text: #ifndef STAN_MATH_PRIM_ERR_CHECK_POS_DEFINITE_HPP
  #define STAN_MATH_PRIM_ERR_CHECK_POS_DEFINITE_HPP
  
  #include <stan/math/prim/mat/fun/Eigen.hpp>
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/err/check_not_nan.hpp>
  #include <stan/math/prim/err/throw_domain_error.hpp>
  #include <stan/math/prim/err/check_symmetric.hpp>
  #include <stan/math/prim/err/constraint_tolerance.hpp>
  #include <stan/math/prim/err/check_positive.hpp>
  #include <stan/math/prim/mat/fun/value_of_rec.hpp>
  
  namespace stan {
  namespace math {
  
  /**
   * Check if the specified square, symmetric matrix is positive definite.
   * @tparam T_y Type of scalar of the matrix
   * @param function Function name (for error messages)
   * @param name Variable name (for error messages)
   * @param y Matrix to test
   * @throw <code>std::invalid_argument</code> if the matrix is not square
   * or if the matrix has 0 size.
   * @throw <code>std::domain_error</code> if the matrix is not symmetric,
   * if it is not positive definite, or if any element is <code>NaN</code>
   */
  template <typename T_y>
  inline void check_pos_definite(const char* function, const char* name,
                                 const Eigen::Matrix<T_y, -1, -1>& y) {
    check_symmetric(function, name, y);
    check_positive(function, name, "rows", y.rows());
    check_not_nan(function, name, y);
  
    if (y.rows() == 1 && !(y(0, 0) > CONSTRAINT_TOLERANCE)) {
      throw_domain_error(function, name, "is not positive definite.", "");
    }
  
    Eigen::LDLT<Eigen::MatrixXd> cholesky = value_of_rec(y).ldlt();
    if (cholesky.info() != Eigen::Success || !cholesky.isPositive()
        || (cholesky.vectorD().array() <= 0.0).any()) {
      throw_domain_error(function, name, "is not positive definite.", "");
    }
  }
  
  /**
   * Check if the specified LDLT transform of a matrix is positive definite.
   * @tparam Derived Derived type of the Eigen::LDLT transform.
   * @param function Function name (for error messages)
   * @param name Variable name (for error messages)
   * @param cholesky Eigen::LDLT to test, whose progenitor
   * must not have any NaN elements
   * @throw <code>std::domain_error</code> if the matrix is not
   * positive definite
   */
  template <typename Derived>
  inline void check_pos_definite(const char* function, const char* name,
                                 const Eigen::LDLT<Derived>& cholesky) {
    if (cholesky.info() != Eigen::Success || !cholesky.isPositive()
        || !(cholesky.vectorD().array() > 0.0).all()) {
      throw_domain_error(function, "LDLT decomposition of", " failed", name);
    }
  }
  
  /**
   * Check if the specified LLT decomposition transform resulted in
   * <code>Eigen::Success</code>
   * @tparam Derived Derived type of the Eigen::LLT transform.
   * @param function Function name (for error messages)
   * @param name Variable name (for error messages)
   * @param cholesky Eigen::LLT to test, whose progenitor
   * must not have any NaN elements
   * @throw <code>std::domain_error</code> if the diagonal of the
   * L matrix is not positive
   */
  template <typename Derived>
  inline void check_pos_definite(const char* function, const char* name,
                                 const Eigen::LLT<Derived>& cholesky) {
    if (cholesky.info() != Eigen::Success
        || !(cholesky.matrixLLT().diagonal().array() > 0.0).all()) {
      throw_domain_error(function, "Matrix", " is not positive definite", name);
    }
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  