MatrixBase.h
Go to the documentation of this file.
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
59 
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 
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 
97 #endif // not EIGEN_PARSED_BY_DOXYGEN
98 
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 
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 
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>
146  Derived& operator=(const DenseBase<OtherDerived>& other);
147 
148  template <typename OtherDerived>
150  Derived& operator=(const EigenBase<OtherDerived>& other);
151 
152  template<typename OtherDerived>
154  Derived& operator=(const ReturnByValue<OtherDerived>& other);
155 
156  template<typename OtherDerived>
158  Derived& operator+=(const MatrixBase<OtherDerived>& other);
159  template<typename OtherDerived>
161  Derived& operator-=(const MatrixBase<OtherDerived>& other);
162 
163  template<typename OtherDerived>
166  operator*(const MatrixBase<OtherDerived> &other) const;
167 
168  template<typename OtherDerived>
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>
185  operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
186 
187  template<typename OtherDerived>
190  dot(const MatrixBase<OtherDerived>& other) const;
191 
194  RealScalar stableNorm() const;
195  RealScalar blueNorm() const;
196  RealScalar hypotNorm() const;
201 
204 
208 
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>
219 
220  template<int Index>
223 
226 
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>
238  template<unsigned int Mode>
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>
248  template<unsigned int UpLo>
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;
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 
266 
268  Derived& setIdentity();
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 
279 
280  template<typename OtherDerived>
282  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
283  bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
284 
289  template<typename OtherDerived>
291  { return cwiseEqual(other).all(); }
292 
297  template<typename OtherDerived>
299  { return cwiseNotEqual(other).any(); }
300 
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 
311 
312  template<int p> EIGEN_DEVICE_FUNC RealScalar lpNorm() const;
313 
315  EIGEN_DEVICE_FUNC const MatrixBase<Derived>& matrix() const { return *this; }
316 
323 
325 
326  inline const FullPivLU<PlainObject> fullPivLu() const;
327  inline const PartialPivLU<PlainObject> partialPivLu() const;
328 
329  inline const PartialPivLU<PlainObject> lu() const;
330 
332  inline const Inverse<Derived> inverse() const;
333 
334  template<typename ResultType>
335  inline void computeInverseAndDetWithCheck(
336  ResultType& inverse,
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 
350  Scalar determinant() const;
351 
353 
354  inline const LLT<PlainObject> llt() const;
355  inline const LDLT<PlainObject> ldlt() const;
356 
358 
359  inline const HouseholderQR<PlainObject> householderQr() const;
363 
365 
366  inline EigenvaluesReturnType eigenvalues() const;
367  inline RealScalar operatorNorm() const;
368 
370 
371  inline JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
372  inline BDCSVD<PlainObject> bdcSvd(unsigned int computationOptions = 0) const;
373 
375 
376  #ifndef EIGEN_PARSED_BY_DOXYGEN
377  template<typename OtherDerived> struct cross_product_return_type {
381  };
382  #endif // EIGEN_PARSED_BY_DOXYGEN
383  template<typename OtherDerived>
385 #ifndef EIGEN_PARSED_BY_DOXYGEN
387 #else
388  inline PlainObject
389 #endif
390  cross(const MatrixBase<OtherDerived>& other) const;
391 
392  template<typename OtherDerived>
394  inline PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
395 
397  inline PlainObject unitOrthogonal(void) const;
398 
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 (?)
