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

#include <MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:

Classes
struct	ConstDiagonalIndexReturnType

struct	ConstSelfAdjointViewReturnType

struct	ConstTriangularViewReturnType

struct	cross_product_return_type

struct	DiagonalIndexReturnType

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, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime)>	SquareMatrixType

typedef Base::PlainObject	PlainObject

typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, PlainObject >	ConstantReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	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 internal::add_const< Diagonal< constDerived > >::type	ConstDiagonalReturnType

typedef Diagonal< Derived, DynamicIndex >	DiagonalDynamicIndexReturnType

typedef internal::add_const< Diagonal< constDerived, DynamicIndex > >::type	ConstDiagonalDynamicIndexReturnType

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 , MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime , MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime , MaxSizeAtCompileTime , IsVectorAtCompileTime , NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2 , 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.

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 internal::conditional< internal::is_same< typenameinternal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray >::type	PlainObject
	The plain matrix or array type corresponding to this expression.

typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, PlainObject >	ConstantReturnType

typedef CwiseNullaryOp< internal::linspaced_op< Scalar >, PlainObject >	RandomAccessLinSpacedReturnType

typedef Matrix< typename NumTraits< typename internal::traits< Derived >::Scalar >::Real, internal::traits< Derived >::ColsAtCompileTime, 1 >	EigenvaluesReturnType

typedef Transpose< Derived >	TransposeReturnType

typedef internal::add_const< Transpose< constDerived > >::type	ConstTransposeReturnType

typedef internal::add_const_on_value_type< typenameinternal::eval< Derived >::type >::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 internal::conditional<(Flags &DirectAccessBit)==DirectAccessBit, internal::pointer_based_stl_iterator< Derived >, internal::generic_randaccess_stl_iterator< Derived > >::type	iterator_type

typedef internal::conditional<(Flags &DirectAccessBit)==DirectAccessBit, internal::pointer_based_stl_iterator< constDerived >, internal::generic_randaccess_stl_iterator< constDerived > >::type	const_iterator_type

typedef internal::conditional< IsVectorAtCompileTime, iterator_type, void >::type	iterator

typedef internal::conditional< IsVectorAtCompileTime, const_iterator_type, void >::type	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 OtherDerived >
EIGEN_DEVICE_FUNC ScalarBinaryOpTraits< typenameinternal::traits< Derived >::Scalar, typenameinternal::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 ConstDiagonalReturnType	diagonal () const

template<int Index>
EIGEN_DEVICE_FUNC DiagonalIndexReturnType< Index >::Type	diagonal ()

template<int Index>
EIGEN_DEVICE_FUNC ConstDiagonalIndexReturnType< Index >::Type	diagonal () const

EIGEN_DEVICE_FUNC DiagonalDynamicIndexReturnType	diagonal (Index index)

EIGEN_DEVICE_FUNC ConstDiagonalDynamicIndexReturnType	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 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.

EIGEN_DEVICE_FUNC Derived &	setUnit (Index i)
	Set the coefficients of `*this` to the i-th unit (basis) vector.

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

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

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

const FullPivLU< PlainObject >	fullPivLu () const

const PartialPivLU< PlainObject >	partialPivLu () const

const PartialPivLU< PlainObject >	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

const ColPivHouseholderQR< PlainObject >	colPivHouseholderQr () const

const FullPivHouseholderQR< PlainObject >	fullPivHouseholderQr () const

const CompleteOrthogonalDecomposition< PlainObject >	completeOrthogonalDecomposition () const

EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix.

RealScalar	operatorNorm () const
	Computes the L2 operator norm.

JacobiSVD< PlainObject >	jacobiSvd (unsigned int computationOptions=0) const

BDCSVD< PlainObject >	bdcSvd (unsigned int computationOptions=0) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC cross_product_return_type< OtherDerived >::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_DEVICE_FUNC Matrix< Scalar, 3, 1 >	eulerAngles (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

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.

