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

Inheritance diagram for Eigen::MatrixBase< Derived >:

Classes
struct	ConstSelfAdjointViewReturnType

struct	ConstTriangularViewReturnType

struct	SelfAdjointViewReturnType

struct	TriangularViewReturnType

Public Types
enum	{ HomogeneousReturnTypeDirection }

enum	{ SizeMinusOne }

typedef Diagonal< const Derived >	ConstDiagonalReturnType

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

typedef Diagonal< Derived >	DiagonalReturnType

typedef Homogeneous< Derived, HomogeneousReturnTypeDirection >	HomogeneousReturnType

typedef Base::PlainObject	PlainObject

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

Public Types inherited from Eigen::DenseBase< Derived >
enum	{ RowsAtCompileTime , ColsAtCompileTime , SizeAtCompileTime , MaxRowsAtCompileTime , MaxColsAtCompileTime , MaxSizeAtCompileTime , IsVectorAtCompileTime , NumDimensions , Flags , IsRowMajor , InnerSizeAtCompileTime , InnerStrideAtCompileTime , OuterStrideAtCompileTime }

enum	{ IsPlainObjectBase }

typedef DenseCoeffsBase< Derived, internal::accessors_level< Derived >::value >	Base

typedef Base::CoeffReturnType	CoeffReturnType

typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType

typedef random_access_iterator_type	const_iterator

typedef const VectorwiseOp< const Derived, Vertical >	ConstColwiseReturnType

typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType

typedef const VectorwiseOp< const Derived, Horizontal >	ConstRowwiseReturnType

typedef Transpose< const Derived >	ConstTransposeReturnType

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

typedef random_access_iterator_type	iterator

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

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

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

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

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

typedef NumTraits< Scalar >::Real	RealScalar

typedef Reverse< Derived, BothDirections >	ReverseReturnType

typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType

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

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

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

typedef Transpose< Derived >	TransposeReturnType

typedef Scalar	value_type

Public Types inherited from Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >
typedef DenseCoeffsBase< Derived, WriteAccessors >	Base

typedef NumTraits< Scalar >::Real	RealScalar

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

Public Types inherited from Eigen::DenseCoeffsBase< Derived, WriteAccessors >
typedef DenseCoeffsBase< Derived, ReadOnlyAccessors >	Base

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

typedef NumTraits< Scalar >::Real	RealScalar

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

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

Public Types inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
typedef EigenBase< Derived >	Base

typedef std::conditional_t< bool(internal::traits< Derived >::Flags &LvalueBit), const Scalar &, std::conditional_t< internal::is_arithmetic< Scalar >::value, Scalar, const Scalar > >	CoeffReturnType

typedef internal::add_const_on_value_type_if_arithmetic< typename internal::packet_traits< Scalar >::type >::type	PacketReturnType

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

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

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

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...

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

Public Member Functions
const MatrixFunctionReturnValue< Derived >	acosh () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh . More...

const AdjointReturnType	adjoint () const

void	adjointInPlace ()

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

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

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

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

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

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

ArrayWrapper< Derived >	array ()

const ArrayWrapper< const Derived >	array () const

const DiagonalWrapper< const Derived >	asDiagonal () const

const MatrixFunctionReturnValue< Derived >	asinh () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh . More...

const PermutationWrapper< const Derived >	asPermutation () const

const SkewSymmetricWrapper< const Derived >	asSkewSymmetric () const

const MatrixFunctionReturnValue< Derived >	atanh () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh . More...

template<int Options = 0>
BDCSVD< PlainObject, Options >	bdcSvd () const

template<int Options>
BDCSVD< typename MatrixBase< Derived >::PlainObject, Options >	bdcSvd () const

template<int Options = 0>
EIGEN_DEPRECATED BDCSVD< PlainObject, Options >	bdcSvd (unsigned int computationOptions) const

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

RealScalar	blueNorm () const

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

template<typename PermutationIndex = DefaultPermutationIndex>
const ColPivHouseholderQR< PlainObject, PermutationIndex >	colPivHouseholderQr () const

template<typename PermutationIndexType >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType >	colPivHouseholderQr () const

template<typename PermutationIndex = DefaultPermutationIndex>
const CompleteOrthogonalDecomposition< PlainObject, PermutationIndex >	completeOrthogonalDecomposition () const

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

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

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

const MatrixFunctionReturnValue< Derived >	cos () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos . More...

const MatrixFunctionReturnValue< Derived >	cosh () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh . More...

