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 
84     typedef typename Base::CoeffReturnType CoeffReturnType;
85     typedef typename Base::ConstTransposeReturnType ConstTransposeReturnType;
86     typedef typename Base::RowXpr RowXpr;
87     typedef typename Base::ColXpr ColXpr;
88 #endif // not EIGEN_PARSED_BY_DOXYGEN
89 
90 
91 
92 #ifndef EIGEN_PARSED_BY_DOXYGEN
93     /** type of the equivalent square matrix */
94     typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
95                           EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
96 #endif // not EIGEN_PARSED_BY_DOXYGEN
97 
98     /** \returns the size of the main diagonal, which is min(rows(),cols()).
99       * \sa rows(), cols(), SizeAtCompileTime. */
100     EIGEN_DEVICE_FUNC
diagonalSize()101     inline Index diagonalSize() const { return (numext::mini)(rows(),cols()); }
102 
103     typedef typename Base::PlainObject PlainObject;
104 
105 #ifndef EIGEN_PARSED_BY_DOXYGEN
106     /** \internal Represents a matrix with all coefficients equal to one another*/
107     typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,PlainObject> ConstantReturnType;
108     /** \internal the return type of MatrixBase::adjoint() */
109     typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
110                         CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
111                         ConstTransposeReturnType
112                      >::type AdjointReturnType;
113     /** \internal Return type of eigenvalues() */
114     typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
115     /** \internal the return type of identity */
116     typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,PlainObject> IdentityReturnType;
117     /** \internal the return type of unit vectors */
118     typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
119                   internal::traits<Derived>::RowsAtCompileTime,
120                   internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
121 #endif // not EIGEN_PARSED_BY_DOXYGEN
122 
123 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
124 #define EIGEN_DOC_UNARY_ADDONS(X,Y)
125 #   include "../plugins/CommonCwiseUnaryOps.h"
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 #ifdef __CUDACC__
164     template<typename OtherDerived>
165     EIGEN_DEVICE_FUNC
166     const Product<Derived,OtherDerived,LazyProduct>
167     operator*(const MatrixBase<OtherDerived> &other) const
168     { return this->lazyProduct(other); }
169 #else
170 
171     template<typename OtherDerived>
172     const Product<Derived,OtherDerived>
173     operator*(const MatrixBase<OtherDerived> &other) const;
174 
175 #endif
176 
177     template<typename OtherDerived>
178     EIGEN_DEVICE_FUNC
179     const Product<Derived,OtherDerived,LazyProduct>
180     lazyProduct(const MatrixBase<OtherDerived> &other) const;
181 
182     template<typename OtherDerived>
183     Derived& operator*=(const EigenBase<OtherDerived>& other);
184 
185     template<typename OtherDerived>
186     void applyOnTheLeft(const EigenBase<OtherDerived>& other);
187 
188     template<typename OtherDerived>
189     void applyOnTheRight(const EigenBase<OtherDerived>& other);
190 
191     template<typename DiagonalDerived>
192     EIGEN_DEVICE_FUNC
193     const Product<Derived, DiagonalDerived, LazyProduct>
194     operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
195 
196     template<typename OtherDerived>
197     EIGEN_DEVICE_FUNC
198     typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
199     dot(const MatrixBase<OtherDerived>& other) const;
200 
201     EIGEN_DEVICE_FUNC RealScalar squaredNorm() const;
202     EIGEN_DEVICE_FUNC RealScalar norm() const;
203     RealScalar stableNorm() const;
204     RealScalar blueNorm() const;
205     RealScalar hypotNorm() const;
206     EIGEN_DEVICE_FUNC const PlainObject normalized() const;
207     EIGEN_DEVICE_FUNC const PlainObject stableNormalized() const;
208     EIGEN_DEVICE_FUNC void normalize();
209     EIGEN_DEVICE_FUNC void stableNormalize();
210 
211     EIGEN_DEVICE_FUNC const AdjointReturnType adjoint() const;
212     EIGEN_DEVICE_FUNC void adjointInPlace();
213 
214     typedef Diagonal<Derived> DiagonalReturnType;
215     EIGEN_DEVICE_FUNC
216     DiagonalReturnType diagonal();
217 
218     typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
219     EIGEN_DEVICE_FUNC
220     ConstDiagonalReturnType diagonal() const;
221 
222     template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
223     template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
224 
225     template<int Index>
226     EIGEN_DEVICE_FUNC
227     typename DiagonalIndexReturnType<Index>::Type diagonal();
228 
229     template<int Index>
230     EIGEN_DEVICE_FUNC
231     typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
232 
233     typedef Diagonal<Derived,DynamicIndex> DiagonalDynamicIndexReturnType;
234     typedef typename internal::add_const<Diagonal<const Derived,DynamicIndex> >::type ConstDiagonalDynamicIndexReturnType;
235 
236     EIGEN_DEVICE_FUNC
237     DiagonalDynamicIndexReturnType diagonal(Index index);
238     EIGEN_DEVICE_FUNC
239     ConstDiagonalDynamicIndexReturnType diagonal(Index index) const;
240 
241     template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
242     template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
243 
244     template<unsigned int Mode>
245     EIGEN_DEVICE_FUNC
246     typename TriangularViewReturnType<Mode>::Type triangularView();
247     template<unsigned int Mode>
248     EIGEN_DEVICE_FUNC
249     typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
250 
251     template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
252     template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
253 
254     template<unsigned int UpLo>
255     EIGEN_DEVICE_FUNC
256     typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
257     template<unsigned int UpLo>
258     EIGEN_DEVICE_FUNC
259     typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
260 
261     const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
262                                          const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
263     EIGEN_DEVICE_FUNC static const IdentityReturnType Identity();
