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

#include <MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:

Classes
struct	CastXpr

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 internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	AdjointReturnType

typedef DenseBase< Derived >	Base

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

typedef Base::CoeffReturnType	CoeffReturnType

typedef Base::ColXpr	ColXpr

typedef internal::conditional< NumTraits< Scalar >::IsComplex, const CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, const Derived >, const Derived & >::type	ConjugateReturnType

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

typedef internal::add_const< Diagonal< const Derived, DynamicIndex > >::type	ConstDiagonalDynamicIndexReturnType

typedef internal::add_const< Diagonal< const Derived > >::type	ConstDiagonalReturnType

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

typedef Base::ConstTransposeReturnType	ConstTransposeReturnType

typedef CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Derived >	CwiseAbs2ReturnType

typedef CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived >	CwiseAbsReturnType

typedef CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const Derived >	CwiseInverseReturnType

typedef CwiseBinaryOp< internal::scalar_cmp_op< Scalar, Scalar, internal::cmp_EQ >, const Derived, const ConstantReturnType >	CwiseScalarEqualReturnType

typedef CwiseUnaryOp< internal::scalar_sign_op< Scalar >, const Derived >	CwiseSignReturnType

typedef CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Derived >	CwiseSqrtReturnType

typedef Diagonal< Derived, DynamicIndex >	DiagonalDynamicIndexReturnType

typedef Diagonal< Derived >	DiagonalReturnType

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

typedef Homogeneous< Derived, HomogeneousReturnTypeDirection >	HomogeneousReturnType

typedef CwiseNullaryOp< internal::scalar_identity_op< Scalar >, PlainObject >	IdentityReturnType

typedef CwiseUnaryOp< internal::scalar_imag_op< Scalar >, const Derived >	ImagReturnType

typedef CwiseUnaryOp< internal::scalar_opposite_op< Scalar >, const Derived >	NegativeReturnType

typedef CwiseUnaryView< internal::scalar_imag_ref_op< Scalar >, Derived >	NonConstImagReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryView< internal::scalar_real_ref_op< Scalar >, Derived >, Derived & >::type	NonConstRealReturnType

typedef internal::packet_traits< Scalar >::type	PacketScalar

typedef Base::PlainObject	PlainObject

typedef internal::conditional< NumTraits< Scalar >::IsComplex, const CwiseUnaryOp< internal::scalar_real_op< Scalar >, const Derived >, const Derived & >::type	RealReturnType

typedef NumTraits< Scalar >::Real	RealScalar

typedef Base::RowXpr	RowXpr

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

typedef Matrix< Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime)>	SquareMatrixType

typedef internal::stem_function< Scalar >::type	StemFunction

typedef MatrixBase	StorageBaseType

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

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

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, 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 DenseCoeffsBase< Derived >	Base

typedef Block< Derived >	BlockXpr

typedef Base::CoeffReturnType	CoeffReturnType

typedef Block< Derived, internal::traits< Derived >::RowsAtCompileTime, Dynamic,!IsRowMajor >	ColsBlockXpr

typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType

typedef Block< Derived, internal::traits< Derived >::RowsAtCompileTime, 1,!IsRowMajor >	ColXpr

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

typedef const Block< const Derived >	ConstBlockXpr

typedef const Block< const Derived, internal::traits< Derived >::RowsAtCompileTime, Dynamic,!IsRowMajor >	ConstColsBlockXpr

typedef const VectorwiseOp< const Derived, Vertical >	ConstColwiseReturnType

typedef const Block< const Derived, internal::traits< Derived >::RowsAtCompileTime, 1,!IsRowMajor >	ConstColXpr

typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType

typedef const Block< const Derived, Dynamic, internal::traits< Derived >::ColsAtCompileTime, IsRowMajor >	ConstRowsBlockXpr

typedef const VectorwiseOp< const Derived, Horizontal >	ConstRowwiseReturnType

typedef const Block< const Derived, 1, internal::traits< Derived >::ColsAtCompileTime, IsRowMajor >	ConstRowXpr

typedef const VectorBlock< const Derived >	ConstSegmentReturnType

typedef internal::add_const< Transpose< const Derived > >::type	ConstTransposeReturnType

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

typedef internal::add_const_on_value_type< typename internal::eval< Derived >::type >::type	EvalReturnType

typedef Eigen::InnerIterator< Derived >	InnerIterator

typedef internal::find_best_packet< Scalar, SizeAtCompileTime >::type	PacketScalar

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

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

typedef CwiseNullaryOp< internal::scalar_random_op< Scalar >, PlainObject >	RandomReturnType

typedef NumTraits< Scalar >::Real	RealScalar

typedef Reverse< Derived, BothDirections >	ReverseReturnType

typedef Block< Derived, Dynamic, internal::traits< Derived >::ColsAtCompileTime, IsRowMajor >	RowsBlockXpr

typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType

typedef Block< Derived, 1, internal::traits< Derived >::ColsAtCompileTime, IsRowMajor >	RowXpr

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

typedef VectorBlock< Derived >	SegmentReturnType

typedef CwiseNullaryOp< internal::linspaced_op< Scalar, PacketScalar >, PlainObject >	SequentialLinSpacedReturnType

typedef internal::traits< Derived >::StorageIndex	StorageIndex
	The type used to store indices. More...

