Eigen::MatrixBase< Derived > Class Template Reference

Base class for all dense matrices, vectors, and expressions. More...

#include <MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:

Classes
struct	ConstSelfAdjointViewReturnType
struct	ConstTriangularViewReturnType
struct	SelfAdjointViewReturnType
struct	TriangularViewReturnType

Public Types
enum	{ HomogeneousReturnTypeDirection }
enum	{ SizeMinusOne = SizeAtCompileTime == Dynamic ? Dynamic : SizeAtCompileTime - 1 }
typedef MatrixBase	StorageBaseType
typedef internal::traits< Derived >::StorageKind	StorageKind
typedef internal::traits< Derived >::StorageIndex	StorageIndex
typedef internal::traits< Derived >::Scalar	Scalar
typedef internal::packet_traits< Scalar >::type	PacketScalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef DenseBase< Derived >	Base
typedef Base::CoeffReturnType	CoeffReturnType
typedef Base::ConstTransposeReturnType	ConstTransposeReturnType
typedef Base::RowXpr	RowXpr
typedef Base::ColXpr	ColXpr
typedef Matrix< Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime), internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)>	SquareMatrixType
typedef Base::PlainObject	PlainObject
typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, PlainObject >	ConstantReturnType
typedef std::conditional_t< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >	AdjointReturnType
typedef Matrix< std::complex< RealScalar >, internal::traits< Derived >::ColsAtCompileTime, 1, ColMajor >	EigenvaluesReturnType
typedef CwiseNullaryOp< internal::scalar_identity_op< Scalar >, PlainObject >	IdentityReturnType
typedef Block< const CwiseNullaryOp< internal::scalar_identity_op< Scalar >, SquareMatrixType >, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime >	BasisReturnType
typedef Diagonal< Derived >	DiagonalReturnType
typedef Diagonal< const Derived >	ConstDiagonalReturnType
typedef Homogeneous< Derived, HomogeneousReturnTypeDirection >	HomogeneousReturnType
typedef Block< const Derived, internal::traits< Derived >::ColsAtCompileTime==1 ? SizeMinusOne :1, internal::traits< Derived >::ColsAtCompileTime==1 ? 1 :SizeMinusOne >	ConstStartMinusOne
typedef internal::stem_function< Scalar >::type	StemFunction
Public Types inherited from Eigen::DenseBase< Derived >
enum	{   RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime , ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime , SizeAtCompileTime = (internal::size_of_xpr_at_compile_time<Derived>::ret) , MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime ,   MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime , MaxSizeAtCompileTime , IsVectorAtCompileTime , NumDimensions ,   Flags = internal::traits<Derived>::Flags , IsRowMajor = int(Flags) & RowMajorBit , InnerSizeAtCompileTime , InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret ,   OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret }
enum	{ IsPlainObjectBase = 0 }
typedef Eigen::InnerIterator< Derived >	InnerIterator
typedef internal::traits< Derived >::StorageKind	StorageKind
typedef internal::traits< Derived >::StorageIndex	StorageIndex
	The type used to store indices. More...
typedef internal::traits< Derived >::Scalar	Scalar
typedef Scalar	value_type
typedef NumTraits< Scalar >::Real	RealScalar
typedef DenseCoeffsBase< Derived, internal::accessors_level< Derived >::value >	Base
typedef Base::CoeffReturnType	CoeffReturnType
typedef internal::find_best_packet< Scalar, SizeAtCompileTime >::type	PacketScalar
typedef Matrix< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime >	PlainMatrix
typedef Array< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime >	PlainArray
typedef std::conditional_t< internal::is_same< typename internal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray >	PlainObject
	The plain matrix or array type corresponding to this expression. More...
typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, PlainObject >	ConstantReturnType
typedef CwiseNullaryOp< internal::scalar_zero_op< Scalar >, PlainObject >	ZeroReturnType
typedef CwiseNullaryOp< internal::linspaced_op< Scalar >, PlainObject >	RandomAccessLinSpacedReturnType
typedef CwiseNullaryOp< internal::equalspaced_op< Scalar >, PlainObject >	RandomAccessEqualSpacedReturnType
typedef Matrix< typename NumTraits< typename internal::traits< Derived >::Scalar >::Real, internal::traits< Derived >::ColsAtCompileTime, 1 >	EigenvaluesReturnType
typedef Transpose< Derived >	TransposeReturnType
typedef Transpose< const Derived >	ConstTransposeReturnType
typedef internal::add_const_on_value_type_t< typename internal::eval< Derived >::type >	EvalReturnType
typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType
typedef const VectorwiseOp< const Derived, Horizontal >	ConstRowwiseReturnType
typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType
typedef const VectorwiseOp< const Derived, Vertical >	ConstColwiseReturnType
typedef CwiseNullaryOp< internal::scalar_random_op< Scalar >, PlainObject >	RandomReturnType
typedef Reverse< Derived, BothDirections >	ReverseReturnType
typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType
typedef std::conditional_t<(Flags &DirectAccessBit)==DirectAccessBit, internal::pointer_based_stl_iterator< Derived >, internal::generic_randaccess_stl_iterator< Derived > >	iterator_type
typedef std::conditional_t<(Flags &DirectAccessBit)==DirectAccessBit, internal::pointer_based_stl_iterator< const Derived >, internal::generic_randaccess_stl_iterator< const Derived > >	const_iterator_type
typedef std::conditional_t< IsVectorAtCompileTime, iterator_type, void >	iterator
typedef std::conditional_t< IsVectorAtCompileTime, const_iterator_type, void >	const_iterator

