cholesky_factor_constrain.hpp

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#ifndef STAN_MATH_REV_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
#define STAN_MATH_REV_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
 
#include <stan/math/rev/core.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/sum.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <cmath>
#include <stdexcept>
#include <vector>
 
namespace stan {
namespace math {
 
template <typename T, require_var_vector_t<T>* = nullptr>
var_value<Eigen::MatrixXd> cholesky_factor_constrain(const T& x, int M, int N) {
  using std::exp;
  check_greater_or_equal("cholesky_factor_constrain",
                         "num rows (must be greater or equal to num cols)", M,
                         N);
  check_size_match("cholesky_factor_constrain", "x.size()", x.size(),
                   "((N * (N + 1)) / 2 + (M - N) * N)",
                   ((N * (N + 1)) / 2 + (M - N) * N));
  arena_t<Eigen::MatrixXd> y_val = Eigen::MatrixXd::Zero(M, N);
 
  int pos = 0;
  for (int m = 0; m < N; ++m) {
    y_val.row(m).head(m) = x.val().segment(pos, m);
    pos += m;
    y_val.coeffRef(m, m) = exp(x.val().coeff(pos));
    pos++;
  }
 
  for (int m = N; m < M; ++m) {
    y_val.row(m) = x.val().segment(pos, N);
    pos += N;
  }
 
  var_value<Eigen::MatrixXd> y = y_val;
 
  reverse_pass_callback([x, M, N, y]() mutable {
    int pos = x.size();
    for (int m = M - 1; m >= N; --m) {
      pos -= N;
      x.adj().segment(pos, N) += y.adj().row(m);
    }
 
    for (int m = N - 1; m >= 0; --m) {
      pos--;
      x.adj().coeffRef(pos) += y.adj().coeff(m, m) * y.val().coeff(m, m);
      pos -= m;
      x.adj().segment(pos, m) += y.adj().row(m).head(m);
    }
  });
 
  return y;
}
 
template <typename T, require_var_vector_t<T>* = nullptr>
var_value<Eigen::MatrixXd> cholesky_factor_constrain(const T& x, int M, int N,
                                                     scalar_type_t<T>& lp) {
  check_size_match("cholesky_factor_constrain", "x.size()", x.size(),
                   "((N * (N + 1)) / 2 + (M - N) * N)",
                   ((N * (N + 1)) / 2 + (M - N) * N));
  int pos = 0;
  double lp_val = 0.0;
  for (int n = 0; n < N; ++n) {
    pos += n;
    lp_val += x.val().coeff(pos);
    pos++;
  }
  lp += lp_val;
 
  reverse_pass_callback([x, N, lp]() mutable {
    int pos = 0;
    for (int n = 0; n < N; ++n) {
      pos += n;
      x.adj().coeffRef(pos) += lp.adj();
      pos++;
    }
  });
 
  return cholesky_factor_constrain(x, M, N);
}
 
}  // namespace math
}  // namespace stan
 
#endif