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

typedef Transpose< Derived >	TransposeReturnType

typedef Scalar	value_type

Public Member Functions
EIGEN_DEVICE_FUNC const AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC void	adjointInPlace ()

template<typename EssentialPart >
void	applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)

template<typename EssentialPart >
void	applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)

template<typename OtherDerived >
void	applyOnTheLeft (const EigenBase< OtherDerived > &other)

template<typename OtherScalar >
void	applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)

template<typename OtherDerived >
void	applyOnTheRight (const EigenBase< OtherDerived > &other)

template<typename OtherScalar >
void	applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper< Derived >	array ()

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const ArrayWrapper< const Derived >	array () const

EIGEN_DEVICE_FUNC const DiagonalWrapper< const Derived >	asDiagonal () const

const PermutationWrapper< const Derived >	asPermutation () const

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

template<typename CustomBinaryOp , typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< CustomBinaryOp, const Derived, const OtherDerived >	binaryExpr (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const

RealScalar	blueNorm () const

template<typename NewType >
EIGEN_DEVICE_FUNC CastXpr< NewType >::Type	cast () const

const ColPivHouseholderQR< PlainObject >	colPivHouseholderQr () const

const CompleteOrthogonalDecomposition< PlainObject >	completeOrthogonalDecomposition () 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 ConjugateReturnType	conjugate () const

const MatrixFunctionReturnValue< Derived >	cos () const

const MatrixFunctionReturnValue< Derived >	cosh () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type	cross (const MatrixBase< OtherDerived > &other) 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 EIGEN_STRONG_INLINE const CwiseAbsReturnType	cwiseAbs () const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseAbs2ReturnType	cwiseAbs2 () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const CwiseBinaryOp< std::equal_to< Scalar >, const Derived, const OtherDerived >	cwiseEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

EIGEN_DEVICE_FUNC const CwiseScalarEqualReturnType	cwiseEqual (const Scalar &s) const

EIGEN_DEVICE_FUNC const CwiseInverseReturnType	cwiseInverse () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar >, const Derived, const OtherDerived >	cwiseMax (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar >, const Derived, const ConstantReturnType >	cwiseMax (const Scalar &other) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar >, const Derived, const OtherDerived >	cwiseMin (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar >, const Derived, const ConstantReturnType >	cwiseMin (const Scalar &other) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const CwiseBinaryOp< std::not_equal_to< Scalar >, const Derived, const OtherDerived >	cwiseNotEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const Derived, const OtherDerived >	cwiseQuotient (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

EIGEN_DEVICE_FUNC const CwiseSignReturnType	cwiseSign () const

EIGEN_DEVICE_FUNC const CwiseSqrtReturnType	cwiseSqrt () const

Scalar	determinant () const

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

EIGEN_DEVICE_FUNC Index	diagonalSize () 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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const	EIGEN_CWISE_BINARY_RETURN_TYPE (Derived, OtherDerived, product) cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

typedef	EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE (ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType

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

EIGEN_DEVICE_FUNC Matrix< Scalar, 3, 1 >	eulerAngles (Index a0, Index a1, Index a2) const

const MatrixExponentialReturnValue< Derived >	exp () const

const Derived &	forceAlignedAccess () const

Derived &	forceAlignedAccess ()

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

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

template<bool Enable>
const Derived &	forceAlignedAccessIf () const

template<bool Enable>
Derived &	forceAlignedAccessIf ()

const FullPivHouseholderQR< PlainObject >	fullPivHouseholderQr () const

const FullPivLU< PlainObject >	fullPivLu () const

EIGEN_DEVICE_FUNC const HNormalizedReturnType	hnormalized () const
	homogeneous normalization More...

EIGEN_DEVICE_FUNC HomogeneousReturnType	homogeneous () const

const HouseholderQR< PlainObject >	householderQr () const

RealScalar	hypotNorm () const

EIGEN_DEVICE_FUNC const ImagReturnType	imag () const

EIGEN_DEVICE_FUNC NonConstImagReturnType	imag ()

const Inverse< Derived >	inverse () const

bool	isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

bool	isIdentity (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

bool	isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const Product< Derived, OtherDerived, LazyProduct >	lazyProduct (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived >
const Product< Derived, OtherDerived, LazyProduct >	lazyProduct (const MatrixBase< OtherDerived > &other) const

const LDLT< PlainObject >	ldlt () const

const LLT< PlainObject >	llt () const

const MatrixLogarithmReturnValue< Derived >	log () const

template<int p>
NumTraits< typename internal::traits< Derived >::Scalar >::Real	lpNorm () const

template<int p>
EIGEN_DEVICE_FUNC RealScalar	lpNorm () const

const PartialPivLU< PlainObject >	lu () const

template<typename EssentialPart >
void	makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const

void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)

EIGEN_DEVICE_FUNC MatrixBase< Derived > &	matrix ()

EIGEN_DEVICE_FUNC const MatrixBase< Derived > &	matrix () const

const MatrixFunctionReturnValue< Derived >	matrixFunction (StemFunction f) const

NoAlias< Derived, Eigen::MatrixBase >	noalias ()

EIGEN_DEVICE_FUNC RealScalar	norm () const

EIGEN_DEVICE_FUNC void	normalize ()

EIGEN_DEVICE_FUNC const PlainObject	normalized () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	operator!= (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const CwiseBinaryOp< internal::scalar_boolean_and_op, const Derived, const OtherDerived >	operator&& (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

template<typename DiagonalDerived >
const Product< Derived, DiagonalDerived, LazyProduct >	operator* (const DiagonalBase< DiagonalDerived > &a_diagonal) const

template<typename OtherDerived >
const Product< Derived, OtherDerived >	operator* (const MatrixBase< OtherDerived > &other) const

template<typename DiagonalDerived >
EIGEN_DEVICE_FUNC const Product< Derived, DiagonalDerived, LazyProduct >	operator* (const DiagonalBase< DiagonalDerived > &diagonal) const

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

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

template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator+= (const MatrixBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC const NegativeReturnType	operator- () const

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

template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator-= (const MatrixBase< OtherDerived > &other)

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)

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 bool	operator== (const MatrixBase< OtherDerived > &other) const

RealScalar	operatorNorm () const
	Computes the L2 operator norm. More...

template<typename OtherDerived >
EIGEN_DEVICE_FUNC const CwiseBinaryOp< internal::scalar_boolean_or_op, const Derived, const OtherDerived >	operator\|\| (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

const PartialPivLU< PlainObject >	partialPivLu () const

const MatrixPowerReturnValue< Derived >	pow (const RealScalar &p) const

const MatrixComplexPowerReturnValue< Derived >	pow (const std::complex< RealScalar > &p) const