Public Member Functions
EIGEN_DEVICE_FUNC Index	diagonalSize () const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const MatrixBase &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const ReturnByValue< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator+= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator-= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC const Product< Derived, OtherDerived >	operator* (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC const Product< Derived, OtherDerived, LazyProduct >	lazyProduct (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
Derived &	operator*= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
void	applyOnTheLeft (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
void	applyOnTheRight (const EigenBase< OtherDerived > &other)
template<typename DiagonalDerived >
EIGEN_DEVICE_FUNC const Product< Derived, DiagonalDerived, LazyProduct >	operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
template<typename SkewDerived >
EIGEN_DEVICE_FUNC const Product< Derived, SkewDerived, LazyProduct >	operator* (const SkewSymmetricBase< SkewDerived > &skew) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType	dot (const MatrixBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC RealScalar	squaredNorm () const
EIGEN_DEVICE_FUNC RealScalar	norm () const
RealScalar	stableNorm () const
RealScalar	blueNorm () const
RealScalar	hypotNorm () const
EIGEN_DEVICE_FUNC const PlainObject	normalized () const
EIGEN_DEVICE_FUNC const PlainObject	stableNormalized () const
EIGEN_DEVICE_FUNC void	normalize ()
EIGEN_DEVICE_FUNC void	stableNormalize ()
EIGEN_DEVICE_FUNC const AdjointReturnType	adjoint () const
EIGEN_DEVICE_FUNC void	adjointInPlace ()
EIGEN_DEVICE_FUNC DiagonalReturnType	diagonal ()
EIGEN_DEVICE_FUNC const ConstDiagonalReturnType	diagonal () const
template<int Index>
EIGEN_DEVICE_FUNC Diagonal< Derived, Index >	diagonal ()
template<int Index>
EIGEN_DEVICE_FUNC const Diagonal< const Derived, Index >	diagonal () const
EIGEN_DEVICE_FUNC Diagonal< Derived, DynamicIndex >	diagonal (Index index)
EIGEN_DEVICE_FUNC const Diagonal< const Derived, DynamicIndex >	diagonal (Index index) const
template<unsigned int Mode>
EIGEN_DEVICE_FUNC TriangularViewReturnType< Mode >::Type	triangularView ()
template<unsigned int Mode>
EIGEN_DEVICE_FUNC ConstTriangularViewReturnType< Mode >::Type	triangularView () const
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC SelfAdjointViewReturnType< UpLo >::Type	selfadjointView ()
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC ConstSelfAdjointViewReturnType< UpLo >::Type	selfadjointView () const
const SparseView< Derived >	sparseView (const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC const DiagonalWrapper< const Derived >	asDiagonal () const
const PermutationWrapper< const Derived >	asPermutation () const
EIGEN_DEVICE_FUNC const SkewSymmetricWrapper< const Derived >	asSkewSymmetric () const
EIGEN_DEVICE_FUNC Derived &	setIdentity ()
EIGEN_DEVICE_FUNC Derived &	setIdentity (Index rows, Index cols)
	Resizes to the given size, and writes the identity expression (not necessarily square) into *this. More...
EIGEN_DEVICE_FUNC Derived &	setUnit (Index i)
	Set the coefficients of *this to the i-th unit (basis) vector. More...
EIGEN_DEVICE_FUNC Derived &	setUnit (Index newSize, Index i)
	Resizes to the given newSize, and writes the i-th unit (basis) vector into *this. More...
bool	isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool	isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool	isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool	isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool	isSkewSymmetric (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool	isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool	isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	operator== (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	operator!= (const MatrixBase< OtherDerived > &other) const
NoAlias< Derived, Eigen::MatrixBase > EIGEN_DEVICE_FUNC	noalias ()
const Derived &	forceAlignedAccess () const
Derived &	forceAlignedAccess ()
template<bool Enable>
const Derived &	forceAlignedAccessIf () const
template<bool Enable>
Derived &	forceAlignedAccessIf ()
EIGEN_DEVICE_FUNC Scalar	trace () const
template<int p>
EIGEN_DEVICE_FUNC RealScalar	lpNorm () const
EIGEN_DEVICE_FUNC MatrixBase< Derived > &	matrix ()
EIGEN_DEVICE_FUNC const MatrixBase< Derived > &	matrix () const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper< Derived >	array ()
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper< const Derived >	array () const
template<typename PermutationIndex = DefaultPermutationIndex>
const FullPivLU< PlainObject, PermutationIndex >	fullPivLu () const
template<typename PermutationIndex = DefaultPermutationIndex>
const PartialPivLU< PlainObject, PermutationIndex >	partialPivLu () const
template<typename PermutationIndex = DefaultPermutationIndex>
const PartialPivLU< PlainObject, PermutationIndex >	lu () const
EIGEN_DEVICE_FUNC const Inverse< Derived >	inverse () const
template<typename ResultType >
void	computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
template<typename ResultType >
void	computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC Scalar	determinant () const
const LLT< PlainObject >	llt () const
const LDLT< PlainObject >	ldlt () const
const HouseholderQR< PlainObject >	householderQr () const
template<typename PermutationIndex = DefaultPermutationIndex>
const ColPivHouseholderQR< PlainObject, PermutationIndex >	colPivHouseholderQr () const
template<typename PermutationIndex = DefaultPermutationIndex>
const FullPivHouseholderQR< PlainObject, PermutationIndex >	fullPivHouseholderQr () const
template<typename PermutationIndex = DefaultPermutationIndex>
const CompleteOrthogonalDecomposition< PlainObject, PermutationIndex >	completeOrthogonalDecomposition () const
EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix. More...
RealScalar	operatorNorm () const
	Computes the L2 operator norm. More...
template<int Options = 0>
JacobiSVD< PlainObject, Options >	jacobiSvd () const
template<int Options = 0>
EIGEN_DEPRECATED JacobiSVD< PlainObject, Options >	jacobiSvd (unsigned int computationOptions) const
template<int Options = 0>
BDCSVD< PlainObject, Options >	bdcSvd () const
template<int Options = 0>
EIGEN_DEPRECATED BDCSVD< PlainObject, Options >	bdcSvd (unsigned int computationOptions) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC internal::cross_impl< Derived, OtherDerived >::return_type	cross (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC PlainObject	cross3 (const MatrixBase< OtherDerived > &other) const
EIGEN_DEVICE_FUNC PlainObject	unitOrthogonal (void) const
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Matrix< Scalar, 3, 1 >	eulerAngles (Index a0, Index a1, Index a2) const
EIGEN_DEVICE_FUNC Matrix< Scalar, 3, 1 >	canonicalEulerAngles (Index a0, Index a1, Index a2) const
EIGEN_DEVICE_FUNC HomogeneousReturnType	homogeneous () const
typedef	EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE (ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType
EIGEN_DEVICE_FUNC const HNormalizedReturnType	hnormalized () const
	homogeneous normalization More...
EIGEN_DEVICE_FUNC void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
template<typename EssentialPart >
EIGEN_DEVICE_FUNC void	makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
template<typename EssentialPart >
EIGEN_DEVICE_FUNC void	applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename EssentialPart >
EIGEN_DEVICE_FUNC void	applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename OtherScalar >
EIGEN_DEVICE_FUNC void	applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherScalar >
EIGEN_DEVICE_FUNC void	applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherDerived >
EIGEN_STRONG_INLINE const SparseMatrixBase< OtherDerived >::template CwiseProductDenseReturnType< Derived >::Type	cwiseProduct (const SparseMatrixBase< OtherDerived > &other) const
const MatrixFunctionReturnValue< Derived >	matrixFunction (StemFunction f) const
	Helper function for the unsupported MatrixFunctions module. More...
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const ReturnByValue< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType	dot (const MatrixBase< OtherDerived > &other) const
template<int p>
EIGEN_DEVICE_FUNC NumTraits< typename internal::traits< Derived >::Scalar >::Real	lpNorm () const
template<bool Enable>
add_const_on_value_type_t< std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > >	forceAlignedAccessIf () const
template<bool Enable>
std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf ()
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product< Derived, OtherDerived >	operator* (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product< Derived, OtherDerived, LazyProduct >	lazyProduct (const MatrixBase< OtherDerived > &other) const
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type	selfadjointView () const
template<unsigned int UpLo>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type	selfadjointView ()
template<unsigned int Mode>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type	triangularView ()
template<unsigned int Mode>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type	triangularView () const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::cross_impl< Derived, OtherDerived >::return_type	cross (const MatrixBase< OtherDerived > &other) const
template<typename PermutationIndex >
const FullPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex >	fullPivLu () const
template<typename PermutationIndex >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex >	partialPivLu () const
template<typename PermutationIndex >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex >	lu () const
template<typename PermutationIndexType >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType >	colPivHouseholderQr () const
template<typename PermutationIndex >
const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject, PermutationIndex >	completeOrthogonalDecomposition () const
template<typename PermutationIndex >
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndex >	fullPivHouseholderQr () const
template<int Options>
BDCSVD< typename MatrixBase< Derived >::PlainObject, Options >	bdcSvd () const
template<int Options>
BDCSVD< typename MatrixBase< Derived >::PlainObject, Options >	bdcSvd (unsigned int computationOptions) const
template<int Options>
JacobiSVD< typename MatrixBase< Derived >::PlainObject, Options >	jacobiSvd () const
template<int Options>
JacobiSVD< typename MatrixBase< Derived >::PlainObject, Options >	jacobiSvd (unsigned int computationOptions) const
Public Member Functions inherited from Eigen::DenseBase< Derived >
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	outerSize () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	innerSize () const
EIGEN_DEVICE_FUNC void	resize (Index newSize)
EIGEN_DEVICE_FUNC void	resize (Index rows, Index cols)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const DenseBase< OtherDerived > &other)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const DenseBase &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const EigenBase< OtherDerived > &other)
	Copies the generic expression other into *this. More...
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator+= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator-= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator= (const ReturnByValue< OtherDerived > &func)
template<typename OtherDerived >
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived &	lazyAssign (const DenseBase< OtherDerived > &other)
EIGEN_DEVICE_FUNC CommaInitializer< Derived >	operator<< (const Scalar &s)
template<unsigned int Added, unsigned int Removed>
EIGEN_DEPRECATED const Derived &	flagged () const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC CommaInitializer< Derived >	operator<< (const DenseBase< OtherDerived > &other)
EIGEN_DEVICE_FUNC TransposeReturnType	transpose ()
EIGEN_DEVICE_FUNC const ConstTransposeReturnType	transpose () const
EIGEN_DEVICE_FUNC void	transposeInPlace ()
EIGEN_DEVICE_FUNC void	fill (const Scalar &value)
EIGEN_DEVICE_FUNC Derived &	setConstant (const Scalar &value)
EIGEN_DEVICE_FUNC Derived &	setLinSpaced (Index size, const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector. More...
EIGEN_DEVICE_FUNC Derived &	setLinSpaced (const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector. More...
EIGEN_DEVICE_FUNC Derived &	setEqualSpaced (Index size, const Scalar &low, const Scalar &step)
EIGEN_DEVICE_FUNC Derived &	setEqualSpaced (const Scalar &low, const Scalar &step)
EIGEN_DEVICE_FUNC Derived &	setZero ()
EIGEN_DEVICE_FUNC Derived &	setOnes ()
EIGEN_DEVICE_FUNC Derived &	setRandom ()
template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	isMuchSmallerThan (const RealScalar &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_DEVICE_FUNC bool	hasNaN () const
EIGEN_DEVICE_FUNC bool	allFinite () const
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator*= (const Scalar &other)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator/= (const Scalar &other)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType	eval () const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void	swap (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void	swap (PlainObjectBase< OtherDerived > &other)
EIGEN_DEVICE_FUNC const NestByValue< Derived >	nestByValue () const
EIGEN_DEVICE_FUNC const ForceAlignedAccess< Derived >	forceAlignedAccess () const
EIGEN_DEVICE_FUNC ForceAlignedAccess< Derived >	forceAlignedAccess ()
template<bool Enable>
EIGEN_DEVICE_FUNC const std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf () const
template<bool Enable>
EIGEN_DEVICE_FUNC std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf ()
EIGEN_DEVICE_FUNC Scalar	sum () const
EIGEN_DEVICE_FUNC Scalar	mean () const
EIGEN_DEVICE_FUNC Scalar	trace () const
EIGEN_DEVICE_FUNC Scalar	prod () const
template<int NaNPropagation>
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff () const
template<int NaNPropagation>
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff () const
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff () const
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff () const
template<int NaNPropagation, typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff (IndexType *row, IndexType *col) const
template<int NaNPropagation, typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff (IndexType *row, IndexType *col) const
template<int NaNPropagation, typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff (IndexType *index) const
template<int NaNPropagation, typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff (IndexType *index) const
template<typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff (IndexType *index) const
template<typename IndexType >
EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff (IndexType *index) const
template<typename BinaryOp >
EIGEN_DEVICE_FUNC Scalar	redux (const BinaryOp &func) const
template<typename Visitor >
EIGEN_DEVICE_FUNC void	visit (Visitor &func) const
const WithFormat< Derived >	format (const IOFormat &fmt) const
EIGEN_DEVICE_FUNC CoeffReturnType	value () const
EIGEN_DEVICE_FUNC bool	all () const
EIGEN_DEVICE_FUNC bool	any () const
EIGEN_DEVICE_FUNC Index	count () const
EIGEN_DEVICE_FUNC ConstRowwiseReturnType	rowwise () const
EIGEN_DEVICE_FUNC RowwiseReturnType	rowwise ()
EIGEN_DEVICE_FUNC ConstColwiseReturnType	colwise () const
EIGEN_DEVICE_FUNC ColwiseReturnType	colwise ()
template<typename ThenDerived , typename ElseDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, Scalar >, ThenDerived, ElseDerived, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
template<typename ThenDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ThenDerived >::Scalar, Scalar >, ThenDerived, typename DenseBase< ThenDerived >::ConstantReturnType, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const typename DenseBase< ThenDerived >::Scalar &elseScalar) const
template<typename ElseDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ElseDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, Scalar >, typename DenseBase< ElseDerived >::ConstantReturnType, ElseDerived, Derived >	select (const typename DenseBase< ElseDerived >::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
template<int p>
RealScalar	lpNorm () const
template<int RowFactor, int ColFactor>
EIGEN_DEVICE_FUNC const Replicate< Derived, RowFactor, ColFactor >	replicate () const
EIGEN_DEVICE_FUNC const Replicate< Derived, Dynamic, Dynamic >	replicate (Index rowFactor, Index colFactor) const
EIGEN_DEVICE_FUNC ReverseReturnType	reverse ()
EIGEN_DEVICE_FUNC ConstReverseReturnType	reverse () const
EIGEN_DEVICE_FUNC void	reverseInPlace ()
iterator	begin ()
const_iterator	begin () const
const_iterator	cbegin () const
iterator	end ()
const_iterator	end () const
const_iterator	cend () const
template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &) const
template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	lazyAssign (const DenseBase< OtherDerived > &other)
template<typename CustomNullaryOp >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject >	NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject >	NullaryExpr (Index size, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject >	NullaryExpr (const CustomNullaryOp &func)
template<typename Derived >
EIGEN_DEVICE_FUNC bool	isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const
template<typename Func >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar	redux (const Func &func) const
template<typename ThenDerived , typename ElseDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, typename DenseBase< Derived >::Scalar >, ThenDerived, ElseDerived, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
template<typename ThenDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ThenDerived >::Scalar, typename DenseBase< Derived >::Scalar >, ThenDerived, typename DenseBase< ThenDerived >::ConstantReturnType, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const typename DenseBase< ThenDerived >::Scalar &elseScalar) const
template<typename ElseDerived >
EIGEN_DEVICE_FUNC CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ElseDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, typename DenseBase< Derived >::Scalar >, typename DenseBase< ElseDerived >::ConstantReturnType, ElseDerived, Derived >	select (const typename DenseBase< ElseDerived >::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const

