cart-elc

Source code for CART-ELC
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MatrixBase.h (23856B)


      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
      5 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 #ifndef EIGEN_MATRIXBASE_H
     12 #define EIGEN_MATRIXBASE_H
     13 
     14 namespace Eigen {
     15 
     16 /** \class MatrixBase
     17   * \ingroup Core_Module
     18   *
     19   * \brief Base class for all dense matrices, vectors, and expressions
     20   *
     21   * This class is the base that is inherited by all matrix, vector, and related expression
     22   * types. Most of the Eigen API is contained in this class, and its base classes. Other important
     23   * classes for the Eigen API are Matrix, and VectorwiseOp.
     24   *
     25   * Note that some methods are defined in other modules such as the \ref LU_Module LU module
     26   * for all functions related to matrix inversions.
     27   *
     28   * \tparam Derived is the derived type, e.g. a matrix type, or an expression, etc.
     29   *
     30   * When writing a function taking Eigen objects as argument, if you want your function
     31   * to take as argument any matrix, vector, or expression, just let it take a
     32   * MatrixBase argument. As an example, here is a function printFirstRow which, given
     33   * a matrix, vector, or expression \a x, prints the first row of \a x.
     34   *
     35   * \code
     36     template<typename Derived>
     37     void printFirstRow(const Eigen::MatrixBase<Derived>& x)
     38     {
     39       cout << x.row(0) << endl;
     40     }
     41   * \endcode
     42   *
     43   * This class can be extended with the help of the plugin mechanism described on the page
     44   * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
     45   *
     46   * \sa \blank \ref TopicClassHierarchy
     47   */
     48 template<typename Derived> class MatrixBase
     49   : public DenseBase<Derived>
     50 {
     51   public:
     52 #ifndef EIGEN_PARSED_BY_DOXYGEN
     53     typedef MatrixBase StorageBaseType;
     54     typedef typename internal::traits<Derived>::StorageKind StorageKind;
     55     typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
     56     typedef typename internal::traits<Derived>::Scalar Scalar;
     57     typedef typename internal::packet_traits<Scalar>::type PacketScalar;
     58     typedef typename NumTraits<Scalar>::Real RealScalar;
     59 
     60     typedef DenseBase<Derived> Base;
     61     using Base::RowsAtCompileTime;
     62     using Base::ColsAtCompileTime;
     63     using Base::SizeAtCompileTime;
     64     using Base::MaxRowsAtCompileTime;
     65     using Base::MaxColsAtCompileTime;
     66     using Base::MaxSizeAtCompileTime;
     67     using Base::IsVectorAtCompileTime;
     68     using Base::Flags;
     69 
     70     using Base::derived;
     71     using Base::const_cast_derived;
     72     using Base::rows;
     73     using Base::cols;
     74     using Base::size;
     75     using Base::coeff;
     76     using Base::coeffRef;
     77     using Base::lazyAssign;
     78     using Base::eval;
     79     using Base::operator-;
     80     using Base::operator+=;
     81     using Base::operator-=;
     82     using Base::operator*=;
     83     using Base::operator/=;
     84 
     85     typedef typename Base::CoeffReturnType CoeffReturnType;
     86     typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
     87     typedef typename Base::RowXpr RowXpr;
     88     typedef typename Base::ColXpr ColXpr;
     89 #endif // not EIGEN_PARSED_BY_DOXYGEN
     90 
     91 
     92 
     93 #ifndef EIGEN_PARSED_BY_DOXYGEN
     94     /** type of the equivalent square matrix */
     95     typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
     96                           EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
     97 #endif // not EIGEN_PARSED_BY_DOXYGEN
     98 
     99     /** \returns the size of the main diagonal, which is min(rows(),cols()).
