sum_to_zero_constrain.hpp

Go to the documentation of this file.

#ifndef STAN_MATH_PRIM_CONSTRAINT_SUM_TO_ZERO_CONSTRAIN_HPP
#define STAN_MATH_PRIM_CONSTRAINT_SUM_TO_ZERO_CONSTRAIN_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/inv_sqrt.hpp>
#include <stan/math/prim/functor/apply_vector_unary.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename Vec, require_eigen_col_vector_t<Vec>* = nullptr,
          require_not_st_var<Vec>* = nullptr>
inline plain_type_t<Vec> sum_to_zero_constrain(const Vec& y) {
  const auto N = y.size();
 
  plain_type_t<Vec> z = Eigen::VectorXd::Zero(N + 1);
  if (unlikely(N == 0)) {
    return z;
  }
 
  auto&& y_ref = to_ref(y);
 
  value_type_t<Vec> sum_w(0);
  for (int i = N; i > 0; --i) {
    double n = static_cast<double>(i);
    auto w = y_ref.coeff(i - 1) * inv_sqrt(n * (n + 1));
    sum_w += w;
 
    z.coeffRef(i - 1) += sum_w;
    z.coeffRef(i) -= w * n;
  }
 
  return z;
}
 
template <typename Mat, require_eigen_matrix_dynamic_t<Mat>* = nullptr,
          require_not_st_var<Mat>* = nullptr>
inline plain_type_t<Mat> sum_to_zero_constrain(const Mat& x) {
  const auto N = x.rows();
  const auto M = x.cols();
 
  plain_type_t<Mat> Z = Eigen::MatrixXd::Zero(N + 1, M + 1);
  if (unlikely(N == 0 || M == 0)) {
    return Z;
  }
  auto&& x_ref = to_ref(x);
 
  Eigen::Matrix<value_type_t<Mat>, -1, 1> beta = Eigen::VectorXd::Zero(N);
 
  for (int j = M - 1; j >= 0; --j) {
    value_type_t<Mat> ax_previous(0);
 
    double a_j = inv_sqrt((j + 1.0) * (j + 2.0));
    double b_j = (j + 1.0) * a_j;
 
    for (int i = N - 1; i >= 0; --i) {
      double a_i = inv_sqrt((i + 1.0) * (i + 2.0));
      double b_i = (i + 1.0) * a_i;
 
      auto b_i_x = b_i * x_ref.coeff(i, j) - ax_previous;
 
      Z.coeffRef(i, j) = (b_j * b_i_x) - beta.coeff(i);
      beta.coeffRef(i) += a_j * b_i_x;
 
      Z.coeffRef(N, j) -= Z.coeff(i, j);
      Z.coeffRef(i, M) -= Z.coeff(i, j);
 
      ax_previous += a_i * x_ref.coeff(i, j);
    }
    Z.coeffRef(N, M) -= Z.coeff(N, j);
  }
 
  return Z;
}
 
template <typename T, typename Lp, require_not_st_var<T>* = nullptr>
inline plain_type_t<T> sum_to_zero_constrain(const T& y, Lp& lp) {
  return sum_to_zero_constrain(y);
}
 
template <typename T, require_std_vector_t<T>* = nullptr>
inline auto sum_to_zero_constrain(const T& y) {
  return apply_vector_unary<T>::apply(
      y, [](auto&& v) { return sum_to_zero_constrain(v); });
}
 
template <typename T, typename Lp, require_std_vector_t<T>* = nullptr,
          require_convertible_t<return_type_t<T>, Lp>* = nullptr>
inline auto sum_to_zero_constrain(const T& y, Lp& lp) {
  return apply_vector_unary<T>::apply(
      y, [](auto&& v) { return sum_to_zero_constrain(v); });
}
 
template <bool Jacobian, typename T, typename Lp>
inline plain_type_t<T> sum_to_zero_constrain(const T& y, Lp& lp) {
  return sum_to_zero_constrain(y);
}
 
}  // namespace math
}  // namespace stan
 
#endif