407  inline HomogeneousReturnType homogeneous() const;
408 
409  enum {
411  };
412  typedef Block<const Derived,
415  typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne,Scalar,quotient) HNormalizedReturnType;
417  inline const HNormalizedReturnType hnormalized() const;
418 
420 
423  template<typename EssentialPart>
425  void makeHouseholder(EssentialPart& essential,
426  Scalar& tau, RealScalar& beta) const;
427  template<typename EssentialPart>
429  void applyHouseholderOnTheLeft(const EssentialPart& essential,
430  const Scalar& tau,
431  Scalar* workspace);
432  template<typename EssentialPart>
434  void applyHouseholderOnTheRight(const EssentialPart& essential,
435  const Scalar& tau,
436  Scalar* workspace);
437 
439 
440  template<typename OtherScalar>
443  template<typename OtherScalar>
446 
448 
449  template<typename OtherDerived>
452  {
453  return other.cwiseProduct(derived());
454  }
455 
457 
459 #define EIGEN_MATRIX_FUNCTION(ReturnType, Name, Description) \
460  \
461  const ReturnType<Derived> Name() const;
462 #define EIGEN_MATRIX_FUNCTION_1(ReturnType, Name, Description, Argument) \
463  \
464  const ReturnType<Derived> Name(Argument) const;
465 
466  EIGEN_MATRIX_FUNCTION(MatrixExponentialReturnValue, exp, exponential)
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:
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 
512 template<typename Derived>
513 template<typename OtherDerived>
514 inline Derived&
516 {
517  other.derived().applyThisOnTheRight(derived());
518  return derived();
519 }
520 
526 template<typename Derived>
527 template<typename OtherDerived>
529 {
530  other.derived().applyThisOnTheRight(derived());
531 }
532 
538 template<typename Derived>
539 template<typename OtherDerived>
541 {
542  other.derived().applyThisOnTheLeft(derived());
543 }
544 
545 } // end namespace Eigen
546 
547 #endif // EIGEN_MATRIXBASE_H
Eigen::Inverse
Expression of the inverse of another expression.
Definition: Inverse.h:43
Eigen::MatrixBase::lu
const PartialPivLU< PlainObject > lu() const
Definition: PartialPivLU.h:617
Eigen::MatrixBase::computeInverseWithCheck
void computeInverseWithCheck(ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition: InverseImpl.h:418
Eigen::MatrixBase::jacobiSvd
JacobiSVD< PlainObject > jacobiSvd(unsigned int computationOptions=0) const
Definition: JacobiSVD.h:805
Eigen::MatrixBase::UnitX
static const EIGEN_DEVICE_FUNC BasisReturnType UnitX()
Definition: CwiseNullaryOp.h:930
Eigen::MatrixBase::DiagonalIndexReturnType::Type
Diagonal< Derived, Index > Type
Definition: MatrixBase.h:213
Eigen::MatrixBase::Base
DenseBase< Derived > Base
Definition: MatrixBase.h:60
Eigen::DenseBase::PlainObject
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:210
Eigen::MatrixBase::computeInverseAndDetWithCheck
void computeInverseAndDetWithCheck(ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition: InverseImpl.h:377
Eigen::MatrixBase::operator+=
Derived & operator+=(const ArrayBase< OtherDerived > &)
Definition: MatrixBase.h:493
Eigen::MatrixBase::StemFunction
internal::stem_function< Scalar >::type StemFunction
Definition: MatrixBase.h:458
EIGEN_DEVICE_FUNC
#define EIGEN_DEVICE_FUNC
Definition: Macros.h:976
Eigen::MatrixBase::ConstDiagonalReturnType
internal::add_const< Diagonal< const Derived > >::type ConstDiagonalReturnType
Definition: MatrixBase.h:209
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
Eigen::MatrixBase::cross_product_return_type::Scalar
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType Scalar
Definition: MatrixBase.h:379
Eigen::MatrixBase::applyHouseholderOnTheLeft
EIGEN_DEVICE_FUNC void applyHouseholderOnTheLeft(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition: Householder.h:116
RowXpr
Block< Derived, 1, internal::traits< Derived >::ColsAtCompileTime, IsRowMajor > RowXpr
Definition: BlockMethods.h:17
Eigen::PartialPivLU
LU decomposition of a matrix with partial pivoting, and related features.