    100       * \sa rows(), cols(), SizeAtCompileTime. */
    101     EIGEN_DEVICE_FUNC
    102     inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); }
    103 
    104     typedef typename Base::PlainObject PlainObject;
    105 
    106 #ifndef EIGEN_PARSED_BY_DOXYGEN
    107     /** \internal Represents a matrix with all coefficients equal to one another*/
    108     typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
    109     /** \internal the return type of MatrixBase::adjoint() */
    110     typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
    111                         CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
    112                         ConstTransposeReturnType
    113                      >::type AdjointReturnType;
    114     /** \internal Return type of eigenvalues() */
    115     typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
    116     /** \internal the return type of identity */
    117     typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,PlainObject> IdentityReturnType;
    118     /** \internal the return type of unit vectors */
    119     typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
    120                   internal::traits<Derived>::RowsAtCompileTime,
    121                   internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
    122 #endif // not EIGEN_PARSED_BY_DOXYGEN
    123 
    124 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
    125 #define EIGEN_DOC_UNARY_ADDONS(X,Y)
    126 #   include "../plugins/CommonCwiseBinaryOps.h"
    127 #   include "../plugins/MatrixCwiseUnaryOps.h"
    128 #   include "../plugins/MatrixCwiseBinaryOps.h"
    129 #   ifdef EIGEN_MATRIXBASE_PLUGIN
    130 #     include EIGEN_MATRIXBASE_PLUGIN
    131 #   endif
    132 #undef EIGEN_CURRENT_STORAGE_BASE_CLASS
    133 #undef EIGEN_DOC_UNARY_ADDONS
    134 
    135     /** Special case of the template operator=, in order to prevent the compiler
    136       * from generating a default operator= (issue hit with g++ 4.1)
    137       */
    138     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    139     Derived& operator=(const MatrixBase& other);
    140 
    141     // We cannot inherit here via Base::operator= since it is causing
    142     // trouble with MSVC.
    143 
    144     template <typename OtherDerived>
    145     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    146     Derived& operator=(const DenseBase<OtherDerived>& other);
    147 
    148     template <typename OtherDerived>
    149     EIGEN_DEVICE_FUNC
    150     Derived& operator=(const EigenBase<OtherDerived>& other);
    151 
    152     template<typename OtherDerived>
    153     EIGEN_DEVICE_FUNC
    154     Derived& operator=(const ReturnByValue<OtherDerived>& other);
    155 
    156     template<typename OtherDerived>
    157     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    158     Derived& operator+=(const MatrixBase<OtherDerived>& other);
    159     template<typename OtherDerived>
    160     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
    161     Derived& operator-=(const MatrixBase<OtherDerived>& other);
    162 
    163     template<typename OtherDerived>
    164     EIGEN_DEVICE_FUNC
    165     const Product<Derived,OtherDerived>
    166     operator*(const MatrixBase<OtherDerived> &other) const;
    167 
    168     template<typename OtherDerived>
    169     EIGEN_DEVICE_FUNC
    170     const Product<Derived,OtherDerived,LazyProduct>
    171     lazyProduct(const MatrixBase<OtherDerived> &other) const;
    172 
    173     template<typename OtherDerived>
    174     Derived& operator*=(const EigenBase<OtherDerived>& other);
    175 
    176     template<typename OtherDerived>
    177     void applyOnTheLeft(const EigenBase<OtherDerived>& other);
    178 
    179     template<typename OtherDerived>
    180     void applyOnTheRight(const EigenBase<OtherDerived>& other);
    181 
    182     template<typename DiagonalDerived>
    183     EIGEN_DEVICE_FUNC
    184     const Product<Derived, DiagonalDerived, LazyProduct>
    185     operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
    186 
    187     template<typename OtherDerived>
    188     EIGEN_DEVICE_FUNC
    189     typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
    190     dot(const MatrixBase<OtherDerived>& other) const;
    191 
    192     EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
    193     EIGEN_DEVICE_FUNC RealScalar norm() const;
    194     RealScalar stableNorm() const;
    195     RealScalar blueNorm() const;
    196     RealScalar hypotNorm() const;
    197     EIGEN_DEVICE_FUNC const PlainObject normalized() const;
    198     EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
    199     EIGEN_DEVICE_FUNC void normalize();
    200     EIGEN_DEVICE_FUNC void stableNormalize();
    201 