Static Public Member Functions
static EIGEN_DEVICE_FUNC const IdentityReturnType	Identity ()
static EIGEN_DEVICE_FUNC const IdentityReturnType	Identity (Index rows, Index cols)
static EIGEN_DEVICE_FUNC const BasisReturnType	Unit (Index size, Index i)
static EIGEN_DEVICE_FUNC const BasisReturnType	Unit (Index i)
static EIGEN_DEVICE_FUNC const BasisReturnType	UnitX ()
static EIGEN_DEVICE_FUNC const BasisReturnType	UnitY ()
static EIGEN_DEVICE_FUNC const BasisReturnType	UnitZ ()
static EIGEN_DEVICE_FUNC const BasisReturnType	UnitW ()
Static Public Member Functions inherited from Eigen::DenseBase< Derived >
static EIGEN_DEVICE_FUNC const ConstantReturnType	Constant (Index rows, Index cols, const Scalar &value)
static EIGEN_DEVICE_FUNC const ConstantReturnType	Constant (Index size, const Scalar &value)
static EIGEN_DEVICE_FUNC const ConstantReturnType	Constant (const Scalar &value)
EIGEN_DEPRECATED static EIGEN_DEVICE_FUNC const RandomAccessLinSpacedReturnType	LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
EIGEN_DEPRECATED static EIGEN_DEVICE_FUNC const RandomAccessLinSpacedReturnType	LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static EIGEN_DEVICE_FUNC const RandomAccessLinSpacedReturnType	LinSpaced (Index size, const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector. More...
static EIGEN_DEVICE_FUNC const RandomAccessLinSpacedReturnType	LinSpaced (const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector. More...
static EIGEN_DEVICE_FUNC const RandomAccessEqualSpacedReturnType	EqualSpaced (Index size, const Scalar &low, const Scalar &step)
static EIGEN_DEVICE_FUNC const RandomAccessEqualSpacedReturnType	EqualSpaced (const Scalar &low, const Scalar &step)
template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (Index size, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (const CustomNullaryOp &func)
static EIGEN_DEVICE_FUNC const ZeroReturnType	Zero (Index rows, Index cols)
static EIGEN_DEVICE_FUNC const ZeroReturnType	Zero (Index size)
static EIGEN_DEVICE_FUNC const ZeroReturnType	Zero ()
static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones (Index rows, Index cols)
static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones (Index size)
static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones ()
static const RandomReturnType	Random (Index rows, Index cols)
static const RandomReturnType	Random (Index size)
static const RandomReturnType	Random ()

Protected Member Functions
template<typename OtherDerived >
Derived &	operator+= (const ArrayBase< OtherDerived > &)
template<typename OtherDerived >
Derived &	operator-= (const ArrayBase< OtherDerived > &)
Protected Member Functions inherited from Eigen::DenseBase< Derived >
constexpr EIGEN_DEVICE_FUNC	DenseBase ()=default

Private Member Functions
EIGEN_DEVICE_FUNC	MatrixBase (int)
EIGEN_DEVICE_FUNC	MatrixBase (int, int)
template<typename OtherDerived >
EIGEN_DEVICE_FUNC	MatrixBase (const MatrixBase< OtherDerived > &)

Additional Inherited Members
Public Attributes inherited from Eigen::DenseBase< Derived >
EIGEN_DEPRECATED typedef CwiseNullaryOp< internal::linspaced_op< Scalar >, PlainObject >	SequentialLinSpacedReturnType
Related Functions inherited from Eigen::DenseBase< Derived >
template<typename Derived >
std::ostream &	operator<< (std::ostream &s, const DenseBase< Derived > &m)

Detailed Description

template<typename Derived>
class Eigen::MatrixBase< Derived >

Base class for all dense matrices, vectors, and expressions.

This class is the base that is inherited by all matrix, vector, and related expression types. Most of the Eigen API is contained in this class, and its base classes. Other important classes for the Eigen API are Matrix, and VectorwiseOp.

Note that some methods are defined in other modules such as the LU_Module LU module for all functions related to matrix inversions.

Template Parameters

Derived

is the derived type, e.g. a matrix type, or an expression, etc.

When writing a function taking Eigen objects as argument, if you want your function to take as argument any matrix, vector, or expression, just let it take a MatrixBase argument. As an example, here is a function printFirstRow which, given a matrix, vector, or expression x, prints the first row of x.

template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
  cout << x.row(0) << endl;
}

This class can be extended with the help of the plugin mechanism described on the page Extending MatrixBase (and other classes) by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN.

See also

\blank The class hierarchy

Member Typedef Documentation

AdjointReturnType

template<typename Derived >

typedef std::conditional_t<NumTraits<Scalar>::IsComplex, CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, ConstTransposeReturnType>, ConstTransposeReturnType> Eigen::MatrixBase< Derived >::AdjointReturnType

the return type of MatrixBase::adjoint()

Base

template<typename Derived >

typedef DenseBase<Derived> Eigen::MatrixBase< Derived >::Base

BasisReturnType

template<typename Derived >

typedef Block<const CwiseNullaryOp<internal::scalar_identity_op<Scalar>, SquareMatrixType>, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime> Eigen::MatrixBase< Derived >::BasisReturnType

the return type of unit vectors

CoeffReturnType

template<typename Derived >

typedef Base::CoeffReturnType Eigen::MatrixBase< Derived >::CoeffReturnType

ColXpr

template<typename Derived >

typedef Base::ColXpr Eigen::MatrixBase< Derived >::ColXpr

ConstantReturnType

template<typename Derived >

typedef CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> Eigen::MatrixBase< Derived >::ConstantReturnType

Represents a matrix with all coefficients equal to one another

ConstDiagonalReturnType

template<typename Derived >

typedef Diagonal<const Derived> Eigen::MatrixBase< Derived >::ConstDiagonalReturnType

ConstStartMinusOne

template<typename Derived >

typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime == 1 ? SizeMinusOne : 1, internal::traits<Derived>::ColsAtCompileTime == 1 ? 1 : SizeMinusOne> Eigen::MatrixBase< Derived >::ConstStartMinusOne

ConstTransposeReturnType

template<typename Derived >

typedef Base::ConstTransposeReturnType Eigen::MatrixBase< Derived >::ConstTransposeReturnType

DiagonalReturnType

template<typename Derived >

typedef Diagonal<Derived> Eigen::MatrixBase< Derived >::DiagonalReturnType

EigenvaluesReturnType

template<typename Derived >

typedef Matrix<std::complex<RealScalar>, internal::traits<Derived>::ColsAtCompileTime, 1, ColMajor> Eigen::MatrixBase< Derived >::EigenvaluesReturnType

Return type of eigenvalues()

HomogeneousReturnType

template<typename Derived >

typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> Eigen::MatrixBase< Derived >::HomogeneousReturnType

IdentityReturnType

template<typename Derived >

typedef CwiseNullaryOp<internal::scalar_identity_op<Scalar>, PlainObject> Eigen::MatrixBase< Derived >::IdentityReturnType

the return type of identity

PacketScalar

template<typename Derived >

typedef internal::packet_traits<Scalar>::type Eigen::MatrixBase< Derived >::PacketScalar

PlainObject

template<typename Derived >

typedef Base::PlainObject Eigen::MatrixBase< Derived >::PlainObject

RealScalar

template<typename Derived >

typedef NumTraits<Scalar>::Real Eigen::MatrixBase< Derived >::RealScalar

RowXpr

template<typename Derived >

typedef Base::RowXpr Eigen::MatrixBase< Derived >::RowXpr

Scalar

template<typename Derived >

typedef internal::traits<Derived>::Scalar Eigen::MatrixBase< Derived >::Scalar

SquareMatrixType

template<typename Derived >

typedef Matrix<Scalar, internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime), internal::max_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime)> Eigen::MatrixBase< Derived >::SquareMatrixType

type of the equivalent square matrix

StemFunction

template<typename Derived >

typedef internal::stem_function<Scalar>::type Eigen::MatrixBase< Derived >::StemFunction

StorageBaseType

template<typename Derived >

typedef MatrixBase Eigen::MatrixBase< Derived >::StorageBaseType

StorageIndex

template<typename Derived >

typedef internal::traits<Derived>::StorageIndex Eigen::MatrixBase< Derived >::StorageIndex

StorageKind

template<typename Derived >

typedef internal::traits<Derived>::StorageKind Eigen::MatrixBase< Derived >::StorageKind

Member Enumeration Documentation

anonymous enum

template<typename Derived >

anonymous enum

Enumerator
HomogeneousReturnTypeDirection

       {
    HomogeneousReturnTypeDirection =
        ColsAtCompileTime == 1 && RowsAtCompileTime == 1
            ? ((internal::traits<Derived>::Flags & RowMajorBit) == RowMajorBit ? Horizontal : Vertical)
        : ColsAtCompileTime == 1 ? Vertical
                                 : Horizontal
  };

anonymous enum

template<typename Derived >

anonymous enum

Enumerator
SizeMinusOne

{ SizeMinusOne = SizeAtCompileTime == Dynamic ? Dynamic : SizeAtCompileTime - 1 };

Constructor & Destructor Documentation

MatrixBase() [1/3]

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::MatrixBase< Derived >::MatrixBase ( int  )

explicitprivate

MatrixBase() [2/3]

template<typename Derived >

EIGEN_DEVICE_FUNC Eigen::MatrixBase< Derived >::MatrixBase ( int  , int    )

private

MatrixBase() [3/3]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Eigen::MatrixBase< Derived >::MatrixBase ( const MatrixBase< OtherDerived > &  )

explicitprivate

Member Function Documentation

adjoint()

template<typename Derived >

EIGEN_DEVICE_FUNC const MatrixBase< Derived >::AdjointReturnType Eigen::MatrixBase< Derived >::adjoint

inline

Returns

an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

Matrix2cf m = Matrix2cf::Random();
cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;

Output:

Warning

If you want to replace a matrix by its own adjoint, do NOT do this:

m = m.adjoint(); // bug!!! caused by aliasing effect

Instead, use the adjointInPlace() method:

m.adjointInPlace();

which gives Eigen good opportunities for optimization, or alternatively you can also do:

m = m.adjoint().eval();

See also

adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op

                                                                                                                {
  return AdjointReturnType(this->transpose());
}

adjointInPlace()

template<typename Derived >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::adjointInPlace

inline

This is the "in place" version of adjoint(): it replaces *this by its own transpose. Thus, doing

m.adjointInPlace();

has the same effect on m as doing

m = m.adjoint().eval();

and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.

Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().

Note

if the matrix is not square, then *this must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.

See also

transpose(), adjoint(), transposeInPlace()

                                                                  {
  derived() = adjoint().eval();
}

References adjoint().

applyHouseholderOnTheLeft()

template<typename Derived >

template<typename EssentialPart >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::applyHouseholderOnTheLeft	(	const EssentialPart &	essential,
		const Scalar &	tau,
		Scalar *	workspace
	)

Apply the elementary reflector H given by \( H = I - tau v v^*\) with \( v^T = [1 essential^T] \) from the left to a vector or matrix.

On input:

Parameters

essential	the essential part of the vector v
tau	the scaling factor of the Householder transformation
workspace	a pointer to working space with at least this->cols() entries

See also

MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()

                                                                                         {
  if (rows() == 1) {
    *this *= Scalar(1) - tau;
  } else if (!numext::is_exactly_zero(tau)) {
    Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace, cols());
    Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows() - 1,
                                                                                        cols());
    tmp.noalias() = essential.adjoint() * bottom;
    tmp += this->row(0);
    this->row(0) -= tau * tmp;
    bottom.noalias() -= tau * essential * tmp;
  }
}

References cols, Eigen::numext::is_exactly_zero(), row(), rows, and tmp.

applyHouseholderOnTheRight()

template<typename Derived >

template<typename EssentialPart >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::applyHouseholderOnTheRight	(	const EssentialPart &	essential,
		const Scalar &	tau,
		Scalar *	workspace
	)

Apply the elementary reflector H given by \( H = I - tau v v^*\) with \( v^T = [1 essential^T] \) from the right to a vector or matrix.

On input:

Parameters

essential	the essential part of the vector v
tau	the scaling factor of the Householder transformation
workspace	a pointer to working space with at least this->rows() entries

See also

MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()

                                                                                                             {
  if (cols() == 1) {
    *this *= Scalar(1) - tau;
  } else if (!numext::is_exactly_zero(tau)) {
    Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace, rows());
    Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(),
                                                                                       cols() - 1);
    tmp.noalias() = right * essential;
    tmp += this->col(0);
    this->col(0) -= tau * tmp;
    right.noalias() -= tau * tmp * essential.adjoint();
  }
}

References col(), cols, Eigen::numext::is_exactly_zero(), rows, and tmp.

applyOnTheLeft() [1/2]

template<typename Derived >

template<typename OtherDerived >

void Eigen::MatrixBase< Derived >::applyOnTheLeft ( const EigenBase< OtherDerived > &  other )

inline

replaces *this by other * *this.

Example:

Matrix3f A = Matrix3f::Random(3, 3), B;
B << 0, 1, 0, 0, 0, 1, 1, 0, 0;
cout << "At start, A = " << endl << A << endl;
A.applyOnTheLeft(B);
cout << "After applyOnTheLeft, A = " << endl << A << endl;

Output:

         : \verbinclude MatrixBase_applyOnTheLeft.out
 */
template <typename Derived>

applyOnTheLeft() [2/2]

template<typename Derived >

template<typename OtherScalar >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::applyOnTheLeft ( Index  p, Index  q, const JacobiRotation< OtherScalar > &  j  )

inline

\jacobi_module Applies the rotation in the plane j to the rows p and q of *this, i.e., it computes B = J * B, with \( B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \).

See also

class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()

                                                                                                        {
  RowXpr x(this->row(p));
  RowXpr y(this->row(q));
  internal::apply_rotation_in_the_plane(x, y, j);
}

References Eigen::internal::apply_rotation_in_the_plane(), j, row(), plotDoE::x, and y.

applyOnTheRight() [1/2]

template<typename Derived >

template<typename OtherDerived >

void Eigen::MatrixBase< Derived >::applyOnTheRight ( const EigenBase< OtherDerived > &  other )

inline

replaces *this by *this * other. It is equivalent to MatrixBase::operator*=().

Example:

Matrix3f A = Matrix3f::Random(3, 3), B;
B << 0, 1, 0, 0, 0, 1, 1, 0, 0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

         : \verbinclude MatrixBase_applyOnTheRight.out
 */
template <typename Derived>

applyOnTheRight() [2/2]

template<typename Derived >

template<typename OtherScalar >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::applyOnTheRight ( Index  p, Index  q, const JacobiRotation< OtherScalar > &  j  )

inline

\jacobi_module Applies the rotation in the plane j to the columns p and q of *this, i.e., it computes B = B * J with \( B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \).

See also

class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()

                                                                                                         {
  ColXpr x(this->col(p));
  ColXpr y(this->col(q));
  internal::apply_rotation_in_the_plane(x, y, j.transpose());
}

References Eigen::internal::apply_rotation_in_the_plane(), col(), j, plotDoE::x, and y.

array() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper<Derived> Eigen::MatrixBase< Derived >::array ( )

inline

Returns

an Array expression of this matrix

See also

ArrayBase::matrix()

{ return ArrayWrapper<Derived>(derived()); }

array() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper<const Derived> Eigen::MatrixBase< Derived >::array ( ) const

inline

Returns

a const Array expression of this matrix

See also

ArrayBase::matrix()

                                                                                        {
    return ArrayWrapper<const Derived>(derived());
  }

asDiagonal()

template<typename Derived >

EIGEN_DEVICE_FUNC const DiagonalWrapper< const Derived > Eigen::MatrixBase< Derived >::asDiagonal

inline

Returns

a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients

\only_for_vectors

Example:

cout << Matrix3i(Vector3i(2, 5, 6).asDiagonal()) << endl;

Output:

See also

class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()

                                                                                                    {
  return DiagonalWrapper<const Derived>(derived());
}

Referenced by Eigen::Transform< Scalar_, Dim_, Mode_, Options_ >::fromPositionOrientationScale(), Eigen::Transform< Scalar_, Dim_, Mode_, Options_ >::prescale(), Eigen::Transform< Scalar_, Dim_, Mode_, Options_ >::scale(), and Eigen::Scaling().

asPermutation()

template<typename Derived >

const PermutationWrapper< const Derived > Eigen::MatrixBase< Derived >::asPermutation

                                                                                 {
  return derived();
}

asSkewSymmetric()

template<typename Derived >

EIGEN_DEVICE_FUNC const SkewSymmetricWrapper< const Derived > Eigen::MatrixBase< Derived >::asSkewSymmetric

inline

Returns

a pseudo-expression of a skew symmetric matrix with *this as vector of coefficients

\only_for_vectors

See also

class SkewSymmetricWrapper, class SkewSymmetricMatrix3, vector(), isSkewSymmetric()

                                                                                                              {
  return SkewSymmetricWrapper<const Derived>(derived());
}

bdcSvd() [1/4]

template<typename Derived >

template<int Options = 0>

BDCSVD<PlainObject, Options> Eigen::MatrixBase< Derived >::bdcSvd ( ) const

inline

bdcSvd() [2/4]

template<typename Derived >

template<int Options>

BDCSVD<typename MatrixBase<Derived>::PlainObject, Options> Eigen::MatrixBase< Derived >::bdcSvd

(

)

const

\svd_module

Returns

the singular value decomposition of *this computed by Divide & Conquer algorithm

See also

class BDCSVD

                                                                                           {
  return BDCSVD<PlainObject, Options>(*this);
}

bdcSvd() [3/4]

template<typename Derived >

template<int Options = 0>

EIGEN_DEPRECATED BDCSVD<PlainObject, Options> Eigen::MatrixBase< Derived >::bdcSvd ( unsigned int  computationOptions ) const

inline

bdcSvd() [4/4]

template<typename Derived >

template<int Options>

BDCSVD<typename MatrixBase<Derived>::PlainObject, Options> Eigen::MatrixBase< Derived >::bdcSvd

(

unsigned int

computationOptions

)

const

\svd_module

Returns

the singular value decomposition of *this computed by Divide & Conquer algorithm

See also

class BDCSVD

                                           {
  return BDCSVD<PlainObject, Options>(*this, computationOptions);
}

blueNorm()

template<typename Derived >

NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::blueNorm

inline

Returns

the l2 norm of *this using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

For architecture/scalar types without vectorization, this version is much faster than stableNorm(). Otherwise the stableNorm() is faster.

See also

norm(), stableNorm(), hypotNorm()

                                                                                                          {
  return internal::blueNorm_impl(*this);
}

References Eigen::internal::blueNorm_impl().

colPivHouseholderQr() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const ColPivHouseholderQR<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::colPivHouseholderQr ( ) const

inline

colPivHouseholderQr() [2/2]

template<typename Derived >

template<typename PermutationIndexType >

const ColPivHouseholderQR<typename MatrixBase<Derived>::PlainObject, PermutationIndexType> Eigen::MatrixBase< Derived >::colPivHouseholderQr

(

)

const

Returns

the column-pivoting Householder QR decomposition of *this.

See also

class ColPivHouseholderQR

                                               {
  return ColPivHouseholderQR<PlainObject, PermutationIndexType>(eval());
}

References eval().

completeOrthogonalDecomposition() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const CompleteOrthogonalDecomposition<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition ( ) const

inline

completeOrthogonalDecomposition() [2/2]

template<typename Derived >

template<typename PermutationIndex >

const CompleteOrthogonalDecomposition<typename MatrixBase<Derived>::PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition

(

)

const

Returns

the complete orthogonal decomposition of *this.

