Eigen  3.3.7
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>::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 
94  typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime),
95  EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;
96 #endif // not EIGEN_PARSED_BY_DOXYGEN
97 
100  EIGEN_DEVICE_FUNC
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 
109  typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
112  >::type AdjointReturnType;
114  typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> EigenvaluesReturnType;
119  internal::traits<Derived>::RowsAtCompileTime,
120  internal::traits<Derived>::ColsAtCompileTime> BasisReturnType;
121 #endif // not EIGEN_PARSED_BY_DOXYGEN
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 
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.
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);
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
166  operator*(const MatrixBase<OtherDerived> &other) const;
167 
168  template<typename OtherDerived>
169  EIGEN_DEVICE_FUNC
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
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 
206  EIGEN_DEVICE_FUNC
208 
209  typedef typename internal::add_const<Diagonal<const Derived> >::type ConstDiagonalReturnType;
210  EIGEN_DEVICE_FUNC
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 
272  bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
273  bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
274 
275  bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
276  bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
277 
278  template<typename OtherDerived>
279  bool isOrthogonal(const MatrixBase<OtherDerived>& other,
280  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
281  bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
282 
287  template<typename OtherDerived>
288  EIGEN_DEVICE_FUNC inline bool operator==(const MatrixBase<OtherDerived>& other) const
289  { return cwiseEqual(other).all(); }
290 
295  template<typename OtherDerived>
296  EIGEN_DEVICE_FUNC inline bool operator!=(const MatrixBase<OtherDerived>& other) const
297  { return cwiseNotEqual(other).any(); }
298 
300 
301  // TODO forceAlignedAccess is temporarily disabled
302  // Need to find a nicer workaround.
303  inline const Derived& forceAlignedAccess() const { return derived(); }
304  inline Derived& forceAlignedAccess() { return derived(); }
305  template<bool Enable> inline const Derived& forceAlignedAccessIf() const { return derived(); }
306  template<bool Enable> inline Derived& forceAlignedAccessIf() { return derived(); }
307 
308  EIGEN_DEVICE_FUNC Scalar trace() const;
309 
310  template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
311 
312  EIGEN_DEVICE_FUNC MatrixBase<Derived>& matrix() { return *this; }
313  EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
314 
317  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> array() { return ArrayWrapper<Derived>(derived()); }
320  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> array() const { return ArrayWrapper<const Derived>(derived()); }
321 
323 
324  inline const FullPivLU<PlainObject> fullPivLu() const;
325  inline const PartialPivLU<PlainObject> partialPivLu() const;
326 
327  inline const PartialPivLU<PlainObject> lu() const;
328 
329  inline const Inverse<Derived> inverse() const;
330 
331  template<typename ResultType>
332  inline void computeInverseAndDetWithCheck(
333  ResultType& inverse,
334  typename ResultType::Scalar& determinant,
335  bool& invertible,
336  const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
337  ) const;
338  template<typename ResultType>
339  inline void computeInverseWithCheck(
340  ResultType& inverse,
341  bool& invertible,
342  const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
343  ) const;
344  Scalar determinant() const;
345 
347 
348  inline const LLT<PlainObject> llt() const;
349  inline const LDLT<PlainObject> ldlt() const;
350 
352 
353  inline const HouseholderQR<PlainObject> householderQr() const;
357 
359 
360  inline EigenvaluesReturnType eigenvalues() const;
361  inline RealScalar operatorNorm() const;
362 
364 
365  inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
366  inline BDCSVD<PlainObject> bdcSvd(unsigned int computationOptions = 0) const;
367 
369 
370  #ifndef EIGEN_PARSED_BY_DOXYGEN
371  template<typename OtherDerived> struct cross_product_return_type {
373  typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
375  };
376  #endif // EIGEN_PARSED_BY_DOXYGEN
377  template<typename OtherDerived>
378  EIGEN_DEVICE_FUNC
379 #ifndef EIGEN_PARSED_BY_DOXYGEN
380  inline typename cross_product_return_type<OtherDerived>::type
381 #else
382  inline PlainObject
383 #endif
384  cross(const MatrixBase<OtherDerived>& other) const;
385 
386  template<typename OtherDerived>
387  EIGEN_DEVICE_FUNC
388  inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
389 
390  EIGEN_DEVICE_FUNC
391  inline PlainObject unitOrthogonal(void) const;
392 
393  EIGEN_DEVICE_FUNC
394  inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
395 
396  // put this as separate enum value to work around possible GCC 4.3 bug (?)