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

template<typename OtherDerived >
std::conditional_t< SizeAtCompileTime==2, Scalar, PlainObject >	cross (const MatrixBase< OtherDerived > &other) const

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

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

Scalar	determinant () const

DiagonalReturnType	diagonal ()

template<int Index>
Diagonal< Derived, Index >	diagonal ()

const ConstDiagonalReturnType	diagonal () const

template<int Index>
const Diagonal< const Derived, Index >	diagonal () const

Diagonal< Derived, DynamicIndex >	diagonal (Index index)

const Diagonal< const Derived, DynamicIndex >	diagonal (Index index) const

Index	diagonalSize () const

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

typedef	EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE (ConstStartMinusOne, Scalar, quotient) HNormalizedReturnType

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

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

const MatrixExponentialReturnValue< Derived >	exp () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp . More...

Derived &	forceAlignedAccess ()

const Derived &	forceAlignedAccess () const

template<bool Enable>
std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf ()

template<bool Enable>
Derived &	forceAlignedAccessIf ()

template<bool Enable>
add_const_on_value_type_t< std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > >	forceAlignedAccessIf () const

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

template<typename PermutationIndex = DefaultPermutationIndex>
const FullPivHouseholderQR< PlainObject, PermutationIndex >	fullPivHouseholderQr () const

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

template<typename PermutationIndex = DefaultPermutationIndex>
const FullPivLU< PlainObject, PermutationIndex >	fullPivLu () const

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

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

HomogeneousReturnType	homogeneous () const

const HouseholderQR< PlainObject >	householderQr () const

RealScalar	hypotNorm () const

const Inverse< Derived >	inverse () const

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

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

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

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

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

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

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

template<int Options = 0>
JacobiSVD< PlainObject, Options >	jacobiSvd () const

template<int Options>
JacobiSVD< typename MatrixBase< Derived >::PlainObject, Options >	jacobiSvd () const

template<int Options = 0>
EIGEN_DEPRECATED JacobiSVD< PlainObject, Options >	jacobiSvd (unsigned int computationOptions) const

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

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

const LDLT< PlainObject >	ldlt () const

const LLT< PlainObject >	llt () const

const MatrixLogarithmReturnValue< Derived >	log () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log . More...

template<int p>
RealScalar	lpNorm () const

template<typename PermutationIndex = DefaultPermutationIndex>
const PartialPivLU< PlainObject, PermutationIndex >	lu () const

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

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

void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)

MatrixBase< Derived > &	matrix ()

const MatrixBase< Derived > &	matrix () const

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

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

RealScalar	norm () const

void	normalize ()

const PlainObject	normalized () const

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

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

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

template<typename SkewDerived >
const Product< Derived, SkewDerived, LazyProduct >	operator* (const SkewSymmetricBase< SkewDerived > &skew) const

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

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

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

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

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

Derived &	operator= (const MatrixBase &other)

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

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

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

template<typename PermutationIndex = DefaultPermutationIndex>
const PartialPivLU< PlainObject, PermutationIndex >	partialPivLu () const

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

const MatrixPowerReturnValue< Derived >	pow (const RealScalar &p) const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to `p` use ArrayBase::pow . More...

const MatrixComplexPowerReturnValue< Derived >	pow (const std::complex< RealScalar > &p) const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to `p` use ArrayBase::pow . More...

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

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

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

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

Derived &	setIdentity ()

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

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

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

const MatrixFunctionReturnValue< Derived >	sin () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin . More...

const MatrixFunctionReturnValue< Derived >	sinh () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh . More...