EIGEN_DEVICE_FUNC RealReturnType	real () const

EIGEN_DEVICE_FUNC NonConstRealReturnType	real ()

template<unsigned int UpLo>
EIGEN_DEVICE_FUNC SelfAdjointViewReturnType< UpLo >::Type	selfadjointView ()

template<unsigned int UpLo>
EIGEN_DEVICE_FUNC ConstSelfAdjointViewReturnType< UpLo >::Type	selfadjointView () const

template<unsigned int UpLo>
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type	selfadjointView () const

template<unsigned int UpLo>
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type	selfadjointView ()

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...

const MatrixFunctionReturnValue< Derived >	sin () const

const MatrixFunctionReturnValue< Derived >	sinh () const

const SparseView< Derived >	sparseView (const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const

const MatrixSquareRootReturnValue< Derived >	sqrt () const

EIGEN_DEVICE_FUNC RealScalar	squaredNorm () const

RealScalar	stableNorm () const

EIGEN_DEVICE_FUNC void	stableNormalize ()

EIGEN_DEVICE_FUNC const PlainObject	stableNormalized () const

EIGEN_DEVICE_FUNC Scalar	trace () 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 Mode>
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type	triangularView ()

template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type	triangularView () const

template<typename CustomUnaryOp >
EIGEN_DEVICE_FUNC const CwiseUnaryOp< CustomUnaryOp, const Derived >	unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
	Apply a unary operator coefficient-wise. More...

template<typename CustomViewOp >
EIGEN_DEVICE_FUNC const CwiseUnaryView< CustomViewOp, const Derived >	unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const

EIGEN_DEVICE_FUNC PlainObject	unitOrthogonal (void) const

Public Member Functions inherited from Eigen::DenseBase< Derived >
EIGEN_DEVICE_FUNC bool	all () const

bool	allFinite () const

EIGEN_DEVICE_FUNC bool	any () const

EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC BlockXpr	block (Index startRow, Index startCol, Index blockRows, Index blockCols)

EIGEN_DEVICE_FUNC const ConstBlockXpr	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
	This is the const version of block(Index,Index,Index,Index). */. More...

template<int NRows, int NCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC FixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol)

template<int NRows, int NCols>
EIGEN_DEVICE_FUNC const ConstFixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol) const
	This is the const version of block<>(Index, Index). */. More...

template<int NRows, int NCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL FixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol, Index blockRows, Index blockCols)

template<int NRows, int NCols>
const ConstFixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
	This is the const version of block<>(Index, Index, Index, Index). More...

EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC BlockXpr	bottomLeftCorner (Index cRows, Index cCols)

EIGEN_DEVICE_FUNC const ConstBlockXpr	bottomLeftCorner (Index cRows, Index cCols) const
	This is the const version of bottomLeftCorner(Index, Index). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC FixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner ()

template<int CRows, int CCols>
EIGEN_DEVICE_FUNC const ConstFixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner () const
	This is the const version of bottomLeftCorner<int, int>(). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL FixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner (Index cRows, Index cCols) const
	This is the const version of bottomLeftCorner<int, int>(Index, Index). More...

EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC BlockXpr	bottomRightCorner (Index cRows, Index cCols)

EIGEN_DEVICE_FUNC const ConstBlockXpr	bottomRightCorner (Index cRows, Index cCols) const
	This is the const version of bottomRightCorner(Index, Index). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC FixedBlockXpr< CRows, CCols >::Type	bottomRightCorner ()

template<int CRows, int CCols>
EIGEN_DEVICE_FUNC const ConstFixedBlockXpr< CRows, CCols >::Type	bottomRightCorner () const
	This is the const version of bottomRightCorner<int, int>(). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL FixedBlockXpr< CRows, CCols >::Type	bottomRightCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomRightCorner (Index cRows, Index cCols) const
	This is the const version of bottomRightCorner<int, int>(Index, Index). More...

EIGEN_DEVICE_FUNC RowsBlockXpr	bottomRows (Index n)

EIGEN_DEVICE_FUNC ConstRowsBlockXpr	bottomRows (Index n) const
	This is the const version of bottomRows(Index). More...

template<int N>
EIGEN_DEVICE_FUNC NRowsBlockXpr< N >::Type	bottomRows (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr< N >::Type	bottomRows (Index n=N) const
	This is the const version of bottomRows<int>(). More...

EIGEN_DEVICE_FUNC ColXpr	col (Index i)

EIGEN_DEVICE_FUNC ConstColXpr	col (Index i) const
	This is the const version of col(). More...

EIGEN_DEVICE_FUNC ConstColwiseReturnType	colwise () const

EIGEN_DEVICE_FUNC ColwiseReturnType	colwise ()

EIGEN_DEVICE_FUNC Index	count () const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType	eval () const

template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &) const

EIGEN_DEVICE_FUNC void	fill (const Scalar &value)

template<unsigned int Added, unsigned int Removed>
EIGEN_DEPRECATED const Derived &	flagged () 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 ()

const WithFormat< Derived >	format (const IOFormat &fmt) const

bool	hasNaN () const

EIGEN_DEVICE_FUNC SegmentReturnType	head (Index n)

EIGEN_DEVICE_FUNC ConstSegmentReturnType	head (Index n) const
	This is the const version of head(Index). More...

template<int N>
EIGEN_DEVICE_FUNC FixedSegmentReturnType< N >::Type	head (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType< N >::Type	head (Index n=N) const
	This is the const version of head<int>(). More...

EIGEN_DEVICE_FUNC Index	innerSize () const

template<typename OtherDerived >
bool	isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC bool	isApprox (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

template<typename Derived >
bool	isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const

template<typename OtherDerived >
bool	isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec) 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	isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

EIGEN_DEVICE_FUNC bool	isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

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

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

EIGEN_DEVICE_FUNC ColsBlockXpr	leftCols (Index n)

EIGEN_DEVICE_FUNC ConstColsBlockXpr	leftCols (Index n) const
	This is the const version of leftCols(Index). More...

template<int N>
EIGEN_DEVICE_FUNC NColsBlockXpr< N >::Type	leftCols (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNColsBlockXpr< N >::Type	leftCols (Index n=N) const
	This is the const version of leftCols<int>(). More...

template<int p>
RealScalar	lpNorm () const

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	maxCoeff () 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	maxCoeff (IndexType *index) const

EIGEN_DEVICE_FUNC Scalar	mean () const

EIGEN_DEVICE_FUNC ColsBlockXpr	middleCols (Index startCol, Index numCols)

EIGEN_DEVICE_FUNC ConstColsBlockXpr	middleCols (Index startCol, Index numCols) const
	This is the const version of middleCols(Index,Index). More...

template<int N>
EIGEN_DEVICE_FUNC NColsBlockXpr< N >::Type	middleCols (Index startCol, Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNColsBlockXpr< N >::Type	middleCols (Index startCol, Index n=N) const
	This is the const version of middleCols<int>(). More...

