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

#include <src/eigen/Eigen/src/Core/MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:

Collaboration diagram for Eigen::MatrixBase< Derived >:

Classes
struct	ConstDiagonalIndexReturnType

struct	ConstSelfAdjointViewReturnType

struct	ConstTriangularViewReturnType

struct	cross_product_return_type

struct	DiagonalIndexReturnType

struct	SelfAdjointViewReturnType

struct	TriangularViewReturnType

Public Types
enum	{ HomogeneousReturnTypeDirection }

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

typedef MatrixBase	StorageBaseType

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

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

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

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

typedef NumTraits< Scalar >::Real	RealScalar

typedef DenseBase< Derived >	Base

typedef Base::CoeffReturnType	CoeffReturnType

typedef Base::ConstTransposeReturnType	ConstTransposeReturnType

typedef Base::RowXpr	RowXpr

typedef Base::ColXpr	ColXpr

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

typedef Base::PlainObject	PlainObject

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

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

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

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

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

typedef Diagonal< Derived >	DiagonalReturnType

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

typedef Diagonal< Derived, DynamicIndex >	DiagonalDynamicIndexReturnType

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

typedef Homogeneous< Derived, HomogeneousReturnTypeDirection >	HomogeneousReturnType

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

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

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 Eigen::InnerIterator< Derived >	InnerIterator

typedef Scalar	value_type

typedef Matrix< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign\|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime >	PlainMatrix

typedef Array< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign\|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime >	PlainArray

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

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

typedef Transpose< Derived >	TransposeReturnType

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

typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType

typedef const VectorwiseOp< const Derived, Horizontal >	ConstRowwiseReturnType

typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType

typedef const VectorwiseOp< const Derived, Vertical >	ConstColwiseReturnType

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

typedef Reverse< Derived, BothDirections >	ReverseReturnType

typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType

Public Member Functions
EIGEN_DEVICE_FUNC Index	diagonalSize () const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived &	operator= (const MatrixBase &other)

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

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

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

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

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

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

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

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

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

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

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

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

EIGEN_DEVICE_FUNC RealScalar	squaredNorm () const

EIGEN_DEVICE_FUNC RealScalar	norm () const

RealScalar	stableNorm () const

RealScalar	blueNorm () const

RealScalar	hypotNorm () const

EIGEN_DEVICE_FUNC const PlainObject	normalized () const

EIGEN_DEVICE_FUNC const PlainObject	stableNormalized () const

EIGEN_DEVICE_FUNC void	normalize ()

EIGEN_DEVICE_FUNC void	stableNormalize ()

EIGEN_DEVICE_FUNC const AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC void	adjointInPlace ()

EIGEN_DEVICE_FUNC DiagonalReturnType	diagonal ()

EIGEN_DEVICE_FUNC ConstDiagonalReturnType	diagonal () const

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

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

EIGEN_DEVICE_FUNC DiagonalDynamicIndexReturnType	diagonal (Index index)

EIGEN_DEVICE_FUNC ConstDiagonalDynamicIndexReturnType	diagonal (Index index) const

template<unsigned int Mode>
EIGEN_DEVICE_FUNC TriangularViewReturnType< Mode >::Type	triangularView ()

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

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

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

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

EIGEN_DEVICE_FUNC const DiagonalWrapper< const Derived >	asDiagonal () const

const PermutationWrapper< const Derived >	asPermutation () const

EIGEN_DEVICE_FUNC Derived &	setIdentity ()

EIGEN_DEVICE_FUNC Derived &	setIdentity (Index rows, Index cols)
	Resizes to the given size, and writes the identity expression (not necessarily square) into *this.

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

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

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

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

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

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

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

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

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

const Derived &	forceAlignedAccess () const

Derived &	forceAlignedAccess ()

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

template<bool Enable>
Derived &	forceAlignedAccessIf ()

EIGEN_DEVICE_FUNC Scalar	trace () const

template<int p>
EIGEN_DEVICE_FUNC RealScalar	lpNorm () const

EIGEN_DEVICE_FUNC MatrixBase< Derived > &	matrix ()

EIGEN_DEVICE_FUNC const MatrixBase< Derived > &	matrix () const

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE ArrayWrapper< Derived >	array ()

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

const FullPivLU< PlainObject >	fullPivLu () const

const PartialPivLU< PlainObject >	partialPivLu () const

const PartialPivLU< PlainObject >	lu () const

const Inverse< Derived >	inverse () const

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

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

Scalar	determinant () const

const LLT< PlainObject >	llt () const

const LDLT< PlainObject >	ldlt () const

const HouseholderQR< PlainObject >	householderQr () const

const ColPivHouseholderQR< PlainObject >	colPivHouseholderQr () const

const FullPivHouseholderQR< PlainObject >	fullPivHouseholderQr () const

const CompleteOrthogonalDecomposition< PlainObject >	completeOrthogonalDecomposition () const

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

RealScalar	operatorNorm () const
	Computes the L2 operator norm.

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

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

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

template<typename OtherDerived >
EIGEN_DEVICE_FUNC PlainObject	cross3 (const MatrixBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC PlainObject	unitOrthogonal (void) const

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

EIGEN_DEVICE_FUNC HomogeneousReturnType	homogeneous () const

typedef	EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE (ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType

EIGEN_DEVICE_FUNC const HNormalizedReturnType	hnormalized () const
	homogeneous normalization

void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)

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

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

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

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

const MatrixFunctionReturnValue< Derived >	matrixFunction (StemFunction f) const
	Helper function for the unsupported MatrixFunctions module.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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 Derived &	lazyAssign (const DenseBase< OtherDerived > &other)

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

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvalReturnType	eval () const

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

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

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

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

EIGEN_DEVICE_FUNC Index	nonZeros () const

EIGEN_DEVICE_FUNC Index	outerSize () const

EIGEN_DEVICE_FUNC Index	innerSize () const

EIGEN_DEVICE_FUNC void	resize (Index newSize)

EIGEN_DEVICE_FUNC void	resize (Index rows, Index cols)

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

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

EIGEN_DEVICE_FUNC TransposeReturnType	transpose ()

EIGEN_DEVICE_FUNC ConstTransposeReturnType	transpose () const

EIGEN_DEVICE_FUNC void	transposeInPlace ()

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 void	fill (const Scalar &value)

EIGEN_DEVICE_FUNC Derived &	setConstant (const Scalar &value)

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

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

EIGEN_DEVICE_FUNC Derived &	setZero ()

EIGEN_DEVICE_FUNC Derived &	setOnes ()

EIGEN_DEVICE_FUNC Derived &	setRandom ()

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

template<typename OtherDerived >
bool	isApprox (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

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	isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

EIGEN_DEVICE_FUNC bool	isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

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

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

bool	hasNaN () const

bool	allFinite () const

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 const NestByValue< Derived >	nestByValue () const

EIGEN_DEVICE_FUNC Scalar	sum () const

EIGEN_DEVICE_FUNC Scalar	mean () const

EIGEN_DEVICE_FUNC Scalar	prod () const

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 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

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

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

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

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

EIGEN_DEVICE_FUNC CoeffReturnType	value () const

EIGEN_DEVICE_FUNC bool	all () const

EIGEN_DEVICE_FUNC bool	any () const

EIGEN_DEVICE_FUNC Index	count () const

EIGEN_DEVICE_FUNC ConstRowwiseReturnType	rowwise () const

EIGEN_DEVICE_FUNC RowwiseReturnType	rowwise ()

EIGEN_DEVICE_FUNC ConstColwiseReturnType	colwise () const

EIGEN_DEVICE_FUNC ColwiseReturnType	colwise ()

template<typename ThenDerived , typename ElseDerived >
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

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

template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor >	replicate () const

EIGEN_DEVICE_FUNC ReverseReturnType	reverse ()

EIGEN_DEVICE_FUNC ConstReverseReturnType	reverse () const

EIGEN_DEVICE_FUNC void	reverseInPlace ()

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

Static Public Member Functions
static EIGEN_DEVICE_FUNC const IdentityReturnType	Identity ()

static EIGEN_DEVICE_FUNC const IdentityReturnType	Identity (Index rows, Index cols)

static EIGEN_DEVICE_FUNC const BasisReturnType	Unit (Index size, Index i)

static EIGEN_DEVICE_FUNC const BasisReturnType	Unit (Index i)

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitX ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitY ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitZ ()

static EIGEN_DEVICE_FUNC const BasisReturnType	UnitW ()

static 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.