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<int Index_>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template DiagonalIndexReturnType< Index_ >::Type	diagonal ()

template<int Index_>
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index_ >::Type	diagonal () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarBinaryOpTraits< typenameinternal::traits< Derived >::Scalar, typenameinternal::traits< OtherDerived >::Scalar >::ReturnType	dot (const MatrixBase< OtherDerived > &other) const

template<int p>
EIGEN_DEVICE_FUNC NumTraits< typenameinternal::traits< Derived >::Scalar >::Real	lpNorm () const

template<bool Enable>
internal::add_const_on_value_type< typenameinternal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type	forceAlignedAccessIf () const

template<bool Enable>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type	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 MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type	cross (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived >
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived &	lazyAssign (const DenseBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	lazyAssign (const DenseBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType	eval () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator+= (const EigenBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC Derived &	operator-= (const EigenBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator*= (const Scalar &other)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator/= (const Scalar &other)

Public Member Functions inherited from Eigen::DenseBase< Derived >
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	nonZeros () const

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.

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 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.

EIGEN_DEVICE_FUNC Derived &	setLinSpaced (const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector.

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

bool	hasNaN () const

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 internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type	forceAlignedAccessIf () const

template<bool Enable>
EIGEN_DEVICE_FUNC internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type	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 const Select< Derived, ThenDerived, ElseDerived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const

template<typename ThenDerived >
EIGEN_DEVICE_FUNC const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType >	select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const

template<typename ElseDerived >
EIGEN_DEVICE_FUNC const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived >	select (const typename 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<int NaNPropagation>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar	minCoeff () const

template<int NaNPropagation>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar	maxCoeff () 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.

static EIGEN_DEVICE_FUNC const RandomAccessLinSpacedReturnType	LinSpaced (const Scalar &low, const Scalar &high)
	Sets a linearly spaced vector.

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 ConstantReturnType	Zero (Index rows, Index cols)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Zero (Index size)

static EIGEN_DEVICE_FUNC const ConstantReturnType	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 >
EIGEN_DEVICE_FUNC	DenseBase ()

Additional Inherited Members
Public Attributes inherited from Eigen::DenseBase< Derived >
EIGEN_DEPRECATED typedef CwiseNullaryOp< internal::linspaced_op< Scalar >, PlainObject >	SequentialLinSpacedReturnType

Related Symbols 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 internal::conditional<NumTraits<Scalar>::IsComplex,CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,ConstTransposeReturnType>,ConstTransposeReturnType>::type Eigen::MatrixBase< Derived >::AdjointReturnType

◆ 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

◆ 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

◆ ConstDiagonalDynamicIndexReturnType

template<typename Derived >

typedef internal::add_const<Diagonal<constDerived,DynamicIndex>>::type Eigen::MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType

◆ ConstDiagonalReturnType

template<typename Derived >

typedef internal::add_const<Diagonal<constDerived>>::type 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

◆ DiagonalDynamicIndexReturnType

template<typename Derived >

typedef Diagonal<Derived,DynamicIndex> Eigen::MatrixBase< Derived >::DiagonalDynamicIndexReturnType

◆ 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

◆ 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

◆ 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,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime), EIGEN_SIZE_MAX(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

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
SizeMinusOne

Member Function Documentation

◆ adjoint()

template<typename Derived >

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

inline

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

Example:

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

m
Matrix3f m
Definition AngleAxis_mimic_euler.cpp:1

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

◆ 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()

◆ 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()

◆ 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()

◆ 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:

Output:

◆ 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()

◆ applyOnTheRight()

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:

Output:

◆ 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()

◆ 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()

◆ asDiagonal()

template<typename Derived >

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

inline

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

\only_for_vectors

Example:

Output:

See also: class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()

◆ asPermutation()

template<typename Derived >

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

◆ bdcSvd()

template<typename Derived >

BDCSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::bdcSvd ( unsigned int computationOptions = 0 ) const

inline

\svd_module

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

See also: class BDCSVD

◆ blueNorm()

template<typename Derived >

NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::blueNorm ( ) const

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()

◆ colPivHouseholderQr()

template<typename Derived >

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

inline

Returns: the column-pivoting Householder QR decomposition of *this.

See also: class ColPivHouseholderQR

◆ completeOrthogonalDecomposition()

template<typename Derived >

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

inline

Returns: the complete orthogonal decomposition of *this.