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

const MatrixSquareRootReturnValue< Derived >	sqrt () const
	This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt . More...

RealScalar	squaredNorm () const

RealScalar	stableNorm () const

void	stableNormalize ()

const PlainObject	stableNormalized () const

Scalar	trace () const

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

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

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

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

PlainObject	unitOrthogonal (void) const

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

bool	allFinite () const

bool	any () const

iterator	begin ()

const_iterator	begin () const

const_iterator	cbegin () const

const_iterator	cend () const

ColwiseReturnType	colwise ()

ConstColwiseReturnType	colwise () const

Index	count () const

iterator	end ()

const_iterator	end () const

EvalReturnType	eval () const

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

void	fill (const Scalar &value)

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

ForceAlignedAccess< Derived >	forceAlignedAccess ()

const ForceAlignedAccess< Derived >	forceAlignedAccess () const

template<bool Enable>
std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf ()

template<bool Enable>
const std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & >	forceAlignedAccessIf () const

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

bool	hasNaN () const

EIGEN_CONSTEXPR Index	innerSize () const

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

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

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

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

bool	isMuchSmallerThan (const RealScalar &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const

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

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

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

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

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

template<int p>
RealScalar	lpNorm () const

template<int NaNPropagation>
internal::traits< Derived >::Scalar	maxCoeff () const

internal::traits< Derived >::Scalar	maxCoeff () const

template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar	maxCoeff (IndexType *index) const

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

template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar	maxCoeff (IndexType row, IndexType col) const

template<typename IndexType >
internal::traits< Derived >::Scalar	maxCoeff (IndexType row, IndexType col) const

Scalar	mean () const

template<int NaNPropagation>
internal::traits< Derived >::Scalar	minCoeff () const

internal::traits< Derived >::Scalar	minCoeff () const

template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar	minCoeff (IndexType *index) const

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

template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar	minCoeff (IndexType row, IndexType col) const

template<typename IndexType >
internal::traits< Derived >::Scalar	minCoeff (IndexType row, IndexType col) const

const NestByValue< Derived >	nestByValue () const

Derived &	operator*= (const Scalar &other)

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

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

Derived &	operator/= (const Scalar &other)

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

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

Derived &	operator= (const DenseBase &other)

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

template<typename OtherDerived >
Derived &	operator= (const EigenBase< OtherDerived > &other)
	Copies the generic expression other into *this. More...

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

EIGEN_CONSTEXPR Index	outerSize () const

Scalar	prod () const

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

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

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

const Replicate< Derived, Dynamic, Dynamic >	replicate (Index rowFactor, Index colFactor) const

void	resize (Index newSize)

void	resize (Index rows, Index cols)

ReverseReturnType	reverse ()

ConstReverseReturnType	reverse () const

void	reverseInPlace ()

RowwiseReturnType	rowwise ()

ConstRowwiseReturnType	rowwise () const

template<typename ThenDerived , typename ElseDerived >
CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, Scalar >, ThenDerived, ElseDerived, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const

template<typename ThenDerived , typename ElseDerived >
CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, typename DenseBase< Derived >::Scalar >, ThenDerived, ElseDerived, Derived >	select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const

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

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

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

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

Derived &	setConstant (const Scalar &value)

Derived &	setEqualSpaced (const Scalar &low, const Scalar &step)

Derived &	setEqualSpaced (Index size, const Scalar &low, const Scalar &step)

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

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

Derived &	setOnes ()

Derived &	setRandom ()

Derived &	setZero ()

Scalar	sum () const

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

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

Scalar	trace () const

TransposeReturnType	transpose ()

const ConstTransposeReturnType	transpose () const

void	transposeInPlace ()

CoeffReturnType	value () const

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

Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	colStride () const EIGEN_NOEXCEPT

Derived &	derived ()

const Derived &	derived () const

EIGEN_CONSTEXPR Index	innerStride () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	outerStride () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	rowStride () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	stride () const EIGEN_NOEXCEPT

Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, WriteAccessors >
Scalar &	coeffRef (Index index)

Scalar &	coeffRef (Index row, Index col)

Scalar &	coeffRefByOuterInner (Index outer, Index inner)

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	derived ()

const Derived &	derived () const

Scalar &	operator() (Index index)

Scalar &	operator() (Index row, Index col)

Scalar &	operator[] (Index index)

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

Scalar &	w ()

Scalar &	x ()

Scalar &	y ()

Scalar &	z ()

Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
CoeffReturnType	coeff (Index index) const

CoeffReturnType	coeff (Index row, Index col) const

CoeffReturnType	coeffByOuterInner (Index outer, Index inner) const

Index	colIndexByOuterInner (Index outer, Index inner) const

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	derived ()

const Derived &	derived () const

CoeffReturnType	operator() (Index index) const

CoeffReturnType	operator() (Index row, Index col) const

CoeffReturnType	operator[] (Index index) const

template<int LoadMode>
PacketReturnType	packet (Index index) const

template<int LoadMode>
PacketReturnType	packet (Index row, Index col) const

template<int LoadMode>
PacketReturnType	packetByOuterInner (Index outer, Index inner) const

Index	rowIndexByOuterInner (Index outer, Index inner) const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

CoeffReturnType	w () const

CoeffReturnType	x () const

CoeffReturnType	y () const

CoeffReturnType	z () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
template<typename Dest >
void	addTo (Dest &dst) const

template<typename Dest >
void	applyThisOnTheLeft (Dest &dst) const

template<typename Dest >
void	applyThisOnTheRight (Dest &dst) const

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	const_cast_derived () const

const Derived &	const_derived () const

Derived &	derived ()

const Derived &	derived () const

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

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

template<typename Dest >
void	subTo (Dest &dst) const

Static Public Member Functions
static const IdentityReturnType	Identity ()

static const IdentityReturnType	Identity (Index rows, Index cols)

static const BasisReturnType	Unit (Index i)

static const BasisReturnType	Unit (Index size, Index i)

static const BasisReturnType	UnitW ()

static const BasisReturnType	UnitX ()

static const BasisReturnType	UnitY ()

static const BasisReturnType	UnitZ ()

Static Public Member Functions inherited from Eigen::DenseBase< Derived >
static const ConstantReturnType	Constant (const Scalar &value)

static const ConstantReturnType	Constant (Index rows, Index cols, const Scalar &value)

static const ConstantReturnType	Constant (Index size, const Scalar &value)

static const RandomAccessEqualSpacedReturnType	EqualSpaced (const Scalar &low, const Scalar &step)

static const RandomAccessEqualSpacedReturnType	EqualSpaced (Index size, const Scalar &low, const Scalar &step)

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

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

static EIGEN_DEPRECATED const RandomAccessLinSpacedReturnType	LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)

static EIGEN_DEPRECATED const RandomAccessLinSpacedReturnType	LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)

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

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

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

static const ConstantReturnType	Ones ()

static const ConstantReturnType	Ones (Index rows, Index cols)

static const ConstantReturnType	Ones (Index size)

static const RandomReturnType	Random ()

static const RandomReturnType	Random (Index rows, Index cols)

static const RandomReturnType	Random (Index size)

static const ConstantReturnType	Zero ()

static const ConstantReturnType	Zero (Index rows, Index cols)

static const ConstantReturnType	Zero (Index size)

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

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

Protected Member Functions inherited from Eigen::DenseBase< Derived >
constexpr	DenseBase ()

Protected Member Functions inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
void	coeffRef ()

void	coeffRefByOuterInner ()

void	colStride ()

void	copyCoeff ()

void	copyCoeffByOuterInner ()

void	copyPacket ()

void	copyPacketByOuterInner ()

void	innerStride ()

void	outerStride ()

void	rowStride ()

void	stride ()

void	writePacket ()

void	writePacketByOuterInner ()

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

	MatrixBase (int)

	MatrixBase (int, int)

Additional Inherited Members
Related Functions inherited from Eigen::DenseBase< Derived >
template<typename Derived >
std::ostream &	operator<< (std::ostream &s, const DenseBase< Derived > &m)

Detailed Description

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

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

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

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

Template Parameters

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

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

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

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

See also: The class hierarchy

Definition at line 50 of file MatrixBase.h.