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.

template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)

template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (Index size, const CustomNullaryOp &func)

template<typename CustomNullaryOp >
static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject >	NullaryExpr (const CustomNullaryOp &func)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Zero (Index rows, Index cols)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Zero (Index size)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Zero ()

static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones (Index rows, Index cols)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones (Index size)

static EIGEN_DEVICE_FUNC const ConstantReturnType	Ones ()

static const RandomReturnType	Random (Index rows, Index cols)

static const RandomReturnType	Random (Index size)

static const RandomReturnType	Random ()

Protected Member Functions
EIGEN_DEVICE_FUNC	MatrixBase ()

template<typename OtherDerived >
Derived &	operator+= (const ArrayBase< OtherDerived > &)

template<typename OtherDerived >
Derived &	operator-= (const ArrayBase< OtherDerived > &)

Private Member Functions
EIGEN_DEVICE_FUNC	MatrixBase (int)

EIGEN_DEVICE_FUNC	MatrixBase (int, int)

template<typename OtherDerived >
EIGEN_DEVICE_FUNC	MatrixBase (const MatrixBase< OtherDerived > &)

Related Symbols
(Note that these are not member symbols.)
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: \blank TopicClassHierarchy

Class Documentation

◆ Eigen::MatrixBase::ConstDiagonalIndexReturnType

struct Eigen::MatrixBase::ConstDiagonalIndexReturnType

template<typename Derived>
template<int Index>
struct Eigen::MatrixBase< Derived >::ConstDiagonalIndexReturnType< Index >

Class Members
typedef const Diagonal< const Derived, Index >	Type

◆ Eigen::MatrixBase::ConstSelfAdjointViewReturnType

struct Eigen::MatrixBase::ConstSelfAdjointViewReturnType

template<typename Derived>
template<unsigned int UpLo>
struct Eigen::MatrixBase< Derived >::ConstSelfAdjointViewReturnType< UpLo >

Class Members
typedef const SelfAdjointView< const Derived, UpLo >	Type

◆ Eigen::MatrixBase::ConstTriangularViewReturnType

struct Eigen::MatrixBase::ConstTriangularViewReturnType

template<typename Derived>
template<unsigned int Mode>
struct Eigen::MatrixBase< Derived >::ConstTriangularViewReturnType< Mode >

Class Members
typedef const TriangularView< const Derived, Mode >	Type

◆ Eigen::MatrixBase::cross_product_return_type

struct Eigen::MatrixBase::cross_product_return_type

template<typename Derived>
template<typename OtherDerived>
struct Eigen::MatrixBase< Derived >::cross_product_return_type< OtherDerived >

Class Members
typedef Scalar, Scalar >::ReturnType	Scalar
typedef Matrix< Scalar, RowsAtCompileTime, ColsAtCompileTime >	type

◆ Eigen::MatrixBase::DiagonalIndexReturnType

struct Eigen::MatrixBase::DiagonalIndexReturnType

template<typename Derived>
template<int Index>
struct Eigen::MatrixBase< Derived >::DiagonalIndexReturnType< Index >

Class Members
typedef Diagonal< Derived, Index >	Type

◆ Eigen::MatrixBase::SelfAdjointViewReturnType

struct Eigen::MatrixBase::SelfAdjointViewReturnType

template<typename Derived>
template<unsigned int UpLo>
struct Eigen::MatrixBase< Derived >::SelfAdjointViewReturnType< UpLo >

Class Members
typedef SelfAdjointView< Derived, UpLo >	Type

◆ Eigen::MatrixBase::TriangularViewReturnType

struct Eigen::MatrixBase::TriangularViewReturnType

template<typename Derived>
template<unsigned int Mode>
struct Eigen::MatrixBase< Derived >::TriangularViewReturnType< Mode >

Class Members
typedef TriangularView< Derived, Mode >	Type

Member Typedef Documentation

◆ AdjointReturnType

template<typename Derived >

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

◆ Base

template<typename Derived >

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

◆ BasisReturnType

template<typename Derived >

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

◆ CoeffReturnType

template<typename Derived >

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

◆ ColwiseReturnType

template<typename Derived >

typedef VectorwiseOp<Derived, Vertical> Eigen::DenseBase< Derived >::ColwiseReturnType

inherited

◆ ColXpr

template<typename Derived >

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

◆ ConstantReturnType

template<typename Derived >

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

◆ ConstColwiseReturnType

template<typename Derived >

typedef const VectorwiseOp<const Derived, Vertical> Eigen::DenseBase< Derived >::ConstColwiseReturnType

inherited

◆ ConstDiagonalDynamicIndexReturnType

template<typename Derived >

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

◆ ConstDiagonalReturnType

template<typename Derived >

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

◆ ConstReverseReturnType

template<typename Derived >

typedef const Reverse<const Derived, BothDirections> Eigen::DenseBase< Derived >::ConstReverseReturnType

inherited

◆ ConstRowwiseReturnType

template<typename Derived >

typedef const VectorwiseOp<const Derived, Horizontal> Eigen::DenseBase< Derived >::ConstRowwiseReturnType

inherited

◆ ConstStartMinusOne

template<typename Derived >

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

◆ ConstTransposeReturnType

template<typename Derived >

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

◆ DiagonalDynamicIndexReturnType

template<typename Derived >

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

◆ DiagonalReturnType

template<typename Derived >

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

◆ EigenvaluesReturnType

template<typename Derived >

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

◆ EvalReturnType

template<typename Derived >

typedef internal::add_const_on_value_type<typenameinternal::eval<Derived>::type>::type Eigen::DenseBase< Derived >::EvalReturnType

inherited

◆ HomogeneousReturnType

template<typename Derived >

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

◆ IdentityReturnType

template<typename Derived >

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

◆ InnerIterator

template<typename Derived >

typedef Eigen::InnerIterator<Derived> Eigen::DenseBase< Derived >::InnerIterator

inherited

Inner iterator type to iterate over the coefficients of a row or column.

See also: class InnerIterator

◆ PacketScalar

template<typename Derived >

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

◆ PlainArray

template<typename Derived >

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 > Eigen::DenseBase< Derived >::PlainArray

inherited

The plain array type corresponding to this expression.

See also: PlainObject

◆ PlainMatrix

template<typename Derived >

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 > Eigen::DenseBase< Derived >::PlainMatrix

inherited

The plain matrix type corresponding to this expression.

See also: PlainObject

◆ PlainObject

template<typename Derived >

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

◆ RandomAccessLinSpacedReturnType

template<typename Derived >

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

inherited

◆ RandomReturnType

template<typename Derived >

typedef CwiseNullaryOp<internal::scalar_random_op<Scalar>,PlainObject> Eigen::DenseBase< Derived >::RandomReturnType

inherited

◆ RealScalar

template<typename Derived >

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

◆ ReverseReturnType

template<typename Derived >

typedef Reverse<Derived, BothDirections> Eigen::DenseBase< Derived >::ReverseReturnType

inherited

◆ RowwiseReturnType

template<typename Derived >

typedef VectorwiseOp<Derived, Horizontal> Eigen::DenseBase< Derived >::RowwiseReturnType

inherited

◆ RowXpr

template<typename Derived >

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

◆ Scalar

template<typename Derived >

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

◆ SequentialLinSpacedReturnType

template<typename Derived >

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

inherited

◆ SquareMatrixType

template<typename Derived >

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

type of the equivalent square matrix

◆ StemFunction

template<typename Derived >

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

◆ StorageBaseType

template<typename Derived >

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

◆ StorageIndex

template<typename Derived >

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

◆ StorageKind

template<typename Derived >

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

◆ TransposeReturnType

template<typename Derived >

typedef Transpose<Derived> Eigen::DenseBase< Derived >::TransposeReturnType

inherited

◆ value_type

template<typename Derived >

typedef Scalar Eigen::DenseBase< Derived >::value_type

inherited

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

It is an alias for the Scalar type

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

inherited

Enumerator
RowsAtCompileTime	The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant. See also MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime
ColsAtCompileTime	The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant. See also MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime
SizeAtCompileTime	This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time. See also RowsAtCompileTime, ColsAtCompileTime
MaxRowsAtCompileTime	This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. See also RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
MaxColsAtCompileTime	This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. See also ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
MaxSizeAtCompileTime	This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. See also SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
IsVectorAtCompileTime	This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row).
Flags	This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags.
IsRowMajor	True if this expression has row-major storage order.
InnerSizeAtCompileTime
InnerStrideAtCompileTime
OuterStrideAtCompileTime

         {
 
      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
                                                   internal::traits<Derived>::ColsAtCompileTime>::ret),
      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
                                                      internal::traits<Derived>::MaxColsAtCompileTime>::ret),
      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
                           || internal::traits<Derived>::MaxColsAtCompileTime == 1,
      Flags = internal::traits<Derived>::Flags,
      IsRowMajor = int(Flags) & RowMajorBit, 
      InnerSizeAtCompileTime = int(IsVectorAtCompileTime) ? int(SizeAtCompileTime)
                             : int(IsRowMajor) ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
 
      InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
      OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
    };

◆ anonymous enum

template<typename Derived >

anonymous enum

inherited

Enumerator
IsPlainObjectBase

176{ IsPlainObjectBase = 0 };

Eigen::DenseBase::IsPlainObjectBase

@ IsPlainObjectBase

Definition DenseBase.h:176

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
HomogeneousReturnTypeDirection

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

398 : ColsAtCompileTime==1 ? Vertical : Horizontal };

Eigen::MatrixBase::HomogeneousReturnTypeDirection

@ HomogeneousReturnTypeDirection

Definition MatrixBase.h:397

Eigen::MatrixBase::ColsAtCompileTime

@ ColsAtCompileTime

Definition DenseBase.h:106

Eigen::MatrixBase::RowsAtCompileTime

@ RowsAtCompileTime

Definition DenseBase.h:100

Eigen::Horizontal

@ Horizontal

Definition Constants.h:268

Eigen::Vertical

@ Vertical

Definition Constants.h:265

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
SizeMinusOne

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

Constructor & Destructor Documentation

◆ MatrixBase() [1/4]

template<typename Derived >

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

inlineprotected

467: Base() {}

Eigen::MatrixBase::Base

DenseBase< Derived > Base

Definition MatrixBase.h:60

◆ MatrixBase() [2/4]

template<typename Derived >

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

explicitprivate

◆ MatrixBase() [3/4]

template<typename Derived >

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

private

◆ MatrixBase() [4/4]

template<typename Derived >

template<typename OtherDerived >

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

explicitprivate

Member Function Documentation

◆ adjoint()

template<typename Derived >

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

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

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

◆ adjointInPlace()

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()

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

◆ all()

template<typename Derived >

bool Eigen::DenseBase< Derived >::all

inlineinherited

Returns: true if all coefficients are true

Example:

Output:

See also: any(), Cwise::operator<()

{
  typedef internal::evaluator<Derived> Evaluator;
  enum {
    unroll = SizeAtCompileTime != Dynamic
          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
  };
  Evaluator evaluator(derived());
  if(unroll)
    return internal::all_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);
  else
  {
    for(Index j = 0; j < cols(); ++j)
      for(Index i = 0; i < rows(); ++i)
        if (!evaluator.coeff(i, j)) return false;
    return true;
  }
}

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

◆ allFinite()

template<typename Derived >

bool Eigen::DenseBase< Derived >::allFinite

inlineinherited

Returns: true if *this contains only finite numbers, i.e., no NaN and no +/-INF values.