EIGEN_DEVICE_FUNC RowsBlockXpr	middleRows (Index startRow, Index n)

EIGEN_DEVICE_FUNC ConstRowsBlockXpr	middleRows (Index startRow, Index n) const
	This is the const version of middleRows(Index,Index). More...

template<int N>
EIGEN_DEVICE_FUNC NRowsBlockXpr< N >::Type	middleRows (Index startRow, Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr< N >::Type	middleRows (Index startRow, Index n=N) const
	This is the const version of middleRows<int>(). More...

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar	minCoeff () 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	minCoeff (IndexType *index) const

EIGEN_DEVICE_FUNC const NestByValue< Derived >	nestByValue () const

EIGEN_DEVICE_FUNC Index	nonZeros () const

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_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)

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

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)

template<typename OtherDerived >
CommaInitializer< Derived >	operator<< (const DenseBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC CommaInitializer< Derived >	operator<< (const Scalar &s)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC CommaInitializer< Derived >	operator<< (const DenseBase< OtherDerived > &other)

template<typename OtherDerived >
Derived &	operator= (const ReturnByValue< OtherDerived > &other)

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 ReturnByValue< OtherDerived > &func)

EIGEN_DEVICE_FUNC Index	outerSize () const

EIGEN_DEVICE_FUNC Scalar	prod () const

template<typename Func >
internal::traits< Derived >::Scalar	redux (const Func &func) const

template<typename BinaryOp >
EIGEN_DEVICE_FUNC Scalar	redux (const BinaryOp &func) const

template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor >	replicate () 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 void	resize (Index newSize)

EIGEN_DEVICE_FUNC void	resize (Index rows, Index cols)

EIGEN_DEVICE_FUNC ReverseReturnType	reverse ()

EIGEN_DEVICE_FUNC ConstReverseReturnType	reverse () const

EIGEN_DEVICE_FUNC void	reverseInPlace ()

EIGEN_DEVICE_FUNC ColsBlockXpr	rightCols (Index n)

EIGEN_DEVICE_FUNC ConstColsBlockXpr	rightCols (Index n) const
	This is the const version of rightCols(Index). More...

template<int N>
EIGEN_DEVICE_FUNC NColsBlockXpr< N >::Type	rightCols (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNColsBlockXpr< N >::Type	rightCols (Index n=N) const
	This is the const version of rightCols<int>(). More...

EIGEN_DEVICE_FUNC RowXpr	row (Index i)

EIGEN_DEVICE_FUNC ConstRowXpr	row (Index i) const
	This is the const version of row(). */. More...

EIGEN_DEVICE_FUNC ConstRowwiseReturnType	rowwise () const

EIGEN_DEVICE_FUNC RowwiseReturnType	rowwise ()

EIGEN_DEVICE_FUNC SegmentReturnType	segment (Index start, Index n)

EIGEN_DEVICE_FUNC ConstSegmentReturnType	segment (Index start, Index n) const
	This is the const version of segment(Index,Index). More...

template<int N>
EIGEN_DEVICE_FUNC FixedSegmentReturnType< N >::Type	segment (Index start, Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType< N >::Type	segment (Index start, Index n=N) const
	This is the const version of segment<int>(Index). More...

template<typename ThenDerived , typename ElseDerived >
const Select< Derived, ThenDerived, ElseDerived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const

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

template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived >	select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const

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 &	setOnes ()

EIGEN_DEVICE_FUNC Derived &	setRandom ()

EIGEN_DEVICE_FUNC Derived &	setZero ()

EIGEN_DEVICE_FUNC Scalar	sum () const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC void	swap (const DenseBase< OtherDerived > &other)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC void	swap (PlainObjectBase< OtherDerived > &other)

EIGEN_DEVICE_FUNC SegmentReturnType	tail (Index n)

EIGEN_DEVICE_FUNC ConstSegmentReturnType	tail (Index n) const
	This is the const version of tail(Index). More...

template<int N>
EIGEN_DEVICE_FUNC FixedSegmentReturnType< N >::Type	tail (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType< N >::Type	tail (Index n=N) const
	This is the const version of tail<int>. More...

EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC BlockXpr	topLeftCorner (Index cRows, Index cCols)

EIGEN_DEVICE_FUNC const ConstBlockXpr	topLeftCorner (Index cRows, Index cCols) const
	This is the const version of topLeftCorner(Index, Index). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC FixedBlockXpr< CRows, CCols >::Type	topLeftCorner ()

template<int CRows, int CCols>
EIGEN_DEVICE_FUNC const ConstFixedBlockXpr< CRows, CCols >::Type	topLeftCorner () const
	This is the const version of topLeftCorner<int, int>(). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL FixedBlockXpr< CRows, CCols >::Type	topLeftCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topLeftCorner (Index cRows, Index cCols) const
	This is the const version of topLeftCorner<int, int>(Index, Index). More...

EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC BlockXpr	topRightCorner (Index cRows, Index cCols)

EIGEN_DEVICE_FUNC const ConstBlockXpr	topRightCorner (Index cRows, Index cCols) const
	This is the const version of topRightCorner(Index, Index). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL EIGEN_DEVICE_FUNC FixedBlockXpr< CRows, CCols >::Type	topRightCorner ()

template<int CRows, int CCols>
EIGEN_DEVICE_FUNC const ConstFixedBlockXpr< CRows, CCols >::Type	topRightCorner () const
	This is the const version of topRightCorner<int, int>(). More...

template<int CRows, int CCols>
EIGEN_DOC_BLOCK_ADDONS_NOT_INNER_PANEL FixedBlockXpr< CRows, CCols >::Type	topRightCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topRightCorner (Index cRows, Index cCols) const
	This is the const version of topRightCorner<int, int>(Index, Index). More...