Member Typedef Documentation

◆ ConstDiagonalReturnType

template<typename Derived >

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

Definition at line 216 of file MatrixBase.h.

◆ 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

Definition at line 420 of file MatrixBase.h.

◆ DiagonalReturnType

template<typename Derived >

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

Definition at line 212 of file MatrixBase.h.

◆ HomogeneousReturnType

template<typename Derived >

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

Definition at line 411 of file MatrixBase.h.

◆ PlainObject

template<typename Derived >

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

Definition at line 106 of file MatrixBase.h.

◆ StemFunction

template<typename Derived >

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

Definition at line 464 of file MatrixBase.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
HomogeneousReturnTypeDirection

Definition at line 409 of file MatrixBase.h.

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

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

Eigen::DenseBase::ColsAtCompileTime

@ ColsAtCompileTime

Definition: DenseBase.h:101

Eigen::DenseBase::RowsAtCompileTime

@ RowsAtCompileTime

Definition: DenseBase.h:95

Eigen::MatrixBase::HomogeneousReturnTypeDirection

@ HomogeneousReturnTypeDirection

Definition: MatrixBase.h:409

Eigen::Horizontal

@ Horizontal

Definition: Constants.h:269

Eigen::Vertical

@ Vertical

Definition: Constants.h:266

Eigen::RowMajorBit

const unsigned int RowMajorBit

Definition: Constants.h:68

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
SizeMinusOne

Definition at line 415 of file MatrixBase.h.

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

Constructor & Destructor Documentation

◆ MatrixBase() [1/3]

template<typename Derived >

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

explicitprivate

◆ MatrixBase() [2/3]

template<typename Derived >

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

private

◆ MatrixBase() [3/3]

template<typename Derived >

template<typename OtherDerived >

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

explicitprivate

Member Function Documentation

◆ acosh()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .

Returns: an expression of the matrix inverse hyperbolic cosine of *this.

◆ 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:

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

Output:

Here is the 2x2 complex matrix m:
 (-0.211,0.68) (-0.605,0.823)
 (0.597,0.566)  (0.536,-0.33)
Here is the adjoint of m:
 (-0.211,-0.68)  (0.597,-0.566)
(-0.605,-0.823)    (0.536,0.33)

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

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

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

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

Definition at line 223 of file Transpose.h.

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

◆ adjointInPlace()

template<typename Derived >

void Eigen::MatrixBase< Derived >::adjointInPlace

inline

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

m.adjointInPlace();

has the same effect on m as doing

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

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

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

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

See also: transpose(), adjoint(), transposeInPlace()

Definition at line 377 of file Transpose.h.

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

◆ 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() entries

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

Definition at line 118 of file Householder.h.

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

◆ 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->rows() entries

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

Definition at line 156 of file Householder.h.

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

◆ applyOnTheLeft() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by other * *this.

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After applyOnTheLeft, A = 
-0.211  0.823  0.536
 0.566 -0.605 -0.444
  0.68  0.597  -0.33

Definition at line 544 of file MatrixBase.h.

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

◆ applyOnTheLeft() [2/2]

template<typename Derived >

template<typename OtherScalar >

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

inline

This is defined in the Jacobi module.

#include <Eigen/Jacobi>

Jacobi

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

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

Definition at line 297 of file Jacobi.h.

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

◆ applyOnTheRight()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566

Definition at line 532 of file MatrixBase.h.

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

◆ array() [1/2]

template<typename Derived >

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

inline

Returns: an Array expression of this matrix

See also: ArrayBase::matrix()

Definition at line 324 of file MatrixBase.h.