See also: hasNaN()

{
#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
  return derived().array().isFinite().all();
#else
  return !((derived()-derived()).hasNaN());
#endif
}

◆ any()

template<typename Derived >

bool Eigen::DenseBase< Derived >::any

inlineinherited

Returns: true if at least one coefficient is true

See also: all()

{
  typedef internal::evaluator<Derived> Evaluator;
  enum {
    unroll = SizeAtCompileTime != Dynamic
          && SizeAtCompileTime * (Evaluator::CoeffReadCost + NumTraits<Scalar>::AddCost) <= EIGEN_UNROLLING_LIMIT
  };
  Evaluator evaluator(derived());
  if(unroll)
    return internal::any_unroller<Evaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(evaluator);
  else
  {
    for(Index j = 0; j < cols(); ++j)
      for(Index i = 0; i < rows(); ++i)
        if (evaluator.coeff(i, j)) return true;
    return false;
  }
}

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

◆ applyHouseholderOnTheLeft()

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()

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

References row().

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◆ applyHouseholderOnTheRight()

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()

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

References col().

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◆ applyOnTheLeft() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by other * *this.

Example:

Output:

{
  other.derived().applyThisOnTheLeft(derived());
}

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

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◆ applyOnTheLeft() [2/2]

template<typename Derived >

template<typename OtherScalar >

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

inline

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

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

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

References Eigen::internal::apply_rotation_in_the_plane(), and row().

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◆ applyOnTheRight() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

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

Example:

Output:

{
  other.derived().applyThisOnTheRight(derived());
}

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

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◆ applyOnTheRight() [2/2]

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()

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

References Eigen::internal::apply_rotation_in_the_plane(), col(), and Eigen::JacobiRotation< Scalar >::transpose().

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◆ array() [1/2]

template<typename Derived >

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

inline

Returns: an Array expression of this matrix

See also: ArrayBase::matrix()

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

Referenced by igl::barycentric_coordinates(), igl::copyleft::cgal::mesh_boolean(), igl::copyleft::cgal::minkowski_sum(), igl::normalize_row_sums(), igl::pso(), igl::random_search(), and Eigen::internal::lpNorm_selector< Derived, p >::run().

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◆ array() [2/2]

template<typename Derived >

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

inline

Returns: a const Array expression of this matrix

See also: ArrayBase::matrix()

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

◆ asDiagonal()

template<typename Derived >

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

inline

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

\only_for_vectors

Example:

Output:

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

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

Referenced by Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::prescale(), Eigen::Transform< _Scalar, _Dim, _Mode, _Options >::scale(), and Eigen::Scaling().

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◆ asPermutation()

template<typename Derived >

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

{
  return derived();
}

◆ bdcSvd()

template<typename Derived >

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

inline

\svd_module

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

See also: class BDCSVD

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

◆ blueNorm()

template<typename Derived >

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

inline

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

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

See also: norm(), stableNorm(), hypotNorm()

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

References Eigen::internal::blueNorm_impl().

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◆ colPivHouseholderQr()

template<typename Derived >

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

inline

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

See also: class ColPivHouseholderQR

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

◆ colwise() [1/2]

template<typename Derived >

DenseBase< Derived >::ColwiseReturnType Eigen::DenseBase< Derived >::colwise

inlineinherited

Returns: a writable VectorwiseOp wrapper of *this providing additional partial reduction operations

See also: rowwise(), class VectorwiseOp, TutorialReductionsVisitorsBroadcasting

{
  return ColwiseReturnType(derived());
}

◆ colwise() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC ConstColwiseReturnType Eigen::DenseBase< Derived >::colwise ( ) const

inlineinherited

Returns: a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Output:

See also: rowwise(), class VectorwiseOp, TutorialReductionsVisitorsBroadcasting

                                                                    {
      return ConstColwiseReturnType(derived());
    }

Referenced by igl::bounding_box(), igl::copyleft::offset_surface(), and Eigen::umeyama().

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◆ completeOrthogonalDecomposition()

template<typename Derived >

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

inline

Returns: the complete orthogonal decomposition of *this.

See also: class CompleteOrthogonalDecomposition

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

◆ computeInverseAndDetWithCheck()

template<typename Derived >

template<typename ResultType >

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

inline

\lu_module

Computation of matrix inverse and determinant, with invertibility check.

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

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()

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

References eigen_assert, and inverse().

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◆ computeInverseWithCheck()

template<typename Derived >

template<typename ResultType >

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

inline

\lu_module

Computation of matrix inverse, with invertibility check.

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

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()

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

References eigen_assert, and inverse().

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◆ Constant() [1/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant ( const Scalar & value )

staticinherited

Returns: an expression of a constant matrix of value value

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

The template parameter CustomNullaryOp is the type of the functor.

See also: class CwiseNullaryOp

{
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
  return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value));
}

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

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◆ Constant() [2/3]

template<typename Derived >

EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant	(	Index	rows,
		Index	cols,
		const Scalar &	value
	)

staticinherited

Returns: an expression of a constant matrix of value value

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase 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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also: class CwiseNullaryOp

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

References Eigen::DenseBase< Derived >::NullaryExpr().

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◆ Constant() [3/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant	(	Index	size,
		const Scalar &	value
	)

staticinherited

Returns: an expression of a constant matrix of value value

The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.

\only_for_vectors

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also: class CwiseNullaryOp

{
  return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value));
}

References Eigen::DenseBase< Derived >::NullaryExpr().

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◆ count()

template<typename Derived >

Eigen::Index Eigen::DenseBase< Derived >::count

inlineinherited

Returns: the number of coefficients which evaluate to true

See also: all(), any()

{
  return derived().template cast<bool>().template cast<Index>().sum();
}

◆ cross()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC cross_product_return_type< OtherDerived >::type Eigen::MatrixBase< Derived >::cross ( const MatrixBase< OtherDerived > & other ) const

inline

◆ cwiseProduct()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

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◆ determinant()

template<typename Derived >

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

inline

\lu_module

Returns: the determinant of this matrix

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

References eigen_assert.

◆ diagonal() [1/6]

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

{
  return DiagonalReturnType(derived());
}

◆ diagonal() [2/6]

template<typename Derived >

template<int Index>

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

◆ diagonal() [3/6]

template<typename Derived >

MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index_ >::Type Eigen::MatrixBase< Derived >::diagonal

inline

This is the const version of diagonal().

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

{
  return ConstDiagonalReturnType(derived());
}

◆ diagonal() [4/6]

template<typename Derived >

template<int Index>

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

◆ diagonal() [5/6]

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

{
  return DiagonalDynamicIndexReturnType(derived(), index);
}

◆ diagonal() [6/6]

template<typename Derived >

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

inline

This is the const version of diagonal(Index).

{
  return ConstDiagonalDynamicIndexReturnType(derived(), index);
}

◆ diagonalSize()

template<typename Derived >

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

inline

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

See also: rows(), cols(), SizeAtCompileTime.

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

Eigen::numext::mini

EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE T mini(const T &x, const T &y)

Definition MathFunctions.h:815

References Eigen::numext::mini().

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◆ dot() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))
  typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
#endif
  
  eigen_assert(size() == other.size());
 
  return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
}

References eigen_assert, EIGEN_CHECK_BINARY_COMPATIBILIY, EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE, EIGEN_STATIC_ASSERT_VECTOR_ONLY, and Eigen::internal::dot_nocheck< T, U, NeedToTranspose >::run().

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◆ dot() [2/2]

template<typename Derived >

template<typename OtherDerived >

Eigen::MatrixBase< Derived >::dot ( const MatrixBase< OtherDerived > & other ) const

Returns: the dot product of *this with other.

\only_for_vectors

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

See also: squaredNorm(), norm()

◆ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE()

template<typename Derived >

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

◆ eigenvalues()

template<typename Derived >

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

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

Output:

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

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

◆ eval()

template<typename Derived >

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

inline

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

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

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

    {
      // Even though MSVC does not honor strong inlining when the return type
      // is a dynamic matrix, we desperately need strong inlining for fixed
      // size types on MSVC.
      return typename internal::eval<Derived>::type(derived());
    }

Referenced by Eigen::internal::generic_product_impl< Lhs, Homogeneous< RhsArg, Vertical >, TriangularShape, HomogeneousShape, ProductTag >::evalTo(), igl::min_quad_with_fixed_solve(), and igl::ramer_douglas_peucker().