See also: class CompleteOrthogonalDecomposition

◆ 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:

Output:

See also: inverse(), computeInverseWithCheck()

◆ 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:

Output:

See also: inverse(), computeInverseAndDetWithCheck()

◆ cross()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC cross_product_return_type< OtherDerived >::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

◆ determinant()

template<typename Derived >

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant ( ) const

inline

\lu_module

Returns: the determinant of this matrix

◆ diagonal() [1/8]

template<typename Derived >

template<int Index_>

EIGEN_DEVICE_FUNC MatrixBase< Derived >::template DiagonalIndexReturnType< Index_ >::Type Eigen::MatrixBase< Derived >::diagonal ( )

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:

Output:

See also: MatrixBase::diagonal(), class Diagonal

◆ diagonal() [2/8]

template<typename Derived >

EIGEN_DEVICE_FUNC MatrixBase< Derived >::DiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( )

inline

Returns: an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

Output:

See also: class Diagonal

◆ diagonal() [3/8]

template<typename Derived >

template<int Index>

EIGEN_DEVICE_FUNC DiagonalIndexReturnType< Index >::Type Eigen::MatrixBase< Derived >::diagonal ( )

◆ diagonal() [4/8]

template<typename Derived >

template<int Index_>

EIGEN_DEVICE_FUNC MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index_ >::Type Eigen::MatrixBase< Derived >::diagonal ( ) const

inline

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

◆ diagonal() [5/8]

template<typename Derived >

EIGEN_DEVICE_FUNC MatrixBase< Derived >::ConstDiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( ) const

inline

This is the const version of diagonal().

◆ diagonal() [6/8]

template<typename Derived >

template<int Index>

EIGEN_DEVICE_FUNC ConstDiagonalIndexReturnType< Index >::Type Eigen::MatrixBase< Derived >::diagonal ( ) const

◆ diagonal() [7/8]

template<typename Derived >

EIGEN_DEVICE_FUNC MatrixBase< Derived >::DiagonalDynamicIndexReturnType 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:

Output:

See also: MatrixBase::diagonal(), class Diagonal

◆ diagonal() [8/8]

template<typename Derived >

EIGEN_DEVICE_FUNC MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType Eigen::MatrixBase< Derived >::diagonal ( Index index ) const

inline

This is the const version of diagonal(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.

◆ dot() [1/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ScalarBinaryOpTraits< typenameinternal::traits< Derived >::Scalar, typenameinternal::traits< OtherDerived >::Scalar >::ReturnType Eigen::MatrixBase< Derived >::dot ( const MatrixBase< OtherDerived > & other ) const

◆ 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 ( ) const

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:

Output:

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

◆ eval()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType Eigen::DenseBase< Derived >::eval ( ) const

inline

Returns: the matrix or vector obtained by evaluating this expression.

Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.

Warning: Be careful with eval() and the auto C++ keyword, as detailed in this page .

◆ 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

◆ forceAlignedAccess() [2/2]

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(),class ForceAlignedAccess

◆ forceAlignedAccessIf() [1/4]

template<typename Derived >

template<bool Enable>

internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( )

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

◆ forceAlignedAccessIf() [2/4]

template<typename Derived >

template<bool Enable>

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

inline

◆ forceAlignedAccessIf() [3/4]

template<typename Derived >

template<bool Enable>

internal::add_const_on_value_type< typenameinternal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( ) const

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

◆ forceAlignedAccessIf() [4/4]

template<typename Derived >

template<bool Enable>

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

inline

◆ fullPivHouseholderQr()

template<typename Derived >

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

inline

Returns: the full-pivoting Householder QR decomposition of *this.

See also: class FullPivHouseholderQR

◆ fullPivLu()

template<typename Derived >

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

inline

\lu_module

Returns: the full-pivoting LU decomposition of *this.

See also: class FullPivLU

◆ householderQr()

template<typename Derived >

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

inline

Returns: the Householder QR decomposition of *this.

