MatrixBase.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {

  *
  * This class can be extended with the help of the plugin mechanism described on the page
  * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
  *
  * \sa \blank \ref TopicClassHierarchy
  */
template <typename Derived>
class MatrixBase : public DenseBase<Derived> {
 public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
  using StorageBaseType = MatrixBase;
  using StorageKind = typename internal::traits<Derived>::StorageKind;
  using StorageIndex = typename internal::traits<Derived>::StorageIndex;
  using Scalar = typename internal::traits<Derived>::Scalar;
  using PacketScalar = typename internal::packet_traits<Scalar>::type;
  using RealScalar = typename NumTraits<Scalar>::Real;
 
  using Base = DenseBase<Derived>;
  using Base::ColsAtCompileTime;
  using Base::Flags;
  using Base::IsVectorAtCompileTime;
  using Base::MaxColsAtCompileTime;
  using Base::MaxRowsAtCompileTime;
  using Base::MaxSizeAtCompileTime;
  using Base::RowsAtCompileTime;
  using Base::SizeAtCompileTime;
 
  using Base::coeff;
  using Base::coeffRef;
  using Base::cols;
  using Base::const_cast_derived;
  using Base::derived;
  using Base::eval;
  using Base::lazyAssign;
  using Base::rows;
  using Base::size;
  using Base::operator-;
  using Base::operator+=;
  using Base::operator-=;
  using Base::operator*=;
  using Base::operator/=;
 
  using CoeffReturnType = typename Base::CoeffReturnType;
  using ConstTransposeReturnType = typename Base::ConstTransposeReturnType;
  using RowXpr = typename Base::RowXpr;
  using ColXpr = typename Base::ColXpr;
#endif  // not EIGEN_PARSED_BY_DOXYGEN
 
#ifndef EIGEN_PARSED_BY_DOXYGEN
  using SquareMatrixType = Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
                                  internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)>;
#endif  // not EIGEN_PARSED_BY_DOXYGEN

  /** \returns the size of the main diagonal, which is min(rows(),cols()).
   * \sa rows(), cols(), SizeAtCompileTime. */
  EIGEN_DEVICE_FUNC constexpr Index diagonalSize() const { return (numext::mini)(rows(), cols()); }
 
  using PlainObject = typename Base::PlainObject;
 
#ifndef EIGEN_PARSED_BY_DOXYGEN
  /** \internal Represents a matrix with all coefficients equal to one another*/
  using ConstantReturnType = CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject>;
  using AdjointReturnType =
      std::conditional_t<NumTraits<Scalar>::IsComplex,
                         CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
                         ConstTransposeReturnType>;
  using EigenvaluesReturnType =
      Matrix<internal::make_complex_t<Scalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor>;
  using IdentityReturnType = CwiseNullaryOp<internal::scalar_identity_op<Scalar>, PlainObject>;
  using BasisReturnType =
      Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
            internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime>;
#endif  // not EIGEN_PARSED_BY_DOXYGEN
 
#define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
#define EIGEN_DOC_UNARY_ADDONS(X, Y)
#include "../plugins/CommonCwiseBinaryOps.inc"
#include "../plugins/MatrixCwiseUnaryOps.inc"
#include "../plugins/MatrixCwiseBinaryOps.inc"
#ifdef EIGEN_MATRIXBASE_PLUGIN
#include EIGEN_MATRIXBASE_PLUGIN
#endif
#undef EIGEN_CURRENT_STORAGE_BASE_CLASS
#undef EIGEN_DOC_UNARY_ADDONS


  EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE Derived& operator=(const MatrixBase& other);
 
  // We cannot inherit here via Base::operator= since it is causing
  // trouble with MSVC.
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE Derived& operator=(const DenseBase<OtherDerived>& other);
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC constexpr Derived& operator=(const EigenBase<OtherDerived>& other);
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC constexpr Derived& operator=(const ReturnByValue<OtherDerived>& other);
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator+=(const MatrixBase<OtherDerived>& other);
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator-=(const MatrixBase<OtherDerived>& other);
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived> operator*(const MatrixBase<OtherDerived>& other) const;
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived, LazyProduct> lazyProduct(
      const MatrixBase<OtherDerived>& other) const;
 
  template <typename OtherDerived>
  Derived& operator*=(const EigenBase<OtherDerived>& other);
 
  template <typename OtherDerived>
  void applyOnTheLeft(const EigenBase<OtherDerived>& other);
 