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◆ evalTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::evalTo ( Dest & ) const

inlineinherited

    {
      EIGEN_STATIC_ASSERT((internal::is_same<Dest,void>::value),THE_EVAL_EVALTO_FUNCTION_SHOULD_NEVER_BE_CALLED_FOR_DENSE_OBJECTS);
    }

References EIGEN_STATIC_ASSERT.

◆ fill()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void Eigen::DenseBase< Derived >::fill ( const Scalar & val )

inherited

Alias for setConstant(): sets all coefficients in this expression to val.

See also: setConstant(), Constant(), class CwiseNullaryOp

{
  setConstant(val);
}

◆ flagged()

template<typename Derived >

template<unsigned int Added, unsigned int Removed>

EIGEN_DEPRECATED const Derived & Eigen::DenseBase< Derived >::flagged ( ) const

inlineinherited

313 { return derived(); }

◆ forceAlignedAccess() [1/2]

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(), class ForceAlignedAccess

304{ return derived(); }

◆ forceAlignedAccess() [2/2]

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(),class ForceAlignedAccess

303{ return derived(); }

◆ forceAlignedAccessIf() [1/4]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

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

◆ forceAlignedAccessIf() [2/4]

template<typename Derived >

template<bool Enable>

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

inline

306{ return derived(); }

◆ forceAlignedAccessIf() [3/4]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

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

◆ forceAlignedAccessIf() [4/4]

template<typename Derived >

template<bool Enable>

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

inline

305{ return derived(); }

◆ format()

template<typename Derived >

const WithFormat< Derived > Eigen::DenseBase< Derived >::format ( const IOFormat & fmt ) const

inlineinherited

Returns: a WithFormat proxy object allowing to print a matrix the with given format fmt.

See class IOFormat for some examples.

See also: class IOFormat, class WithFormat

    {
      return WithFormat<Derived>(derived(), fmt);
    }

Referenced by igl::matlab_format(), and igl::writeOBJ().

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◆ fullPivHouseholderQr()

template<typename Derived >

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

inline

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

See also: class FullPivHouseholderQR

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

◆ fullPivLu()

template<typename Derived >

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

inline

\lu_module

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

See also: class FullPivLU

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

◆ hasNaN()

template<typename Derived >

bool Eigen::DenseBase< Derived >::hasNaN

inlineinherited

Returns: true is *this contains at least one Not A Number (NaN).

See also: allFinite()

{
#if EIGEN_COMP_MSVC || (defined __FAST_MATH__)
  return derived().array().isNaN().any();
#else
  return !((derived().array()==derived().array()).all());
#endif
}

◆ householderQr()

template<typename Derived >

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

inline

Returns: the Householder QR decomposition of *this.

See also: class HouseholderQR

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

◆ hypotNorm()

template<typename Derived >

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

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()

{
  return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
}

References cwiseAbs().

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◆ Identity() [1/2]

template<typename Derived >

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

static

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

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

Example:

Output:

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

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

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

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◆ Identity() [2/2]

template<typename Derived >

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

static

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

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

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

Example:

Output:

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

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

References Eigen::DenseBase< Derived >::NullaryExpr().

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◆ innerSize()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::DenseBase< Derived >::innerSize ( ) const

inlineinherited

Returns: the inner size.

Note: For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension with respect to the storage order, i.e., the number of rows for a column-major matrix, and the number of columns for a row-major matrix.

    {
      return IsVectorAtCompileTime ? this->size()
           : int(IsRowMajor) ? this->cols() : this->rows();
    }

References Eigen::DenseBase< Derived >::IsRowMajor, and Eigen::DenseBase< Derived >::IsVectorAtCompileTime.

◆ inverse()

template<typename Derived >

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

inline

\lu_module

Returns: the matrix inverse of this matrix.

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

Note

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

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

Example:

Output:

See also: computeInverseAndDetWithCheck()

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

References eigen_assert, and EIGEN_STATIC_ASSERT.

Referenced by Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::transform().

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◆ isApprox() [1/2]

template<typename Derived >

template<typename OtherDerived >

bool Eigen::DenseBase< Derived >::isApprox	(	const DenseBase< OtherDerived > &	other,
		const RealScalar &	prec
	)		const

inherited

Returns: true if *this is approximately equal to other, within the precision determined by prec.

Note: The fuzzy compares are done multiplicatively. Two vectors and are considered to be approximately equal within precision if
$\Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert).$
For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm L2 norm).; Because of the multiplicativeness of this comparison, one can't use this function to check whether *this is approximately equal to the zero matrix or vector. Indeed, isApprox(zero) returns false unless *this itself is exactly the zero matrix or vector. If you want to test whether *this is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.

See also: internal::isMuchSmallerThan(const RealScalar&, RealScalar) const

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

References Eigen::internal::isApprox_selector< Derived, OtherDerived, is_integer >::run().

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◆ isApprox() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isApprox	(	const DenseBase< OtherDerived > &	other,
		const RealScalar &	prec = `NumTraits< Scalar >::dummy_precision()`
	)		const

inherited

◆ isApproxToConstant()

template<typename Derived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isApproxToConstant	(	const Scalar &	val,
		const RealScalar &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inherited

Returns: true if all coefficients in this matrix are approximately equal to val, to within precision prec

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

References Eigen::internal::isApprox().

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◆ isConstant()

template<typename Derived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isConstant	(	const Scalar &	val,
		const RealScalar &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inherited

This is just an alias for isApproxToConstant().

Returns: true if all coefficients in this matrix are approximately equal to value, to within precision prec

{
  return isApproxToConstant(val, prec);
}

◆ isDiagonal()

template<typename Derived >

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

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

Example:

Output:

See also: asDiagonal()

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

References Eigen::numext::abs(), and Eigen::internal::isMuchSmallerThan().

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◆ isIdentity()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isIdentity ( const RealScalar & prec = NumTraits<Scalar>::dummy_precision() ) const

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

Example:

Output:

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

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

References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().

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◆ isLowerTriangular()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isLowerTriangular ( const RealScalar & prec = NumTraits<Scalar>::dummy_precision() ) const

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

See also: isUpperTriangular()

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

References Eigen::numext::abs(), Eigen::TriangularView< _MatrixType, _Mode >::cols(), Eigen::numext::mini(), and Eigen::TriangularView< _MatrixType, _Mode >::rows().

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◆ isMuchSmallerThan() [1/4]

template<typename Derived >

template<typename OtherDerived >

bool Eigen::DenseBase< Derived >::isMuchSmallerThan	(	const DenseBase< OtherDerived > &	other,
		const RealScalar &	prec
	)		const

inherited

Returns: true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.

Note: The fuzzy compares are done multiplicatively. A vector is considered to be much smaller than a vector within precision if
$\Vert v \Vert \leqslant p\,\Vert w\Vert.$
For matrices, the comparison is done using the Hilbert-Schmidt norm.

See also: isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const

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

References Eigen::internal::isMuchSmallerThan_object_selector< Derived, OtherDerived, is_integer >::run().

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◆ isMuchSmallerThan() [2/4]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isMuchSmallerThan	(	const DenseBase< OtherDerived > &	other,
		const RealScalar &	prec = `NumTraits< Scalar >::dummy_precision()`
	)		const

inherited

◆ isMuchSmallerThan() [3/4]

template<typename Derived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isMuchSmallerThan	(	const RealScalar &	other,
		const RealScalar &	prec = `NumTraits< Scalar >::dummy_precision()`
	)		const

inherited

◆ isMuchSmallerThan() [4/4]

template<typename Derived >

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

inherited

Returns: true if the norm of *this is much smaller than other, within the precision determined by prec.

Note: The fuzzy compares are done multiplicatively. A vector is considered to be much smaller than within precision if
$\Vert v \Vert \leqslant p\,\vert x\vert.$

For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.

See also: isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const

{
  return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
}

References Eigen::internal::isMuchSmallerThan_scalar_selector< Derived, is_integer >::run().

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◆ isOnes()

template<typename Derived >

EIGEN_DEVICE_FUNC bool Eigen::DenseBase< Derived >::isOnes ( const RealScalar & prec = NumTraits<Scalar>::dummy_precision() ) const

inherited

Returns: true if *this is approximately equal to the matrix where all coefficients are equal to 1, within the precision given by prec.

Example:

Output:

See also: class CwiseNullaryOp, Ones()

{
  return isApproxToConstant(Scalar(1), prec);
}

◆ isOrthogonal()

template<typename Derived >

template<typename OtherDerived >

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

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

Example:

Output:

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

◆ isUnitary()

template<typename Derived >

bool Eigen::MatrixBase< Derived >::isUnitary ( const RealScalar & prec = NumTraits<Scalar>::dummy_precision() ) const

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

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

Example:

Output:

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

References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().

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◆ isUpperTriangular()

template<typename Derived >

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

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

See also: isLowerTriangular()

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

References Eigen::numext::abs(), Eigen::TriangularView< _MatrixType, _Mode >::cols(), Eigen::numext::mini(), and Eigen::TriangularView< _MatrixType, _Mode >::rows().

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◆ isZero()

template<typename Derived >

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

inherited

Returns: true if *this is approximately equal to the zero matrix, within the precision given by prec.

Example:

Output:

See also: class CwiseNullaryOp, Zero()

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

References Eigen::internal::isMuchSmallerThan().

