laplace_base_rng.hpp

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#ifndef STAN_MATH_MIX_FUNCTOR_LAPLACE_BASE_RNG_HPP
#define STAN_MATH_MIX_FUNCTOR_LAPLACE_BASE_RNG_HPP
 
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/mix/functor/laplace_marginal_density.hpp>
#include <stan/math/prim/prob/multi_normal_cholesky_rng.hpp>
#include <stan/math/prim/prob/multi_normal_rng.hpp>
 
namespace stan {
namespace math {
 
template <typename LLFunc, typename LLArgs, typename CovarFun,
          typename CovarArgs, bool InitTheta, typename RNG,
          require_t<is_all_arithmetic_scalar<CovarArgs, LLArgs>>* = nullptr>
inline Eigen::VectorXd laplace_base_rng(
    LLFunc&& ll_fun, LLArgs&& ll_args, CovarFun&& covariance_function,
    CovarArgs&& covar_args, const laplace_options<InitTheta>& options, RNG& rng,
    std::ostream* msgs) {
  auto md_est = internal::laplace_marginal_density_est(
      ll_fun, std::forward<LLArgs>(ll_args),
      std::forward<CovarFun>(covariance_function),
      to_ref(std::forward<CovarArgs>(covar_args)), options, msgs);
  // Modified R&W method
  auto&& covariance_train = md_est.covariance;
  Eigen::VectorXd mean_train = covariance_train * md_est.theta_grad;
  if (options.solver == 1 || options.solver == 2) {
    Eigen::MatrixXd V_dec
        = md_est.L.template triangularView<Eigen::Lower>().solve(
            md_est.W_r * covariance_train);
    Eigen::MatrixXd Sigma = covariance_train - V_dec.transpose() * V_dec;
    return multi_normal_rng(std::move(mean_train), std::move(Sigma), rng);
  } else {
    Eigen::MatrixXd Sigma
        = covariance_train
          - covariance_train
                * (md_est.W_r
                   - md_est.W_r
                         * md_est.LU.solve(covariance_train * md_est.W_r))
                * covariance_train;
    return multi_normal_rng(std::move(mean_train), std::move(Sigma), rng);
  }
}
 
}  // namespace math
}  // namespace stan
 
#endif