  template <typename OtherDerived>
  void applyOnTheRight(const EigenBase<OtherDerived>& other);
 
  template <typename DiagonalDerived>
  EIGEN_DEVICE_FUNC const Product<Derived, DiagonalDerived, LazyProduct> operator*(
      const DiagonalBase<DiagonalDerived>& diagonal) const;
 
  template <typename SkewDerived>
  EIGEN_DEVICE_FUNC const Product<Derived, SkewDerived, LazyProduct> operator*(
      const SkewSymmetricBase<SkewDerived>& skew) const;
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC constexpr typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
                                                            typename internal::traits<OtherDerived>::Scalar>::ReturnType
  dot(const MatrixBase<OtherDerived>& other) const;
 
  EIGEN_DEVICE_FUNC constexpr RealScalar squaredNorm() const;
  EIGEN_DEVICE_FUNC RealScalar norm() const;
  RealScalar stableNorm() const;
  RealScalar blueNorm() const;
  RealScalar hypotNorm() const;
  EIGEN_DEVICE_FUNC const PlainObject normalized() const;
  EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
  EIGEN_DEVICE_FUNC void normalize();
  EIGEN_DEVICE_FUNC void stableNormalize();
 
  EIGEN_DEVICE_FUNC constexpr const AdjointReturnType adjoint() const;
  EIGEN_DEVICE_FUNC void adjointInPlace();
 
  using DiagonalReturnType = Diagonal<Derived>;
  EIGEN_DEVICE_FUNC constexpr DiagonalReturnType diagonal();
 
  using ConstDiagonalReturnType = Diagonal<const Derived>;
  EIGEN_DEVICE_FUNC constexpr const ConstDiagonalReturnType diagonal() const;
 
  template <int Index>
  EIGEN_DEVICE_FUNC constexpr Diagonal<Derived, Index> diagonal();
 
  template <int Index>
  EIGEN_DEVICE_FUNC constexpr const Diagonal<const Derived, Index> diagonal() const;
 
  EIGEN_DEVICE_FUNC constexpr Diagonal<Derived, DynamicIndex> diagonal(Index index);
  EIGEN_DEVICE_FUNC constexpr const Diagonal<const Derived, DynamicIndex> diagonal(Index index) const;
 
  template <unsigned int Mode>
  struct TriangularViewReturnType {
    using Type = TriangularView<Derived, Mode>;
  };
  template <unsigned int Mode>
  struct ConstTriangularViewReturnType {
    using Type = const TriangularView<const Derived, Mode>;
  };
 
  template <unsigned int Mode>
  EIGEN_DEVICE_FUNC constexpr typename TriangularViewReturnType<Mode>::Type triangularView();
  template <unsigned int Mode>
  EIGEN_DEVICE_FUNC constexpr typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
 
  template <unsigned int UpLo>
  struct SelfAdjointViewReturnType {
    using Type = SelfAdjointView<Derived, UpLo>;
  };
  template <unsigned int UpLo>
  struct ConstSelfAdjointViewReturnType {
    using Type = const SelfAdjointView<const Derived, UpLo>;
  };
 
  template <unsigned int UpLo>
  EIGEN_DEVICE_FUNC constexpr typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
  template <unsigned int UpLo>
  EIGEN_DEVICE_FUNC constexpr typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
 
  const SparseView<Derived> sparseView(
      const Scalar& m_reference = Scalar(0),
      const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
  EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
  EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
  EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
  EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
  EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
  EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
  EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
  EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
 
  EIGEN_DEVICE_FUNC constexpr const DiagonalWrapper<const Derived> asDiagonal() const;
  const PermutationWrapper<const Derived> asPermutation() const;
  EIGEN_DEVICE_FUNC constexpr const SkewSymmetricWrapper<const Derived> asSkewSymmetric() const;
 
  EIGEN_DEVICE_FUNC Derived& setIdentity();
  EIGEN_DEVICE_FUNC Derived& setIdentity(Index rows, Index cols);
  EIGEN_DEVICE_FUNC Derived& setUnit(Index i);
  EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i);
 
  bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
  bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
  bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
  bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
  bool isSkewSymmetric(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
  template <typename OtherDerived>
  bool isOrthogonal(const MatrixBase<OtherDerived>& other,
                    const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
  bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
  /* diagonalView */
  template <int DiagIndex_ = 0>
  EIGEN_DEVICE_FUNC constexpr DiagonalWrapper<Diagonal<Derived, DiagIndex_>> diagonalView();
 
  template <int DiagIndex_ = 0>
  EIGEN_DEVICE_FUNC constexpr DiagonalWrapper<Diagonal<const Derived, DiagIndex_>> diagonalView() const;
 
