inverse.hpp

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#ifndef STAN_MATH_FWD_FUN_INVERSE_HPP
#define STAN_MATH_FWD_FUN_INVERSE_HPP
 
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/fwd/core.hpp>
#include <stan/math/fwd/fun/multiply.hpp>
#include <stan/math/fwd/fun/to_fvar.hpp>
#include <stan/math/fwd/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/inverse.hpp>
 
namespace stan {
namespace math {
 
template <typename EigMat, require_eigen_vt<is_fvar, EigMat>* = nullptr>
inline Eigen::Matrix<value_type_t<EigMat>, EigMat::RowsAtCompileTime,
                     EigMat::ColsAtCompileTime>
inverse(const EigMat& m) {
  using T = typename value_type_t<EigMat>::Scalar;
  constexpr int R = EigMat::RowsAtCompileTime;
  constexpr int C = EigMat::ColsAtCompileTime;
 
  check_square("inverse", "m", m);
  if (m.size() == 0) {
    return {};
  }
 
  Eigen::Matrix<T, R, C> m_deriv(m.rows(), m.cols());
  Eigen::Matrix<T, R, C> m_inv(m.rows(), m.cols());
 
  const Eigen::Ref<const plain_type_t<EigMat>>& m_ref = m;
  for (size_type j = 0; j < m.cols(); j++) {
    for (size_type i = 0; i < m.rows(); i++) {
      m_inv.coeffRef(i, j) = m_ref.coeff(i, j).val_;
      m_deriv.coeffRef(i, j) = m_ref.coeff(i, j).d_;
    }
  }
 
  m_inv = inverse(m_inv);
  m_deriv = -multiply(multiply(m_inv, m_deriv), m_inv);
 
  return to_fvar(m_inv, m_deriv);
}
 
}  // namespace math
}  // namespace stan
#endif