EIGEN_DEVICE_FUNC RowsBlockXpr	topRows (Index n)

EIGEN_DEVICE_FUNC ConstRowsBlockXpr	topRows (Index n) const
	This is the const version of topRows(Index). More...

template<int N>
EIGEN_DEVICE_FUNC NRowsBlockXpr< N >::Type	topRows (Index n=N)

template<int N>
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr< N >::Type	topRows (Index n=N) const
	This is the const version of topRows<int>(). More...

EIGEN_DEVICE_FUNC Scalar	trace () const

EIGEN_DEVICE_FUNC TransposeReturnType	transpose ()

EIGEN_DEVICE_FUNC ConstTransposeReturnType	transpose () const

EIGEN_DEVICE_FUNC void	transposeInPlace ()

EIGEN_DEVICE_FUNC CoeffReturnType	value () const

template<typename Visitor >
EIGEN_DEVICE_FUNC void	visit (Visitor &func) 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	UnitW ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitX ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitY ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitZ ()

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)

static EIGEN_DEVICE_FUNC const SequentialLinSpacedReturnType	LinSpaced (Sequential_t, Index size, 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 SequentialLinSpacedReturnType	LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)

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

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	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 ()

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 ()

Protected Member Functions
EIGEN_DEVICE_FUNC	MatrixBase ()

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 ()

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
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 TopicCustomizing_Plugins by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN.

See also: TopicClassHierarchy

Definition at line 48 of file MatrixBase.h.

Member Typedef Documentation

template<typename Derived>

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

Definition at line 112 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 60 of file MatrixBase.h.

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

Definition at line 120 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 84 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 87 of file MatrixBase.h.

template<typename Derived>

typedef internal::conditional<NumTraits<Scalar>::IsComplex, const CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Derived>, const Derived& >::type Eigen::MatrixBase< Derived >::ConjugateReturnType

Definition at line 20 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 107 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 234 of file MatrixBase.h.

template<typename Derived>

typedef internal::add_const<Diagonal<const Derived> >::type Eigen::MatrixBase< Derived >::ConstDiagonalReturnType

Definition at line 218 of file MatrixBase.h.

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

Definition at line 417 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 85 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::CwiseAbs2ReturnType

Definition at line 17 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::CwiseAbsReturnType

Definition at line 16 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::CwiseInverseReturnType

Definition at line 20 of file MatrixBase.h.

template<typename Derived>

typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar,Scalar,internal::cmp_EQ>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::CwiseScalarEqualReturnType

Definition at line 137 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::CwiseSignReturnType

Definition at line 19 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::CwiseSqrtReturnType

Definition at line 18 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 233 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 214 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 114 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 408 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 116 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_imag_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::ImagReturnType

Definition at line 32 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::NegativeReturnType

Definition at line 36 of file MatrixBase.h.

template<typename Derived>

typedef CwiseUnaryView<internal::scalar_imag_ref_op<Scalar>, Derived> Eigen::MatrixBase< Derived >::NonConstImagReturnType

Definition at line 34 of file MatrixBase.h.

template<typename Derived>

typedef internal::conditional<NumTraits<Scalar>::IsComplex, CwiseUnaryView<internal::scalar_real_ref_op<Scalar>, Derived>, Derived& >::type Eigen::MatrixBase< Derived >::NonConstRealReturnType

Definition at line 30 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 57 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 103 of file MatrixBase.h.

template<typename Derived>

typedef internal::conditional<NumTraits<Scalar>::IsComplex, const CwiseUnaryOp<internal::scalar_real_op<Scalar>, const Derived>, const Derived& >::type Eigen::MatrixBase< Derived >::RealReturnType

Definition at line 25 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 58 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 86 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 56 of file MatrixBase.h.

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

Definition at line 95 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 455 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 53 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 55 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 54 of file MatrixBase.h.

Member Enumeration Documentation

template<typename Derived>

anonymous enum

Enumerator
HomogeneousReturnTypeDirection

Definition at line 406 of file MatrixBase.h.

template<typename Derived>

anonymous enum

Enumerator
SizeMinusOne

Definition at line 412 of file MatrixBase.h.

Constructor & Destructor Documentation

template<typename Derived>

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

inlineprotected

Definition at line 468 of file MatrixBase.h.

template<typename Derived>

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

explicitprivate

template<typename Derived>

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

private

template<typename Derived>

template<typename OtherDerived >

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

explicitprivate

Member Function Documentation

template<typename Derived >

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
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

Definition at line 210 of file Transpose.h.

template<typename Derived >

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()

Definition at line 315 of file Transpose.h.

template<typename Derived >

template<typename EssentialPart >

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() * essential.size() entries

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

Definition at line 113 of file Householder.h.

template<typename Derived >

template<typename EssentialPart >

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->cols() * essential.size() entries

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

Definition at line 150 of file Householder.h.

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by other * *this.

Example:

Output:

Definition at line 523 of file MatrixBase.h.

template<typename Derived >

template<typename OtherScalar >

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

inline

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()

Definition at line 278 of file Jacobi.h.

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:

Definition at line 511 of file MatrixBase.h.

template<typename Derived >

template<typename OtherScalar >

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

inline

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()

Definition at line 293 of file Jacobi.h.

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()

Definition at line 326 of file MatrixBase.h.

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()

Definition at line 329 of file MatrixBase.h.

template<typename Derived >

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

Example:

Output:

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

Definition at line 277 of file DiagonalMatrix.h.

template<typename Derived >

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

Definition at line 620 of file PermutationMatrix.h.

template<typename Derived >

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

inline

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

See also: class BDCSVD

Definition at line 1223 of file BDCSVD.h.

template<typename Derived>

template<typename CustomBinaryOp , typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::binaryExpr	(	const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &	other,
		const CustomBinaryOp &	func = `CustomBinaryOp()`
	)		const

inline

Returns: an expression of the difference of *this and other

Note: If you want to substract a given scalar from all coefficients, see Cwise::operator-().