  EIGEN_DEVICE_FUNC constexpr DiagonalWrapper<Diagonal<Derived, DynamicIndex>> diagonalView(Index index);
 
  EIGEN_DEVICE_FUNC constexpr DiagonalWrapper<Diagonal<const Derived, DynamicIndex>> diagonalView(Index index) const;

  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const {
    return (this->rows() == other.rows()) && (this->cols() == other.cols()) && cwiseEqual(other).all();
  }

  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const {
    return !(*this == other);
  }
 
  NoAlias<Derived, Eigen::MatrixBase> EIGEN_DEVICE_FUNC noalias();
 
  // TODO forceAlignedAccess is temporarily disabled
  // Need to find a nicer workaround.
  constexpr const Derived& forceAlignedAccess() const { return derived(); }
  constexpr Derived& forceAlignedAccess() { return derived(); }
  template <bool Enable>
  constexpr const Derived& forceAlignedAccessIf() const {
    return derived();
  }
  template <bool Enable>
  constexpr Derived& forceAlignedAccessIf() {
    return derived();
  }
 
  EIGEN_DEVICE_FUNC Scalar trace() const;
 
  template <int p>
  EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
 
  EIGEN_DEVICE_FUNC constexpr MatrixBase<Derived>& matrix() { return *this; }
  EIGEN_DEVICE_FUNC constexpr const MatrixBase<Derived>& matrix() const { return *this; }

  EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() {
    return ArrayWrapper<Derived>(derived());
  }

  EIGEN_DEVICE_FUNC constexpr EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const {
    return ArrayWrapper<const Derived>(derived());
  }

 
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline FullPivLU<PlainObject, PermutationIndex> fullPivLu() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline PartialPivLU<PlainObject, PermutationIndex> partialPivLu() const;
 
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline PartialPivLU<PlainObject, PermutationIndex> lu() const;
 
  EIGEN_DEVICE_FUNC inline Inverse<Derived> inverse() const;
 
  template <typename ResultType>
  inline void computeInverseAndDetWithCheck(
      ResultType& inverse, typename ResultType::Scalar& determinant, bool& invertible,
      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const;
 
  template <typename ResultType>
  inline void computeInverseWithCheck(
      ResultType& inverse, bool& invertible,
      const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const;
 
  EIGEN_DEVICE_FUNC Scalar determinant() const;

 
  inline LLT<PlainObject> llt() const;
  inline LDLT<PlainObject> ldlt() const;
  inline BunchKaufman<PlainObject> bunchKaufman() const;

 
  inline HouseholderQR<PlainObject> householderQr() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline ColPivHouseholderQR<PlainObject, PermutationIndex> colPivHouseholderQr() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline FullPivHouseholderQR<PlainObject, PermutationIndex> fullPivHouseholderQr() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline RandColPivHouseholderQR<PlainObject, PermutationIndex> randColPivHouseholderQr() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline CompleteOrthogonalDecomposition<PlainObject, PermutationIndex> completeOrthogonalDecomposition() const;
  template <typename PermutationIndex = DefaultPermutationIndex>
  inline RandCompleteOrthogonalDecomposition<PlainObject, PermutationIndex> randCompleteOrthogonalDecomposition() const;

 
  inline EigenvaluesReturnType eigenvalues() const;
  inline RealScalar operatorNorm() const;

 
  template <int Options = 0>
  inline JacobiSVD<PlainObject, Options> jacobiSvd() const;
  template <int Options = 0>
  EIGEN_DEPRECATED_WITH_REASON("Options should be specified using method's template parameter.")
  inline JacobiSVD<PlainObject, Options> jacobiSvd(unsigned int computationOptions) const;
 
  template <int Options = 0>
  inline BDCSVD<PlainObject, Options> bdcSvd() const;
  template <int Options = 0>
  EIGEN_DEPRECATED_WITH_REASON("Options should be specified using method's template parameter.")
  inline BDCSVD<PlainObject, Options> bdcSvd(unsigned int computationOptions) const;

 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline typename internal::cross_impl<Derived, OtherDerived>::return_type cross(
      const MatrixBase<OtherDerived>& other) const;
 
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
 
  EIGEN_DEVICE_FUNC inline PlainObject unitOrthogonal(void) const;
 