Definition: ForwardDeclarations.h:269
Eigen::Block
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
Eigen::MatrixBase::forceAlignedAccess
const Derived & forceAlignedAccess() const
Definition: MatrixBase.h:305
Eigen::MatrixBase::isOrthogonal
bool isOrthogonal(const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Dot.h:283
Eigen::MatrixBase::llt
const LLT< PlainObject > llt() const
Definition: LLT.h:540
Eigen::MatrixBase::SizeMinusOne
@ SizeMinusOne
Definition: MatrixBase.h:410
Eigen::MatrixBase::fullPivHouseholderQr
const FullPivHouseholderQR< PlainObject > fullPivHouseholderQr() const
Definition: FullPivHouseholderQR.h:706
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR
#define EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(Derived)
Definition: Macros.h:1247
Eigen::MatrixBase::asDiagonal
const EIGEN_DEVICE_FUNC DiagonalWrapper< const Derived > asDiagonal() const
Definition: DiagonalMatrix.h:325
ceres::sin
Jet< T, N > sin(const Jet< T, N > &f)
Definition: jet.h:439
Eigen::Horizontal
@ Horizontal
Definition: Constants.h:267
Eigen::DenseBase::Scalar
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Eigen::MatrixBase::normalized
const EIGEN_DEVICE_FUNC PlainObject normalized() const
Definition: Dot.h:124
c
Scalar Scalar * c
Definition: benchVecAdd.cpp:17
Eigen::MatrixBase::UnitW
static const EIGEN_DEVICE_FUNC BasisReturnType UnitW()
Definition: CwiseNullaryOp.h:960
Eigen::EigenBase
Definition: EigenBase.h:29
Eigen::MatrixBase::HomogeneousReturnTypeDirection
@ HomogeneousReturnTypeDirection
Definition: MatrixBase.h:403
Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition: Constants.h:66
Eigen::MatrixBase::UnitZ
static const EIGEN_DEVICE_FUNC BasisReturnType UnitZ()
Definition: CwiseNullaryOp.h:950
Eigen::MatrixBase::applyOnTheRight
void applyOnTheRight(const EigenBase< OtherDerived > &other)
Definition: MatrixBase.h:528
Eigen::MatrixBase::ConstTriangularViewReturnType::Type
const typedef TriangularView< const Derived, Mode > Type
Definition: MatrixBase.h:233
Eigen::MatrixBase::lpNorm
EIGEN_DEVICE_FUNC RealScalar lpNorm() const
Eigen::MatrixBase::eigenvalues
EigenvaluesReturnType eigenvalues() const
Computes the eigenvalues of a matrix.
Definition: MatrixBaseEigenvalues.h:67
Eigen::internal::stem_function
Definition: ForwardDeclarations.h:313
type
Definition: pytypes.h:1525
Eigen::MatrixBase::selfadjointView
EIGEN_DEVICE_FUNC SelfAdjointViewReturnType< UpLo >::Type selfadjointView()
Eigen::MatrixBase::operator+=
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & operator+=(const MatrixBase< OtherDerived > &other)
Definition: CwiseBinaryOp.h:175
Eigen::MatrixBase::ConstStartMinusOne
Block< const Derived, internal::traits< Derived >::ColsAtCompileTime==1 ? SizeMinusOne :1, internal::traits< Derived >::ColsAtCompileTime==1 ? 1 :SizeMinusOne > ConstStartMinusOne
Definition: MatrixBase.h:414
log
const EIGEN_DEVICE_FUNC LogReturnType log() const
Definition: ArrayCwiseUnaryOps.h:128
Eigen::MatrixBase::applyHouseholderOnTheRight
EIGEN_DEVICE_FUNC void applyHouseholderOnTheRight(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition: Householder.h:154
Eigen::SelfAdjointView
Expression of a selfadjoint matrix from a triangular part of a dense matrix.
Definition: SelfAdjointView.h:49
Eigen::ArrayWrapper
Expression of a mathematical vector or matrix as an array object.
Definition: ArrayWrapper.h:42
Eigen::ScalarBinaryOpTraits
Determines whether the given binary operation of two numeric types is allowed and what the scalar ret...
