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
14namespace Eigen {
15
43 * This class can be extended with the help of the plugin mechanism described on the page
44 * \ref TopicCustomizingEigen by defining the preprocessor symbol \c EIGEN_MATRIXBASE_PLUGIN.
45 *
46 * \sa \ref TopicClassHierarchy
47 */
48template<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;
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 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
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()); }
106
109 typedef Matrix<typename internal::traits<Derived>::Scalar,
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
115 > PlainObject;
116
117#ifndef EIGEN_PARSED_BY_DOXYGEN
119 typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>,Derived> ConstantReturnType;
121 typedef typename internal::conditional<NumTraits<Scalar>::IsComplex,
122 CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>,
123 ConstTransposeReturnType
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;
130 typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>,
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);
158
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#endif // not EIGEN_PARSED_BY_DOXYGEN
166
167 template<typename OtherDerived>
168 Derived& operator+=(const MatrixBase<OtherDerived>& other);
169 template<typename OtherDerived>
170 Derived& operator-=(const MatrixBase<OtherDerived>& other);
171
172 template<typename OtherDerived>
173 const typename ProductReturnType<Derived,OtherDerived>::Type
174 operator*(const MatrixBase<OtherDerived> &other) const;
175
176 template<typename OtherDerived>
177 const typename LazyProductReturnType<Derived,OtherDerived>::Type
178 lazyProduct(const MatrixBase<OtherDerived> &other) const;
179
180 template<typename OtherDerived>
181 Derived& operator*=(const EigenBase<OtherDerived>& other);
182
183 template<typename OtherDerived>
184 void applyOnTheLeft(const EigenBase<OtherDerived>& other);
185
186 template<typename OtherDerived>
187 void applyOnTheRight(const EigenBase<OtherDerived>& other);
188
189 template<typename DiagonalDerived>
190 const DiagonalProduct<Derived, DiagonalDerived, OnTheRight>
191 operator*(const DiagonalBase<DiagonalDerived> &diagonal) const;
192
193 template<typename OtherDerived>
194 typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
195 dot(const MatrixBase<OtherDerived>& other) const;
196
197 #ifdef EIGEN2_SUPPORT
198 template<typename OtherDerived>
199 Scalar eigen2_dot(const MatrixBase<OtherDerived>& other) const;
200 #endif
201
202 RealScalar squaredNorm() const;
203 RealScalar norm() const;
204 RealScalar stableNorm() const;
205 RealScalar blueNorm() const;
206 RealScalar hypotNorm() const;
207 const PlainObject normalized() const;
208 void normalize();
209
210 const AdjointReturnType adjoint() const;
211 void adjointInPlace();
212
213 typedef Diagonal<Derived> DiagonalReturnType;
214 DiagonalReturnType diagonal();
215 typedef const Diagonal<const Derived> ConstDiagonalReturnType;
216 const ConstDiagonalReturnType diagonal() const;
217
218 template<int Index> struct DiagonalIndexReturnType { typedef Diagonal<Derived,Index> Type; };
219 template<int Index> struct ConstDiagonalIndexReturnType { typedef const Diagonal<const Derived,Index> Type; };
220
221 template<int Index> typename DiagonalIndexReturnType<Index>::Type diagonal();
222 template<int Index> typename ConstDiagonalIndexReturnType<Index>::Type diagonal() const;
223
224 // Note: The "MatrixBase::" prefixes are added to help MSVC9 to match these declarations with the later implementations.
225 // On the other hand they confuse MSVC8...
226 #if (defined _MSC_VER) && (_MSC_VER >= 1500) // 2008 or later
227 typename MatrixBase::template DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
228 typename MatrixBase::template ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
229 #else
230 typename DiagonalIndexReturnType<Dynamic>::Type diagonal(Index index);
231 typename ConstDiagonalIndexReturnType<Dynamic>::Type diagonal(Index index) const;
232 #endif
233
234 #ifdef EIGEN2_SUPPORT
235 template<unsigned int Mode> typename internal::eigen2_part_return_type<Derived, Mode>::type part();
236 template<unsigned int Mode> const typename internal::eigen2_part_return_type<Derived, Mode>::type part() const;
237
238 // huuuge hack. make Eigen2's matrix.part<Diagonal>() work in eigen3. Problem: Diagonal is now a class template instead
239 // of an integer constant. Solution: overload the part() method template wrt template parameters list.
