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MatrixBase.h
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 
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>::Index Index;
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;
68  using Base::Flags;
69  using Base::CoeffReadCost;
70 
71  using Base::derived;
72  using Base::const_cast_derived;
73  using Base::rows;
74  using Base::cols;
75  using Base::size;
76  using Base::coeff;
77  using Base::coeffRef;
78  using Base::lazyAssign;
79  using Base::eval;
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 
95  typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
96  EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
97 #endif // not EIGEN_PARSED_BY_DOXYGEN
98 
101  inline Index diagonalSize() const { return (std::min)(rows(),cols()); }
110  internal::traits<Derived>::RowsAtCompileTime,
111  internal::traits<Derived>::ColsAtCompileTime,
112  AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor),
113  internal::traits<Derived>::MaxRowsAtCompileTime,
114  internal::traits<Derived>::MaxColsAtCompileTime
116 
117 #ifndef EIGEN_PARSED_BY_DOXYGEN
118 
119  typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
121  typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
124  >::type AdjointReturnType;
126  typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
128  typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>,Derived> IdentityReturnType;
131  internal::traits<Derived>::RowsAtCompileTime,
132  internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
133 #endif // not EIGEN_PARSED_BY_DOXYGEN
134 
135 #define EIGEN_CURRENT_STORAGE_BASE_CLASS Eigen::MatrixBase
136 # include "../plugins/CommonCwiseUnaryOps.h"
137 # include "../plugins/CommonCwiseBinaryOps.h"
138 # include "../plugins/MatrixCwiseUnaryOps.h"
139 # include "../plugins/MatrixCwiseBinaryOps.h"
140 # ifdef EIGEN_MATRIXBASE_PLUGIN
141 # include EIGEN_MATRIXBASE_PLUGIN
142 # endif
143 #undef EIGEN_CURRENT_STORAGE_BASE_CLASS
144 
148  Derived& operator=(const MatrixBase& other);
149 
150  // We cannot inherit here via Base::operator= since it is causing
151  // trouble with MSVC.
152 
153  template <typename OtherDerived>
154  Derived& operator=(const DenseBase<OtherDerived>& other);
155 
156  template <typename OtherDerived>
157  Derived& operator=(const EigenBase<OtherDerived>& other);
159  template<typename OtherDerived>
160  Derived& operator=(const ReturnByValue<OtherDerived>& other);
161 
162 #ifndef EIGEN_PARSED_BY_DOXYGEN
163  template<typename ProductDerived, typename Lhs, typename Rhs>
164  Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
165 
166  template<typename MatrixPower, typename Lhs, typename Rhs>
167  Derived& lazyAssign(const MatrixPowerProduct<MatrixPower, Lhs,Rhs>& other);
168 #endif // not EIGEN_PARSED_BY_DOXYGEN
169 
170  template<typename OtherDerived>
171  Derived& operator+=(const MatrixBase<OtherDerived>& other);
172  template<typename OtherDerived>
173  Derived& operator-=(const MatrixBase<OtherDerived>& other);
174 
175  template<typename OtherDerived>
177  operator*(const MatrixBase<OtherDerived> &other) const;
178 
179  template<typename OtherDerived>
181  lazyProduct(const MatrixBase<OtherDerived> &other) const;
182 
183  template<typename OtherDerived>
184  Derived& operator*=(const EigenBase<OtherDerived>& other);
185 
186  template<typename OtherDerived>
187  void applyOnTheLeft(const EigenBase<OtherDerived>& other);
188 
189  template<typename OtherDerived>
190  void applyOnTheRight(const EigenBase<OtherDerived>& other);
191 
192  template<typename DiagonalDerived>
193  const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
194  operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
195 
196  template<typename OtherDerived>
197  typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
198  dot(const MatrixBase<OtherDerived>& other) const;
199 
200  #ifdef EIGEN2_SUPPORT
201  template<typename OtherDerived>
202  Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
203  #endif
204 
205  RealScalar squaredNorm() const;
206  RealScalar norm() const;
207  RealScalar stableNorm() const;
208  RealScalar blueNorm() const;
209  RealScalar hypotNorm() const;
210  const PlainObject normalized() const;
211  void normalize();
212 
213  const AdjointReturnType adjoint() const;
214  void adjointInPlace();
215 
218  typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
220 
221  template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
222  template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
223 
224  template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
225  template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
226 
227  // Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
228  // On the other hand they confuse MSVC8...