264     EIGEN_DEVICE_FUNC static const IdentityReturnType Identity(Index rows, Index cols);
265     EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index size, Index i);
266     EIGEN_DEVICE_FUNC static const BasisReturnType Unit(Index i);
267     EIGEN_DEVICE_FUNC static const BasisReturnType UnitX();
268     EIGEN_DEVICE_FUNC static const BasisReturnType UnitY();
269     EIGEN_DEVICE_FUNC static const BasisReturnType UnitZ();
270     EIGEN_DEVICE_FUNC static const BasisReturnType UnitW();
271 
272     EIGEN_DEVICE_FUNC
273     const DiagonalWrapper<const Derived> asDiagonal() const;
274     const PermutationWrapper<const Derived> asPermutation() const;
275 
276     EIGEN_DEVICE_FUNC
277     Derived& setIdentity();
278     EIGEN_DEVICE_FUNC
279     Derived& setIdentity(Index rows, Index cols);
280 
281     bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
282     bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
283 
284     bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
285     bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
286 
287     template<typename OtherDerived>
288     bool isOrthogonal(const MatrixBase<OtherDerived>& other,
289                       const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
290     bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
291 
292     /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
293       * \warning When using floating point scalar values you probably should rather use a
294       *          fuzzy comparison such as isApprox()
295       * \sa isApprox(), operator!= */
296     template<typename OtherDerived>
297     EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const
298     { return cwiseEqual(other).all(); }
299 
300     /** \returns true if at least one pair of coefficients of \c *this and \a other are not exactly equal to each other.
301       * \warning When using floating point scalar values you probably should rather use a
302       *          fuzzy comparison such as isApprox()
303       * \sa isApprox(), operator== */
304     template<typename OtherDerived>
305     EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const
306     { return cwiseNotEqual(other).any(); }
307 
308     NoAlias<Derived,Eigen::MatrixBase > noalias();
309 
310     // TODO forceAlignedAccess is temporarily disabled
311     // Need to find a nicer workaround.
forceAlignedAccess()312     inline const Derived& forceAlignedAccess() const { return derived(); }
forceAlignedAccess()313     inline Derived& forceAlignedAccess() { return derived(); }
forceAlignedAccessIf()314     template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }
forceAlignedAccessIf()315     template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }
316 
317     EIGEN_DEVICE_FUNC Scalar trace() const;
318 
319     template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
320 
matrix()321     EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
matrix()322     EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
323 
324     /** \returns an \link Eigen::ArrayBase Array \endlink expression of this matrix
325       * \sa ArrayBase::matrix() */
array()326     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
327     /** \returns a const \link Eigen::ArrayBase Array \endlink expression of this matrix
328       * \sa ArrayBase::matrix() */
array()329     EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }
330 
331 /////////// LU module ///////////
332 
333     inline const FullPivLU<PlainObject> fullPivLu() const;
334     inline const PartialPivLU<PlainObject> partialPivLu() const;
335 
336     inline const PartialPivLU<PlainObject> lu() const;
337 
338     inline const Inverse<Derived> inverse() const;
339 
340     template<typename ResultType>
341     inline void computeInverseAndDetWithCheck(
342       ResultType& inverse,
343       typename ResultType::Scalar& determinant,
344       bool& invertible,
345       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
346     ) const;
347     template<typename ResultType>
348     inline void computeInverseWithCheck(
349       ResultType& inverse,
350       bool& invertible,
351       const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
352     ) const;
353     Scalar determinant() const;
354 
355 /////////// Cholesky module ///////////
356 
357     inline const LLT<PlainObject>  llt() const;
358     inline const LDLT<PlainObject> ldlt() const;
359 
360 /////////// QR module ///////////
361 
362     inline const HouseholderQR<PlainObject> householderQr() const;
363     inline const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
364     inline const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
365     inline const CompleteOrthogonalDecomposition<PlainObject> completeOrthogonalDecomposition() const;
366 
367 /////////// Eigenvalues module ///////////
368 
369     inline EigenvaluesReturnType eigenvalues() const;
370     inline RealScalar operatorNorm() const;
371 
372 /////////// SVD module ///////////
373 
374     inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
375     inline BDCSVD<PlainObject>    bdcSvd(unsigned int computationOptions = 0) const;
376 
377 /////////// Geometry module ///////////
378 
379     #ifndef EIGEN_PARSED_BY_DOXYGEN
380     /// \internal helper struct to form the return type of the cross product
381     template<typename OtherDerived> struct cross_product_return_type {
382       typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
383       typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
384     };
385     #endif // EIGEN_PARSED_BY_DOXYGEN
386     template<typename OtherDerived>
387     EIGEN_DEVICE_FUNC
388 #ifndef EIGEN_PARSED_BY_DOXYGEN
389     inline typename cross_product_return_type<OtherDerived>::type
390 #else
391     inline PlainObject
392 #endif
393     cross(const MatrixBase<OtherDerived>& other) const;
394 
395     template<typename OtherDerived>
396     EIGEN_DEVICE_FUNC
397     inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
398 
399     EIGEN_DEVICE_FUNC
400     inline PlainObject unitOrthogonal(void) const;
401 
402     EIGEN_DEVICE_FUNC
403     inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
404 
405     // put this as separate enum value to work around possible GCC 4.3 bug (?)