    202     EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
    203     EIGEN_DEVICE_FUNC void adjointInPlace();
    204 
    205     typedef Diagonal<Derived> DiagonalReturnType;
    206     EIGEN_DEVICE_FUNC
    207     DiagonalReturnType diagonal();
    208 
    209     typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
    210     EIGEN_DEVICE_FUNC
    211     ConstDiagonalReturnType diagonal() const;
    212 
    213     template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
    214     template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
    215 
    216     template<int Index>
    217     EIGEN_DEVICE_FUNC
    218     typename DiagonalIndexReturnType<Index>::Type diagonal();
    219 
    220     template<int Index>
    221     EIGEN_DEVICE_FUNC
    222     typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
    223 
    224     typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
    225     typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
    226 
    227     EIGEN_DEVICE_FUNC
    228     DiagonalDynamicIndexReturnType diagonal(Index index);
    229     EIGEN_DEVICE_FUNC
    230     ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
    231 
    232     template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
    233     template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
    234 
    235     template<unsigned int Mode>
    236     EIGEN_DEVICE_FUNC
    237     typename TriangularViewReturnType<Mode>::Type triangularView();
    238     template<unsigned int Mode>
    239     EIGEN_DEVICE_FUNC
    240     typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
    241 
    242     template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
    243     template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
    244 
    245     template<unsigned int UpLo>
    246     EIGEN_DEVICE_FUNC
    247     typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
    248     template<unsigned int UpLo>
    249     EIGEN_DEVICE_FUNC
    250     typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
    251 
    252     const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
    253                                          const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
    254     EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
    255     EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
    256     EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
    257     EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
    258     EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
    259     EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
    260     EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
    261     EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
    262 
    263     EIGEN_DEVICE_FUNC
    264     const DiagonalWrapper<const Derived> asDiagonal() const;
    265     const PermutationWrapper<const Derived> asPermutation() const;
    266 
    267     EIGEN_DEVICE_FUNC
    268     Derived& setIdentity();
    269     EIGEN_DEVICE_FUNC
    270     Derived& setIdentity(Index rows, Index cols);
    271     EIGEN_DEVICE_FUNC Derived& setUnit(Index i);
    272     EIGEN_DEVICE_FUNC Derived& setUnit(Index newSize, Index i);
    273 
    274     bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    275     bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    276 
    277     bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    278     bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    279 
    280     template<typename OtherDerived>
    281     bool isOrthogonal(const MatrixBase<OtherDerived>& other,
    282                       const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    283     bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
    284 
    285     /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
    286       * \warning When using floating point scalar values you probably should rather use a
    287       *          fuzzy comparison such as isApprox()
    288       * \sa isApprox(), operator!= */
    289     template<typename OtherDerived>
    290     EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const
    291     { return cwiseEqual(other).all(); }
    292 
    293     /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
    294       * \warning When using floating point scalar values you probably should rather use a
    295       *          fuzzy comparison such as isApprox()
    296       * \sa isApprox(), operator== */
    297     template<typename OtherDerived>
    298     EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const
    299     { return cwiseNotEqual(other).any(); }
    300 
    301     NoAlias<Derived,Eigen::MatrixBase > EIGEN_DEVICE_FUNC noalias();
    302 
    303     // TODO forceAlignedAccess is temporarily disabled
    304     // Need to find a nicer workaround.