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◆ jacobiSvd()

template<typename Derived >

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

inline

\svd_module

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

See also: class JacobiSVD

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

◆ lazyAssign() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

{
  enum{
    SameType = internal::is_same<typename Derived::Scalar,typename OtherDerived::Scalar>::value
  };
 
  EIGEN_STATIC_ASSERT_LVALUE(Derived)
  EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(Derived,OtherDerived)
  EIGEN_STATIC_ASSERT(SameType,YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
 
  eigen_assert(rows() == other.rows() && cols() == other.cols());
  internal::call_assignment_no_alias(derived(),other.derived());
  
  return derived();
}

◆ lazyAssign() [2/2]

template<typename Derived >

template<typename OtherDerived >

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

◆ lazyProduct() [1/2]

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&)

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

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

◆ lazyProduct() [2/2]

template<typename Derived >

template<typename OtherDerived >

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

◆ ldlt()

template<typename Derived >

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

inline

\cholesky_module

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

See also: SelfAdjointView::ldlt()

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

◆ LinSpaced() [1/4]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced	(	const Scalar &	low,
		const Scalar &	high
	)

staticinherited

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

\only_for_vectors

Example:

Output:

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

Output:

See also: setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp Special version for fixed size types which does not require the size parameter.

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
}

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

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◆ LinSpaced() [2/4]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced	(	Index	size,
		const Scalar &	low,
		const Scalar &	high
	)

staticinherited

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

\only_for_vectors

Example:

Output:

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

Output:

See also: setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
}

◆ LinSpaced() [3/4]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced	(	Sequential_t	,
		const Scalar &	low,
		const Scalar &	high
	)

staticinherited

See also: LinSpaced(Scalar,Scalar)

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
  return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime));
}

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

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◆ LinSpaced() [4/4]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced	(	Sequential_t	,
		Index	size,
		const Scalar &	low,
		const Scalar &	high
	)

staticinherited

See also: LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size));
}

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

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◆ llt()

template<typename Derived >

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

inline

\cholesky_module

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

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

◆ lpNorm() [1/2]

template<typename Derived >

template<int p>

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

inline

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

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

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

See also: norm()

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

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

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◆ lpNorm() [2/2]

template<typename Derived >

template<int p>

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

◆ lu()

template<typename Derived >

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

inline

\lu_module

Synonym of partialPivLu().

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

See also: class PartialPivLU

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

◆ makeHouseholder()

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()

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY, sqrt(), and tail().

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◆ makeHouseholderInPlace()

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()

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

◆ matrix() [1/2]

template<typename Derived >

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

inline

312{ return *this; }

◆ matrix() [2/2]

template<typename Derived >

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

inline

313{ return *this; }

◆ matrixFunction()

template<typename Derived >

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

Helper function for the unsupported MatrixFunctions module.

◆ maxCoeff() [1/3]

template<typename Derived >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::maxCoeff

inherited

Returns: the maximum of all coefficients of *this.

Warning: the result is undefined if *this contains NaN.

{
  return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar>());
}

Referenced by igl::copyleft::cgal::half_space_box(), igl::isolines(), igl::min_quad_with_fixed_precompute(), igl::octree(), Eigen::internal::lpNorm_selector< Derived, Infinity >::run(), and igl::slice().

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◆ maxCoeff() [2/3]

template<typename Derived >

template<typename IndexType >

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

inherited

Returns: the maximum of all coefficients of *this and puts in *index its location.

Warning: the result is undefined if *this contains NaN.

See also: DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  internal::max_coeff_visitor<Derived> maxVisitor;
  this->visit(maxVisitor);
  *index = (RowsAtCompileTime==1) ? maxVisitor.col : maxVisitor.row;
  return maxVisitor.res;
}

References Eigen::internal::coeff_visitor< Derived >::col, EIGEN_STATIC_ASSERT_VECTOR_ONLY, Eigen::internal::coeff_visitor< Derived >::res, and Eigen::internal::coeff_visitor< Derived >::row.

◆ maxCoeff() [3/3]

template<typename Derived >

template<typename IndexType >

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::maxCoeff	(	IndexType *	rowId,
		IndexType *	colId
	)		const

inherited

Returns: the maximum of all coefficients of *this and puts in *row and *col its location.

Warning: the result is undefined if *this contains NaN.

See also: DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()

{
  internal::max_coeff_visitor<Derived> maxVisitor;
  this->visit(maxVisitor);
  *rowPtr = maxVisitor.row;
  if (colPtr) *colPtr = maxVisitor.col;
  return maxVisitor.res;
}

References Eigen::internal::coeff_visitor< Derived >::col, Eigen::internal::coeff_visitor< Derived >::res, and Eigen::internal::coeff_visitor< Derived >::row.

◆ mean()

template<typename Derived >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::mean

inherited

Returns: the mean of all coefficients of *this

See also: trace(), prod(), sum()

{
#ifdef __INTEL_COMPILER
  #pragma warning push
  #pragma warning ( disable : 2259 )
#endif
  return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());
#ifdef __INTEL_COMPILER
  #pragma warning pop
#endif
}

◆ minCoeff() [1/3]

template<typename Derived >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::minCoeff

inherited

Returns: the minimum of all coefficients of *this.

Warning: the result is undefined if *this contains NaN.

{
  return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar>());
}

Referenced by igl::copyleft::cgal::half_space_box(), igl::isolines(), igl::min_quad_with_fixed_precompute(), igl::octree(), and igl::slice().

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◆ minCoeff() [2/3]

template<typename Derived >

template<typename IndexType >

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

inherited

Returns: the minimum of all coefficients of *this and puts in *index its location.

Warning: the result is undefined if *this contains NaN.

See also: DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::minCoeff()

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  internal::min_coeff_visitor<Derived> minVisitor;
  this->visit(minVisitor);
  *index = IndexType((RowsAtCompileTime==1) ? minVisitor.col : minVisitor.row);
  return minVisitor.res;
}

References Eigen::internal::coeff_visitor< Derived >::col, EIGEN_STATIC_ASSERT_VECTOR_ONLY, Eigen::internal::coeff_visitor< Derived >::res, and Eigen::internal::coeff_visitor< Derived >::row.

◆ minCoeff() [3/3]

template<typename Derived >

template<typename IndexType >

EIGEN_DEVICE_FUNC internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::minCoeff	(	IndexType *	rowId,
		IndexType *	colId
	)		const

inherited

Returns: the minimum of all coefficients of *this and puts in *row and *col its location.

Warning: the result is undefined if *this contains NaN.

See also: DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()

{
  internal::min_coeff_visitor<Derived> minVisitor;
  this->visit(minVisitor);
  *rowId = minVisitor.row;
  if (colId) *colId = minVisitor.col;
  return minVisitor.res;
}

References Eigen::internal::coeff_visitor< Derived >::col, Eigen::internal::coeff_visitor< Derived >::res, and Eigen::internal::coeff_visitor< Derived >::row.

◆ nestByValue()

template<typename Derived >

const NestByValue< Derived > Eigen::DenseBase< Derived >::nestByValue

inlineinherited

Returns: an expression of the temporary version of *this.

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

◆ noalias()

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

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

◆ nonZeros()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::DenseBase< Derived >::nonZeros ( ) const

inlineinherited

Returns: the number of nonzero coefficients which is in practice the number of stored coefficients.

210{ return size(); }

◆ norm()

template<typename Derived >

EIGEN_STRONG_INLINE NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm

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

See also: lpNorm(), dot(), squaredNorm()

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

References Eigen::numext::sqrt().

Referenced by Eigen::internal::lpNorm_selector< Derived, 2 >::run().

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◆ normalize()

template<typename Derived >

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

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

\only_for_vectors

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

See also: norm(), normalized()

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

References Eigen::numext::sqrt().

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◆ normalized()

template<typename Derived >

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

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

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

\only_for_vectors

See also: norm(), normalize()

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

References Eigen::numext::sqrt().

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◆ NullaryExpr() [1/6]

template<typename Derived >

template<typename CustomNullaryOp >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr ( const CustomNullaryOp & func )

inherited

Returns: an expression of a matrix defined by a custom functor func

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

The template parameter CustomNullaryOp is the type of the functor.

See also: class CwiseNullaryOp

{
  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func);
}

◆ NullaryExpr() [2/6]

template<typename Derived >

template<typename CustomNullaryOp >

static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject > Eigen::DenseBase< Derived >::NullaryExpr ( const CustomNullaryOp & func )

staticinherited

◆ NullaryExpr() [3/6]

template<typename Derived >

template<typename CustomNullaryOp >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr	(	Index	rows,
		Index	cols,
		const CustomNullaryOp &	func
	)

inherited

Returns: an expression of a matrix defined by a custom functor func

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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also: class CwiseNullaryOp

{
  return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func);
}

◆ NullaryExpr() [4/6]

template<typename Derived >

template<typename CustomNullaryOp >

static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject > Eigen::DenseBase< Derived >::NullaryExpr	(	Index	rows,
		Index	cols,
		const CustomNullaryOp &	func
	)

staticinherited

Referenced by Eigen::DenseBase< Derived >::Constant(), Eigen::DenseBase< Derived >::Constant(), Eigen::DenseBase< Derived >::Constant(), Eigen::MatrixBase< Derived >::Identity(), Eigen::MatrixBase< Derived >::Identity(), Eigen::DenseBase< Derived >::LinSpaced(), Eigen::DenseBase< Derived >::LinSpaced(), and Eigen::DenseBase< Derived >::LinSpaced().