See also: class CwiseBinaryOp, operator-=()

Returns: an expression of the sum of *this and other

Note: If you want to add a given scalar to all coefficients, see Cwise::operator+().

See also: class CwiseBinaryOp, operator+=()

Returns: an expression of a custom coefficient-wise operator func of *this and other

The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)

Here is an example illustrating the use of custom functors:

Output:

See also: class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()

Definition at line 44 of file MatrixBase.h.

template<typename Derived >

NumTraits< typename internal::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()

Definition at line 202 of file StableNorm.h.

template<typename Derived>

template<typename NewType >

EIGEN_DEVICE_FUNC CastXpr<NewType>::Type Eigen::MatrixBase< Derived >::cast ( ) const

inline

Returns: an expression of *this with the Scalar type casted to NewScalar.

The template parameter NewScalar is the type we are casting the scalars to.

See also: class CwiseUnaryOp

Definition at line 63 of file MatrixBase.h.

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

Definition at line 646 of file ColPivHouseholderQR.h.

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

Definition at line 556 of file CompleteOrthogonalDecomposition.h.

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

Computation of matrix inverse and determinant, with invertibility check.

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

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()

Definition at line 362 of file InverseImpl.h.

template<typename Derived >

template<typename ResultType >

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

inline

Computation of matrix inverse, with invertibility check.

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

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()

Definition at line 401 of file InverseImpl.h.

template<typename Derived>

EIGEN_DEVICE_FUNC ConjugateReturnType Eigen::MatrixBase< Derived >::conjugate ( ) const

inline

Returns: an expression of the complex conjugate of *this.

See also: Math functions, MatrixBase::adjoint()

Definition at line 75 of file MatrixBase.h.

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::cos ( ) const

Definition at line 555 of file MatrixFunction.h.

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::cosh ( ) const

Definition at line 571 of file MatrixFunction.h.

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

template<typename Derived>

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseAbsReturnType Eigen::MatrixBase< Derived >::cwiseAbs ( ) const

inline

Returns: an expression of the coefficient-wise absolute value of *this

Example:

Output:

See also: cwiseAbs2()

Definition at line 33 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseAbs2ReturnType Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const

inline

Returns: an expression of the coefficient-wise squared absolute value of *this

Example:

Output:

See also: cwiseAbs()

Definition at line 46 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise == operator of *this and other

Warning: this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

See also: cwiseNotEqual(), isApprox(), isMuchSmallerThan()

Definition at line 44 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const CwiseScalarEqualReturnType Eigen::MatrixBase< Derived >::cwiseEqual ( const Scalar & s ) const

inline

Returns: an expression of the coefficient-wise == operator of *this and a scalar s

Warning: this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

See also: cwiseEqual(const MatrixBase<OtherDerived> &) const

Definition at line 150 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const CwiseInverseReturnType Eigen::MatrixBase< Derived >::cwiseInverse ( ) const

inline

Returns: an expression of the coefficient-wise inverse of *this.

Example:

Output:

See also: cwiseProduct()

Definition at line 84 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMax ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise max of *this and other

Example:

Output:

See also: class CwiseBinaryOp, min()

Definition at line 105 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMax ( const Scalar & other ) const

inline

Returns: an expression of the coefficient-wise max of *this and scalar other

See also: class CwiseBinaryOp, min()

Definition at line 116 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMin ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise min of *this and other

Example:

Output:

See also: class CwiseBinaryOp, max()

Definition at line 79 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMin ( const Scalar & other ) const

inline

Returns: an expression of the coefficient-wise min of *this and scalar other

See also: class CwiseBinaryOp, min()

Definition at line 90 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseNotEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise != operator of *this and other

Warning: this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

See also: cwiseEqual(), isApprox(), isMuchSmallerThan()

Definition at line 64 of file MatrixBase.h.

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

Definition at line 448 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseQuotient ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise quotient of *this and other

Example:

Output:

See also: class CwiseBinaryOp, cwiseProduct(), cwiseInverse()

Definition at line 132 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const CwiseSignReturnType Eigen::MatrixBase< Derived >::cwiseSign ( ) const

inline

Returns: an expression of the coefficient-wise signum of *this.

Example:

Output:

Definition at line 70 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const CwiseSqrtReturnType Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const

inline

Returns: an expression of the coefficient-wise square root of *this.

Example:

Output:

See also: cwisePow(), cwiseSquare()

Definition at line 59 of file MatrixBase.h.

template<typename Derived >

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

inline

Returns: the determinant of this matrix

Definition at line 92 of file Determinant.h.

template<typename Derived >

MatrixBase< Derived >::template DiagonalIndexReturnType< Index_ >::Type 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

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

Definition at line 188 of file Diagonal.h.

template<typename Derived >

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

inline

This is the const version of diagonal().

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

Definition at line 196 of file Diagonal.h.

template<typename Derived>

template<int Index>

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

template<typename Derived>

template<int Index>

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

template<typename Derived >

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

Definition at line 214 of file Diagonal.h.

template<typename Derived >

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

inline

This is the const version of diagonal(Index).

Definition at line 222 of file Diagonal.h.

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.

Definition at line 101 of file MatrixBase.h.

template<typename Derived >

template<typename OtherDerived >

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

Returns: the dot product of *this with other.

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()

Definition at line 69 of file Dot.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Eigen::MatrixBase< Derived >::EIGEN_CWISE_BINARY_RETURN_TYPE	(	Derived	,
		OtherDerived	,
		product
	)		const

inline

Returns: an expression of the Schur product (coefficient wise product) of *this and other

Example:

Output:

See also: class CwiseBinaryOp, cwiseAbs2

Definition at line 23 of file MatrixBase.h.

template<typename Derived>

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

template<typename Derived >

MatrixBase< Derived >::EigenvaluesReturnType Eigen::MatrixBase< Derived >::eigenvalues ( ) const

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

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()

Definition at line 67 of file MatrixBaseEigenvalues.h.

template<typename Derived >

const MatrixExponentialReturnValue< Derived > Eigen::MatrixBase< Derived >::exp ( ) const

Definition at line 424 of file MatrixExponential.h.

