simplex_constrain.hpp

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#ifndef STAN_MATH_REV_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
#define STAN_MATH_REV_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
 
#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core/reverse_pass_callback.hpp>
#include <stan/math/rev/core/arena_matrix.hpp>
#include <stan/math/rev/fun/value_of.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/inv_logit.hpp>
#include <stan/math/prim/fun/log1p_exp.hpp>
#include <cmath>
#include <tuple>
#include <vector>
 
namespace stan {
namespace math {
 
template <typename T, require_rev_col_vector_t<T>* = nullptr>
inline auto simplex_constrain(const T& y) {
  using ret_type = plain_type_t<T>;
 
  size_t N = y.size();
  arena_t<T> arena_y = y;
  arena_t<Eigen::VectorXd> arena_z(N);
  Eigen::VectorXd x_val(N + 1);
 
  double stick_len(1.0);
  for (Eigen::Index k = 0; k < N; ++k) {
    double log_N_minus_k = std::log(N - k);
    arena_z.coeffRef(k) = inv_logit(arena_y.val().coeff(k) - log_N_minus_k);
    x_val.coeffRef(k) = stick_len * arena_z.coeff(k);
    stick_len -= x_val(k);
  }
  x_val.coeffRef(N) = stick_len;
 
  arena_t<ret_type> arena_x = x_val;
 
  if (unlikely(N == 0)) {
    return ret_type(arena_x);
  }
 
  reverse_pass_callback([arena_y, arena_x, arena_z]() mutable {
    int N = arena_y.size();
    double stick_len_val = arena_x.val().coeff(N);
    double stick_len_adj = arena_x.adj().coeff(N);
    for (Eigen::Index k = N; k-- > 0;) {
      arena_x.adj().coeffRef(k) -= stick_len_adj;
      stick_len_val += arena_x.val().coeff(k);
      stick_len_adj += arena_x.adj().coeff(k) * arena_z.coeff(k);
      double arena_z_adj = arena_x.adj().coeff(k) * stick_len_val;
      arena_y.adj().coeffRef(k)
          += arena_z_adj * arena_z.coeff(k) * (1.0 - arena_z.coeff(k));
    }
  });
 
  return ret_type(arena_x);
}
 
template <typename T, require_rev_col_vector_t<T>* = nullptr>
auto simplex_constrain(const T& y, scalar_type_t<T>& lp) {
  using ret_type = plain_type_t<T>;
 
  size_t N = y.size();
  arena_t<T> arena_y = y;
  arena_t<Eigen::VectorXd> arena_z(N);
  Eigen::VectorXd x_val(N + 1);
 
  double stick_len(1.0);
  for (Eigen::Index k = 0; k < N; ++k) {
    double log_N_minus_k = std::log(N - k);
    double adj_y_k = arena_y.val().coeff(k) - log_N_minus_k;
    arena_z.coeffRef(k) = inv_logit(adj_y_k);
    x_val.coeffRef(k) = stick_len * arena_z.coeff(k);
    lp += log(stick_len);
    lp -= log1p_exp(-adj_y_k);
    lp -= log1p_exp(adj_y_k);
    stick_len -= x_val(k);
  }
  x_val.coeffRef(N) = stick_len;
 
  arena_t<ret_type> arena_x = x_val;
 
  if (unlikely(N == 0)) {
    return ret_type(arena_x);
  }
 
  reverse_pass_callback([arena_y, arena_x, arena_z, lp]() mutable {
    int N = arena_y.size();
    double stick_len_val = arena_x.val().coeff(N);
    double stick_len_adj = arena_x.adj().coeff(N);
    for (Eigen::Index k = N; k-- > 0;) {
      arena_x.adj().coeffRef(k) -= stick_len_adj;
      stick_len_val += arena_x.val().coeff(k);
      double log_N_minus_k = std::log(N - k);
      double adj_y_k = arena_y.val().coeff(k) - log_N_minus_k;
      arena_y.adj().coeffRef(k) -= lp.adj() * inv_logit(adj_y_k);
      arena_y.adj().coeffRef(k) += lp.adj() * inv_logit(-adj_y_k);
      stick_len_adj += lp.adj() / stick_len_val;
      stick_len_adj += arena_x.adj().coeff(k) * arena_z.coeff(k);
      double arena_z_adj = arena_x.adj().coeff(k) * stick_len_val;
      arena_y.adj().coeffRef(k)
          += arena_z_adj * arena_z.coeff(k) * (1.0 - arena_z.coeff(k));
    }
  });
 
  return ret_type(arena_x);
}
 
}  // namespace math
}  // namespace stan
#endif