240 template<template<typename T, int N> class U>
241 const DiagonalWrapper<ConstDiagonalReturnType> part() const
242 { return diagonal().asDiagonal(); }
243 #endif // EIGEN2_SUPPORT
244
245 template<unsigned int Mode> struct TriangularViewReturnType { typedef TriangularView<Derived, Mode> Type; };
246 template<unsigned int Mode> struct ConstTriangularViewReturnType { typedef const TriangularView<const Derived, Mode> Type; };
247
248 template<unsigned int Mode> typename TriangularViewReturnType<Mode>::Type triangularView();
249 template<unsigned int Mode> 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> typename SelfAdjointViewReturnType<UpLo>::Type selfadjointView();
255 template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
256
257 const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
258 typename NumTraits<Scalar>::Real m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
259 static const IdentityReturnType Identity();
260 static const IdentityReturnType Identity(Index rows, Index cols);
261 static const BasisReturnType Unit(Index size, Index i);
262 static const BasisReturnType Unit(Index i);
263 static const BasisReturnType UnitX();
264 static const BasisReturnType UnitY();
265 static const BasisReturnType UnitZ();
266 static const BasisReturnType UnitW();
267
268 const DiagonalWrapper<const Derived> asDiagonal() const;
269 const PermutationWrapper<const Derived> asPermutation() const;
270
271 Derived& setIdentity();
272 Derived& setIdentity(Index rows, Index cols);
273
274 bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
275 bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
276
277 bool isUpperTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
278 bool isLowerTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
279
280 template<typename OtherDerived>
281 bool isOrthogonal(const MatrixBase<OtherDerived>& other,
282 RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
283 bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
284
287 * fuzzy comparison such as isApprox()
288 * \sa isApprox(), operator!= */
289 template<typename OtherDerived>
290 inline bool operator==(const MatrixBase<OtherDerived>& other) const
291 { return cwiseEqual(other).all(); }
292
297 template<typename OtherDerived>
298 inline bool operator!=(const MatrixBase<OtherDerived>& other) const
299 { return cwiseNotEqual(other).any(); }
300
301 NoAlias<Derived,Eigen::MatrixBase > noalias();
302
303 inline const ForceAlignedAccess<Derived> forceAlignedAccess() const;
304 inline ForceAlignedAccess<Derived> forceAlignedAccess();
305 template<bool Enable> inline typename internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type forceAlignedAccessIf() const;
306 template<bool Enable> inline typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type forceAlignedAccessIf();
307
308 Scalar trace() const;
309
311
312 template<int p> RealScalar lpNorm() const;
313
314 MatrixBase<Derived>& matrix() { return *this; }
315 const MatrixBase<Derived>& matrix() const { return *this; }
316
319 ArrayWrapper<Derived> array() { return derived(); }
320 const ArrayWrapper<const Derived> array() const { return derived(); }
321
323
324 const FullPivLU<PlainObject> fullPivLu() const;
325 const PartialPivLU<PlainObject> partialPivLu() const;
326
327 #if EIGEN2_SUPPORT_STAGE < STAGE20_RESOLVE_API_CONFLICTS
328 const LU<PlainObject> lu() const;
329 #endif
330
331 #ifdef EIGEN2_SUPPORT
332 const LU<PlainObject> eigen2_lu() const;
333 #endif
334
335 #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
336 const PartialPivLU<PlainObject> lu() const;
337 #endif
338
339 #ifdef EIGEN2_SUPPORT
340 template<typename ResultType>
341 void computeInverse(MatrixBase<ResultType> *result) const {
342 *result = this->inverse();
343 }
344 #endif
345
346 const internal::inverse_impl<Derived> inverse() const;
347 template<typename ResultType>
348 void computeInverseAndDetWithCheck(
349 ResultType& inverse,
350 typename ResultType::Scalar& determinant,
351 bool& invertible,
352 const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
353 ) const;
354 template<typename ResultType>
355 void computeInverseWithCheck(
356 ResultType& inverse,
357 bool& invertible,
358 const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()
359 ) const;
360 Scalar determinant() const;
361
363
364 const LLT<PlainObject> llt() const;
365 const LDLT<PlainObject> ldlt() const;
366
368
369 const HouseholderQR<PlainObject> householderQr() const;
370 const ColPivHouseholderQR<PlainObject> colPivHouseholderQr() const;
371 const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr() const;
372
373 #ifdef EIGEN2_SUPPORT
374 const QR<PlainObject> qr() const;
375 #endif
376
377 EigenvaluesReturnType eigenvalues() const;
378 RealScalar operatorNorm() const;
379
381
382 JacobiSVD<PlainObject> jacobiSvd(unsigned int computationOptions = 0) const;
383
384 #ifdef EIGEN2_SUPPORT
385 SVD<PlainObject> svd() const;
386 #endif
387
389
390 #ifndef EIGEN_PARSED_BY_DOXYGEN
392 template<typename OtherDerived> struct cross_product_return_type {
393 typedef typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
394 typedef Matrix<Scalar,MatrixBase::RowsAtCompileTime,MatrixBase::ColsAtCompileTime> type;
395 };
396 #endif // EIGEN_PARSED_BY_DOXYGEN
397 template<typename OtherDerived>
398 typename cross_product_return_type<OtherDerived>::type
399 cross(const MatrixBase<OtherDerived>& other) const;
400 template<typename OtherDerived>
401 PlainObject cross3(const MatrixBase<OtherDerived>& other) const;
402 PlainObject unitOrthogonal(void) const;
403 Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
404
405 #if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS
406 ScalarMultipleReturnType operator*(const UniformScaling<Scalar>& s) const;
407 // put this as separate enum value to work around possible GCC 4.3 bug (?)