  EIGEN_DEPRECATED_WITH_REASON("Use .canonicalEulerAngles() instead.")
  EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> eulerAngles(Index a0, Index a1, Index a2) const;
 
  EIGEN_DEVICE_FUNC inline Matrix<Scalar, 3, 1> canonicalEulerAngles(Index a0, Index a1, Index a2) const;
 
  enum {
    HomogeneousReturnTypeDirection =
        ColsAtCompileTime == 1 && RowsAtCompileTime == 1
            ? ((internal::traits<Derived>::Flags & RowMajorBit) == RowMajorBit ? Horizontal : Vertical)
        : ColsAtCompileTime == 1 ? Vertical
                                 : Horizontal
  };
  using HomogeneousReturnType = Homogeneous<Derived, HomogeneousReturnTypeDirection>;
  EIGEN_DEVICE_FUNC inline HomogeneousReturnType homogeneous() const;
 
  enum { SizeMinusOne = SizeAtCompileTime == Dynamic ? Dynamic : SizeAtCompileTime - 1 };
  using ConstStartMinusOne = Block<const Derived, internal::traits<Derived>::ColsAtCompileTime == 1 ? SizeMinusOne : 1,
                                   internal::traits<Derived>::ColsAtCompileTime == 1 ? 1 : SizeMinusOne>;
  using HNormalizedReturnType = EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne, Scalar,
                                                                       internal::scalar_quotient_op);
  EIGEN_DEVICE_FUNC inline const HNormalizedReturnType hnormalized() const;

 
  EIGEN_DEVICE_FUNC void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
  template <typename EssentialPart>
  EIGEN_DEVICE_FUNC void makeHouseholder(EssentialPart& essential, Scalar& tau, RealScalar& beta) const;
  template <typename EssentialPart>
  EIGEN_DEVICE_FUNC void applyHouseholderOnTheLeft(const EssentialPart& essential, const Scalar& tau,
                                                   Scalar* workspace);
  template <typename EssentialPart>
  EIGEN_DEVICE_FUNC void applyHouseholderOnTheRight(const EssentialPart& essential, const Scalar& tau,
                                                    Scalar* workspace);

 
  template <typename OtherScalar>
  EIGEN_DEVICE_FUNC void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
  template <typename OtherScalar>
  EIGEN_DEVICE_FUNC void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);

 
  template <typename OtherDerived>
  EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
  cwiseProduct(const SparseMatrixBase<OtherDerived>& other) const {
    return other.cwiseProduct(derived());
  }

 
  using StemFunction = typename internal::stem_function<Scalar>::type;
#define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description)                                                \
                                                \
  const ReturnType<Derived> Name() const;
#define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument)                                    \
                                                \
  const ReturnType<Derived> Name(Argument) const;
 
  EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
  const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic tangent)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
  EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
  EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
  EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
  EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const internal::make_complex_t<Scalar>& p)
 
 protected:
  EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)
  EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase)
 
 private:
  EIGEN_DEVICE_FUNC explicit MatrixBase(int);
  EIGEN_DEVICE_FUNC MatrixBase(int, int);
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
 
 protected:
  // mixing arrays and matrices is not legal
  template <typename OtherDerived>
  Derived& operator+=(const ArrayBase<OtherDerived>&) {
    EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
                        YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
    return *this;
  }
  // mixing arrays and matrices is not legal
  template <typename OtherDerived>
  Derived& operator-=(const ArrayBase<OtherDerived>&) {
    EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar)) == -1,
                        YOU_CANNOT_MIX_ARRAYS_AND_MATRICES);
    return *this;
  }
};
 
/***************************************************************************
 * Implementation of matrix base methods
 ***************************************************************************/

 * Output: \verbinclude MatrixBase_applyOnTheRight.out
 */
template <typename Derived>
template <typename OtherDerived>
inline Derived& MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived>& other) {
  other.derived().applyThisOnTheRight(derived());
  return derived();
}

 * Output: \verbinclude MatrixBase_applyOnTheRight.out
 */
template <typename Derived>
template <typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived>& other) {
  other.derived().applyThisOnTheRight(derived());
}

 * Output: \verbinclude MatrixBase_applyOnTheLeft.out
 */
template <typename Derived>
template <typename OtherDerived>
inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived>& other) {
  other.derived().applyThisOnTheLeft(derived());
}
 
}  // end namespace Eigen
 
#endif  // EIGEN_MATRIXBASE_H