simplex_constrain.hpp

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#ifndef STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
#define STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/inv_logit.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1p_exp.hpp>
#include <stan/math/prim/fun/logit.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename Vec, require_eigen_vector_t<Vec>* = nullptr,
          require_not_st_var<Vec>* = nullptr>
inline plain_type_t<Vec> simplex_constrain(const Vec& y) {
  // cut & paste simplex_constrain(Eigen::Matrix, T) w/o Jacobian
  using std::log;
  using T = value_type_t<Vec>;
 
  int Km1 = y.size();
  plain_type_t<Vec> x(Km1 + 1);
  T stick_len(1.0);
  for (Eigen::Index k = 0; k < Km1; ++k) {
    T z_k = inv_logit(y.coeff(k) - log(Km1 - k));
    x.coeffRef(k) = stick_len * z_k;
    stick_len -= x.coeff(k);
  }
  x.coeffRef(Km1) = stick_len;
  return x;
}
 
template <typename Vec, typename Lp, require_eigen_vector_t<Vec>* = nullptr,
          require_not_st_var<Vec>* = nullptr,
          require_convertible_t<value_type_t<Vec>, Lp>* = nullptr>
inline plain_type_t<Vec> simplex_constrain(const Vec& y, Lp& lp) {
  using Eigen::Dynamic;
  using Eigen::Matrix;
  using std::log;
  using T = value_type_t<Vec>;
 
  int Km1 = y.size();  // K = Km1 + 1
  plain_type_t<Vec> x(Km1 + 1);
  T stick_len(1.0);
  for (Eigen::Index k = 0; k < Km1; ++k) {
    double eq_share = -log(Km1 - k);  // = logit(1.0/(Km1 + 1 - k));
    T adj_y_k = y.coeff(k) + eq_share;
    T z_k = inv_logit(adj_y_k);
    x.coeffRef(k) = stick_len * z_k;
    lp += log(stick_len);
    lp -= log1p_exp(-adj_y_k);
    lp -= log1p_exp(adj_y_k);
    stick_len -= x.coeff(k);  // equivalently *= (1 - z_k);
  }
  x.coeffRef(Km1) = stick_len;  // no Jacobian contrib for last dim
  return x;
}
 
template <typename T, require_std_vector_t<T>* = nullptr>
inline auto simplex_constrain(const T& y) {
  return apply_vector_unary<T>::apply(
      y, [](auto&& v) { return simplex_constrain(v); });
}
 
template <typename T, typename Lp, require_std_vector_t<T>* = nullptr,
          require_convertible_t<return_type_t<T>, Lp>* = nullptr>
inline auto simplex_constrain(const T& y, Lp& lp) {
  return apply_vector_unary<T>::apply(
      y, [&lp](auto&& v) { return simplex_constrain(v, lp); });
}
 
template <bool Jacobian, typename Vec, typename Lp,
          require_convertible_t<return_type_t<Vec>, Lp>* = nullptr>
inline plain_type_t<Vec> simplex_constrain(const Vec& y, Lp& lp) {
  if constexpr (Jacobian) {
    return simplex_constrain(y, lp);
  } else {
    return simplex_constrain(y);
  }
}
 
}  // namespace math
}  // namespace stan
 
#endif