408 enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal };
409 typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType;
410 HomogeneousReturnType homogeneous() const;
411 #endif
412
413 enum {
414 SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1
415 };
416 typedef Block<const Derived,
417 internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1,
418 internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne;
419 typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>,
420 const ConstStartMinusOne > HNormalizedReturnType;
421
422 const HNormalizedReturnType hnormalized() const;
423
425
426 void makeHouseholderInPlace(Scalar& tau, RealScalar& beta);
427 template<typename EssentialPart>
428 void makeHouseholder(EssentialPart& essential,
429 Scalar& tau, RealScalar& beta) const;
430 template<typename EssentialPart>
431 void applyHouseholderOnTheLeft(const EssentialPart& essential,
432 const Scalar& tau,
433 Scalar* workspace);
434 template<typename EssentialPart>
435 void applyHouseholderOnTheRight(const EssentialPart& essential,
436 const Scalar& tau,
437 Scalar* workspace);
438
440
441 template<typename OtherScalar>
442 void applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j);
443 template<typename OtherScalar>
444 void applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j);
445
447
448 typedef typename internal::stem_function<Scalar>::type StemFunction;
449 const MatrixExponentialReturnValue<Derived> exp() const;
450 const MatrixFunctionReturnValue<Derived> matrixFunction(StemFunction f) const;
451 const MatrixFunctionReturnValue<Derived> cosh() const;
452 const MatrixFunctionReturnValue<Derived> sinh() const;
453 const MatrixFunctionReturnValue<Derived> cos() const;
454 const MatrixFunctionReturnValue<Derived> sin() const;
455 const MatrixSquareRootReturnValue<Derived> sqrt() const;
456 const MatrixLogarithmReturnValue<Derived> log() const;
457
458#ifdef EIGEN2_SUPPORT
459 template<typename ProductDerived, typename Lhs, typename Rhs>
460 Derived& operator+=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
461 EvalBeforeAssigningBit>& other);
462
463 template<typename ProductDerived, typename Lhs, typename Rhs>
464 Derived& operator-=(const Flagged<ProductBase<ProductDerived, Lhs,Rhs>, 0,
465 EvalBeforeAssigningBit>& other);
466
469 template<typename OtherDerived>
470 Derived& lazyAssign(const Flagged<OtherDerived, 0, EvalBeforeAssigningBit>& other)
471 { return lazyAssign(other._expression()); }
472
473 template<unsigned int Added>
474 const Flagged<Derived, Added, 0> marked() const;
475 const Flagged<Derived, 0, EvalBeforeAssigningBit> lazy() const;
476
477 inline const Cwise<Derived> cwise() const;
478 inline Cwise<Derived> cwise();
479
480 VectorBlock<Derived> start(Index size);
481 const VectorBlock<const Derived> start(Index size) const;
482 VectorBlock<Derived> end(Index size);
483 const VectorBlock<const Derived> end(Index size) const;
484 template<int Size> VectorBlock<Derived,Size> start();
485 template<int Size> const VectorBlock<const Derived,Size> start() const;
486 template<int Size> VectorBlock<Derived,Size> end();
487 template<int Size> const VectorBlock<const Derived,Size> end() const;
488
489 Minor<Derived> minor(Index row, Index col);
490 const Minor<Derived> minor(Index row, Index col) const;
491#endif
492
493 protected:
494 MatrixBase() : Base() {}
495
496 private:
497 explicit MatrixBase(int);
498 MatrixBase(int,int);
499 template<typename OtherDerived> explicit MatrixBase(const MatrixBase<OtherDerived>&);
500 protected:
501 // mixing arrays and matrices is not legal
502 template<typename OtherDerived> Derived& operator+=(const ArrayBase<OtherDerived>& )
503 {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
504 // mixing arrays and matrices is not legal
505 template<typename OtherDerived> Derived& operator-=(const ArrayBase<OtherDerived>& )
506 {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}
507};
508
509} // end namespace Eigen
510
511#endif // EIGEN_MATRIXBASE_H
Eigen::Block
Expression of a fixed-size or dynamic-size block.