Definition: XprHelper.h:801
Eigen::MatrixBase::ConstSelfAdjointViewReturnType
Definition: MatrixBase.h:243
Eigen::MatrixBase::matrix
EIGEN_DEVICE_FUNC MatrixBase< Derived > & matrix()
Definition: MatrixBase.h:314
Eigen::MatrixBase::operator-=
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & operator-=(const MatrixBase< OtherDerived > &other)
Definition: CwiseBinaryOp.h:162
Eigen::MatrixBase::matrixFunction
const MatrixFunctionReturnValue< Derived > matrixFunction(StemFunction f) const
Helper function for the unsupported MatrixFunctions module.
Definition: MatrixFunction.h:529
EIGEN_SIZE_MAX
#define EIGEN_SIZE_MAX(a, b)
Definition: Macros.h:1310
exp
const EIGEN_DEVICE_FUNC ExpReturnType exp() const
Definition: ArrayCwiseUnaryOps.h:97
Eigen::NoAlias
Pseudo expression providing an operator = assuming no aliasing.
Definition: NoAlias.h:31
Eigen::MatrixBase::cross
EIGEN_DEVICE_FUNC cross_product_return_type< OtherDerived >::type cross(const MatrixBase< OtherDerived > &other) const
Eigen::JacobiRotation
Rotation given by a cosine-sine pair.
Definition: ForwardDeclarations.h:283
Eigen::MatrixBase::fullPivLu
const FullPivLU< PlainObject > fullPivLu() const
Definition: FullPivLU.h:870
Eigen::FullPivLU
LU decomposition of a matrix with complete pivoting, and related features.
Definition: ForwardDeclarations.h:268
Eigen::MatrixBase::MatrixBase
EIGEN_DEVICE_FUNC MatrixBase(int)
Eigen::MatrixBase::eulerAngles
EIGEN_DEVICE_FUNC Matrix< Scalar, 3, 1 > eulerAngles(Index a0, Index a1, Index a2) const
Definition: Eigen/src/Geometry/EulerAngles.h:37
beta
double beta(double a, double b)
Definition: beta.c:61
Eigen::MatrixBase::colPivHouseholderQr
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
Definition: ColPivHouseholderQR.h:667
Eigen::DenseBase::eval
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType eval() const
Definition: DenseBase.h:407
rows
int rows
Definition: Tutorial_commainit_02.cpp:1
ceres::cos
Jet< T, N > cos(const Jet< T, N > &f)
Definition: jet.h:426
Eigen::MatrixBase::operator!=
EIGEN_DEVICE_FUNC bool operator!=(const MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:298
Eigen::MatrixBase::makeHouseholder
EIGEN_DEVICE_FUNC void makeHouseholder(EssentialPart &essential, Scalar &tau, RealScalar &beta) const
Definition: Householder.h:67
Eigen::CwiseNullaryOp
Generic expression of a matrix where all coefficients are defined by a functor.
Definition: CwiseNullaryOp.h:60
Eigen::MatrixBase::forceAlignedAccessIf
const Derived & forceAlignedAccessIf() const
Definition: MatrixBase.h:307
Eigen::Homogeneous
Expression of one (or a set of) homogeneous vector(s)
Definition: ForwardDeclarations.h:298
size
Scalar Scalar int size
Definition: benchVecAdd.cpp:17
Eigen::MatrixBase::asPermutation
const PermutationWrapper< const Derived > asPermutation() const
Definition: PermutationMatrix.h:592
cosh
const EIGEN_DEVICE_FUNC CoshReturnType cosh() const
Definition: ArrayCwiseUnaryOps.h:353
Eigen::MatrixBase::BasisReturnType
Block< const CwiseNullaryOp< internal::scalar_identity_op< Scalar >, SquareMatrixType >, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime > BasisReturnType
Definition: MatrixBase.h:121
Eigen::DenseBase::IsVectorAtCompileTime
@ IsVectorAtCompileTime
Definition: DenseBase.h:153
Eigen::MatrixBase::UnitY
static const EIGEN_DEVICE_FUNC BasisReturnType UnitY()
Definition: CwiseNullaryOp.h:940
Eigen::MatrixBase::ConstDiagonalDynamicIndexReturnType
internal::add_const< Diagonal< const Derived, DynamicIndex > >::type ConstDiagonalDynamicIndexReturnType
Definition: MatrixBase.h:225
Eigen::MatrixBase::hypotNorm
RealScalar hypotNorm() const
Definition: StableNorm.h:241
align_3::a1
Point2 a1
Definition: testPose2.cpp:769
Eigen::MatrixBase::inverse
const EIGEN_DEVICE_FUNC Inverse< Derived > inverse() const
Definition: InverseImpl.h:348
Eigen::internal::true_type
Definition: Meta.h:96
Eigen::FullPivHouseholderQR
Householder rank-revealing QR decomposition of a matrix with full pivoting.
