Eigen/src/LU/Determinant.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_DETERMINANT_H
#define EIGEN_DETERMINANT_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename Derived>
EIGEN_DEVICE_FUNC inline const typename Derived::Scalar bruteforce_det3_helper(const MatrixBase<Derived>& matrix, int a,
                                                                               int b, int c) {
  return matrix.coeff(0, a) * (matrix.coeff(1, b) * matrix.coeff(2, c) - matrix.coeff(1, c) * matrix.coeff(2, b));
}

template <typename Derived, int DeterminantType = Derived::RowsAtCompileTime>
struct determinant_impl {
  static inline typename traits<Derived>::Scalar run(const Derived& m) {
    if (Derived::ColsAtCompileTime == Dynamic && m.rows() == 0) return typename traits<Derived>::Scalar(1);
    return m.partialPivLu().determinant();
  }
};

template <typename Derived>
struct determinant_impl<Derived, 1> {
  static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m) { return m.coeff(0, 0); }
};

template <typename Derived>
struct determinant_impl<Derived, 2> {
  static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m) {
    return m.coeff(0, 0) * m.coeff(1, 1) - m.coeff(1, 0) * m.coeff(0, 1);
  }
};

template <typename Derived>
struct determinant_impl<Derived, 3> {
  static inline EIGEN_DEVICE_FUNC typename traits<Derived>::Scalar run(const Derived& m) {
    return bruteforce_det3_helper(m, 0, 1, 2) - bruteforce_det3_helper(m, 1, 0, 2) + bruteforce_det3_helper(m, 2, 0, 1);
  }
};

template <typename Derived>
struct determinant_impl<Derived, 4> {
  typedef typename traits<Derived>::Scalar Scalar;
  static EIGEN_DEVICE_FUNC Scalar run(const Derived& m) {
    Scalar d2_01 = det2(m, 0, 1);
    Scalar d2_02 = det2(m, 0, 2);
    Scalar d2_03 = det2(m, 0, 3);
    Scalar d2_12 = det2(m, 1, 2);
    Scalar d2_13 = det2(m, 1, 3);
    Scalar d2_23 = det2(m, 2, 3);
    Scalar d3_0 = det3(m, 1, d2_23, 2, d2_13, 3, d2_12);
    Scalar d3_1 = det3(m, 0, d2_23, 2, d2_03, 3, d2_02);
    Scalar d3_2 = det3(m, 0, d2_13, 1, d2_03, 3, d2_01);
    Scalar d3_3 = det3(m, 0, d2_12, 1, d2_02, 2, d2_01);
    return internal::pmadd(static_cast<Scalar>(-m(0, 3)), d3_0, static_cast<Scalar>(m(1, 3) * d3_1)) +
           internal::pmadd(static_cast<Scalar>(-m(2, 3)), d3_2, static_cast<Scalar>(m(3, 3) * d3_3));
  }

 protected:
  static EIGEN_DEVICE_FUNC Scalar det2(const Derived& m, Index i0, Index i1) {
    return m(i0, 0) * m(i1, 1) - m(i1, 0) * m(i0, 1);
  }

  static EIGEN_DEVICE_FUNC Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1,
                                       Index i2, const Scalar& d2) {
    return internal::pmadd(m(i0, 2), d0,
                           internal::pmadd(static_cast<Scalar>(-m(i1, 2)), d1, static_cast<Scalar>(m(i2, 2) * d2)));
  }
};

}  // end namespace internal

/** \lu_module
 *
 * \returns the determinant of this matrix
 */
template <typename Derived>
EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const {
  eigen_assert(rows() == cols());
  typedef typename internal::nested_eval<Derived, Base::RowsAtCompileTime>::type Nested;
  return internal::determinant_impl<internal::remove_all_t<Nested>>::run(derived());
}

}  // end namespace Eigen

#endif  // EIGEN_DETERMINANT_H