See also

class CompleteOrthogonalDecomposition

                                                           {
  return CompleteOrthogonalDecomposition<PlainObject>(eval());
}

References eval().

computeInverseAndDetWithCheck()

template<typename Derived >

template<typename ResultType >

void Eigen::MatrixBase< Derived >::computeInverseAndDetWithCheck ( ResultType &  inverse, typename ResultType::Scalar &  determinant, bool &  invertible, const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()  ) const

inline

\lu_module

Computation of matrix inverse and determinant, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Notice that it will trigger a copy of input matrix when trying to do the inverse in place.

Parameters

inverse	Reference to the matrix in which to store the inverse.
determinant	Reference to the variable in which to store the determinant.
invertible	Reference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThreshold	Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
double determinant;
m.computeInverseAndDetWithCheck(inverse, determinant, invertible);
cout << "Its determinant is " << determinant << endl;
if (invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
} else {
  cout << "It is not invertible." << endl;
}

Output:

See also

inverse(), computeInverseWithCheck()

                                                                                                                {
  // i'd love to put some static assertions there, but SFINAE means that they have no effect...
  eigen_assert(rows() == cols());
  // for 2x2, it's worth giving a chance to avoid evaluating.
  // for larger sizes, evaluating has negligible cost and limits code size.
  typedef std::conditional_t<RowsAtCompileTime == 2,
                             internal::remove_all_t<typename internal::nested_eval<Derived, 2>::type>, PlainObject>
      MatrixType;
  internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run(derived(), absDeterminantThreshold, inverse,
                                                                            determinant, invertible);
}

References cols, determinant(), eigen_assert, inverse(), rows, and run().

computeInverseWithCheck()

template<typename Derived >

template<typename ResultType >

void Eigen::MatrixBase< Derived >::computeInverseWithCheck ( ResultType &  inverse, bool &  invertible, const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()  ) const

inline

\lu_module

Computation of matrix inverse, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Notice that it will trigger a copy of input matrix when trying to do the inverse in place.

Parameters

inverse	Reference to the matrix in which to store the inverse.
invertible	Reference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThreshold	Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
m.computeInverseWithCheck(inverse, invertible);
if (invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
} else {
  cout << "It is not invertible." << endl;
}

Output:

See also

inverse(), computeInverseAndDetWithCheck()

                                                                                                          {
  Scalar determinant;
  // i'd love to put some static assertions there, but SFINAE means that they have no effect...
  eigen_assert(rows() == cols());
  computeInverseAndDetWithCheck(inverse, determinant, invertible, absDeterminantThreshold);
}

cross()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC internal::cross_impl<Derived, OtherDerived>::return_type Eigen::MatrixBase< Derived >::cross ( const MatrixBase< OtherDerived > &  other ) const

inline

cwiseProduct()

template<typename Derived >

template<typename OtherDerived >

EIGEN_STRONG_INLINE const SparseMatrixBase<OtherDerived>::template CwiseProductDenseReturnType<Derived>::Type Eigen::MatrixBase< Derived >::cwiseProduct ( const SparseMatrixBase< OtherDerived > &  other ) const

inline

                                                                  {
    return other.cwiseProduct(derived());
  }

References Eigen::SparseMatrixBase< Derived >::cwiseProduct().

determinant()

template<typename Derived >

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant

inline

\lu_module

Returns

the determinant of this matrix

                                                                                                       {
  eigen_assert(rows() == cols());
  typedef typename internal::nested_eval<Derived, Base::RowsAtCompileTime>::type Nested;
  return internal::determinant_impl<internal::remove_all_t<Nested>>::run(derived());
}

References cols, eigen_assert, rows, and Eigen::run().

diagonal() [1/6]

template<typename Derived >

EIGEN_DEVICE_FUNC Diagonal< Derived, Index_ > Eigen::MatrixBase< Derived >::diagonal

inline

Returns

an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the main diagonal of m:" << endl << m.diagonal() << endl;

Output:

See also

class Diagonal

Returns

an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal<1>().transpose() << endl
     << m.diagonal<-2>().transpose() << endl;

Output:

See also

MatrixBase::diagonal(), class Diagonal

                                                                                                      {
  return DiagonalReturnType(derived());
}

diagonal() [2/6]

template<typename Derived >

template<int Index>

EIGEN_DEVICE_FUNC Diagonal<Derived, Index> Eigen::MatrixBase< Derived >::diagonal

(

)

diagonal() [3/6]

template<typename Derived >

EIGEN_DEVICE_FUNC const Diagonal< const Derived, Index_ > Eigen::MatrixBase< Derived >::diagonal

inline

This is the const version of diagonal().

This is the const version of diagonal<int>().

          {
  return ConstDiagonalReturnType(derived());
}

diagonal() [4/6]

template<typename Derived >

template<int Index>

EIGEN_DEVICE_FUNC const Diagonal<const Derived, Index> Eigen::MatrixBase< Derived >::diagonal

(

)

const

diagonal() [5/6]

template<typename Derived >

EIGEN_DEVICE_FUNC Diagonal< Derived, DynamicIndex > Eigen::MatrixBase< Derived >::diagonal ( Index  index )

inline

Returns

an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal(1).transpose() << endl
     << m.diagonal(-2).transpose() << endl;

Output:

See also

MatrixBase::diagonal(), class Diagonal

                                                                                                  {
  return Diagonal<Derived, DynamicIndex>(derived(), index);
}

diagonal() [6/6]

template<typename Derived >

EIGEN_DEVICE_FUNC const Diagonal< const Derived, DynamicIndex > Eigen::MatrixBase< Derived >::diagonal ( Index  index ) const

inline

This is the const version of diagonal(Index).

                                                                                                                    {
  return Diagonal<const Derived, DynamicIndex>(derived(), index);
}

diagonalSize()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::MatrixBase< Derived >::diagonalSize ( ) const

inline

Returns

the size of the main diagonal, which is min(rows(),cols()).

See also

rows(), cols(), SizeAtCompileTime.

{ return (numext::mini)(rows(), cols()); }

References cols, Eigen::numext::mini(), and rows.

dot() [1/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar, typename internal::traits<OtherDerived>::Scalar>::ReturnType Eigen::MatrixBase< Derived >::dot

(

const MatrixBase< OtherDerived > &

other

)

const

                                                                        {
  return internal::dot_impl<Derived, OtherDerived>::run(derived(), other.derived());
}

References Eigen::internal::default_inner_product_impl< Lhs, Rhs, true >::run().

dot() [2/2]

template<typename Derived >

template<typename OtherDerived >

Eigen::MatrixBase< Derived >::dot

(

const MatrixBase< OtherDerived > &

other

)

const

Returns

the dot product of *this with other.

\only_for_vectors

Note

If the scalar type is complex numbers, then this function returns the hermitian (sesquilinear) dot product, conjugate-linear in the first variable and linear in the second variable.

See also

squaredNorm(), norm()

EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE()

template<typename Derived >

typedef Eigen::MatrixBase< Derived >::EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE	(	ConstStartMinusOne	,
		Scalar	,
		quotient
	)

eigenvalues()

template<typename Derived >

MatrixBase< Derived >::EigenvaluesReturnType Eigen::MatrixBase< Derived >::eigenvalues

inline

Computes the eigenvalues of a matrix.

Returns

Column vector containing the eigenvalues.

\eigenvalues_module This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).

The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

MatrixXd ones = MatrixXd::Ones(3, 3);
VectorXcd eivals = ones.eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

See also

EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()

                                                                                                {
  return internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived());
}

References Eigen::run().

forceAlignedAccess() [1/2]

template<typename Derived >

ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess

inline

Returns

an expression of *this with forced aligned access

See also

forceAlignedAccessIf(), class ForceAlignedAccess

{ return derived(); }

forceAlignedAccess() [2/2]

template<typename Derived >

const ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess

inline

Returns

an expression of *this with forced aligned access

See also

forceAlignedAccessIf(),class ForceAlignedAccess

{ return derived(); }

forceAlignedAccessIf() [1/4]

template<typename Derived >

template<bool Enable>

std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( )

inline

Returns

an expression of *this with forced aligned access if Enable is true.

See also

forceAlignedAccess(), class ForceAlignedAccess

                                                                                                                 {
  return derived();  // FIXME This should not work but apparently is never used
}

forceAlignedAccessIf() [2/4]

template<typename Derived >

template<bool Enable>

Derived& Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( )

inline

                                         {
    return derived();
  }

forceAlignedAccessIf() [3/4]

template<typename Derived >

template<bool Enable>

add_const_on_value_type_t<std::conditional_t<Enable, ForceAlignedAccess<Derived>, Derived&> > Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( ) const

inline

Returns

an expression of *this with forced aligned access if Enable is true.

See also

forceAlignedAccess(), class ForceAlignedAccess

                                                {
  return derived();  // FIXME This should not work but apparently is never used
}

forceAlignedAccessIf() [4/4]

template<typename Derived >

template<bool Enable>

const Derived& Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( ) const

inline

                                                     {
    return derived();
  }

fullPivHouseholderQr() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const FullPivHouseholderQR<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::fullPivHouseholderQr ( ) const

inline

fullPivHouseholderQr() [2/2]

template<typename Derived >

template<typename PermutationIndex >

const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::fullPivHouseholderQr

(

)

const

Returns

the full-pivoting Householder QR decomposition of *this.

See also

class FullPivHouseholderQR

                                                {
  return FullPivHouseholderQR<PlainObject, PermutationIndex>(eval());
}

References eval().

fullPivLu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const FullPivLU<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::fullPivLu ( ) const

inline

fullPivLu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

const FullPivLU<typename MatrixBase<Derived>::PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::fullPivLu ( ) const

inline

\lu_module

Returns

the full-pivoting LU decomposition of *this.

See also

class FullPivLU

          {
  return FullPivLU<PlainObject, PermutationIndex>(eval());
}

References eval().

householderQr()

template<typename Derived >

const HouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::householderQr

inline

Returns

the Householder QR decomposition of *this.

See also

class HouseholderQR

                                                                                                      {
  return HouseholderQR<PlainObject>(eval());
}

References eval().

hypotNorm()

template<typename Derived >

NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::hypotNorm

inline

Returns

the l2 norm of *this avoiding underflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.

See also

norm(), stableNorm()

                                                                                                           {
  if (size() == 1)
    return numext::abs(coeff(0, 0));
  else
    return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
}

References Eigen::numext::abs(), and size.

Identity() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity

static

Returns

an expression of the identity matrix (not necessarily square).

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.

Example:

cout << Matrix<double, 3, 4>::Identity() << endl;

Output:

See also

Identity(Index,Index), setIdentity(), isIdentity()

                              {
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
  return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>());
}

References EIGEN_STATIC_ASSERT_FIXED_SIZE, and Eigen::DenseBase< Derived >::NullaryExpr().

