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/prim/fun/Eigen.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/constraint/sum_to_zero_constrain.hpp>
#include <stan/math/prim/constraint/simplex_constrain.hpp>
#include <cmath>
 
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>;
 
  const auto N = y.size();
  arena_t<T> arena_y = y;
 
  arena_t<ret_type> arena_x = simplex_constrain(arena_y.val());
 
  if (unlikely(N == 0)) {
    return ret_type(arena_x);
  }
 
  reverse_pass_callback([arena_y, arena_x]() mutable {
    auto&& res_val = arena_x.val();
 
    // backprop for softmax
    Eigen::VectorXd x_pre_softmax_adj = -res_val * arena_x.adj().dot(res_val)
                                        + res_val.cwiseProduct(arena_x.adj());
 
    // backprop for sum_to_zero_constrain
    internal::sum_to_zero_vector_backprop(arena_y.adj(), x_pre_softmax_adj);
  });
 
  return ret_type(arena_x);
}
 
template <typename T, require_rev_col_vector_t<T>* = nullptr>
inline auto simplex_constrain(const T& y, scalar_type_t<T>& lp) {
  using ret_type = plain_type_t<T>;
 
  const auto N = y.size();
  arena_t<T> arena_y = y;
 
  double lp_val = 0.0;
  arena_t<ret_type> arena_x = simplex_constrain(arena_y.val(), lp_val);
  lp += lp_val;
 
  if (unlikely(N == 0)) {
    return ret_type(arena_x);
  }
 
  reverse_pass_callback([arena_y, arena_x, lp]() mutable {
    auto&& res_val = arena_x.val();
 
    // backprop for log jacobian contribution to log density is equivalent to
    // arena_x.adj().array() += lp.adj() / res_val.array();
    // but is folded into the following to avoid needing to modify the adjoints
    // in-place
 
    // backprop for softmax
    Eigen::VectorXd x_pre_softmax_adj
        = -res_val * (arena_x.adj().dot(res_val) + res_val.size() * lp.adj())
          + (res_val.cwiseProduct(arena_x.adj()).array() + lp.adj()).matrix();
 
    // backprop for sum_to_zero_constrain
    internal::sum_to_zero_vector_backprop(arena_y.adj(), x_pre_softmax_adj);
  });
 
  return ret_type(arena_x);
}
 
}  // namespace math
}  // namespace stan
#endif