    305     inline const Derived& forceAlignedAccess() const { return derived(); }
    306     inline Derived& forceAlignedAccess() { return derived(); }
    307     template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }
    308     template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }
    309 
    310     EIGEN_DEVICE_FUNC Scalar trace() const;
    311 
    312     template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
    313 
    314     EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
    315     EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
    316 
    317     /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
    318       * \sa ArrayBase::matrix() */
    319     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
    320     /** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix
    321       * \sa ArrayBase::matrix() */
    322     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }
    323 
    324 /////////// LU module ///////////
    325 
    326     inline const FullPivLU<PlainObject> fullPivLu() const;
    327     inline const PartialPivLU<PlainObject> partialPivLu() const;
    328 
    329     inline const PartialPivLU<PlainObject> lu() const;
    330 
    331     EIGEN_DEVICE_FUNC
    332     inline const Inverse<Derived> inverse() const;
    333 
    334     template<typename ResultType>
    335     inline void computeInverseAndDetWithCheck(
    336       ResultType& inverse,
    337       typename ResultType::Scalar& determinant,
    338       bool& invertible,
    339       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
    340     ) const;
    341 
    342     template<typename ResultType>
    343     inline void computeInverseWithCheck(
    344       ResultType& inverse,
    345       bool& invertible,
    346       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
    347     ) const;
    348 
    349     EIGEN_DEVICE_FUNC
    350     Scalar determinant() const;
    351 
    352 /////////// Cholesky module ///////////
    353 
    354     inline const LLT<PlainObject>  llt() const;
    355     inline const LDLT<PlainObject> ldlt() const;
    356 
    357 /////////// QR module ///////////
    358 
    359     inline const HouseholderQR<PlainObject> householderQr() const;
    360     inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
    361     inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
    362     inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;
    363 
    364 /////////// Eigenvalues module ///////////
    365 
    366     inline EigenvaluesReturnType eigenvalues() const;
    367     inline RealScalar operatorNorm() const;
    368 
    369 /////////// SVD module ///////////
    370 
    371     inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
    372     inline BDCSVD<PlainObject>    bdcSvd(unsigned int computationOptions = 0) const;
    373 
    374 /////////// Geometry module ///////////
    375 
    376     #ifndef EIGEN_PARSED_BY_DOXYGEN
    377     /// \internal helper struct to form the return type of the cross product
    378     template<typename OtherDerived> struct cross_product_return_type {
    379       typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
    380       typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
    381     };
    382     #endif // EIGEN_PARSED_BY_DOXYGEN
    383     template<typename OtherDerived>
    384     EIGEN_DEVICE_FUNC
    385 #ifndef EIGEN_PARSED_BY_DOXYGEN
    386     inline typename cross_product_return_type<OtherDerived>::type
    387 #else
    388     inline PlainObject
    389 #endif
    390     cross(const MatrixBase<OtherDerived>& other) const;
    391 
    392     template<typename OtherDerived>
    393     EIGEN_DEVICE_FUNC
    394     inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
    395 
    396     EIGEN_DEVICE_FUNC
    397     inline PlainObject unitOrthogonal(void) const;
    398 
    399     EIGEN_DEVICE_FUNC
    400     inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
    401 
    402     // put this as separate enum value to work around possible GCC 4.3 bug (?)