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◆ NullaryExpr() [5/6]

template<typename Derived >

template<typename CustomNullaryOp >

EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr	(	Index	size,
		const CustomNullaryOp &	func
	)

inherited

Returns: an expression of a matrix defined by a custom functor func

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

\only_for_vectors

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

Here is an example with C++11 random generators:

Output:

See also: class CwiseNullaryOp

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func);
  else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func);
}

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

◆ NullaryExpr() [6/6]

template<typename Derived >

template<typename CustomNullaryOp >

static EIGEN_DEVICE_FUNC const CwiseNullaryOp< CustomNullaryOp, PlainObject > Eigen::DenseBase< Derived >::NullaryExpr	(	Index	size,
		const CustomNullaryOp &	func
	)

staticinherited

◆ Ones() [1/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones

staticinherited

Returns: an expression of a fixed-size matrix or vector where all coefficients equal one.

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

Example:

Output:

See also: Ones(Index), Ones(Index,Index), isOnes(), class Ones

{
  return Constant(Scalar(1));
}

◆ Ones() [2/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones	(	Index	rows,
		Index	cols
	)

staticinherited

Returns: an expression of a matrix where all coefficients equal one.

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 Ones() should be used instead.

Example:

Output:

See also: Ones(), Ones(Index), isOnes(), class Ones

{
  return Constant(rows, cols, Scalar(1));
}

◆ Ones() [3/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones ( Index newSize )

staticinherited

Returns: an expression of a vector where all coefficients equal one.

The parameter newSize is the size of the returned vector. Must be compatible with this MatrixBase type.

\only_for_vectors

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.

Example:

Output:

See also: Ones(), Ones(Index,Index), isOnes(), class Ones

{
  return Constant(newSize, Scalar(1));
}

◆ operator!=()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

See also: isApprox(), operator==

297 { return cwiseNotEqual(other).any(); }

cwiseNotEqual

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

Definition MatrixCwiseBinaryOps.h:63

References cwiseNotEqual().

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◆ operator*() [1/4]

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.

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

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

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◆ operator*() [2/4]

template<typename Derived >

template<typename DiagonalDerived >

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

◆ operator*() [3/4]

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*()

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

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

◆ operator*() [4/4]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator*=() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by *this * other.

Returns: a reference to *this

Example:

Output:

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

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

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◆ operator*=() [2/2]

template<typename Derived >

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

{
  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar,Scalar>());
  return derived();
}

◆ operator+=() [1/4]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

476 {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}

References EIGEN_STATIC_ASSERT.

◆ operator+=() [2/4]

template<typename Derived >

template<typename OtherDerived >

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

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

◆ operator+=() [3/4]

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

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

◆ operator+=() [4/4]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator-=() [1/4]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

479 {EIGEN_STATIC_ASSERT(std::ptrdiff_t(sizeof(typename OtherDerived::Scalar))==-1,YOU_CANNOT_MIX_ARRAYS_AND_MATRICES); return *this;}

References EIGEN_STATIC_ASSERT.

◆ operator-=() [2/4]

template<typename Derived >

template<typename OtherDerived >

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

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

◆ operator-=() [3/4]

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

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

◆ operator-=() [4/4]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator/=()

template<typename Derived >

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

{
  internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar,Scalar>());
  return derived();
}

◆ operator<<() [1/3]

template<typename Derived >

template<typename OtherDerived >

CommaInitializer< Derived > Eigen::DenseBase< Derived >::operator<< ( const DenseBase< OtherDerived > & other )

inlineinherited

See also: operator<<(const Scalar&)

{
  return CommaInitializer<Derived>(*static_cast<Derived *>(this), other);
}

◆ operator<<() [2/3]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC CommaInitializer< Derived > Eigen::DenseBase< Derived >::operator<< ( const DenseBase< OtherDerived > & other )

inherited

◆ operator<<() [3/3]

template<typename Derived >

CommaInitializer< Derived > Eigen::DenseBase< Derived >::operator<< ( const Scalar & s )

inlineinherited

Convenient operator to set the coefficients of a matrix.

The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.

Example:

Output:

Note: According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.

See also: CommaInitializer::finished(), class CommaInitializer

{
  return CommaInitializer<Derived>(*static_cast<Derived*>(this), s);
}

◆ operator=() [1/6]

template<typename Derived >

template<typename OtherDerived >

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

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

References Eigen::internal::call_assignment().

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◆ operator=() [2/6]

template<typename Derived >

template<typename OtherDerived >

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

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

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

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◆ operator=() [3/6]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator=() [4/6]

template<typename Derived >

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

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

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

References Eigen::internal::call_assignment().

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◆ operator=() [5/6]

template<typename Derived >

template<typename OtherDerived >

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

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

References Eigen::ReturnByValue< Derived >::evalTo().

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◆ operator=() [6/6]

template<typename Derived >

template<typename OtherDerived >

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

◆ operator==()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

See also: isApprox(), operator!=

289 { return cwiseEqual(other).all(); }

cwiseEqual

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

Definition MatrixCwiseBinaryOps.h:43

References cwiseEqual().

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◆ operatorNorm()

template<typename Derived >

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

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

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

$\|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2}$

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

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

Example:

Output:

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

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

References sqrt().

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◆ outerSize()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::DenseBase< Derived >::outerSize ( ) const

inlineinherited

Returns: the outer size.

Note: For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension with respect to the storage order, i.e., the number of columns for a column-major matrix, and the number of rows for a row-major matrix.

    {
      return IsVectorAtCompileTime ? 1
           : int(IsRowMajor) ? this->rows() : this->cols();
    }

References Eigen::DenseBase< Derived >::IsRowMajor, and Eigen::DenseBase< Derived >::IsVectorAtCompileTime.

◆ partialPivLu()

template<typename Derived >

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

inline

\lu_module

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

See also: class PartialPivLU

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

◆ prod()

template<typename Derived >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::prod

inherited

Returns: the product of all coefficients of *this

Example:

Output:

See also: sum(), mean(), trace()

{
  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
    return Scalar(1);
  return derived().redux(Eigen::internal::scalar_product_op<Scalar>());
}

References Eigen::Dynamic.

◆ Random() [1/3]

template<typename Derived >

const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random

inlinestaticinherited

Returns: a fixed-size random matrix or vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

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

Example:

Output:

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

\not_reentrant

See also: DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)

{
  return NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_random_op<Scalar>());
}

◆ Random() [2/3]

template<typename Derived >

const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random	(	Index	rows,
		Index	cols
	)

inlinestaticinherited

Returns: a random matrix expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

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

\not_reentrant

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 Random() should be used instead.

Example:

Output:

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.

See also: DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()

{
  return NullaryExpr(rows, cols, internal::scalar_random_op<Scalar>());
}

◆ Random() [3/3]

template<typename Derived >

const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random ( Index size )

inlinestaticinherited

Returns: a random vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

\only_for_vectors \not_reentrant

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.

Example:

Output:

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See also: DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()

{
  return NullaryExpr(size, internal::scalar_random_op<Scalar>());
}

◆ redux() [1/2]

template<typename Derived >

template<typename BinaryOp >

EIGEN_DEVICE_FUNC Scalar Eigen::DenseBase< Derived >::redux ( const BinaryOp & func ) const

inherited

Referenced by Eigen::internal::member_redux< BinaryOp, Scalar >::operator()().

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◆ redux() [2/2]

template<typename Derived >

template<typename Func >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::redux ( const Func & func ) const

inherited

Returns: the result of a full redux operation on the whole matrix or vector using func

The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current C++98 and C++11 functor styles are handled.

See also: DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()

{
  eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
 
  typedef typename internal::redux_evaluator<Derived> ThisEvaluator;
  ThisEvaluator thisEval(derived());
  
  return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func);
}

References eigen_assert.

◆ replicate() [1/3]

template<typename Derived >

template<int RowFactor, int ColFactor>

EIGEN_DEVICE_FUNC const Replicate< Derived, RowFactor, ColFactor > Eigen::DenseBase< Derived >::replicate ( ) const

inherited

Referenced by igl::min_quad_with_fixed_solve().

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◆ replicate() [2/3]

template<typename Derived >

template<int RowFactor, int ColFactor>

const Replicate< Derived, RowFactor, ColFactor > Eigen::DenseBase< Derived >::replicate ( ) const

inherited

Returns: an expression of the replication of *this

Example:

Output:

See also: VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate

{
  return Replicate<Derived,RowFactor,ColFactor>(derived());
}

◆ replicate() [3/3]

template<typename Derived >

EIGEN_DEVICE_FUNC const Replicate< Derived, Dynamic, Dynamic > Eigen::DenseBase< Derived >::replicate	(	Index	rowFactor,
		Index	colFactor
	)		const

inlineinherited

Returns: an expression of the replication of *this

Example:

Output:

See also: VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate

    {
      return Replicate<Derived, Dynamic, Dynamic>(derived(), rowFactor, colFactor);
    }

◆ resize() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::resize ( Index newSize )

inlineinherited

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

    {
      EIGEN_ONLY_USED_FOR_DEBUG(newSize);
      eigen_assert(newSize == this->size()
                && "DenseBase::resize() does not actually allow to resize.");
    }

References eigen_assert, and EIGEN_ONLY_USED_FOR_DEBUG.

Referenced by Eigen::TriangularBase< Derived >::evalToLazy(), igl::find(), and igl::slice_tets().

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◆ resize() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::resize	(	Index	rows,
		Index	cols
	)

inlineinherited

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

    {
      EIGEN_ONLY_USED_FOR_DEBUG(rows);
      EIGEN_ONLY_USED_FOR_DEBUG(cols);
      eigen_assert(rows == this->rows() && cols == this->cols()
                && "DenseBase::resize() does not actually allow to resize.");
    }

References eigen_assert, and EIGEN_ONLY_USED_FOR_DEBUG.