229  #if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
230  typename MatrixBase::template DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
231  typename MatrixBase::template ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
232  #else
233  typename DiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index);
234  typename ConstDiagonalIndexReturnType<DynamicIndex>::Type diagonal(Index index) const;
235  #endif
236 
237  #ifdef EIGEN2_SUPPORT
238  template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
239  template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
240 
241  // huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
242  // of an integer constant. Solution: overload the part() method template wrt template parameters list.
243  template<template<typename T, int N> class U>
244  const DiagonalWrapper<ConstDiagonalReturnType> part() const
245  { return diagonal().asDiagonal(); }
246  #endif // EIGEN2_SUPPORT
247 
248  template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
249  template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
250 
251  template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
252  template<unsigned int Mode> typename ConstTriangularViewReturnType<Mode>::Type triangularView() const;
253 
254  template<unsigned int UpLo> struct SelfAdjointViewReturnType { typedef SelfAdjointView<Derived, UpLo> Type; };
255  template<unsigned int UpLo> struct ConstSelfAdjointViewReturnType { typedef const SelfAdjointView<const Derived, UpLo> Type; };
256 
257  template<unsigned int UpLo> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
258  template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
259 
260  const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
261  const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
262  static const IdentityReturnType Identity();
263  static const IdentityReturnType Identity(Index rows, Index cols);
264  static const BasisReturnType Unit(Index size, Index i);
265  static const BasisReturnType Unit(Index i);
266  static const BasisReturnType UnitX();
267  static const BasisReturnType UnitY();
268  static const BasisReturnType UnitZ();
269  static const BasisReturnType UnitW();
270 
271  const DiagonalWrapper<const Derived> asDiagonal() const;
272  const PermutationWrapper<const Derived> asPermutation() const;
273 
274  Derived& setIdentity();
275  Derived& setIdentity(Index rows, Index cols);
276 
277  bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
278  bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
279 
280  bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
281  bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
282 
283  template<typename OtherDerived>
284  bool isOrthogonal(const MatrixBase<OtherDerived>& other,
285  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
286  bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
287 
292  template<typename OtherDerived>
293  inline bool operator==(const MatrixBase<OtherDerived>& other) const
294  { return cwiseEqual(other).all(); }
295 
300  template<typename OtherDerived>
301  inline bool operator!=(const MatrixBase<OtherDerived>& other) const
302  { return cwiseNotEqual(other).any(); }
303 
305 
306  inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
308  template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
309  template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
310 
311  Scalar trace() const;
312 
314 
315  template<int p> RealScalar lpNorm() const;
316 
317  MatrixBase<Derived>& matrix() { return *this; }
318  const MatrixBase<Derived>& matrix() const { return *this; }
319 
322  ArrayWrapper<Derived> array() { return derived(); }
323  const ArrayWrapper<const Derived> array() const { return derived(); }
324 
326 
327  const FullPivLU<PlainObject> fullPivLu() const;
328  const PartialPivLU<PlainObject> partialPivLu() const;
329 
330  #if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
331  const LU<PlainObject> lu() const;
332  #endif
333 
334  #ifdef EIGEN2_SUPPORT
335  const LU<PlainObject> eigen2_lu() const;
336  #endif
337 
338  #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
339  const PartialPivLU<PlainObject> lu() const;
340  #endif
341 
342  #ifdef EIGEN2_SUPPORT
343  template<typename ResultType>
344  void computeInverse(MatrixBase<ResultType> *result) const {
345  *result = this->inverse();
346  }
347  #endif
348 
349  const internal::inverse_impl<Derived> inverse() const;
350  template<typename ResultType>
352  ResultType& inverse,
353  typename ResultType::Scalar& determinant,
354  bool& invertible,
355  const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
356  ) const;
357  template<typename ResultType>
359  ResultType& inverse,
360  bool& invertible,
361  const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
362  ) const;
363  Scalar determinant() const;
364 
366 
367  const LLT<PlainObject> llt() const;
368  const LDLT<PlainObject> ldlt() const;
369 
371 
372  const HouseholderQR<PlainObject> householderQr() const;
373  const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
374  const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
375 
376  #ifdef EIGEN2_SUPPORT
377  const QR<PlainObject> qr() const;
378  #endif
379 
380  EigenvaluesReturnType eigenvalues() const;
381  RealScalar operatorNorm() const;
382 
384 
385  JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
386 
387  #ifdef EIGEN2_SUPPORT
388  SVD<PlainObject> svd() const;
389  #endif
390 
392 
393  #ifndef EIGEN_PARSED_BY_DOXYGEN
394 
395  template<typename OtherDerived> struct cross_product_return_type {
396  typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
397  typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
398  };
399  #endif // EIGEN_PARSED_BY_DOXYGEN
400  template<typename OtherDerived>
401  typename cross_product_return_type<OtherDerived>::type
402  cross(const MatrixBase<OtherDerived>& other) const;
403  template<typename OtherDerived>
404  PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
405  PlainObject unitOrthogonal(void) const;
406  Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
407 
408  #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
409  ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
410  // put this as separate enum value to work around possible GCC 4.3 bug (?)