Identity() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( Index  rows, Index  cols  )

static

Returns

an expression of the identity matrix (not necessarily square).

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.

This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.

Example:

cout << MatrixXd::Identity(4, 3) << endl;

Output:

See also

Identity(), setIdentity(), isIdentity()

                                                    {
  return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>());
}

References cols, Eigen::DenseBase< Derived >::NullaryExpr(), and rows.

inverse()

template<typename Derived >

EIGEN_DEVICE_FUNC const Inverse< Derived > Eigen::MatrixBase< Derived >::inverse

inline

\lu_module

Returns

the matrix inverse of this matrix.

For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.

Note

This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following:

• for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
• for the general case, use class FullPivLU.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << endl;

Output:

See also

computeInverseAndDetWithCheck()

                                                                                   {
  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
  eigen_assert(rows() == cols());
  return Inverse<Derived>(derived());
}

References cols, eigen_assert, EIGEN_STATIC_ASSERT, and rows.

isDiagonal()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isDiagonal

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately equal to a diagonal matrix, within the precision given by prec.

Example:

Matrix3d m = 10000 * Matrix3d::Identity();
m(0, 2) = 1;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl;
cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;

Output:

See also

asDiagonal()

                                                                 {
  if (cols() != rows()) return false;
  RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
  for (Index j = 0; j < cols(); ++j) {
    RealScalar absOnDiagonal = numext::abs(coeff(j, j));
    if (absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
  }
  for (Index j = 0; j < cols(); ++j)
    for (Index i = 0; i < j; ++i) {
      if (!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
      if (!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
    }
  return true;
}

References Eigen::numext::abs(), cols, i, Eigen::internal::isMuchSmallerThan(), j, and rows.

isIdentity()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isIdentity

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.

Example:

Matrix3d m = Matrix3d::Identity();
m(0, 2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isIdentity() returns: " << m.isIdentity() << endl;
cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;

Output:

See also

class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()

                                                                 {
  typename internal::nested_eval<Derived, 1>::type self(derived());
  for (Index j = 0; j < cols(); ++j) {
    for (Index i = 0; i < rows(); ++i) {
      if (i == j) {
        if (!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec)) return false;
      } else {
        if (!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec)) return false;
      }
    }
  }
  return true;
}

References cols, i, Eigen::internal::isApprox(), Eigen::internal::isMuchSmallerThan(), j, and rows.

isLowerTriangular()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isLowerTriangular

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.

See also

isUpperTriangular()

                                                                        {
  RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
  for (Index j = 0; j < cols(); ++j)
    for (Index i = j; i < rows(); ++i) {
      RealScalar absValue = numext::abs(coeff(i, j));
      if (absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
    }
  RealScalar threshold = maxAbsOnLowerPart * prec;
  for (Index j = 1; j < cols(); ++j) {
    Index maxi = numext::mini(j, rows() - 1);
    for (Index i = 0; i < maxi; ++i)
      if (numext::abs(coeff(i, j)) > threshold) return false;
  }
  return true;
}

References Eigen::numext::abs(), cols, i, j, Eigen::numext::maxi(), Eigen::numext::mini(), and rows.

isOrthogonal()

template<typename Derived >

template<typename OtherDerived >

bool Eigen::MatrixBase< Derived >::isOrthogonal	(	const MatrixBase< OtherDerived > &	other,
		const RealScalar &	prec = NumTraits<Scalar>::dummy_precision()
	)		const

Returns

true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

Vector3d v(1, 0, 0);
Vector3d w(1e-4, 0, 1);
cout << "Here's the vector v:" << endl << v << endl;
cout << "Here's the vector w:" << endl << w << endl;
cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl;
cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w, 1e-3) << endl;

Output:

                                                                                                          {
  typename internal::nested_eval<Derived, 2>::type nested(derived());
  typename internal::nested_eval<OtherDerived, 2>::type otherNested(other.derived());
  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
}

References Eigen::numext::abs2().

isSkewSymmetric()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isSkewSymmetric

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately equal to a skew symmetric matrix, within the precision given by prec.

                                                                      {
  if (cols() != rows()) return false;
  return (this->transpose() + *this).isZero(prec);
}

References cols, rows, and anonymous_namespace{skew_symmetric_matrix3.cpp}::transpose().

isUnitary()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isUnitary

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately an unitary matrix, within the precision given by prec. In the case where the Scalar type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.

Note

This can be used to check whether a family of vectors forms an orthonormal basis. Indeed, m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.

Example:

Matrix3d m = Matrix3d::Identity();
m(0, 2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isUnitary() returns: " << m.isUnitary() << endl;
cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;

Output:

                                                                {
  typename internal::nested_eval<Derived, 1>::type self(derived());
  for (Index i = 0; i < cols(); ++i) {
    if (!internal::isApprox(self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec)) return false;
    for (Index j = 0; j < i; ++j)
      if (!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), static_cast<Scalar>(1), prec)) return false;
  }
  return true;
}

References col(), cols, dot(), i, Eigen::internal::isApprox(), Eigen::internal::isMuchSmallerThan(), and j.

isUpperTriangular()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isUpperTriangular

(

const RealScalar &

prec = NumTraits<Scalar>::dummy_precision()

)

const

Returns

true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.

See also

isLowerTriangular()

                                                                        {
  RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
  for (Index j = 0; j < cols(); ++j) {
    Index maxi = numext::mini(j, rows() - 1);
    for (Index i = 0; i <= maxi; ++i) {
      RealScalar absValue = numext::abs(coeff(i, j));
      if (absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
    }
  }
  RealScalar threshold = maxAbsOnUpperPart * prec;
  for (Index j = 0; j < cols(); ++j)
    for (Index i = j + 1; i < rows(); ++i)
      if (numext::abs(coeff(i, j)) > threshold) return false;
  return true;
}

References Eigen::numext::abs(), cols, i, j, Eigen::numext::maxi(), Eigen::numext::mini(), and rows.

jacobiSvd() [1/4]

template<typename Derived >

template<int Options = 0>

JacobiSVD<PlainObject, Options> Eigen::MatrixBase< Derived >::jacobiSvd ( ) const

inline

jacobiSvd() [2/4]

template<typename Derived >

template<int Options>

JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> Eigen::MatrixBase< Derived >::jacobiSvd

(

)

const

\svd_module

Returns

the singular value decomposition of *this computed by two-sided Jacobi transformations.

See also

class JacobiSVD

                                                                                                 {
  return JacobiSVD<PlainObject, Options>(*this);
}

jacobiSvd() [3/4]

template<typename Derived >

template<int Options = 0>

EIGEN_DEPRECATED JacobiSVD<PlainObject, Options> Eigen::MatrixBase< Derived >::jacobiSvd ( unsigned int  computationOptions ) const

inline

jacobiSvd() [4/4]

template<typename Derived >

template<int Options>

JacobiSVD<typename MatrixBase<Derived>::PlainObject, Options> Eigen::MatrixBase< Derived >::jacobiSvd

(

unsigned int

computationOptions

)

const

                                           {
  return JacobiSVD<PlainObject, Options>(*this, computationOptions);
}

lazyProduct() [1/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived, LazyProduct> Eigen::MatrixBase< Derived >::lazyProduct

(

const MatrixBase< OtherDerived > &

other

)

const

Returns

an expression of the matrix product of *this and other without implicit evaluation.

The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.

Warning

This version of the matrix product can be much much slower. So use it only if you know what you are doing and that you measured a true speed improvement.

See also

operator*(const MatrixBase&)

                                                                            {
  enum {
    ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
  };
  // note to the lost user:
  //    * for a dot product use: v1.dot(v2)
  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
  EIGEN_STATIC_ASSERT(
      ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
                      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
 
  return Product<Derived, OtherDerived, LazyProduct>(derived(), other.derived());
}

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, EIGEN_STATIC_ASSERT, and int().

lazyProduct() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived, LazyProduct> Eigen::MatrixBase< Derived >::lazyProduct

(

const MatrixBase< OtherDerived > &

other

)

const

ldlt()

template<typename Derived >

const LDLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::ldlt

inline

\cholesky_module

Returns

the Cholesky decomposition with full pivoting without square root of *this

See also

SelfAdjointView::ldlt()

                                                                                           {
  return LDLT<PlainObject>(derived());
}

References Eigen::SolverBase< LDLT< MatrixType_, UpLo_ > >::derived().

llt()

template<typename Derived >

const LLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::llt

inline

\cholesky_module

Returns

the LLT decomposition of *this

See also

SelfAdjointView::llt()

                                                                                         {
  return LLT<PlainObject>(derived());
}

References Eigen::SolverBase< LLT< MatrixType_, UpLo_ > >::derived().

lpNorm() [1/2]

template<typename Derived >

template<int p>

EIGEN_DEVICE_FUNC NumTraits<typename internal::traits<Derived>::Scalar>::Real Eigen::MatrixBase< Derived >::lpNorm ( ) const

inline

Returns

the coefficient-wise \( \ell^p \) norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values of the coefficients of *this. If p is the special value Eigen::Infinity, this function returns the \( \ell^\infty \) norm, that is the maximum of the absolute values of the coefficients of *this.

In all cases, if *this is empty, then the value 0 is returned.

Note

For matrices, this function does not compute the operator-norm. That is, if *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \(\infty\)-norm matrix operator norms using partial reductions .

See also

norm()

                                  {
  return internal::lpNorm_selector<Derived, p>::run(*this);
}

References Eigen::internal::lpNorm_selector< Derived, p >::run().

lpNorm() [2/2]

template<typename Derived >

template<int p>

EIGEN_DEVICE_FUNC RealScalar Eigen::MatrixBase< Derived >::lpNorm

(

)

const

lu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const PartialPivLU<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::lu ( ) const

inline

lu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

const PartialPivLU<typename MatrixBase<Derived>::PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::lu ( ) const

inline

\lu_module

Synonym of partialPivLu().

Returns

the partial-pivoting LU decomposition of *this.