406     enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
407                                           : ColsAtCompileTime==1 ? Vertical : Horizontal };
408     typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
409     EIGEN_DEVICE_FUNC
410     inline HomogeneousReturnType homogeneous() const;
411 
412     enum {
413       SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
414     };
415     typedef Block<const Derived,
416                   internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
417                   internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
418     typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
419     EIGEN_DEVICE_FUNC
420     inline const HNormalizedReturnType hnormalized() const;
421 
422 ////////// Householder module ///////////
423 
424     void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
425     template<typename EssentialPart>
426     void makeHouseholder(EssentialPart& essential,
427                          Scalar& tau, RealScalar& beta) const;
428     template<typename EssentialPart>
429     void applyHouseholderOnTheLeft(const EssentialPart& essential,
430                                    const Scalar& tau,
431                                    Scalar* workspace);
432     template<typename EssentialPart>
433     void applyHouseholderOnTheRight(const EssentialPart& essential,
434                                     const Scalar& tau,
435                                     Scalar* workspace);
436 
437 ///////// Jacobi module /////////
438 
439     template<typename OtherScalar>
440     void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
441     template<typename OtherScalar>
442     void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
443 
444 ///////// SparseCore module /////////
445 
446     template<typename OtherDerived>
447     EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
cwiseProduct(const SparseMatrixBase<OtherDerived> & other)448     cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
449     {
450       return other.cwiseProduct(derived());
451     }
452 
453 ///////// MatrixFunctions module /////////
454 
455     typedef typename internal::stem_function<Scalar>::type StemFunction;
456     const MatrixExponentialReturnValue<Derived> exp() const;
457     const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
458     const MatrixFunctionReturnValue<Derived> cosh() const;
459     const MatrixFunctionReturnValue<Derived> sinh() const;
460     const MatrixFunctionReturnValue<Derived> cos() const;
461     const MatrixFunctionReturnValue<Derived> sin() const;
462     const MatrixSquareRootReturnValue<Derived> sqrt() const;
463     const MatrixLogarithmReturnValue<Derived> log() const;
464     const MatrixPowerReturnValue<Derived> pow(const RealScalar& p) const;
465     const MatrixComplexPowerReturnValue<Derived> pow(const std::complex<RealScalar>& p) const;
466 
467   protected:
MatrixBase()468     EIGEN_DEVICE_FUNC MatrixBase() : Base() {}
469 
470   private:
471     EIGEN_DEVICE_FUNC explicit MatrixBase(int);
472     EIGEN_DEVICE_FUNC MatrixBase(int,int);
473     template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
474   protected:
475     // mixing arrays and matrices is not legal
476     template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
477     {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
478     // mixing arrays and matrices is not legal
479     template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
480     {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
481 };
482 
483 
484 /***************************************************************************
485 * Implementation of matrix base methods
486 ***************************************************************************/
487 
488 /** replaces \c *this by \c *this * \a other.
489   *
490   * \returns a reference to \c *this
491   *
492   * Example: \include MatrixBase_applyOnTheRight.cpp
493   * Output: \verbinclude MatrixBase_applyOnTheRight.out
494   */
495 template<typename Derived>
496 template<typename OtherDerived>
497 inline Derived&
498 MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived> &other)
499 {
500   other.derived().applyThisOnTheRight(derived());
501   return derived();
502 }
503 
504 /** replaces \c *this by \c *this * \a other. It is equivalent to MatrixBase::operator*=().
505   *
506   * Example: \include MatrixBase_applyOnTheRight.cpp
507   * Output: \verbinclude MatrixBase_applyOnTheRight.out
508   */
509 template<typename Derived>
510 template<typename OtherDerived>
applyOnTheRight(const EigenBase<OtherDerived> & other)511 inline void MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived> &other)
512 {
513   other.derived().applyThisOnTheRight(derived());
514 }
515 
516 /** replaces \c *this by \a other * \c *this.
517   *
518   * Example: \include MatrixBase_applyOnTheLeft.cpp
519   * Output: \verbinclude MatrixBase_applyOnTheLeft.out
520   */
521 template<typename Derived>
522 template<typename OtherDerived>
applyOnTheLeft(const EigenBase<OtherDerived> & other)523 inline void MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived> &other)
524 {
525   other.derived().applyThisOnTheLeft(derived());
526 }
527 
528 } // end namespace Eigen
529 
530 #endif // EIGEN_MATRIXBASE_H
531