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

◆ array() [2/2]

template<typename Derived >

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

inline

Returns: a const Array expression of this matrix

See also: ArrayBase::matrix()

Definition at line 327 of file MatrixBase.h.

327 { 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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Example:

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

Eigen::MatrixBase::asDiagonal

const DiagonalWrapper< const Derived > asDiagonal() const

Definition: DiagonalMatrix.h:384

Eigen::Vector3i

Matrix< int, 3, 1 > Vector3i

3×1 vector of type int.

Definition: Matrix.h:500

Eigen::Matrix3i

Matrix< int, 3, 3 > Matrix3i

3×3 matrix of type int.

Definition: Matrix.h:500

Output:

2 0 0
0 5 0
0 0 6

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

Definition at line 384 of file DiagonalMatrix.h.

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

◆ asinh()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh .

Returns: an expression of the matrix inverse hyperbolic sine of *this.

◆ asPermutation()

template<typename Derived >

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

Definition at line 594 of file PermutationMatrix.h.

 {
   return derived();
 }

◆ asSkewSymmetric()

template<typename Derived >

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

inline

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also: class SkewSymmetricWrapper, class SkewSymmetricMatrix3, vector(), isSkewSymmetric()

Definition at line 349 of file SkewSymmetricMatrix3.h.

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

◆ atanh()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh .

Returns: an expression of the matrix inverse hyperbolic cosine of *this.

◆ bdcSvd() [1/4]

template<typename Derived >

template<int Options = 0>

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

inline

◆ bdcSvd() [2/4]

template<typename Derived >

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

SVD

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

See also: class BDCSVD

Definition at line 1475 of file BDCSVD.h.

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

◆ bdcSvd() [3/4]

template<typename Derived >

template<int Options = 0>

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

inline

◆ bdcSvd() [4/4]

template<typename Derived >

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

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

See also: class BDCSVD

Definition at line 1487 of file BDCSVD.h.

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

◆ blueNorm()

template<typename Derived >

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

inline

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

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

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

Definition at line 231 of file StableNorm.h.

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

◆ colPivHouseholderQr() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ colPivHouseholderQr() [2/2]

template<typename Derived >

template<typename PermutationIndexType >

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

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

See also: class ColPivHouseholderQR

Definition at line 673 of file ColPivHouseholderQR.h.

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

◆ completeOrthogonalDecomposition() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ completeOrthogonalDecomposition() [2/2]

template<typename Derived >

template<typename PermutationIndex >

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

Returns: the complete orthogonal decomposition of *this.

See also: class CompleteOrthogonalDecomposition

Definition at line 645 of file CompleteOrthogonalDecomposition.h.

                                                            {
   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

This is defined in the LU module.

#include <Eigen/LU>

LU

Computation of matrix inverse and determinant, with invertibility check.

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

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

Parameters

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

Example:

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

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its determinant is 0.209
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29

See also: inverse(), computeInverseWithCheck()

Definition at line 379 of file InverseImpl.h.

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

◆ 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

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse, with invertibility check.

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

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

Parameters

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

Example:

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

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29

See also: inverse(), computeInverseAndDetWithCheck()

Definition at line 420 of file InverseImpl.h.

 {
   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);
 }

◆ cos()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos .

Returns: an expression of the matrix cosine of *this.

◆ cosh()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh .

Returns: an expression of the matrix hyperbolic cosine of *this.

◆ cross()

template<typename Derived >

template<typename OtherDerived >

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

inline

◆ cwiseProduct()

template<typename Derived >

template<typename OtherDerived >

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

inline

Definition at line 457 of file MatrixBase.h.

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

◆ determinant()

template<typename Derived >

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Returns: the determinant of this matrix

Definition at line 110 of file Determinant.h.

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

◆ diagonal() [1/6]

template<typename Derived >

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

inline

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

*this is not required to be square.

Example:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here are the coefficients on the main diagonal of m:
 7
 9
-5

See also: class Diagonal

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6

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

Definition at line 189 of file Diagonal.h.