397  enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
399  typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
400  EIGEN_DEVICE_FUNC
401  inline HomogeneousReturnType homogeneous() const;
402 
403  enum {
404  SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
405  };
406  typedef Block<const Derived,
407  internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
408  internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
409  typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
410  EIGEN_DEVICE_FUNC
411  inline const HNormalizedReturnType hnormalized() const;
412 
414 
415  void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
416  template<typename EssentialPart>
417  void makeHouseholder(EssentialPart& essential,
418  Scalar& tau, RealScalar& beta) const;
419  template<typename EssentialPart>
420  void applyHouseholderOnTheLeft(const EssentialPart& essential,
421  const Scalar& tau,
422  Scalar* workspace);
423  template<typename EssentialPart>
424  void applyHouseholderOnTheRight(const EssentialPart& essential,
425  const Scalar& tau,
426  Scalar* workspace);
427 
429 
430  template<typename OtherScalar>
431  void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
432  template<typename OtherScalar>
433  void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
434 
436 
437  template<typename OtherDerived>
438  EIGEN_STRONG_INLINE const typename SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type
439  cwiseProduct(const SparseMatrixBase<OtherDerived> &other) const
440  {
441  return other.cwiseProduct(derived());
442  }
443 
445 
446  typedef typename internal::stem_function<Scalar>::type StemFunction;
447 #define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
448  \
449  const ReturnType<Derived> Name() const;
450 #define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
451  \
452  const ReturnType<Derived> Name(Argument) const;
453 
454  EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
456  const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
457  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cosh, hyperbolic cosine)
458  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sinh, hyperbolic sine)
459  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, cos, cosine)
460  EIGEN_MATRIX_FUNCTION(MatrixFunctionReturnValue, sin, sine)
461  EIGEN_MATRIX_FUNCTION(MatrixSquareRootReturnValue, sqrt, square root)
462  EIGEN_MATRIX_FUNCTION(MatrixLogarithmReturnValue, log, logarithm)
463  EIGEN_MATRIX_FUNCTION_1(MatrixPowerReturnValue, pow, power to \c p, const RealScalar& p)
464  EIGEN_MATRIX_FUNCTION_1(MatrixComplexPowerReturnValue, pow, power to \c p, const std::complex<RealScalar>& p)
465 
466  protected:
467  EIGEN_DEVICE_FUNC MatrixBase() : Base() {}
468 
469  private:
470  EIGEN_DEVICE_FUNC explicit MatrixBase(int);
471  EIGEN_DEVICE_FUNC MatrixBase(int,int);
472  template<typename OtherDerived> EIGEN_DEVICE_FUNC explicit MatrixBase(const MatrixBase<OtherDerived>&);
473  protected:
474  // mixing arrays and matrices is not legal
475  template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
476  {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
477  // mixing arrays and matrices is not legal
478  template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
479  {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
480 };
481 
482 
483 /***************************************************************************
484 * Implementation of matrix base methods
485 ***************************************************************************/
486 
494 template<typename Derived>
495 template<typename OtherDerived>
496 inline Derived&
498 {
499  other.derived().applyThisOnTheRight(derived());
500  return derived();
501 }
502 
508 template<typename Derived>
509 template<typename OtherDerived>
511 {
512  other.derived().applyThisOnTheRight(derived());
513 }
514 
520 template<typename Derived>
521 template<typename OtherDerived>
523 {
524  other.derived().applyThisOnTheLeft(derived());
525 }
526 
527 } // end namespace Eigen
528 
529 #endif // EIGEN_MATRIXBASE_H
const MatrixFunctionReturnValue< Derived > cosh() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperb...
Generic expression of a matrix where all coefficients are defined by a functor.
Definition: CwiseNullaryOp.h:60
Scalar trace() const
Definition: Redux.h:498
Robust Cholesky decomposition of a matrix with pivoting.
Definition: LDLT.h:50
const MatrixPowerReturnValue< Derived > pow(const RealScalar &p) const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power ...
void makeHouseholder(EssentialPart &essential, Scalar &tau, RealScalar &beta) const
Definition: Householder.h:65
RealScalar blueNorm() const
Definition: StableNorm.h:202
Definition: DenseBase.h:100
BDCSVD< PlainObject > bdcSvd(unsigned int computationOptions=0) const
Definition: BDCSVD.h:1269
const CwiseBinaryOp< std::not_equal_to< Scalar >, const Derived, const OtherDerived > cwiseNotEqual(const Eigen::MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:64
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Definition: Constants.h:320
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:71
Expression of a mathematical vector or matrix as an array object.