Definition Block.h:99
Eigen::ColPivHouseholderQR
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
Definition ColPivHouseholderQR.h:38
Eigen::CwiseNullaryOp
Generic expression of a matrix where all coefficients are defined by a functor.
Definition CwiseNullaryOp.h:51
Eigen::CwiseUnaryOp
Generic expression where a coefficient-wise unary operator is applied to an expression.
Definition CwiseUnaryOp.h:61
Eigen::DenseBase::DenseBase
DenseBase()
Definition DenseBase.h:513
Eigen::MatrixBase< MatrixWrapper< ExpressionType > >::Index
internal::traits< MatrixWrapper< ExpressionType > >::Index Index
Definition DenseBase.h:51
Eigen::DiagonalWrapper
Expression of a diagonal matrix.
Definition DiagonalMatrix.h:245
Eigen::Diagonal
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition Diagonal.h:66
Eigen::ForceAlignedAccess
Enforce aligned packet loads and stores regardless of what is requested.
Definition ForceAlignedAccess.h:36
Eigen::FullPivHouseholderQR
Householder rank-revealing QR decomposition of a matrix with full pivoting.
Definition FullPivHouseholderQR.h:50
Eigen::Homogeneous
Expression of one (or a set of) homogeneous vector(s)
Definition Homogeneous.h:63
Eigen::HouseholderQR
Householder QR decomposition of a matrix.
Definition HouseholderQR.h:43
Eigen::JacobiRotation
Rotation given by a cosine-sine pair.
Definition Jacobi.h:35
Eigen::JacobiSVD
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition JacobiSVD.h:479
Eigen::LDLT
Robust Cholesky decomposition of a matrix with pivoting.
Definition LDLT.h:46
Eigen::LLT
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
Definition LLT.h:51
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition MatrixBase.h:50
Eigen::MatrixBase::Identity
static const IdentityReturnType Identity()
Definition CwiseNullaryOp.h:700
Eigen::MatrixBase::normalized
const PlainObject normalized() const
Definition Dot.h:138
Eigen::MatrixBase::partialPivLu
const PartialPivLU< PlainObject > partialPivLu() const
Definition PartialPivLU.h:474
Eigen::MatrixBase::lazyProduct
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct(const MatrixBase< OtherDerived > &other) const
Definition GeneralProduct.h:590
Eigen::MatrixBase::UnitZ
static const BasisReturnType UnitZ()
Definition CwiseNullaryOp.h:849
Eigen::MatrixBase::applyHouseholderOnTheRight
void applyHouseholderOnTheRight(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition Householder.h:146
Eigen::MatrixBase::operator*
const ScalarMultipleReturnType operator*(const Scalar &scalar) const
Definition MatrixBase.h:50
Eigen::MatrixBase::forceAlignedAccessIf
internal::add_const_on_value_type< typenameinternal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf() const
Definition ForceAlignedAccess.h:128
Eigen::MatrixBase::computeInverseWithCheck
void computeInverseWithCheck(ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition Inverse.h:382
Eigen::MatrixBase::operator-=
Derived & operator-=(const MatrixBase< OtherDerived > &other)
Definition CwiseBinaryOp.h:206
Eigen::MatrixBase::hnormalized
const HNormalizedReturnType hnormalized() const
Definition Homogeneous.h:158
Eigen::MatrixBase::asDiagonal
const DiagonalWrapper< const Derived > asDiagonal() const
Definition DiagonalMatrix.h:273
Eigen::MatrixBase::isDiagonal
bool isDiagonal(RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition DiagonalMatrix.h:287
Eigen::MatrixBase::operator==
bool operator==(const MatrixBase< OtherDerived > &other) const
Definition MatrixBase.h:279
Eigen::MatrixBase::homogeneous
HomogeneousReturnType homogeneous() const
Definition Homogeneous.h:127
Eigen::MatrixBase::array
ArrayWrapper< Derived > array()
Definition MatrixBase.h:308
Eigen::MatrixBase::UnitW
static const BasisReturnType UnitW()
Definition CwiseNullaryOp.h:859
Eigen::MatrixBase::UnitX
static const BasisReturnType UnitX()
Definition CwiseNullaryOp.h:829
Eigen::MatrixBase::applyHouseholderOnTheLeft
void applyHouseholderOnTheLeft(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
Definition Householder.h:109
Eigen::MatrixBase::inverse
const internal::inverse_impl< Derived > inverse() const
Definition Inverse.h:316
Eigen::MatrixBase::unitOrthogonal
PlainObject unitOrthogonal(void) const
Definition OrthoMethods.h:210
Eigen::MatrixBase::applyOnTheRight
void applyOnTheRight(const EigenBase< OtherDerived > &other)
Definition EigenBase.h:145
Eigen::MatrixBase::eigenvalues
EigenvaluesReturnType eigenvalues() const
Computes the eigenvalues of a matrix.