 {
   return DiagonalReturnType(derived());
 }

◆ diagonal() [2/6]

template<typename Derived >

template<int Index>

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

◆ diagonal() [3/6]

template<typename Derived >

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

inline

This is the const version of diagonal().

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

Definition at line 198 of file Diagonal.h.

 {
   return ConstDiagonalReturnType(derived());
 }

◆ diagonal() [4/6]

template<typename Derived >

template<int Index>

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

◆ diagonal() [5/6]

template<typename Derived >

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

inline

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6

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

Definition at line 216 of file Diagonal.h.

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

◆ diagonal() [6/6]

template<typename Derived >

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

inline

This is the const version of diagonal(Index).

Definition at line 224 of file Diagonal.h.

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

◆ diagonalSize()

template<typename Derived >

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

inline

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

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

Definition at line 104 of file MatrixBase.h.

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

Eigen::numext::mini

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

Definition: MathFunctions.h:977

◆ dot()

template<typename Derived >

template<typename OtherDerived >

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

inline

Returns: the dot product of *this with other.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

See also: squaredNorm(), norm()

Definition at line 69 of file Dot.h.

 {
   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))
   EIGEN_CHECK_BINARY_COMPATIBILIY(
       Eigen::internal::scalar_conj_product_op<Scalar EIGEN_COMMA typename OtherDerived::Scalar>, 
       Scalar, typename OtherDerived::Scalar);
 #endif
   
   eigen_assert(size() == other.size());
  
   return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
 }

◆ 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.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

Eigenvalues

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

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

Output:

The eigenvalues of the 3x3 matrix of ones are:
(-5.31e-17,0)
        (3,0)
        (0,0)

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

Definition at line 69 of file MatrixBaseEigenvalues.h.

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

◆ exp()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp .

Returns: an expression of the matrix exponential of *this.

◆ 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

Definition at line 311 of file MatrixBase.h.

311 { 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

Definition at line 310 of file MatrixBase.h.

310 { return derived(); }

◆ forceAlignedAccessIf() [1/4]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

Definition at line 145 of file ForceAlignedAccess.h.

 {
   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

Definition at line 313 of file MatrixBase.h.

313 { return derived(); }

◆ forceAlignedAccessIf() [3/4]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

Definition at line 134 of file ForceAlignedAccess.h.

 {
   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

Definition at line 312 of file MatrixBase.h.

312 { return derived(); }

◆ fullPivHouseholderQr() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ fullPivHouseholderQr() [2/2]

template<typename Derived >

template<typename PermutationIndex >

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

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

See also: class FullPivHouseholderQR

Definition at line 731 of file FullPivHouseholderQR.h.

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

◆ fullPivLu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ fullPivLu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

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

inline

This is defined in the LU module.

#include <Eigen/LU>

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

See also: class FullPivLU

Definition at line 870 of file FullPivLU.h.

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

◆ householderQr()

template<typename Derived >

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

inline

Returns: the Householder QR decomposition of *this.

See also: class HouseholderQR

Definition at line 527 of file HouseholderQR.h.

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

◆ hypotNorm()

template<typename Derived >

NumTraits< typename internal::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()

Definition at line 243 of file StableNorm.h.

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

◆ Identity() [1/2]

template<typename Derived >

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

inlinestatic

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

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

Example:

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

Output:

1 0 0 0
0 1 0 0
0 0 1 0

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

Definition at line 828 of file CwiseNullaryOp.h.

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

◆ Identity() [2/2]

template<typename Derived >

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

inlinestatic

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

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

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

Example:

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

Eigen::MatrixBase::Identity

static const IdentityReturnType Identity()

Definition: CwiseNullaryOp.h:828

Output:

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

Definition at line 811 of file CwiseNullaryOp.h.

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

◆ inverse()

template<typename Derived >

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Returns: the matrix inverse of this matrix.