See also

class PartialPivLU

                                                                                                                   {
  return PartialPivLU<PlainObject, PermutationIndex>(eval());
}

References eval().

makeHouseholder()

template<typename Derived >

template<typename EssentialPart >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::makeHouseholder	(	EssentialPart &	essential,
		Scalar &	tau,
		RealScalar &	beta
	)		const

Computes the elementary reflector H such that: \( H *this = [ beta 0 ... 0]^T \) where the transformation H is: \( H = I - tau v v^*\) and the vector v is: \( v^T = [1 essential^T] \)

On output:

Parameters

essential	the essential part of the vector v
tau	the scaling factor of the Householder transformation
beta	the result of H * *this

See also

MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

                                                                                    {
  using numext::conj;
  using numext::sqrt;
 
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
  VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size() - 1);
 
  RealScalar tailSqNorm = size() == 1 ? RealScalar(0) : tail.squaredNorm();
  Scalar c0 = coeff(0);
  const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
 
  if (tailSqNorm <= tol && numext::abs2(numext::imag(c0)) <= tol) {
    tau = RealScalar(0);
    beta = numext::real(c0);
    essential.setZero();
  } else {
    beta = sqrt(numext::abs2(c0) + tailSqNorm);
    if (numext::real(c0) >= RealScalar(0)) beta = -beta;
    essential = tail / (c0 - beta);
    tau = conj((beta - c0) / beta);
  }
}

References Eigen::numext::abs2(), beta, conj(), Eigen::conj(), EIGEN_STATIC_ASSERT_VECTOR_ONLY, imag(), min, size, sqrt(), and Eigen::numext::sqrt().

makeHouseholderInPlace()

template<typename Derived >

EIGEN_DEVICE_FUNC void Eigen::MatrixBase< Derived >::makeHouseholderInPlace	(	Scalar &	tau,
		RealScalar &	beta
	)

Computes the elementary reflector H such that: \( H *this = [ beta 0 ... 0]^T \) where the transformation H is: \( H = I - tau v v^*\) and the vector v is: \( v^T = [1 essential^T] \)

The essential part of the vector v is stored in *this.

On output:

Parameters

tau	the scaling factor of the Householder transformation
beta	the result of H * *this

See also

MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

                                                                                                {
  VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size() - 1);
  makeHouseholder(essentialPart, tau, beta);
}

References beta, and size.

matrix() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC MatrixBase<Derived>& Eigen::MatrixBase< Derived >::matrix ( )

inline

{ return *this; }

matrix() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC const MatrixBase<Derived>& Eigen::MatrixBase< Derived >::matrix ( ) const

inline

{ return *this; }

matrixFunction()

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::matrixFunction

(

StemFunction

f

)

const

Helper function for the unsupported MatrixFunctions module.

                                                                                        {
  eigen_assert(rows() == cols());
  return MatrixFunctionReturnValue<Derived>(derived(), f);
}

References cols, eigen_assert, f(), and rows.

noalias()

template<typename Derived >

NoAlias< Derived, MatrixBase > EIGEN_DEVICE_FUNC Eigen::MatrixBase< Derived >::noalias

Returns

a pseudo expression of *this with an operator= assuming no aliasing between *this and the source expression.

More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only useful when the source expression contains a matrix product.

Here are some examples where noalias is useful:

D.noalias()  = A * B;
D.noalias() += A.transpose() * B;
D.noalias() -= 2 * A * B.adjoint();

On the other hand the following example will lead to a wrong result:

A.noalias() = A * B;

because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:

A = A * B;

See also

class NoAlias

                                                                            {
  return NoAlias<Derived, Eigen::MatrixBase>(derived());
}

norm()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm

Returns

, for vectors, the l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.

See also

lpNorm(), dot(), squaredNorm()

                                {
  return numext::sqrt(squaredNorm());
}

References Eigen::numext::sqrt().

normalize()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Eigen::MatrixBase< Derived >::normalize

Normalizes the vector, i.e. divides it by its own norm.

\only_for_vectors

Warning

If the input vector is too small (i.e., this->norm()==0), then *this is left unchanged.

See also

norm(), normalized()

                                                                          {
  RealScalar z = squaredNorm();
  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
  if (z > RealScalar(0)) derived() /= numext::sqrt(z);
}

References Eigen::numext::sqrt().

normalized()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::normalized

Returns

an expression of the quotient of *this by its own norm.

Warning

If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.

\only_for_vectors

See also

norm(), normalize()

          {
  typedef typename internal::nested_eval<Derived, 2>::type Nested_;
  Nested_ n(derived());
  RealScalar z = n.squaredNorm();
  // NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU
  if (z > RealScalar(0))
    return n / numext::sqrt(z);
  else
    return n;
}

References n, and Eigen::numext::sqrt().

operator!=()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC bool Eigen::MatrixBase< Derived >::operator!= ( const MatrixBase< OtherDerived > &  other ) const

inline

Returns

true if at least one pair of coefficients of *this and other are not exactly equal to each other.

Warning

When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()

See also

isApprox(), operator==

                                                                                        {
    return !(*this == other);
  }

operator*() [1/4]

template<typename Derived >

template<typename DiagonalDerived >

EIGEN_DEVICE_FUNC const Product< Derived, DiagonalDerived, LazyProduct > Eigen::MatrixBase< Derived >::operator* ( const DiagonalBase< DiagonalDerived > &  a_diagonal ) const

inline

Returns

the diagonal matrix product of *this by the diagonal matrix diagonal.

                                                           {
  return Product<Derived, DiagonalDerived, LazyProduct>(derived(), a_diagonal.derived());
}

References Eigen::DiagonalBase< Derived >::derived().

operator*() [2/4]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Product<Derived, OtherDerived> Eigen::MatrixBase< Derived >::operator*

(

const MatrixBase< OtherDerived > &

other

)

const

Returns

the matrix product of *this and other.

Note

If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().

See also

lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()

                                                 {
  // A note regarding the function declaration: In MSVC, this function will sometimes
  // not be inlined since DenseStorage is an unwindable object for dynamic
  // matrices and product types are holding a member to store the result.
  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
  enum {
    ProductIsValid = Derived::ColsAtCompileTime == Dynamic || OtherDerived::RowsAtCompileTime == Dynamic ||
                     int(Derived::ColsAtCompileTime) == int(OtherDerived::RowsAtCompileTime),
    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived, OtherDerived)
  };
  // note to the lost user:
  //    * for a dot product use: v1.dot(v2)
  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
  EIGEN_STATIC_ASSERT(
      ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
                      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
#ifdef EIGEN_DEBUG_PRODUCT
  internal::product_type<Derived, OtherDerived>::debug();
#endif
 
  return Product<Derived, OtherDerived>(derived(), other.derived());
}

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, EIGEN_STATIC_ASSERT, and int().

operator*() [3/4]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const Product<Derived, OtherDerived> Eigen::MatrixBase< Derived >::operator*

(

const MatrixBase< OtherDerived > &

other

)

const

operator*() [4/4]

template<typename Derived >

template<typename SkewDerived >

EIGEN_DEVICE_FUNC const Product< Derived, SkewDerived, LazyProduct > Eigen::MatrixBase< Derived >::operator* ( const SkewSymmetricBase< SkewDerived > &  skew ) const

inline

Returns

the matrix product of *this by the skew symmetric matrix \skew.

                                                      {
  return Product<Derived, SkewDerived, LazyProduct>(derived(), skew.derived());
}

References Eigen::SkewSymmetricBase< Derived >::derived().

operator*=()

template<typename Derived >

template<typename OtherDerived >

Derived & Eigen::MatrixBase< Derived >::operator*= ( const EigenBase< OtherDerived > &  other )

inline

replaces *this by *this * other.

Returns

a reference to *this

Example:

Matrix3f A = Matrix3f::Random(3, 3), B;
B << 0, 1, 0, 0, 0, 1, 1, 0, 0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

         : \verbinclude MatrixBase_applyOnTheRight.out
 */
template <typename Derived>
template <typename OtherDerived>

operator+=() [1/2]

template<typename Derived >

template<typename OtherDerived >

Derived& Eigen::MatrixBase< Derived >::operator+= ( const ArrayBase< OtherDerived > &  )

inlineprotected

          :
  // mixing arrays and matrices is not legal
  template <typename OtherDerived>
  Derived& operator+=(const ArrayBase<OtherDerived>&) {

References EIGEN_STATIC_ASSERT.

operator+=() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::operator+=

(

const MatrixBase< OtherDerived > &

other

)

replaces *this by *this + other.

Returns

a reference to *this

                                                                                                                    {
  call_assignment(derived(), other.derived(), internal::add_assign_op<Scalar, typename OtherDerived::Scalar>());
  return derived();
}

References Eigen::internal::call_assignment().

operator-=() [1/2]

template<typename Derived >

template<typename OtherDerived >

Derived& Eigen::MatrixBase< Derived >::operator-= ( const ArrayBase< OtherDerived > &  )

inlineprotected

                                                      {

operator-=() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::operator-=

(

const MatrixBase< OtherDerived > &

other

)

replaces *this by *this - other.

Returns

a reference to *this

                                                                                                                    {
  call_assignment(derived(), other.derived(), internal::sub_assign_op<Scalar, typename OtherDerived::Scalar>());
  return derived();
}

References Eigen::internal::call_assignment().

operator=() [1/6]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::operator=

(

const DenseBase< OtherDerived > &

other

)

                                                                                                                  {
  internal::call_assignment(derived(), other.derived());
  return derived();
}

References Eigen::internal::call_assignment().

operator=() [2/6]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& Eigen::MatrixBase< Derived >::operator=

(

const EigenBase< OtherDerived > &

other

)

                                                                                                                  {
  internal::call_assignment(derived(), other.derived());
  return derived();
}

References Eigen::internal::call_assignment(), and Eigen::EigenBase< Derived >::derived().

operator=() [3/6]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Derived& Eigen::MatrixBase< Derived >::operator=

(

const EigenBase< OtherDerived > &

other

)

operator=() [4/6]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::operator=

(

const MatrixBase< Derived > &

other

)

Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)

                                                                                                     {
  internal::call_assignment(derived(), other.derived());
  return derived();
}

References Eigen::internal::call_assignment().

operator=() [5/6]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& Eigen::MatrixBase< Derived >::operator=

(

const ReturnByValue< OtherDerived > &

other

)

                                              {
  other.derived().evalTo(derived());
  return derived();
}

operator=() [6/6]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Derived& Eigen::MatrixBase< Derived >::operator=

(

const ReturnByValue< OtherDerived > &

other

)

operator==()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC bool Eigen::MatrixBase< Derived >::operator== ( const MatrixBase< OtherDerived > &  other ) const

inline

Returns

true if each coefficients of *this and other are all exactly equal.

