmp.head(N).real().array() / (N * N * 2); | ||
| ac /= ac(0); | ||
| } | ||
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| /** | ||
| * Write autocovariance estimates for every lag for the specified | ||
| * input sequence into the specified result using the specified FFT | ||
| * engine. Normalizes lag-k autocovariance estimators by N instead | ||
| * of (N - k), yielding biased but more stable estimators as | ||
| * discussed in Geyer (1992); see | ||
| * https://projecteuclid.org/euclid.ss/1177011137. The return vector | ||
| * will be resized to the same length as the input sequence with | ||
| * lags given by array index. | ||
| * | ||
| * <p>The implementation involves a fast Fourier transform, | ||
| * followed by a normalization, followed by an inverse transform. | ||
| * | ||
| * <p>This method is just a light wrapper around the three-argument | ||
| * autocovariance function | ||
| * | ||
| * @tparam T Scalar type. | ||
| * @param y Input sequence. | ||
| * @param acov Autocovariances. | ||
| */ | ||
| template <typename T, typename DerivedA, typename DerivedB> | ||
| void autocovariance(const Eigen::MatrixBase<DerivedA>& y, | ||
| Eigen::MatrixBase<DerivedB>& acov) { | ||
| Eigen::FFT<T> fft; | ||
| autocorrelation(y, acov, fft); | ||
| acov = acov.array() * (y.array() - y.mean()).square().sum() / y.size(); | ||
| } | ||
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| /** | ||
| * Write autocovariance estimates for every lag for the specified | ||
| * input sequence into the specified result using the specified FFT | ||
| * engine. Normalizes lag-k autocovariance estimators by N instead | ||
| * of (N - k), yielding biased but more stable estimators as | ||
| * discussed in Geyer (1992); see | ||
| * https://projecteuclid.org/euclid.ss/1177011137. The return vector | ||
| * will be resized to the same length as the input sequence with | ||
| * lags given by array index. | ||
| * | ||
| * <p>The implementation involves a fast Fourier transform, | ||
| * followed by a normalization, followed by an inverse transform. | ||
| * | ||
| * <p>This method is just a light wrapper around the three-argument | ||
| * autocovariance function | ||
| * | ||
| * @tparam T Scalar type. | ||
| * @param y Input sequence. | ||
| * @param acov Autocovariances. | ||
| */ | ||
| template <typename T> | ||
| void autocovariance(const std::vector<T>& y, std::vector<T>& acov) { | ||
| size_t N = y.size(); | ||
| acov.resize(N); | ||
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| const Eigen::Map<const Eigen::Matrix<T, Eigen::Dynamic, 1>> y_map(&y[0], N); | ||
| Eigen::Map<Eigen::Matrix<T, Eigen::Dynamic, 1> > acov_map(&acov[0], N); | ||
| autocovariance<T>(y_map, acov_map); | ||
| } | ||
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| } // namespace analyze | ||
| } // namespace stan | ||
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| # endif |
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