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

Definition at line 312 of file MatrixBase.h.

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(), class ForceAlignedAccess

Definition at line 313 of file MatrixBase.h.

template<typename Derived>

template<bool Enable>

internal::add_const_on_value_type<typename internal::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

Definition at line 128 of file ForceAlignedAccess.h.

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

Definition at line 139 of file ForceAlignedAccess.h.

template<typename Derived>

template<bool Enable>

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

inline

Definition at line 314 of file MatrixBase.h.

template<typename Derived>

template<bool Enable>

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

inline

Definition at line 315 of file MatrixBase.h.

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

Definition at line 669 of file FullPivHouseholderQR.h.

template<typename Derived >

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

inline

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

See also: class FullPivLU

Definition at line 884 of file FullPivLU.h.

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

Definition at line 402 of file HouseholderQR.h.

template<typename Derived >

NumTraits< typename internal::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()

Definition at line 214 of file StableNorm.h.

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()

Definition at line 700 of file CwiseNullaryOp.h.

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()

Definition at line 683 of file CwiseNullaryOp.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const ImagReturnType Eigen::MatrixBase< Derived >::imag ( ) const

inline

Returns: an read-only expression of the imaginary part of *this.

See also: real()

Definition at line 96 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC NonConstImagReturnType Eigen::MatrixBase< Derived >::imag ( )

inline

Returns: a non const expression of the imaginary part of *this.

See also: real()

Definition at line 164 of file MatrixBase.h.

template<typename Derived >

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

inline

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()

Definition at line 335 of file InverseImpl.h.

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()

Definition at line 291 of file DiagonalMatrix.h.

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()

Definition at line 717 of file CwiseNullaryOp.h.

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()

Definition at line 673 of file TriangularMatrix.h.

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:

Definition at line 280 of file Dot.h.

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:

Definition at line 299 of file Dot.h.

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()

Definition at line 648 of file TriangularMatrix.h.

template<typename Derived >

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

inline

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

See also: class JacobiSVD

Definition at line 797 of file JacobiSVD.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const Product<Derived,OtherDerived,LazyProduct> Eigen::MatrixBase< Derived >::lazyProduct ( const MatrixBase< OtherDerived > & other ) const

template<typename Derived>

template<typename OtherDerived >

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&)

Definition at line 431 of file GeneralProduct.h.

template<typename Derived >

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

inline

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

See also: SelfAdjointView::ldlt()

Definition at line 662 of file LDLT.h.

template<typename Derived >

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

inline

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

Definition at line 516 of file LLT.h.

template<typename Derived >

const MatrixLogarithmReturnValue< Derived > Eigen::MatrixBase< Derived >::log ( ) const

Definition at line 365 of file MatrixLogarithm.h.

template<typename Derived>

template<int p>

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()

Definition at line 264 of file Dot.h.

template<typename Derived>

template<int p>

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

template<typename Derived >

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

inline

Synonym of partialPivLu().

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

See also: class PartialPivLU

Definition at line 604 of file PartialPivLU.h.

template<typename Derived >

template<typename EssentialPart >

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()

Definition at line 65 of file Householder.h.

template<typename Derived >

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()

Definition at line 42 of file Householder.h.

template<typename Derived>

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

inline

Definition at line 321 of file MatrixBase.h.

template<typename Derived>

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

inline

Definition at line 322 of file MatrixBase.h.

template<typename Derived>

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

Definition at line 540 of file MatrixFunction.h.

template<typename Derived >

NoAlias< Derived, MatrixBase > 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 usefull when the source expression contains a matrix product.

Here are some examples where noalias is usefull:

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

Definition at line 101 of file NoAlias.h.

template<typename Derived >

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

inline

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()

Definition at line 105 of file Dot.h.

template<typename Derived >

void Eigen::MatrixBase< Derived >::normalize ( )

inline

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

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

See also: norm(), normalized()

Definition at line 142 of file Dot.h.

template<typename Derived >

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

inline

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.

See also: norm(), normalize()

Definition at line 121 of file Dot.h.

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==

Definition at line 305 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator&& ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise boolean and operator of *this and other

Warning: this operator is for expression of bool only.

Example:

Output:

See also: operator||(), select()

Definition at line 92 of file MatrixBase.h.

template<typename Derived>

template<typename DiagonalDerived >

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.

Definition at line 21 of file DiagonalProduct.h.

template<typename Derived >

template<typename OtherDerived >

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

inline

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*()

Definition at line 387 of file GeneralProduct.h.

template<typename Derived>

template<typename DiagonalDerived >

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

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:

Definition at line 498 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

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

template<typename Derived>

template<typename OtherDerived >

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

replaces *this by *this + other.

Returns: a reference to *this

Definition at line 175 of file CwiseBinaryOp.h.

template<typename Derived>

template<typename OtherDerived >

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

inlineprotected

Definition at line 476 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC const NegativeReturnType Eigen::MatrixBase< Derived >::operator- ( ) const

inline

Returns: an expression of the opposite of *this

Definition at line 46 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

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

template<typename Derived>

template<typename OtherDerived >

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

replaces *this by *this - other.

Returns: a reference to *this

Definition at line 162 of file CwiseBinaryOp.h.

template<typename Derived>

template<typename OtherDerived >

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

inlineprotected

Definition at line 479 of file MatrixBase.h.

template<typename Derived>

template<typename OtherDerived >

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

Definition at line 73 of file Assign.h.

template<typename Derived>

template<typename OtherDerived >

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

Definition at line 82 of file Assign.h.

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)

Definition at line 55 of file Assign.h.

template<typename Derived >

template<typename OtherDerived >

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

Definition at line 64 of file Assign.h.

template<typename Derived>

template<typename OtherDerived >

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

template<typename Derived>

template<typename OtherDerived >

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

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!=

Definition at line 297 of file MatrixBase.h.

template<typename Derived >

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

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

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()

Definition at line 122 of file MatrixBaseEigenvalues.h.

template<typename Derived>

template<typename OtherDerived >

EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator|| ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > & other ) const

inline

Returns: an expression of the coefficient-wise boolean or operator of *this and other

Warning: this operator is for expression of bool only.