Warning

When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()

See also

isApprox(), operator!=

                                                                                        {
    return (this->rows() == other.rows()) && (this->cols() == other.cols()) && cwiseEqual(other).all();
  }

References cols, and rows.

operatorNorm()

template<typename Derived >

MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::operatorNorm

inline

Computes the L2 operator norm.

Returns

Operator norm of the matrix.

\eigenvalues_module This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix \( A \) is defined to be

\[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \]

where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix \( A^*A \).

The current implementation uses the eigenvalues of \( A^*A \), as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

MatrixXd ones = MatrixXd::Ones(3, 3);
cout << "The operator norm of the 3x3 matrix of ones is " << ones.operatorNorm() << endl;

Output:

See also

SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()

                                                                                      {
  using std::sqrt;
  typename Derived::PlainObject m_eval(derived());
  // FIXME if it is really guaranteed that the eigenvalues are already sorted,
  // then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.
  return sqrt((m_eval * m_eval.adjoint()).eval().template selfadjointView<Lower>().eigenvalues().maxCoeff());
}

References sqrt().

partialPivLu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

const PartialPivLU<PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::partialPivLu ( ) const

inline

partialPivLu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

const PartialPivLU<typename MatrixBase<Derived>::PlainObject, PermutationIndex> Eigen::MatrixBase< Derived >::partialPivLu ( ) const

inline

\lu_module

Returns

the partial-pivoting LU decomposition of *this.

See also

class PartialPivLU

                                        {
  return PartialPivLU<PlainObject, PermutationIndex>(eval());
}

References eval().

selfadjointView() [1/4]

template<typename Derived >

template<unsigned int UpLo>

EIGEN_DEVICE_FUNC SelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView

(

)

selfadjointView() [2/4]

template<typename Derived >

template<unsigned int UpLo>

EIGEN_DEVICE_FUNC MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView

(

)

Returns

an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix

The parameter UpLo can be either Upper or Lower

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the symmetric matrix extracted from the upper part of m:" << endl
     << Matrix3i(m.selfadjointView<Upper>()) << endl;
cout << "Here is the symmetric matrix extracted from the lower part of m:" << endl
     << Matrix3i(m.selfadjointView<Lower>()) << endl;

Output:

See also

class SelfAdjointView

                                     {
  return typename SelfAdjointViewReturnType<UpLo>::Type(derived());
}

selfadjointView() [3/4]

template<typename Derived >

template<unsigned int UpLo>

EIGEN_DEVICE_FUNC ConstSelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView

(

)

const

selfadjointView() [4/4]

template<typename Derived >

template<unsigned int UpLo>

EIGEN_DEVICE_FUNC MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView

(

)

const

This is the const version of MatrixBase::selfadjointView()

                                           {
  return typename ConstSelfAdjointViewReturnType<UpLo>::Type(derived());
}

setIdentity() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setIdentity

Writes the identity expression (not necessarily square) into *this.

Example:

Matrix4i m = Matrix4i::Zero();
m.block<3, 3>(1, 0).setIdentity();
cout << m << endl;

Output:

See also

class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()

                                                                                {
  return internal::setIdentity_impl<Derived>::run(derived());
}

References Eigen::internal::setIdentity_impl< Derived, Big >::run().

setIdentity() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setIdentity	(	Index	rows,
		Index	cols
	)

Resizes to the given size, and writes the identity expression (not necessarily square) into *this.

Parameters

rows	the new number of rows
cols	the new number of columns

Example:

MatrixXf m;
m.setIdentity(3, 3);
cout << m << endl;

Output:

See also

MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()

                                                                                                      {
  derived().resize(rows, cols);
  return setIdentity();
}

References cols, rows, and setIdentity().

setUnit() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setUnit

(

Index

i

)

Set the coefficients of *this to the i-th unit (basis) vector.

Parameters

i	index of the unique coefficient to be set to 1

\only_for_vectors

See also

MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)

                                                                                   {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
  eigen_assert(i < size());
  derived().setZero();
  derived().coeffRef(i) = Scalar(1);
  return derived();
}

References eigen_assert, EIGEN_STATIC_ASSERT_VECTOR_ONLY, i, and size.

setUnit() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setUnit	(	Index	newSize,
		Index	i
	)

Resizes to the given newSize, and writes the i-th unit (basis) vector into *this.

Parameters

newSize	the new size of the vector
i	index of the unique coefficient to be set to 1

\only_for_vectors

See also

MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index)

                                                                                                  {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
  eigen_assert(i < newSize);
  derived().resize(newSize);
  return setUnit(i);
}

References eigen_assert, EIGEN_STATIC_ASSERT_VECTOR_ONLY, and i.

squaredNorm()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm

Returns

, for vectors, the squared l2 norm of *this, and for matrices the squared Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this with itself.

See also

dot(), norm(), lpNorm()

                                       {
  return internal::squared_norm_impl<Derived>::run(derived());
}

References Eigen::internal::squared_norm_impl< Derived, Scalar >::run().

stableNorm()

template<typename Derived >

NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::stableNorm

inline

Returns

the l2 norm of *this avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s 2 - compute \( s \Vert \frac{*this}{s} \Vert \) in a standard way

For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.

See also

norm(), blueNorm(), hypotNorm()

                                                                                                            {
  return internal::stable_norm_impl(derived());
}

References Eigen::internal::stable_norm_impl().

stableNormalize()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Eigen::MatrixBase< Derived >::stableNormalize

Normalizes the vector while avoid underflow and overflow

\only_for_vectors

This method is analogue to the normalize() method, but it reduces the risk of underflow and overflow when computing the norm.

Warning

If the input vector is too small (i.e., this->norm()==0), then *this is left unchanged.

See also

stableNorm(), stableNormalized(), normalize()

                                                                                {
  RealScalar w = cwiseAbs().maxCoeff();
  RealScalar z = (derived() / w).squaredNorm();
  if (z > RealScalar(0)) derived() /= numext::sqrt(z) * w;
}

References Eigen::numext::sqrt(), and w.

stableNormalized()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::stableNormalized

Returns

an expression of the quotient of *this by its own norm while avoiding underflow and overflow.

\only_for_vectors

This method is analogue to the normalized() method, but it reduces the risk of underflow and overflow when computing the norm.

Warning

If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.

See also

stableNorm(), stableNormalize(), normalized()

                                            {
  typedef typename internal::nested_eval<Derived, 3>::type Nested_;
  Nested_ n(derived());
  RealScalar w = n.cwiseAbs().maxCoeff();
  RealScalar z = (n / w).squaredNorm();
  if (z > RealScalar(0))
    return n / (numext::sqrt(z) * w);
  else
    return n;
}

References n, Eigen::numext::sqrt(), and w.

trace()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::trace

Returns

the trace of *this, i.e. the sum of the coefficients on the main diagonal.

*this can be any matrix, not necessarily square.

See also

diagonal(), sum()

                                                                                                              {
  return derived().diagonal().sum();
}

triangularView() [1/4]

template<typename Derived >

template<unsigned int Mode>

EIGEN_DEVICE_FUNC TriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView

(

)

triangularView() [2/4]

template<typename Derived >

template<unsigned int Mode>

EIGEN_DEVICE_FUNC MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView

(

)

Returns

an expression of a triangular view extracted from the current matrix

The parameter Mode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the upper-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::Upper>()) << endl;
cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::StrictlyUpper>()) << endl;
cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::UnitLower>()) << endl;
// FIXME need to implement output for triangularViews (Bug 885)

Output:

See also

class TriangularView

                                    {
  return typename TriangularViewReturnType<Mode>::Type(derived());
}

triangularView() [3/4]

template<typename Derived >

template<unsigned int Mode>

EIGEN_DEVICE_FUNC ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView

(

)

const

triangularView() [4/4]

template<typename Derived >

template<unsigned int Mode>

EIGEN_DEVICE_FUNC MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView

(

)

const

This is the const version of MatrixBase::triangularView()

                                          {
  return typename ConstTriangularViewReturnType<Mode>::Type(derived());
}

Unit() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  i )

static

Returns

an expression of the i-th unit (basis) vector.

\only_for_vectors

This variant is for fixed-size vector only.

See also

MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

             {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return BasisReturnType(SquareMatrixType::Identity(), i);
}

References EIGEN_STATIC_ASSERT_VECTOR_ONLY, and i.

Unit() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  newSize, Index  i  )

static

Returns

an expression of the i-th unit (basis) vector.

\only_for_vectors

See also

MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

                            {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return BasisReturnType(SquareMatrixType::Identity(newSize, newSize), i);
}

References EIGEN_STATIC_ASSERT_VECTOR_ONLY, and i.

UnitW()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitW

static

Returns

an expression of the W axis unit vector (0,0,0,1)

\only_for_vectors

See also

MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

                                                                                                                   {
  return Derived::Unit(3);
}

UnitX()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitX

static

Returns

an expression of the X axis unit vector (1{,0}^*)

\only_for_vectors

See also

MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

                                                                                                                   {
  return Derived::Unit(0);
}

UnitY()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitY

static

Returns

an expression of the Y axis unit vector (0,1{,0}^*)

\only_for_vectors

See also

MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

                                                                                                                   {
  return Derived::Unit(1);
}

UnitZ()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitZ

static

Returns

an expression of the Z axis unit vector (0,0,1{,0}^*)

\only_for_vectors

See also

MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

                                                                                                                   {
  return Derived::Unit(2);
}

---

The documentation for this class was generated from the following files:

• MatrixBase.h
• LDLT.h
• LLT.h
• Assign.h
• CwiseBinaryOp.h
• CwiseNullaryOp.h
• Diagonal.h
• DiagonalMatrix.h
• DiagonalProduct.h
• Dot.h
• ForceAlignedAccess.h
• GeneralProduct.h
• NoAlias.h
• PermutationMatrix.h
• Redux.h
• SelfAdjointView.h
• SkewSymmetricMatrix3.h
• StableNorm.h
• Transpose.h
• TriangularMatrix.h
• MatrixBaseEigenvalues.h
• Eigen/src/Geometry/EulerAngles.h
• Homogeneous.h
• OrthoMethods.h
• Householder.h
• Jacobi.h
• Determinant.h
• FullPivLU.h
• InverseImpl.h
• PartialPivLU.h
• ColPivHouseholderQR.h
• CompleteOrthogonalDecomposition.h
• FullPivHouseholderQR.h
• HouseholderQR.h
• SparseView.h
• BDCSVD.h
• JacobiSVD.h
• MatrixFunction.h