Definition: ArrayWrapper.h:42
Householder rank-revealing QR decomposition of a matrix with full pivoting.
Definition: ForwardDeclarations.h:252
const AdjointReturnType adjoint() const
Definition: Transpose.h:210
const CompleteOrthogonalDecomposition< PlainObject > completeOrthogonalDecomposition() const
Definition: CompleteOrthogonalDecomposition.h:556
void applyOnTheLeft(const EigenBase< OtherDerived > &other)
Definition: MatrixBase.h:522
Definition: Constants.h:265
Pseudo expression providing an operator = assuming no aliasing.
Definition: NoAlias.h:31
const CwiseBinaryOp< internal::scalar_product_op< Derived ::Scalar, OtherDerived ::Scalar >, const Derived, const OtherDerived > cwiseProduct(const Eigen::MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:24
Expression of the transpose of a matrix.
Definition: Transpose.h:52
static const BasisReturnType UnitW()
Definition: CwiseNullaryOp.h:861
bool isUnitary(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Dot.h:302
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
Definition: ColPivHouseholderQR.h:646
const CwiseBinaryOp< std::equal_to< Scalar >, const Derived, const OtherDerived > cwiseEqual(const Eigen::MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:44
void applyOnTheRight(const EigenBase< OtherDerived > &other)
Definition: MatrixBase.h:510
LU decomposition of a matrix with partial pivoting, and related features.
Definition: ForwardDeclarations.h:246
Namespace containing all symbols from the Eigen library.
Definition: Core:306
const MatrixFunctionReturnValue< Derived > sinh() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperb...
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_square_op< typename Derived::Scalar >, const Derived > square(const Eigen::ArrayBase< Derived > &x)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:150
const PlainObject normalized() const
Definition: Dot.h:124
const MatrixSquareRootReturnValue< Derived > sqrt() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise square...
Derived & setIdentity()
Definition: CwiseNullaryOp.h:774
Definition: DenseBase.h:113
Matrix< Scalar, 3, 1 > eulerAngles(Index a0, Index a1, Index a2) const
Definition: EulerAngles.h:37
Derived & derived()
Definition: EigenBase.h:45
Complete orthogonal decomposition (COD) of a matrix.
Definition: ForwardDeclarations.h:253
RealScalar stableNorm() const
Definition: StableNorm.h:157
Eigen::Index Index
The interface type of indices.
Definition: EigenBase.h:38
const FullPivLU< PlainObject > fullPivLu() const
Definition: FullPivLU.h:884
const unsigned int RowMajorBit
Definition: Constants.h:61
Base class for all dense matrices, vectors, and arrays.
Definition: DenseBase.h:41
PlainObject cross3(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:82
internal::traits< Derived >::StorageIndex StorageIndex
The type used to store indices.
Definition: DenseBase.h:63
Definition: EigenBase.h:29
void applyHouseholderOnTheLeft(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition: Householder.h:113
PlainObject unitOrthogonal(void) const
Definition: OrthoMethods.h:226
void computeInverseAndDetWithCheck(ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition: InverseImpl.h:362
void normalize()
Definition: Dot.h:145
RealScalar norm() const
Definition: Dot.h:108
Expression of the inverse of another expression.
Definition: Inverse.h:43
bool operator!=(const MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:296
bool isUpperTriangular(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: TriangularMatrix.h:648
static const BasisReturnType UnitX()
Definition: CwiseNullaryOp.h:831
Derived & operator+=(const MatrixBase< OtherDerived > &other)
Definition: CwiseBinaryOp.h:175
void stableNormalize()
Definition: Dot.h:191
const Derived & forceAlignedAccess() const
Definition: MatrixBase.h:303
RealScalar squaredNorm() const
Definition: Dot.h:96
Index size() const
Definition: EigenBase.h:66
JacobiSVD< PlainObject > jacobiSvd(unsigned int computationOptions=0) const
Definition: JacobiSVD.h:797
PlainObject cross(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:34
const MatrixFunctionReturnValue< Derived > cos() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise cosine...
Index rows() const
Definition: EigenBase.h:59
const MatrixLogarithmReturnValue< Derived > log() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise logari...