Definition MatrixBaseEigenvalues.h:67
Eigen::MatrixBase::llt
const LLT< PlainObject > llt() const
Definition LLT.h:471
Eigen::MatrixBase::operator+=
Derived & operator+=(const MatrixBase< OtherDerived > &other)
Definition CwiseBinaryOp.h:220
Eigen::MatrixBase::colPivHouseholderQr
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const
Definition ColPivHouseholderQR.h:519
Eigen::MatrixBase::isOrthogonal
bool isOrthogonal(const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition Dot.h:226
Eigen::MatrixBase::squaredNorm
RealScalar squaredNorm() const
Definition Dot.h:113
Eigen::MatrixBase::fullPivHouseholderQr
const FullPivHouseholderQR< PlainObject > fullPivHouseholderQr() const
Definition FullPivHouseholderQR.h:588
Eigen::MatrixBase::stableNorm
RealScalar stableNorm() const
Definition StableNorm.h:45
Eigen::MatrixBase::norm
RealScalar norm() const
Definition Dot.h:125
Eigen::MatrixBase::jacobiSvd
JacobiSVD< PlainObject > jacobiSvd(unsigned int computationOptions=0) const
Definition JacobiSVD.h:856
Eigen::MatrixBase::operator!=
bool operator!=(const MatrixBase< OtherDerived > &other) const
Definition MatrixBase.h:287
Eigen::MatrixBase::hypotNorm
RealScalar hypotNorm() const
Definition StableNorm.h:170
Eigen::MatrixBase::applyOnTheLeft
void applyOnTheLeft(const EigenBase< OtherDerived > &other)
Definition EigenBase.h:153
Eigen::MatrixBase::trace
Scalar trace() const
Definition Redux.h:399
Eigen::MatrixBase::isUnitary
bool isUnitary(RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition Dot.h:245
Eigen::MatrixBase::cwiseEqual
const CwiseUnaryOp< std::binder1st< std::equal_to< Scalar > >, const Derived > cwiseEqual(const Scalar &s) const
Definition MatrixBase.h:64
Eigen::MatrixBase::makeHouseholder
void makeHouseholder(EssentialPart &essential, Scalar &tau, RealScalar &beta) const
Definition Householder.h:65
Eigen::MatrixBase::isIdentity
bool isIdentity(RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition CwiseNullaryOp.h:717
Eigen::MatrixBase::computeInverseAndDetWithCheck
void computeInverseAndDetWithCheck(ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
Definition Inverse.h:343
Eigen::MatrixBase::adjointInPlace
void adjointInPlace()
Definition Transpose.h:319
Eigen::MatrixBase::makeHouseholderInPlace
void makeHouseholderInPlace(Scalar &tau, RealScalar &beta)
Definition Householder.h:42
Eigen::MatrixBase::dot
internal::scalar_product_traits< typenameinternal::traits< Derived >::Scalar, typenameinternal::traits< OtherDerived >::Scalar >::ReturnType dot(const MatrixBase< OtherDerived > &other) const
Definition Dot.h:63
Eigen::MatrixBase::UnitY
static const BasisReturnType UnitY()
Definition CwiseNullaryOp.h:839
Eigen::MatrixBase< MatrixWrapper< ExpressionType > >::PlainObject
Matrix< typename internal::traits< MatrixWrapper< ExpressionType > >::Scalar, internal::traits< MatrixWrapper< ExpressionType > >::RowsAtCompileTime, internal::traits< MatrixWrapper< ExpressionType > >::ColsAtCompileTime, AutoAlign|(internal::traits< MatrixWrapper< ExpressionType > >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< MatrixWrapper< ExpressionType > >::MaxRowsAtCompileTime, internal::traits< MatrixWrapper< ExpressionType > >::MaxColsAtCompileTime > PlainObject
Definition MatrixBase.h:115
Eigen::MatrixBase::operator*=
Derived & operator*=(const EigenBase< OtherDerived > &other)
Definition EigenBase.h:136
Eigen::MatrixBase::operatorNorm
RealScalar operatorNorm() const
Computes the L2 operator norm.
