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/constants.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/fmax.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/inv_sqrt.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) {
  using T = value_type_t<Vec>;
  const auto N = y.size();
 
  plain_type_t<Vec> z = Eigen::VectorXd::Zero(N + 1);
  if (unlikely(N == 0)) {
    z.coeffRef(0) = 1;
    return z;
  }
 
  auto&& y_ref = to_ref(y);
  T sum_w(0);
 
  T d(0);  // sum of exponentials
  T max_val(0);
  T max_val_old(negative_infinity());
 
  for (int i = N; i > 0; --i) {
    double n = static_cast<double>(i);
    auto w = y_ref(i - 1) * inv_sqrt(n * (n + 1));
    sum_w += w;
 
    z.coeffRef(i - 1) += sum_w;
    z.coeffRef(i) -= w * n;
 
    max_val = fmax(max_val_old, z.coeff(i));
    d = d * exp(max_val_old - max_val) + exp(z.coeff(i) - max_val);
    max_val_old = max_val;
  }
 
  // above loop doesn't reach i==0
  max_val = fmax(max_val_old, z.coeff(0));
  d = d * exp(max_val_old - max_val) + exp(z.coeff(0) - max_val);
 
  z.array() = (z.array() - max_val).exp() / d;
 
  return z;
}
 
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 std::log;
  using T = value_type_t<Vec>;
  const auto N = y.size();
 
  plain_type_t<Vec> z = Eigen::VectorXd::Zero(N + 1);
  if (unlikely(N == 0)) {
    z.coeffRef(0) = 1;
    return z;
  }
 
  auto&& y_ref = to_ref(y);
  T sum_w(0);
 
  T d(0);  // sum of exponentials
  T max_val(0);
  T max_val_old(negative_infinity());
 
  for (int i = N; i > 0; --i) {
    double n = static_cast<double>(i);
    auto w = y_ref(i - 1) * inv_sqrt(n * (n + 1));
    sum_w += w;
 
    z.coeffRef(i - 1) += sum_w;
    z.coeffRef(i) -= w * n;
 
    max_val = fmax(max_val_old, z.coeff(i));
    d = d * exp(max_val_old - max_val) + exp(z.coeff(i) - max_val);
    max_val_old = max_val;
  }
 
  // above loop doesn't reach i==0
  max_val = fmax(max_val_old, z.coeff(0));
  d = d * exp(max_val_old - max_val) + exp(z.coeff(0) - max_val);
 
  z.array() = (z.array() - max_val).exp() / d;
 
  // equivalent to z.log().sum() + 0.5 * log(N + 1)
  lp += -(N + 1) * (max_val + log(d)) + 0.5 * log(N + 1);
 
  return z;
}
 
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