Definition: ForwardDeclarations.h:275
Eigen::MatrixBase::SelfAdjointViewReturnType
Definition: MatrixBase.h:242
Eigen::DenseBase::RealScalar
NumTraits< Scalar >::Real RealScalar
Definition: DenseBase.h:73
Eigen::MatrixBase::operatorNorm
RealScalar operatorNorm() const
Computes the L2 operator norm.
Definition: MatrixBaseEigenvalues.h:120
Eigen::MatrixBase::cross3
EIGEN_DEVICE_FUNC PlainObject cross3(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:83
Eigen::MatrixBase::Identity
static const EIGEN_DEVICE_FUNC IdentityReturnType Identity()
Definition: CwiseNullaryOp.h:799
Eigen::MatrixBase::isDiagonal
bool isDiagonal(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: DiagonalMatrix.h:339
j
std::ptrdiff_t j
Definition: tut_arithmetic_redux_minmax.cpp:2
Eigen::DenseBase::lazyAssign
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived & lazyAssign(const DenseBase< OtherDerived > &other)
Eigen::MatrixBase::normalize
EIGEN_DEVICE_FUNC void normalize()
Definition: Dot.h:145
Eigen::PermutationWrapper
Class to view a vector of integers as a permutation matrix.
Definition: PermutationMatrix.h:486
Eigen::numext::q
EIGEN_DEVICE_FUNC const Scalar & q
Definition: SpecialFunctionsImpl.h:1984
square
const EIGEN_DEVICE_FUNC SquareReturnType square() const
Definition: ArrayCwiseUnaryOps.h:425
Eigen::DenseBase::CoeffReturnType
Base::CoeffReturnType CoeffReturnType
Definition: DenseBase.h:96
Eigen::DenseBase::SizeAtCompileTime
@ SizeAtCompileTime
Definition: DenseBase.h:113
Eigen::MatrixBase::ConstTriangularViewReturnType
Definition: MatrixBase.h:233
Eigen::DenseBase::MaxSizeAtCompileTime
@ MaxSizeAtCompileTime
Definition: DenseBase.h:141
Eigen::MatrixBase::ConstantReturnType
CwiseNullaryOp< internal::scalar_constant_op< Scalar >, PlainObject > ConstantReturnType
Definition: MatrixBase.h:108
Eigen::BDCSVD
class Bidiagonal Divide and Conquer SVD
Definition: ForwardDeclarations.h:279
Eigen::Dynamic
const int Dynamic
Definition: Constants.h:22
Eigen::numext::mini
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T mini(const T &x, const T &y)
Definition: Eigen/src/Core/MathFunctions.h:1085
Eigen::Architecture::Type
Type
Definition: Constants.h:471
Eigen::Diagonal
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition: Diagonal.h:63
Eigen::MatrixBase::DiagonalDynamicIndexReturnType
Diagonal< Derived, DynamicIndex > DiagonalDynamicIndexReturnType
Definition: MatrixBase.h:224
EIGEN_STRONG_INLINE
#define EIGEN_STRONG_INLINE
Definition: Macros.h:917
Eigen::MatrixBase::cross_product_return_type::type
Matrix< Scalar, MatrixBase::RowsAtCompileTime, MatrixBase::ColsAtCompileTime > type
Definition: MatrixBase.h:380
Eigen::internal::add_const
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Definition: MatrixCwiseBinaryOps.h:63
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Complete orthogonal decomposition (COD) of a matrix.