See also: class HouseholderQR

◆ hypotNorm()

template<typename Derived >

NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::hypotNorm ( ) const

inline

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

See also: norm(), stableNorm()

◆ 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:

Output:

See also: Identity(Index,Index), setIdentity(), isIdentity()

◆ 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:

Output:

See also: Identity(), setIdentity(), isIdentity()

◆ inverse()

template<typename Derived >

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

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:

Output:

See also: computeInverseAndDetWithCheck()

◆ 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:

Output:

See also: asDiagonal()

◆ 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:

Output:

See also: class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()

◆ 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()

◆ 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:

Output:

◆ 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:

Output:

◆ 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()

◆ jacobiSvd()

template<typename Derived >

JacobiSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::jacobiSvd ( unsigned int computationOptions = 0 ) const

inline

\svd_module

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

See also: class JacobiSVD

◆ lazyAssign() [1/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEPRECATED EIGEN_DEVICE_FUNC Derived & Eigen::DenseBase< Derived >::lazyAssign ( const DenseBase< OtherDerived > & other )

Deprecated:

◆ lazyAssign() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::lazyAssign ( const DenseBase< OtherDerived > & other )

◆ 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&)

◆ 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 ( ) const

inline

\cholesky_module

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

See also: SelfAdjointView::ldlt()

◆ llt()

template<typename Derived >

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

inline

\cholesky_module

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

◆ lpNorm() [1/2]

template<typename Derived >

template<int p>

EIGEN_DEVICE_FUNC NumTraits< typenameinternal::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()

◆ lpNorm() [2/2]

template<typename Derived >

template<int p>

EIGEN_DEVICE_FUNC RealScalar Eigen::MatrixBase< Derived >::lpNorm ( ) const

◆ lu()

template<typename Derived >

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

inline

\lu_module

Synonym of partialPivLu().

Returns: the partial-pivoting LU decomposition of *this.

See also: class PartialPivLU

◆ 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()

◆ 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()

◆ matrix() [1/2]

template<typename Derived >

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

inline

◆ matrix() [2/2]

template<typename Derived >

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

inline

◆ matrixFunction()

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::matrixFunction ( StemFunction f ) const

Helper function for the unsupported MatrixFunctions module.

◆ 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

◆ norm()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm ( ) const

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()

◆ 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()

◆ normalized()

template<typename Derived >

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

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()

◆ 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==

◆ operator*() [1/3]

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.

◆ operator*() [2/3]

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*()

◆ operator*() [3/3]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const Product< Derived, OtherDerived > Eigen::MatrixBase< Derived >::operator* ( const MatrixBase< OtherDerived > & other ) const

◆ operator*=() [1/2]

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:

Output:

◆ operator*=() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::operator*= ( const Scalar & other )

◆ operator+=() [1/3]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

◆ operator+=() [2/3]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Derived & Eigen::DenseBase< Derived >::operator+= ( const EigenBase< OtherDerived > & other )

◆ operator+=() [3/3]

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

◆ operator-=() [1/3]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

◆ operator-=() [2/3]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC Derived & Eigen::DenseBase< Derived >::operator-= ( const EigenBase< OtherDerived > & other )

◆ operator-=() [3/3]

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

◆ operator/=()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::operator/= ( const Scalar & other )

◆ operator=() [1/6]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator=() [2/6]

template<typename Derived >

template<typename OtherDerived >

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

◆ 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)

◆ operator=() [5/6]

template<typename Derived >

template<typename OtherDerived >

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

◆ 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!=

◆ operatorNorm()

template<typename Derived >

MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::operatorNorm ( ) const

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:

Output:

See also: SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()

◆ partialPivLu()

template<typename Derived >

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

inline

\lu_module

Returns: the partial-pivoting LU decomposition of *this.

See also: class PartialPivLU

◆ 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:

Output:

See also: class SelfAdjointView

◆ 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()

◆ 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:

Output:

See also: class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()

◆ 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:

Output:

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

◆ 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)

◆ 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)

◆ squaredNorm()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm ( ) const

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()

◆ stableNorm()

template<typename Derived >

NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::stableNorm ( ) const

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()

◆ 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()

◆ stableNormalized()

template<typename Derived >

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

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()

◆ trace()

template<typename Derived >

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

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()

◆ 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:

Output:

See also: class TriangularView

◆ 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()

◆ 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()

◆ 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()

◆ 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()

◆ 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()

◆ 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()

◆ 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()

