gp_periodic_cov.hpp

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#ifndef STAN_MATH_PRIM_FUN_GP_PERIODIC_COV_HPP
#define STAN_MATH_PRIM_FUN_GP_PERIODIC_COV_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/distance.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/inv_square.hpp>
#include <stan/math/prim/fun/sin.hpp>
#include <stan/math/prim/fun/square.hpp>
#include <cmath>
#include <vector>
 
namespace stan {
namespace math {
 
template <typename T_x, typename T_sigma, typename T_l, typename T_p>
inline typename Eigen::Matrix<return_type_t<T_x, T_sigma, T_l, T_p>,
                              Eigen::Dynamic, Eigen::Dynamic>
gp_periodic_cov(const std::vector<T_x> &x, const T_sigma &sigma, const T_l &l,
                const T_p &p) {
  using std::exp;
  using std::sin;
  const char *fun = "gp_periodic_cov";
  check_positive(fun, "signal standard deviation", sigma);
  check_positive(fun, "length-scale", l);
  check_positive(fun, "period", p);
  for (size_t n = 0; n < x.size(); ++n) {
    check_not_nan(fun, "element of x", x[n]);
  }
 
  Eigen::Matrix<return_type_t<T_x, T_sigma, T_l, T_p>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x.size(), x.size());
 
  size_t x_size = x.size();
  if (x_size == 0) {
    return cov;
  }
 
  T_sigma sigma_sq = square(sigma);
  T_l neg_two_inv_l_sq = -2.0 * inv_square(l);
  T_p pi_div_p = pi() / p;
  size_t block_size = 10;
 
  for (size_t jb = 0; jb < x_size; jb += block_size) {
    for (size_t ib = jb; ib < x_size; ib += block_size) {
      size_t j_end = std::min(x_size, jb + block_size);
      for (size_t j = jb; j < j_end; ++j) {
        cov.coeffRef(j, j) = sigma_sq;
        size_t i_end = std::min(x_size, ib + block_size);
        for (size_t i = std::max(ib, j + 1); i < i_end; ++i) {
          cov.coeffRef(j, i) = cov.coeffRef(i, j)
              = sigma_sq
                * exp(square(sin(pi_div_p * distance(x[i], x[j])))
                      * neg_two_inv_l_sq);
        }
      }
    }
  }
  return cov;
}
 
template <typename T_x1, typename T_x2, typename T_sigma, typename T_l,
          typename T_p>
inline typename Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l, T_p>,
                              Eigen::Dynamic, Eigen::Dynamic>
gp_periodic_cov(const std::vector<T_x1> &x1, const std::vector<T_x2> &x2,
                const T_sigma &sigma, const T_l &l, const T_p &p) {
  using std::exp;
  using std::sin;
  const char *fun = "gp_periodic_cov";
  check_positive(fun, "signal standard deviation", sigma);
  check_positive(fun, "length-scale", l);
  check_positive(fun, "period", p);
  for (size_t n = 0; n < x1.size(); ++n) {
    check_not_nan(fun, "element of x1", x1[n]);
  }
  for (size_t n = 0; n < x2.size(); ++n) {
    check_not_nan(fun, "element of x2", x2[n]);
  }
 
  Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l, T_p>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x1.size(), x2.size());
  if (x1.size() == 0 || x2.size() == 0) {
    return cov;
  }
 
  T_sigma sigma_sq = square(sigma);
  T_l neg_two_inv_l_sq = -2.0 * inv_square(l);
  T_p pi_div_p = pi() / p;
  size_t block_size = 10;
 
  for (size_t ib = 0; ib < x1.size(); ib += block_size) {
    for (size_t jb = 0; jb < x2.size(); jb += block_size) {
      size_t j_end = std::min(x2.size(), jb + block_size);
      for (size_t j = jb; j < j_end; ++j) {
        size_t i_end = std::min(x1.size(), ib + block_size);
        for (size_t i = ib; i < i_end; ++i) {
          cov.coeffRef(i, j)
              = sigma_sq
                * exp(square(sin(pi_div_p * distance(x1[i], x2[j])))
                      * neg_two_inv_l_sq);
        }
      }
    }
  }
  return cov;
}
}  // namespace math
}  // namespace stan
 
#endif