Example:

Output:

See also: operator&&(), select()

Definition at line 111 of file MatrixBase.h.

template<typename Derived >

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

inline

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

See also: class PartialPivLU

Definition at line 589 of file PartialPivLU.h.

template<typename Derived >

const MatrixPowerReturnValue< Derived > Eigen::MatrixBase< Derived >::pow ( const RealScalar & p ) const

Definition at line 700 of file MatrixPower.h.

template<typename Derived >

const MatrixComplexPowerReturnValue< Derived > Eigen::MatrixBase< Derived >::pow ( const std::complex< RealScalar > & p ) const

Definition at line 704 of file MatrixPower.h.

template<typename Derived>

EIGEN_DEVICE_FUNC RealReturnType Eigen::MatrixBase< Derived >::real ( ) const

inline

Returns: a read-only expression of the real part of *this.

See also: imag()

Definition at line 87 of file MatrixBase.h.

template<typename Derived>

EIGEN_DEVICE_FUNC NonConstRealReturnType Eigen::MatrixBase< Derived >::real ( )

inline

Returns: a non const expression of the real part of *this.

See also: imag()

Definition at line 155 of file MatrixBase.h.

template<typename Derived>

template<unsigned int UpLo>

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

template<typename Derived>

template<unsigned int UpLo>

EIGEN_DEVICE_FUNC ConstSelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView ( ) const

template<typename Derived>

template<unsigned int UpLo>

MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView ( ) const

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

Definition at line 326 of file SelfAdjointView.h.

template<typename Derived>

template<unsigned int UpLo>

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

Definition at line 343 of file SelfAdjointView.h.

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()

Definition at line 774 of file CwiseNullaryOp.h.

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()

Definition at line 790 of file CwiseNullaryOp.h.

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::sin ( ) const

Definition at line 547 of file MatrixFunction.h.

template<typename Derived >

const MatrixFunctionReturnValue< Derived > Eigen::MatrixBase< Derived >::sinh ( ) const

Definition at line 563 of file MatrixFunction.h.

template<typename Derived >

const SparseView< Derived > Eigen::MatrixBase< Derived >::sparseView	(	const Scalar &	reference = `Scalar(0)`,
		const typename NumTraits< Scalar >::Real &	epsilon = `NumTraits<Scalar>::dummy_precision()`
	)		const

Returns: a sparse expression of the dense expression *this with values smaller than reference * epsilon removed.

This method is typically used when prototyping to convert a quickly assembled dense Matrix D to a SparseMatrix S:

MatrixXd D(n,m);
SparseMatrix<double> S;
S = D.sparseView();             // suppress numerical zeros (exact)
S = D.sparseView(reference);
S = D.sparseView(reference,epsilon);

where reference is a meaningful non zero reference value, and epsilon is a tolerance factor defaulting to NumTraits<Scalar>::dummy_precision().

See also: SparseMatrixBase::pruned(), class SparseView

Definition at line 225 of file SparseView.h.

template<typename Derived >

const MatrixSquareRootReturnValue< Derived > Eigen::MatrixBase< Derived >::sqrt ( ) const

Definition at line 362 of file MatrixSquareRoot.h.

template<typename Derived >

EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm ( ) const

Returns: , for vectors, the squared l2 norm of *this, and for matrices the 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()

Definition at line 93 of file Dot.h.

template<typename Derived >

NumTraits< typename internal::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()

Definition at line 157 of file StableNorm.h.

template<typename Derived >

void Eigen::MatrixBase< Derived >::stableNormalize ( )

inline

Normalizes the vector while avoid underflow and overflow

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()

Definition at line 188 of file Dot.h.

template<typename Derived >

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

inline

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

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()

Definition at line 164 of file Dot.h.

template<typename Derived >

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()

Definition at line 498 of file Redux.h.

template<typename Derived>

template<unsigned int Mode>

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

template<typename Derived>

template<unsigned int Mode>

EIGEN_DEVICE_FUNC ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView ( ) const

template<typename Derived>

template<unsigned int Mode>

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

Definition at line 628 of file TriangularMatrix.h.

template<typename Derived>

template<unsigned int Mode>

MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView ( ) const

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

Definition at line 637 of file TriangularMatrix.h.

template<typename Derived>

template<typename CustomUnaryOp >

EIGEN_DEVICE_FUNC const CwiseUnaryOp<CustomUnaryOp, const Derived> Eigen::MatrixBase< Derived >::unaryExpr ( const CustomUnaryOp & func = CustomUnaryOp() ) const

inline

Apply a unary operator coefficient-wise.

Parameters

[in] func Functor implementing the unary operator

Template Parameters

CustomUnaryOp Type of func

Returns: An expression of a custom coefficient-wise unary operator func of *this

The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.

Example:

Output:

Genuine functors allow for more possibilities, for instance it may contain a state.

Example:

Output:

See also: unaryViewExpr, binaryExpr, class CwiseUnaryOp

Definition at line 122 of file MatrixBase.h.

template<typename Derived>

template<typename CustomViewOp >

EIGEN_DEVICE_FUNC const CwiseUnaryView<CustomViewOp, const Derived> Eigen::MatrixBase< Derived >::unaryViewExpr ( const CustomViewOp & func = CustomViewOp() ) const

inline

Returns: an expression of a custom coefficient-wise unary operator func of *this

The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.

Example:

Output:

See also: unaryExpr, binaryExpr class CwiseUnaryOp

Definition at line 143 of file MatrixBase.h.

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.

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

Definition at line 803 of file CwiseNullaryOp.h.

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.

This variant is for fixed-size vector only.

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

Definition at line 818 of file CwiseNullaryOp.h.

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)

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

Definition at line 861 of file CwiseNullaryOp.h.

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}^*)

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

Definition at line 831 of file CwiseNullaryOp.h.

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}^*)

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

Definition at line 841 of file CwiseNullaryOp.h.

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}^*)

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

Definition at line 851 of file CwiseNullaryOp.h.

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

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