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Definition: Dot.h:302
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Robust Cholesky decomposition of a matrix with pivoting.
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Definition: Determinant.h:108
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@ Vertical
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@ Flags
Definition: DenseBase.h:165
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Definition: DiagonalMatrix.h:293
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const EIGEN_DEVICE_FUNC CwiseBinaryOp< numext::equal_to< Scalar >, const Derived, const OtherDerived > cwiseEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
Definition: MatrixCwiseBinaryOps.h:43
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Definition: MatrixBase.h:55
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Definition: Homogeneous.h:132
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Definition: ArrayBase.h:39
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@ MaxRowsAtCompileTime
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Base::PlainObject PlainObject
Definition: MatrixBase.h:104
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homogeneous normalization
Definition: Homogeneous.h:174
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Set the coefficients of *this to the i-th unit (basis) vector.
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Two-sided Jacobi SVD decomposition of a rectangular matrix.
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Base::ConstTransposeReturnType ConstTransposeReturnType
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Definition: MatrixBase.h:232
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Definition: TriangularMatrix.h:690
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Definition: CompleteOrthogonalDecomposition.h:629
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EIGEN_DEVICE_FUNC ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot(const MatrixBase< OtherDerived > &other) const
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Definition: MatrixBase.h:53
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Standard Cholesky decomposition (LL^T) of a matrix and associated features.
Definition: LLT.h:66
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Definition: HouseholderQR.h:427
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Definition: ForwardDeclarations.h:17
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Base class for all dense matrices, vectors, and arrays.
Definition: DenseBase.h:41
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EIGEN_DEVICE_FUNC Index diagonalSize() const
Definition: MatrixBase.h:102
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Definition: StaticAssert.h:127
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Derived & forceAlignedAccessIf()
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Definition: DenseBase.h:327
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Generic expression where a coefficient-wise unary operator is applied to an expression.
Definition: CwiseUnaryOp.h:55
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Expression of a dense or sparse matrix with zero or too small values removed.
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Base::ColXpr ColXpr
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Base class of any sparse matrices or sparse expressions.
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@ RowsAtCompileTime
Definition: DenseBase.h:100
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Definition: MatrixBase.h:451
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EIGEN_DEVICE_FUNC Scalar trace() const
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The matrix class, also used for vectors and row-vectors.
Definition: 3rdparty/Eigen/Eigen/src/Core/Matrix.h:178
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Definition: NoAlias.h:102
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@ ColsAtCompileTime
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Definition: StableNorm.h:213
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Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
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@ MaxColsAtCompileTime
Definition: DenseBase.h:130
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@ ColMajor
Definition: Constants.h:319
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Expression of a triangular part in a matrix.
Definition: TriangularMatrix.h:187
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EIGEN_DEVICE_FUNC DiagonalReturnType diagonal()
Definition: Diagonal.h:187
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Definition: SparseView.h:226
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Definition: PartialPivLU.h:602
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Definition: LDLT.h:681
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Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:232
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Definition: MatrixBase.h:315
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typedef EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType
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Base::RowXpr RowXpr
Definition: MatrixBase.h:87
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EIGEN_DEVICE_FUNC bool operator==(const MatrixBase< OtherDerived > &other) const
Definition: MatrixBase.h:290
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Definition: TriangularMatrix.h:665
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Definition: StableNorm.h:229
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SCALAR Scalar
Definition: bench_gemm.cpp:46
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Householder QR decomposition of a matrix.
Definition: ForwardDeclarations.h:273
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Definition: Householder.h:43
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The Index type as used for the API.
Definition: Meta.h:74
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autogenerated on Fri Nov 1 2024 03:33:41