ArrayWrapper< Derived > array()
Definition: MatrixBase.h:317
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Definition: ForwardDeclarations.h:251
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
Definition: LLT.h:56
const HouseholderQR< PlainObject > householderQr() const
Definition: HouseholderQR.h:402
const ArrayWrapper< const Derived > array() const
Definition: MatrixBase.h:320
bool isDiagonal(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: DiagonalMatrix.h:291
const MatrixFunctionReturnValue< Derived > sin() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine u...
const DiagonalWrapper< const Derived > asDiagonal() const
Definition: DiagonalMatrix.h:277
const MatrixExponentialReturnValue< Derived > exp() const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise expone...
static const BasisReturnType UnitY()
Definition: CwiseNullaryOp.h:841
void adjointInPlace()
Definition: Transpose.h:315
static const BasisReturnType Unit(Index size, Index i)
Definition: CwiseNullaryOp.h:803
Definition: DenseBase.h:106
const PartialPivLU< PlainObject > partialPivLu() const
Definition: PartialPivLU.h:592
class Bidiagonal Divide and Conquer SVD
Definition: ForwardDeclarations.h:255
const LDLT< PlainObject > ldlt() const
Definition: LDLT.h:666
Definition: Constants.h:268
RealScalar operatorNorm() const
Computes the L2 operator norm.
Definition: MatrixBaseEigenvalues.h:120
const PlainObject stableNormalized() const
Definition: Dot.h:167
const Inverse< Derived > inverse() const
Definition: InverseImpl.h:335
bool isLowerTriangular(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: TriangularMatrix.h:673
const HNormalizedReturnType hnormalized() const
homogeneous normalization
Definition: Homogeneous.h:172
internal::conditional< internal::is_same< typename internal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray >::type PlainObject
The plain matrix or array type corresponding to this expression.
Definition: DenseBase.h:205
static const IdentityReturnType Identity()
Definition: CwiseNullaryOp.h:700
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
const SparseView< Derived > sparseView(const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const
Definition: SparseView.h:225
Derived & operator-=(const MatrixBase< OtherDerived > &other)
Definition: CwiseBinaryOp.h:162
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot(const MatrixBase< OtherDerived > &other) const
Definition: Dot.h:72
LU decomposition of a matrix with complete pivoting, and related features.
Definition: ForwardDeclarations.h:245
void applyHouseholderOnTheRight(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition: Householder.h:150
RealScalar lpNorm() const
Definition: Dot.h:267
Householder QR decomposition of a matrix.
Definition: ForwardDeclarations.h:250
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:254
Derived & operator=(const MatrixBase &other)
Definition: Assign.h:55
Derived & forceAlignedAccess()
Definition: MatrixBase.h:304
const LLT< PlainObject > llt() const
Definition: LLT.h:524
Derived & operator*=(const EigenBase< OtherDerived > &other)
Definition: MatrixBase.h:497
DiagonalReturnType diagonal()
Definition: Diagonal.h:191
const MatrixFunctionReturnValue< Derived > matrixFunction(StemFunction f) const
Helper function for the unsupported MatrixFunctions module.
Determines whether the given binary operation of two numeric types is allowed and what the scalar ret...
Definition: XprHelper.h:780
NoAlias< Derived, Eigen::MatrixBase > noalias()
Definition: NoAlias.h:101
bool isOrthogonal(const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Dot.h:283
const PartialPivLU< PlainObject > lu() const
Definition: PartialPivLU.h:607
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition: Diagonal.h:63
void makeHouseholderInPlace(Scalar &tau, RealScalar &beta)
Definition: Householder.h:42
const int Dynamic
Definition: Constants.h:21
bool isIdentity(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: CwiseNullaryOp.h:717
Generic expression where a coefficient-wise unary operator is applied to an expression.
Definition: CwiseUnaryOp.h:55
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:178
void computeInverseWithCheck(ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition: InverseImpl.h:401
HomogeneousReturnType homogeneous() const
Definition: Homogeneous.h:130
Index cols() const
Definition: EigenBase.h:62
bool operator==(const MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:288
Index diagonalSize() const
Definition: MatrixBase.h:101
const FullPivHouseholderQR< PlainObject > fullPivHouseholderQr() const
Definition: FullPivHouseholderQR.h:669
EigenvaluesReturnType eigenvalues() const
Computes the eigenvalues of a matrix.
Definition: MatrixBaseEigenvalues.h:67
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
const CwiseBinaryOp< internal::scalar_product_op< Scalar, T >, Derived, Constant< T > > operator*(const T &scalar) const
Scalar determinant() const
Definition: Determinant.h:92
static const BasisReturnType UnitZ()
Definition: CwiseNullaryOp.h:851
const Product< Derived, OtherDerived, LazyProduct > lazyProduct(const MatrixBase< OtherDerived > &other) const
Definition: GeneralProduct.h:432
RealScalar hypotNorm() const
Definition: StableNorm.h:214