    403     enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
    404                                           : ColsAtCompileTime==1 ? Vertical : Horizontal };
    405     typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
    406     EIGEN_DEVICE_FUNC
    407     inline HomogeneousReturnType homogeneous() const;
    408 
    409     enum {
    410       SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
    411     };
    412     typedef Block<const Derived,
    413                   internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
    414                   internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
    415     typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
    416     EIGEN_DEVICE_FUNC
    417     inline const HNormalizedReturnType hnormalized() const;
    418 
    419 ////////// Householder module ///////////
    420 
    421     EIGEN_DEVICE_FUNC
    422     void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
    423     template<typename EssentialPart>
    424     EIGEN_DEVICE_FUNC
    425     void makeHouseholder(EssentialPart& essential,
    426                          Scalar& tau, RealScalar& beta) const;
    427     template<typename EssentialPart>
    428     EIGEN_DEVICE_FUNC
    429     void applyHouseholderOnTheLeft(const EssentialPart& essential,
    430                                    const Scalar& tau,
    431                                    Scalar* workspace);
    432     template<typename EssentialPart>
    433     EIGEN_DEVICE_FUNC
    434     void applyHouseholderOnTheRight(const EssentialPart& essential,
    435                                     const Scalar& tau,
    436                                     Scalar* workspace);
    437 
    438 ///////// Jacobi module /////////
    439 
    440     template<typename OtherScalar>
    441     EIGEN_DEVICE_FUNC
    442     void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
    443     template<typename OtherScalar>
    444     EIGEN_DEVICE_FUNC
    445     void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
    446 
    447 ///////// SparseCore module /////////
    448 
    449     template<typename OtherDerived>
    450     EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
    451     cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
    452     {
    453       return other.cwiseProduct(derived());
    454     }
    455 
    456 ///////// MatrixFunctions module /////////
    457 
    458     typedef typename internal::stem_function<Scalar>::type StemFunction;
    459 #define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
    460     /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
    461     const ReturnType<Derived> Name() const;
    462 #define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
    463     /** \returns an expression of the matrix Description of \c *this. \brief This function requires the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>. To compute the coefficient-wise Description use ArrayBase::##Name . */ \
    464     const ReturnType<Derived> Name(Argument) const;
    465 
    466     EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
    467     /** \brief Helper function for the <a href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module</a>.*/
    468     const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
    469     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
    470     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
    471 #if EIGEN_HAS_CXX11_MATH
    472     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, atanh, inverse hyperbolic cosine)
    473     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, acosh, inverse hyperbolic cosine)
    474     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, asinh, inverse hyperbolic sine)
    475 #endif
    476     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
    477     EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
    478     EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
    479     EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
    480     EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue,        pow, power to \c p, const RealScalar& p)
    481     EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p)
    482 
    483   protected:
    484     EIGEN_DEFAULT_COPY_CONSTRUCTOR(MatrixBase)
    485     EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(MatrixBase)
    486 
    487   private:
    488     EIGEN_DEVICE_FUNC explicit MatrixBase(int);
    489     EIGEN_DEVICE_FUNC MatrixBase(int,int);
    490     template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
    491   protected:
    492     // mixing arrays and matrices is not legal
    493     template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
    494     {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
    495     // mixing arrays and matrices is not legal
    496     template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
    497     {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
    498 };
    499 
    500 
    501 /***************************************************************************
    502 * Implementation of matrix base methods
    503 ***************************************************************************/
    504 
    505 /** replaces \c *this by \c *this * \a other.
    506   *
    507   * \returns a reference to \c *this
    508   *
    509   * Example: \include MatrixBase_applyOnTheRight.cpp
    510   * Output: \verbinclude MatrixBase_applyOnTheRight.out
    511   */
    512 template<typename Derived>
    513 template<typename OtherDerived>
    514 inline Derived&
    515 MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
    516 {
    517   other.derived().applyThisOnTheRight(derived());
    518   return derived();
    519 }
    520 
    521 /** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
    522   *
    523   * Example: \include MatrixBase_applyOnTheRight.cpp
    524   * Output: \verbinclude MatrixBase_applyOnTheRight.out
    525   */
    526 template<typename Derived>
    527 template<typename OtherDerived>
    528 inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
    529 {
    530   other.derived().applyThisOnTheRight(derived());
    531 }
    532 
    533 /** replaces \c *this by \a other * \c *this.
    534   *
    535   * Example: \include MatrixBase_applyOnTheLeft.cpp
    536   * Output: \verbinclude MatrixBase_applyOnTheLeft.out
    537   */
    538 template<typename Derived>
    539 template<typename OtherDerived>
    540 inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
    541 {
    542   other.derived().applyThisOnTheLeft(derived());
    543 }
    544 
    545 } // end namespace Eigen
    546 
    547 #endif // EIGEN_MATRIXBASE_H