gp_exp_quad_cov.hpp

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#ifndef STAN_MATH_PRIM_FUN_GP_EXP_QUAD_COV_HPP
#define STAN_MATH_PRIM_FUN_GP_EXP_QUAD_COV_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/divide_columns.hpp>
#include <stan/math/prim/fun/squared_distance.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/square.hpp>
#include <cmath>
#include <type_traits>
#include <vector>
 
namespace stan {
namespace math {
 
namespace internal {
 
template <typename T_x, typename T_x_alloc, typename T_sigma, typename T_l>
inline typename Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                              Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<T_x, T_x_alloc> &x, const T_sigma &sigma_sq,
                const T_l &neg_half_inv_l_sq) {
  using std::exp;
  const size_t x_size = x.size();
  Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x_size, x_size);
  cov.diagonal().array() = sigma_sq;
  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) {
        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(i, j)
              = sigma_sq
                * exp(squared_distance(x[i], x[j]) * neg_half_inv_l_sq);
        }
      }
    }
  }
  cov.template triangularView<Eigen::Upper>() = cov.transpose();
  return cov;
}
 
template <typename T_x1, typename T_x1_alloc, typename T_x2, typename T_sigma,
          typename T_l>
inline typename Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l>,
                              Eigen::Dynamic, Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<T_x1, T_x1_alloc> &x1,
                const std::vector<T_x2> &x2, const T_sigma &sigma_sq,
                const T_l &neg_half_inv_l_sq) {
  using std::exp;
  Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x1.size(), x2.size());
  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(squared_distance(x1[i], x2[j]) * neg_half_inv_l_sq);
        }
      }
    }
  }
  return cov;
}
}  // namespace internal
 
template <typename T_x, typename T_x_alloc, typename T_sigma, typename T_l>
inline typename Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                              Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<T_x, T_x_alloc> &x, const T_sigma &sigma,
                const T_l &length_scale) {
  check_positive("gp_exp_quad_cov", "magnitude", sigma);
  check_positive("gp_exp_quad_cov", "length scale", length_scale);
 
  const size_t x_size = x.size();
  Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x_size, x_size);
 
  if (x_size == 0) {
    return cov;
  }
 
  for (size_t n = 0; n < x_size; ++n) {
    check_not_nan("gp_exp_quad_cov", "x", x[n]);
  }
 
  cov = internal::gp_exp_quad_cov(x, square(sigma),
                                  -0.5 / square(length_scale));
  return cov;
}
 
template <typename T_x, typename T_x_alloc, typename T_sigma, typename T_l,
          typename T_l_alloc>
inline typename Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                              Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<Eigen::Matrix<T_x, -1, 1>, T_x_alloc> &x,
                const T_sigma &sigma,
                const std::vector<T_l, T_l_alloc> &length_scale) {
  check_positive_finite("gp_exp_quad_cov", "magnitude", sigma);
  check_positive_finite("gp_exp_quad_cov", "length scale", length_scale);
 
  size_t x_size = x.size();
  Eigen::Matrix<return_type_t<T_x, T_sigma, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x_size, x_size);
  if (x_size == 0) {
    return cov;
  }
 
  check_size_match("gp_exp_quad_cov", "x dimension", x[0].size(),
                   "number of length scales", length_scale.size());
  cov = internal::gp_exp_quad_cov(divide_columns(x, length_scale),
                                  square(sigma), -0.5);
  return cov;
}
 
template <typename T_x1, typename T_x1_alloc, typename T_x2,
          typename T_x2_alloc, typename T_sigma, typename T_l>
inline typename Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l>,
                              Eigen::Dynamic, Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<T_x1, T_x1_alloc> &x1,
                const std::vector<T_x2, T_x2_alloc> &x2, const T_sigma &sigma,
                const T_l &length_scale) {
  const char *function_name = "gp_exp_quad_cov";
  check_positive(function_name, "magnitude", sigma);
  check_positive(function_name, "length scale", length_scale);
 
  const size_t x1_size = x1.size();
  const size_t x2_size = x2.size();
  Eigen::Matrix<return_type_t<T_x1, T_x2, T_sigma, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x1_size, x2_size);
  if (x1_size == 0 || x2_size == 0) {
    return cov;
  }
 
  for (size_t i = 0; i < x1_size; ++i) {
    check_not_nan(function_name, "x1", x1[i]);
  }
  for (size_t i = 0; i < x2_size; ++i) {
    check_not_nan(function_name, "x2", x2[i]);
  }
 
  cov = internal::gp_exp_quad_cov(x1, x2, square(sigma),
                                  -0.5 / square(length_scale));
  return cov;
}
 
template <typename T_x1, typename T_x1_alloc, typename T_x2,
          typename T_x2_alloc, typename T_s, typename T_l, typename T_l_alloc>
inline typename Eigen::Matrix<return_type_t<T_x1, T_x2, T_s, T_l>,
                              Eigen::Dynamic, Eigen::Dynamic>
gp_exp_quad_cov(const std::vector<Eigen::Matrix<T_x1, -1, 1>, T_x1_alloc> &x1,
                const std::vector<Eigen::Matrix<T_x2, -1, 1>, T_x2_alloc> &x2,
                const T_s &sigma,
                const std::vector<T_l, T_l_alloc> &length_scale) {
  size_t x1_size = x1.size();
  size_t x2_size = x2.size();
  size_t l_size = length_scale.size();
 
  Eigen::Matrix<return_type_t<T_x1, T_x2, T_s, T_l>, Eigen::Dynamic,
                Eigen::Dynamic>
      cov(x1_size, x2_size);
 
  if (x1_size == 0 || x2_size == 0) {
    return cov;
  }
 
  const char *function_name = "gp_exp_quad_cov";
  for (size_t i = 0; i < x1_size; ++i) {
    check_not_nan(function_name, "x1", x1[i]);
  }
  for (size_t i = 0; i < x2_size; ++i) {
    check_not_nan(function_name, "x2", x2[i]);
  }
  check_positive_finite(function_name, "magnitude", sigma);
  check_positive_finite(function_name, "length scale", length_scale);
  check_size_match(function_name, "x dimension", x1[0].size(),
                   "number of length scales", l_size);
  check_size_match(function_name, "x dimension", x2[0].size(),
                   "number of length scales", l_size);
  cov = internal::gp_exp_quad_cov(divide_columns(x1, length_scale),
                                  divide_columns(x2, length_scale),
                                  square(sigma), -0.5);
  return cov;
}
 
}  // namespace math
}  // namespace stan
#endif