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

core/util/algorithms/eigen-3.4.0/Eigen/src/Core/MatrixBase.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Cholesky/LDLT.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Cholesky/LLT.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/Assign.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/CwiseBinaryOp.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/CwiseNullaryOp.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/Diagonal.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/DiagonalMatrix.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/DiagonalProduct.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/Dot.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/ForceAlignedAccess.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/GeneralProduct.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/NoAlias.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/PermutationMatrix.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/Redux.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/SelfAdjointView.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/StableNorm.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/Transpose.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Core/TriangularMatrix.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Geometry/EulerAngles.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Geometry/Homogeneous.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Geometry/OrthoMethods.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Householder/Householder.h
core/util/algorithms/eigen-3.4.0/Eigen/src/Jacobi/Jacobi.h
core/util/algorithms/eigen-3.4.0/Eigen/src/LU/Determinant.h
core/util/algorithms/eigen-3.4.0/Eigen/src/LU/FullPivLU.h
core/util/algorithms/eigen-3.4.0/Eigen/src/LU/InverseImpl.h
core/util/algorithms/eigen-3.4.0/Eigen/src/LU/PartialPivLU.h
core/util/algorithms/eigen-3.4.0/Eigen/src/QR/ColPivHouseholderQR.h
core/util/algorithms/eigen-3.4.0/Eigen/src/QR/CompleteOrthogonalDecomposition.h
core/util/algorithms/eigen-3.4.0/Eigen/src/QR/FullPivHouseholderQR.h
core/util/algorithms/eigen-3.4.0/Eigen/src/QR/HouseholderQR.h
core/util/algorithms/eigen-3.4.0/Eigen/src/SparseCore/SparseView.h
core/util/algorithms/eigen-3.4.0/Eigen/src/SVD/BDCSVD.h
core/util/algorithms/eigen-3.4.0/Eigen/src/SVD/JacobiSVD.h
core/util/algorithms/eigen-3.4.0/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ AdjointReturnType

◆ Base

◆ BasisReturnType

◆ CoeffReturnType

◆ ColXpr

◆ ConstantReturnType

◆ ConstDiagonalDynamicIndexReturnType

◆ ConstDiagonalReturnType

◆ ConstStartMinusOne

◆ ConstTransposeReturnType

◆ DiagonalDynamicIndexReturnType

◆ DiagonalReturnType

◆ EigenvaluesReturnType

◆ HomogeneousReturnType

◆ IdentityReturnType

◆ PacketScalar

◆ PlainObject

◆ RealScalar

◆ RowXpr

◆ Scalar

◆ SquareMatrixType

◆ StemFunction

◆ StorageBaseType

◆ StorageIndex

◆ StorageKind

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Member Function Documentation

◆ adjoint()

◆ adjointInPlace()

◆ applyHouseholderOnTheLeft()

◆ applyHouseholderOnTheRight()

◆ applyOnTheLeft() [1/2]

◆ applyOnTheLeft() [2/2]

◆ applyOnTheRight()

◆ array() [1/2]

◆ array() [2/2]

◆ asDiagonal()

◆ asPermutation()

◆ bdcSvd()

◆ blueNorm()

◆ colPivHouseholderQr()

◆ completeOrthogonalDecomposition()

◆ computeInverseAndDetWithCheck()

◆ computeInverseWithCheck()

◆ cross()

◆ cwiseProduct()

◆ determinant()

◆ diagonal() [1/8]

◆ diagonal() [2/8]

◆ diagonal() [3/8]

◆ diagonal() [4/8]

◆ diagonal() [5/8]

◆ diagonal() [6/8]

◆ diagonal() [7/8]

◆ diagonal() [8/8]

◆ diagonalSize()

◆ dot() [1/2]

◆ dot() [2/2]

◆ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE()

◆ eigenvalues()

◆ eval()

◆ forceAlignedAccess() [1/2]

◆ forceAlignedAccess() [2/2]

◆ forceAlignedAccessIf() [1/4]

◆ forceAlignedAccessIf() [2/4]

◆ forceAlignedAccessIf() [3/4]

◆ forceAlignedAccessIf() [4/4]

◆ fullPivHouseholderQr()

◆ fullPivLu()

◆ householderQr()