Quelle Determinant.h Sprache: C

// 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

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(-m(0,3),d3_0, m(1,3)*d3_1) +
           internal::pmadd(-m(2,3),d3_2, 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(-m(i1,2), d1, 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<typename internal::remove_all<Nested>::type>::run(derived());
}

} // end namespace Eigen

#endif // EIGEN_DETERMINANT_H

quality96%

¤ Dauer der Verarbeitung: 0.1 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.