◆ reverse() [1/2]

template<typename Derived >

DenseBase< Derived >::ReverseReturnType Eigen::DenseBase< Derived >::reverse

inlineinherited

Returns: an expression of the reverse of *this.

Example:

Output:

{
  return ReverseReturnType(derived());
}

◆ reverse() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC ConstReverseReturnType Eigen::DenseBase< Derived >::reverse ( ) const

inlineinherited

This is the const version of reverse().

    {
      return ConstReverseReturnType(derived());
    }

◆ reverseInPlace()

template<typename Derived >

void Eigen::DenseBase< Derived >::reverseInPlace

inlineinherited

This is the "in place" version of reverse: it reverses *this.

In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional benefits:

less error prone: doing the same operation with .reverse() requires special care:
m = m.reverse().eval();
this API enables reverse operations without the need for a temporary
it allows future optimizations (cache friendliness, etc.)

See also: VectorwiseOp::reverseInPlace(), reverse()

{
  if(cols()>rows())
  {
    Index half = cols()/2;
    leftCols(half).swap(rightCols(half).reverse());
    if((cols()%2)==1)
    {
      Index half2 = rows()/2;
      col(half).head(half2).swap(col(half).tail(half2).reverse());
    }
  }
  else
  {
    Index half = rows()/2;
    topRows(half).swap(bottomRows(half).reverse());
    if((rows()%2)==1)
    {
      Index half2 = cols()/2;
      row(half).head(half2).swap(row(half).tail(half2).reverse());
    }
  }
}

References bottomRows(), col(), leftCols(), rightCols(), row(), tail(), and topRows().

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◆ rowwise() [1/2]

template<typename Derived >

DenseBase< Derived >::RowwiseReturnType Eigen::DenseBase< Derived >::rowwise

inlineinherited

Returns: a writable VectorwiseOp wrapper of *this providing additional partial reduction operations

See also: colwise(), class VectorwiseOp, TutorialReductionsVisitorsBroadcasting

{
  return RowwiseReturnType(derived());
}

◆ rowwise() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC ConstRowwiseReturnType Eigen::DenseBase< Derived >::rowwise ( ) const

inlineinherited

Returns: a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Output:

See also: colwise(), class VectorwiseOp, TutorialReductionsVisitorsBroadcasting

                                                                    {
      return ConstRowwiseReturnType(derived());
    }

Referenced by igl::normalize_row_sums(), and Eigen::umeyama().

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◆ select() [1/3]

template<typename Derived >

template<typename ThenDerived , typename ElseDerived >

const Select< Derived, ThenDerived, ElseDerived > Eigen::DenseBase< Derived >::select	(	const DenseBase< ThenDerived > &	thenMatrix,
		const DenseBase< ElseDerived > &	elseMatrix
	)		const

inlineinherited

Returns: a matrix where each coefficient (i,j) is equal to thenMatrix(i,j) if *this(i,j), and elseMatrix(i,j) otherwise.

Example:

Output:

See also: class Select

{
  return Select<Derived,ThenDerived,ElseDerived>(derived(), thenMatrix.derived(), elseMatrix.derived());
}

◆ select() [2/3]

template<typename Derived >

template<typename ThenDerived >

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

inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.

See also: DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select

{
  return Select<Derived,ThenDerived,typename ThenDerived::ConstantReturnType>(
    derived(), thenMatrix.derived(), ThenDerived::Constant(rows(),cols(),elseScalar));
}

◆ select() [3/3]

template<typename Derived >

template<typename ElseDerived >

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

inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.

See also: DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select

{
  return Select<Derived,typename ElseDerived::ConstantReturnType,ElseDerived>(
    derived(), ElseDerived::Constant(rows(),cols(),thenScalar), elseMatrix.derived());
}

◆ selfadjointView() [1/4]

template<typename Derived >

template<unsigned int UpLo>

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

◆ selfadjointView() [2/4]

template<typename Derived >

template<unsigned int UpLo>

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

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

References Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >::derived().

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◆ selfadjointView() [3/4]

template<typename Derived >

template<unsigned int UpLo>

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

◆ selfadjointView() [4/4]

template<typename Derived >

template<unsigned int UpLo>

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

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

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

References Eigen::TriangularBase< SelfAdjointView< _MatrixType, UpLo > >::derived().

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◆ setConstant()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::setConstant ( const Scalar & val )

inherited

Sets all coefficients in this expression to value val.

See also: fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()

{
  return derived() = Constant(rows(), cols(), val);
}

Referenced by Eigen::ArrayBase< Derived >::operator=().

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◆ setIdentity() [1/2]

template<typename Derived >

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

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

Example:

Output:

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

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

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

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◆ setIdentity() [2/2]

template<typename Derived >

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

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

Parameters

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

Example:

Output:

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

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

◆ setLinSpaced() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::setLinSpaced	(	const Scalar &	low,
		const Scalar &	high
	)

inherited

Sets a linearly spaced vector.

The function fills *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

\only_for_vectors

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also: LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return setLinSpaced(size(), low, high);
}

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

◆ setLinSpaced() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::setLinSpaced	(	Index	newSize,
		const Scalar &	low,
		const Scalar &	high
	)

inherited

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

\only_for_vectors

Example:

Output:

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also: LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp

{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize));
}

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

◆ setOnes()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::setOnes

inherited

Sets all coefficients in this expression to one.

Example:

Output:

See also: class CwiseNullaryOp, Ones()

{
  return setConstant(Scalar(1));
}

◆ setRandom()

template<typename Derived >

Derived & Eigen::DenseBase< Derived >::setRandom

inlineinherited

Sets all coefficients in this expression to random values.

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

\not_reentrant

Example:

Output:

See also: class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)

{
  return *this = Random(rows(), cols());
}

◆ setZero()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived & Eigen::DenseBase< Derived >::setZero

inherited

Sets all coefficients in this expression to zero.

Example:

Output:

See also: class CwiseNullaryOp, Zero()

{
  return setConstant(Scalar(0));
}

Referenced by Eigen::SPQR< _MatrixType >::_solve_impl(), Eigen::PermutationBase< Derived >::evalTo(), and Eigen::InverseImpl< PermutationType, PermutationStorage >::evalTo().

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◆ sparseView()

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

{
  return SparseView<Derived>(derived(), reference, epsilon);
}

◆ squaredNorm()

template<typename Derived >

EIGEN_STRONG_INLINE NumTraits< typenameinternal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm

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()

{
  return numext::real((*this).cwiseAbs2().sum());
}

◆ stableNorm()

template<typename Derived >

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

inline

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

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

See also: norm(), blueNorm(), hypotNorm()

{
  using std::sqrt;
  using std::abs;
  const Index blockSize = 4096;
  RealScalar scale(0);
  RealScalar invScale(1);
  RealScalar ssq(0); // sum of square
  
  typedef typename internal::nested_eval<Derived,2>::type DerivedCopy;
  typedef typename internal::remove_all<DerivedCopy>::type DerivedCopyClean;
  const DerivedCopy copy(derived());
  
  enum {
    CanAlign = (   (int(DerivedCopyClean::Flags)&DirectAccessBit)
                || (int(internal::evaluator<DerivedCopyClean>::Alignment)>0) // FIXME Alignment)>0 might not be enough
               ) && (blockSize*sizeof(Scalar)*2<EIGEN_STACK_ALLOCATION_LIMIT)
                 && (EIGEN_MAX_STATIC_ALIGN_BYTES>0) // if we cannot allocate on the stack, then let's not bother about this optimization
  };
  typedef typename internal::conditional<CanAlign, Ref<const Matrix<Scalar,Dynamic,1,0,blockSize,1>, internal::evaluator<DerivedCopyClean>::Alignment>,
                                                   typename DerivedCopyClean::ConstSegmentReturnType>::type SegmentWrapper;
  Index n = size();
  
  if(n==1)
    return abs(this->coeff(0));
  
  Index bi = internal::first_default_aligned(copy);
  if (bi>0)
    internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);
  for (; bi<n; bi+=blockSize)
    internal::stable_norm_kernel(SegmentWrapper(copy.segment(bi,numext::mini(blockSize, n - bi))), ssq, scale, invScale);
  return scale * sqrt(ssq);
}

References Eigen::DirectAccessBit, EIGEN_MAX_STATIC_ALIGN_BYTES, EIGEN_STACK_ALLOCATION_LIMIT, Eigen::internal::first_default_aligned(), Eigen::numext::mini(), scale(), sqrt(), and Eigen::internal::stable_norm_kernel().

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◆ stableNormalize()

template<typename Derived >

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

Normalizes the vector while avoid underflow and overflow

\only_for_vectors

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

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

See also: stableNorm(), stableNormalized(), normalize()

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

◆ stableNormalized()

template<typename Derived >

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

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

\only_for_vectors

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

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

See also: stableNorm(), stableNormalize(), normalized()

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

References Eigen::numext::sqrt().

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◆ sum()

template<typename Derived >

EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::sum

inherited

Returns: the sum of all coefficients of *this

If *this is empty, then the value 0 is returned.

See also: trace(), prod(), mean()

{
  if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
    return Scalar(0);
  return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());
}

References Eigen::Dynamic.

Referenced by igl::normalize_row_sums(), and Eigen::internal::lpNorm_selector< Derived, 1 >::run().