Definition MatrixBaseEigenvalues.h:122
Eigen::MatrixBase::normalize
void normalize()
Definition Dot.h:153
Eigen::MatrixBase::fullPivLu
const FullPivLU< PlainObject > fullPivLu() const
Definition FullPivLU.h:729
Eigen::MatrixBase::ldlt
const LDLT< PlainObject > ldlt() const
Definition LDLT.h:592
Eigen::MatrixBase::cross3
PlainObject cross3(const MatrixBase< OtherDerived > &other) const
Definition OrthoMethods.h:74
Eigen::MatrixBase::lu
const PartialPivLU< PlainObject > lu() const
Definition PartialPivLU.h:490
Eigen::MatrixBase::diagonalSize
Index diagonalSize() const
Definition MatrixBase.h:101
Eigen::MatrixBase::operator=
const EIGEN_CWISE_PRODUCT_RETURN_TYPE(Derived, OtherDerived) cwiseProduct(const Eigen Derived & operator=(const DenseBase< OtherDerived > &other)
Eigen::MatrixBase::blueNorm
RealScalar blueNorm() const
Definition StableNorm.h:75
Eigen::MatrixBase::householderQr
const HouseholderQR< PlainObject > householderQr() const
Definition HouseholderQR.h:336
Eigen::MatrixBase::noalias
NoAlias< Derived, Eigen::MatrixBase > noalias()
Definition NoAlias.h:118
Eigen::MatrixBase::Unit
static const BasisReturnType Unit(Index size, Index i)
Definition CwiseNullaryOp.h:801
Eigen::MatrixBase::adjoint
const AdjointReturnType adjoint() const
Definition Transpose.h:237
Eigen::MatrixBase::setIdentity
Derived & setIdentity()
Definition CwiseNullaryOp.h:772
Eigen::MatrixBase::isLowerTriangular
bool isLowerTriangular(RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition TriangularMatrix.h:807
Eigen::MatrixBase::isUpperTriangular
bool isUpperTriangular(RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
Definition TriangularMatrix.h:782
Eigen::MatrixBase::forceAlignedAccess
const ForceAlignedAccess< Derived > forceAlignedAccess() const
Definition ForceAlignedAccess.h:107
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition Matrix.h:129
Eigen::NoAlias
Pseudo expression providing an operator = assuming no aliasing.
Definition NoAlias.h:32
Eigen::PartialPivLU
LU decomposition of a matrix with partial pivoting, and related features.
Definition PartialPivLU.h:48
Eigen::PermutationWrapper
Class to view a vector of integers as a permutation matrix.
Definition PermutationMatrix.h:484
Eigen::SelfAdjointView
Expression of a selfadjoint matrix from a triangular part of a dense matrix.
Definition SelfAdjointView.h:55
Eigen::TriangularView
Base class for triangular part in a matrix.
Definition TriangularMatrix.h:160
Eigen::VectorBlock
Expression of a fixed-size or dynamic-size sub-vector.
Definition VectorBlock.h:61
Eigen::MatrixBase::eulerAngles
Matrix< Scalar, 3, 1 > eulerAngles(Index a0, Index a1, Index a2) const
Definition EulerAngles.h:33
Eigen::RowMajor
@ RowMajor
Definition Constants.h:259
Eigen::ColMajor
@ ColMajor
Definition Constants.h:257
Eigen::Vertical
@ Vertical
Definition Constants.h:204
Eigen::Horizontal
@ Horizontal
Definition Constants.h:207
Eigen::RowMajorBit
const unsigned int RowMajorBit
Definition Constants.h:48
Eigen::EvalBeforeAssigningBit
const unsigned int EvalBeforeAssigningBit
Definition Constants.h:58
Eigen::EigenBase
Definition EigenBase.h:27