411  enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
412  typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
413  HomogeneousReturnType homogeneous() const;
414  #endif
415 
416  enum {
417  SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
418  };
419  typedef Block<const Derived,
420  internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
421  internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
422  typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
423  const ConstStartMinusOne > HNormalizedReturnType;
424 
425  const HNormalizedReturnType hnormalized() const;
426 
428 
429  void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
430  template<typename EssentialPart>
431  void makeHouseholder(EssentialPart& essential,
432  Scalar& tau, RealScalar& beta) const;
433  template<typename EssentialPart>
434  void applyHouseholderOnTheLeft(const EssentialPart& essential,
435  const Scalar& tau,
436  Scalar* workspace);
437  template<typename EssentialPart>
438  void applyHouseholderOnTheRight(const EssentialPart& essential,
439  const Scalar& tau,
440  Scalar* workspace);
441 
443 
444  template<typename OtherScalar>
445  void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
446  template<typename OtherScalar>
447  void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
448 
450 
451  typedef typename internal::stem_function<Scalar>::type StemFunction;
452  const MatrixExponentialReturnValue<Derived> exp() const;
453  const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
454  const MatrixFunctionReturnValue<Derived> cosh() const;
455  const MatrixFunctionReturnValue<Derived> sinh() const;
456  const MatrixFunctionReturnValue<Derived> cos() const;
457  const MatrixFunctionReturnValue<Derived> sin() const;
458  const MatrixSquareRootReturnValue<Derived> sqrt() const;
459  const MatrixLogarithmReturnValue<Derived> log() const;
460  const MatrixPowerReturnValue<Derived> pow(const RealScalar& p) const;
461 
462 #ifdef EIGEN2_SUPPORT
463  template<typename ProductDerived, typename Lhs, typename Rhs>
464  Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
465  EvalBeforeAssigningBit>& other);
466 
467  template<typename ProductDerived, typename Lhs, typename Rhs>
468  Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
469  EvalBeforeAssigningBit>& other);
470 
473  template<typename OtherDerived>
474  Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
475  { return lazyAssign(other._expression()); }
476 
477  template<unsigned int Added>
478  const Flagged<Derived, Added, 0> marked() const;
479  const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
480 
481  inline const Cwise<Derived> cwise() const;
482  inline Cwise<Derived> cwise();
483 
484  VectorBlock<Derived> start(Index size);
485  const VectorBlock<const Derived> start(Index size) const;
486  VectorBlock<Derived> end(Index size);
487  const VectorBlock<const Derived> end(Index size) const;
488  template<int Size> VectorBlock<Derived,Size> start();
489  template<int Size> const VectorBlock<const Derived,Size> start() const;
490  template<int Size> VectorBlock<Derived,Size> end();
491  template<int Size> const VectorBlock<const Derived,Size> end() const;
492 
493  Minor<Derived> minor(Index row, Index col);
494  const Minor<Derived> minor(Index row, Index col) const;
495 #endif
496 
497  protected:
498  MatrixBase() : Base() {}
499 
500  private:
501  explicit MatrixBase(int);
502  MatrixBase(int,int);
503  template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
504  protected:
505  // mixing arrays and matrices is not legal
506  template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
507  {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
508  // mixing arrays and matrices is not legal
509  template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
510  {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
511 };
512 
513 } // end namespace Eigen
514 
515 #endif // EIGEN_MATRIXBASE_H