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◆ swap() [1/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::swap ( const DenseBase< OtherDerived > & other )

inlineinherited

swaps *this with the expression other.

    {
      EIGEN_STATIC_ASSERT(!OtherDerived::IsPlainObjectBase,THIS_EXPRESSION_IS_NOT_A_LVALUE__IT_IS_READ_ONLY);
      eigen_assert(rows()==other.rows() && cols()==other.cols());
      call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
    }

References eigen_assert, and EIGEN_STATIC_ASSERT.

Referenced by Eigen::internal::conservative_resize_like_impl< Derived, OtherDerived, IsVector >::run(), and Eigen::internal::conservative_resize_like_impl< Derived, OtherDerived, IsVector >::run().

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◆ swap() [2/2]

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::swap ( PlainObjectBase< OtherDerived > & other )

inlineinherited

swaps *this with the matrix or array other.

    {
      eigen_assert(rows()==other.rows() && cols()==other.cols());
      call_assignment(derived(), other.derived(), internal::swap_assign_op<Scalar>());
    }

References Eigen::PlainObjectBase< Derived >::cols(), eigen_assert, and Eigen::PlainObjectBase< Derived >::rows().

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◆ trace()

template<typename Derived >

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

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

*this can be any matrix, not necessarily square.

See also: diagonal(), sum()

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

◆ transpose() [1/2]

template<typename Derived >

Transpose< Derived > Eigen::DenseBase< Derived >::transpose

inlineinherited

Returns: an expression of the transpose of *this.

Example:

Output:

Warning: If you want to replace a matrix by its own transpose, do NOT do this:
m = m.transpose(); // bug!!! caused by aliasing effect

Instead, use the transposeInPlace() method:
m.transposeInPlace();

which gives Eigen good opportunities for optimization, or alternatively you can also do:
m = m.transpose().eval();

See also: transposeInPlace(), adjoint()

{
  return TransposeReturnType(derived());
}

Referenced by igl::AABB< DerivedV, DIM >::find(), igl::AABB< DerivedV, DIM >::init(), igl::project(), igl::signed_distance_winding_number(), and igl::unproject().

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◆ transpose() [2/2]

template<typename Derived >

DenseBase< Derived >::ConstTransposeReturnType Eigen::DenseBase< Derived >::transpose

inlineinherited

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also: transposeInPlace(), adjoint()

{
  return ConstTransposeReturnType(derived());
}

◆ transposeInPlace()

template<typename Derived >

void Eigen::DenseBase< Derived >::transposeInPlace

inlineinherited

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

m.transposeInPlace();

has the same effect on m as doing

m = m.transpose().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 transpose. If you just need the transpose of a matrix, use transpose().

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(), adjointInPlace()

{
  eigen_assert((rows() == cols() || (RowsAtCompileTime == Dynamic && ColsAtCompileTime == Dynamic))
               && "transposeInPlace() called on a non-square non-resizable matrix");
  internal::inplace_transpose_selector<Derived>::run(derived());
}

References Eigen::Dynamic, and eigen_assert.

◆ triangularView() [1/4]

template<typename Derived >

template<unsigned int Mode>

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

◆ triangularView() [2/4]

template<typename Derived >

template<unsigned int Mode>

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

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

◆ triangularView() [3/4]

template<typename Derived >

template<unsigned int Mode>

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

◆ triangularView() [4/4]

template<typename Derived >

template<unsigned int Mode>

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

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

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

◆ Unit() [1/2]

template<typename Derived >

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

static

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

\only_for_vectors

This variant is for fixed-size vector only.

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

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

◆ Unit() [2/2]

template<typename Derived >

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

static

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

\only_for_vectors

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

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

◆ UnitW()

template<typename Derived >

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

static

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

\only_for_vectors

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

862{ return Derived::Unit(3); }

◆ UnitX()

template<typename Derived >

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

static

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

\only_for_vectors

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

832{ return Derived::Unit(0); }

◆ UnitY()

template<typename Derived >

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

static

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

\only_for_vectors

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

842{ return Derived::Unit(1); }

◆ UnitZ()

template<typename Derived >

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

static

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

\only_for_vectors

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

852{ return Derived::Unit(2); }

◆ value()

template<typename Derived >

EIGEN_DEVICE_FUNC CoeffReturnType Eigen::DenseBase< Derived >::value ( ) const

inlineinherited

Returns: the unique coefficient of a 1x1 expression

    {
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      return derived().coeff(0,0);
    }

References eigen_assert, and EIGEN_STATIC_ASSERT_SIZE_1x1.

Referenced by igl::find(), and Eigen::ArrayBase< Derived >::operator=().

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◆ visit()

template<typename Derived >

template<typename Visitor >

EIGEN_DEVICE_FUNC void Eigen::DenseBase< Derived >::visit ( Visitor & visitor ) const

inherited

Applies the visitor visitor to the whole coefficients of the matrix or vector.

The template parameter Visitor is the type of the visitor and provides the following interface:

struct MyVisitor {
  // called for the first coefficient
  void init(const Scalar& value, Index i, Index j);
  // called for all other coefficients
  void operator() (const Scalar& value, Index i, Index j);
};

Note: compared to one or two for loops, visitors offer automatic unrolling for small fixed size matrix.

See also: minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()

{
  typedef typename internal::visitor_evaluator<Derived> ThisEvaluator;
  ThisEvaluator thisEval(derived());
  
  enum {
    unroll =  SizeAtCompileTime != Dynamic
           && SizeAtCompileTime * ThisEvaluator::CoeffReadCost + (SizeAtCompileTime-1) * internal::functor_traits<Visitor>::Cost <= EIGEN_UNROLLING_LIMIT
  };
  return internal::visitor_impl<Visitor, ThisEvaluator, unroll ? int(SizeAtCompileTime) : Dynamic>::run(thisEval, visitor);
}

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

◆ Zero() [1/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero

staticinherited

Returns: an expression of a fixed-size zero matrix or vector.

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

Example:

Output:

See also: Zero(Index), Zero(Index,Index)

{
  return Constant(Scalar(0));
}

◆ Zero() [2/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero	(	Index	rows,
		Index	cols
	)

staticinherited

Returns: an expression of a zero matrix.

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 Zero() should be used instead.

Example:

Output:

See also: Zero(), Zero(Index)

{
  return Constant(rows, cols, Scalar(0));
}

◆ Zero() [3/3]

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero ( Index size )

staticinherited

Returns: an expression of a zero vector.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

\only_for_vectors

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

Example:

Output:

See also: Zero(), Zero(Index,Index)

{
  return Constant(size, Scalar(0));
}

Friends And Related Symbol Documentation

◆ operator<<()

template<typename Derived >

std::ostream & operator<<	(	std::ostream &	s,
		const DenseBase< Derived > &	m
	)

If you wish to print the matrix with a format different than the default, use DenseBase::format().

It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.

See also: DenseBase::format()

{
  return internal::print_matrix(s, m.eval(), EIGEN_DEFAULT_IO_FORMAT);
}

References EIGEN_DEFAULT_IO_FORMAT, and Eigen::internal::print_matrix().

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

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Related Symbols

Detailed Description

Class Documentation

◆ Eigen::MatrixBase::ConstDiagonalIndexReturnType

◆ Eigen::MatrixBase::ConstSelfAdjointViewReturnType

◆ Eigen::MatrixBase::ConstTriangularViewReturnType

◆ Eigen::MatrixBase::cross_product_return_type

◆ Eigen::MatrixBase::DiagonalIndexReturnType

◆ Eigen::MatrixBase::SelfAdjointViewReturnType

◆ Eigen::MatrixBase::TriangularViewReturnType

Member Typedef Documentation

◆ AdjointReturnType

◆ Base

◆ BasisReturnType

◆ CoeffReturnType

◆ ColwiseReturnType

◆ ColXpr

◆ ConstantReturnType

◆ ConstColwiseReturnType

◆ ConstDiagonalDynamicIndexReturnType

◆ ConstDiagonalReturnType

◆ ConstReverseReturnType

◆ ConstRowwiseReturnType

◆ ConstStartMinusOne

◆ ConstTransposeReturnType

◆ DiagonalDynamicIndexReturnType

◆ DiagonalReturnType

◆ EigenvaluesReturnType

◆ EvalReturnType

◆ HomogeneousReturnType

◆ IdentityReturnType

◆ InnerIterator

◆ PacketScalar

◆ PlainArray

◆ PlainMatrix

◆ PlainObject

◆ RandomAccessLinSpacedReturnType

◆ RandomReturnType

◆ RealScalar

◆ ReverseReturnType

◆ RowwiseReturnType

◆ RowXpr

◆ Scalar

◆ SequentialLinSpacedReturnType

◆ SquareMatrixType

◆ StemFunction

◆ StorageBaseType

◆ StorageIndex

◆ StorageKind

◆ TransposeReturnType

◆ value_type

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ MatrixBase() [1/4]

◆ MatrixBase() [2/4]

◆ MatrixBase() [3/4]

◆ MatrixBase() [4/4]

Member Function Documentation

◆ adjoint()

◆ adjointInPlace()

◆ all()

◆ allFinite()

◆ any()

◆ applyHouseholderOnTheLeft()

◆ applyHouseholderOnTheRight()

◆ applyOnTheLeft() [1/2]

◆ applyOnTheLeft() [2/2]

◆ applyOnTheRight() [1/2]

◆ applyOnTheRight() [2/2]

◆ array() [1/2]