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

Note

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

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

Example:

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

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29

See also: computeInverseAndDetWithCheck()

Definition at line 350 of file InverseImpl.h.

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

◆ isDiagonal()

template<typename Derived >

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

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

Example:

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

Output:

Here's the matrix m:
1e+04     0     1
    0 1e+04     0
    0     0 1e+04
m.isDiagonal() returns: 0
m.isDiagonal(1e-3) returns: 1

See also: asDiagonal()

Definition at line 398 of file DiagonalMatrix.h.

 {
   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;
 }

◆ isIdentity()

template<typename Derived >

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

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

Example:

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

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1

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

Definition at line 844 of file CwiseNullaryOp.h.

 {
   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;
 }

◆ 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()

Definition at line 692 of file TriangularMatrix.h.

 {
   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;
 }

◆ isOrthogonal()

template<typename Derived >

template<typename OtherDerived >

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

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

Example:

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

Output:

Here's the vector v:
1
0
0
Here's the vector w:
0.0001
     0
     1
v.isOrthogonal(w) returns: 0
v.isOrthogonal(w,1e-3) returns: 1

Definition at line 280 of file Dot.h.

 {
   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();
 }

◆ isSkewSymmetric()

template<typename Derived >

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

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

Definition at line 358 of file SkewSymmetricMatrix3.h.

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

◆ isUnitary()

template<typename Derived >

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

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

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

Example:

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

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isUnitary() returns: 0
m.isUnitary(1e-3) returns: 1

Definition at line 300 of file Dot.h.

 {
   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;
 }

◆ 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()

Definition at line 667 of file TriangularMatrix.h.

 {
   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;
 }

◆ jacobiSvd() [1/4]

template<typename Derived >

template<int Options = 0>

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

inline

◆ jacobiSvd() [2/4]

template<typename Derived >

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

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

See also: class JacobiSVD

Definition at line 830 of file JacobiSVD.h.

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

◆ jacobiSvd() [3/4]

template<typename Derived >

template<int Options = 0>

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

inline

◆ jacobiSvd() [4/4]

template<typename Derived >

template<int Options>

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

Definition at line 836 of file JacobiSVD.h.

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

◆ lazyProduct()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

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

See also: operator*(const MatrixBase&)

Definition at line 444 of file GeneralProduct.h.

 {
   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());
 }

◆ ldlt()

template<typename Derived >

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Cholesky

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

See also: SelfAdjointView::ldlt()

Definition at line 678 of file LDLT.h.

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

◆ llt()

template<typename Derived >

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

Definition at line 537 of file LLT.h.

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

◆ log()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log .

Returns: an expression of the matrix logarithm of *this.

◆ lpNorm()

template<typename Derived >

template<int p>

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

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

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

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

See also: norm()

Definition at line 265 of file Dot.h.

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

◆ lu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ lu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Synonym of partialPivLu().

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

See also: class PartialPivLU

Definition at line 616 of file PartialPivLU.h.

 {
   return PartialPivLU<PlainObject, PermutationIndex>(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()

Definition at line 69 of file Householder.h.

 {
   using numext::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);
   }
 }

◆ 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()

Definition at line 45 of file Householder.h.

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

◆ matrix() [1/2]

template<typename Derived >

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

inline

Definition at line 319 of file MatrixBase.h.

319 { return *this; }

◆ matrix() [2/2]

template<typename Derived >

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

inline

Definition at line 320 of file MatrixBase.h.

320 { return *this; }

◆ matrixFunction()

template<typename Derived >

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

Helper function for the unsupported MatrixFunctions module.

◆ noalias()

template<typename Derived >

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

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

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

Here are some examples where noalias is useful:

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

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

A.noalias() = A * B;

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

A = A * B;

See also: class NoAlias

Definition at line 104 of file NoAlias.h.

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

◆ norm()

template<typename Derived >

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

inline

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

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

Definition at line 106 of file Dot.h.

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

◆ normalize()

template<typename Derived >

void Eigen::MatrixBase< Derived >::normalize

inline

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

See also: norm(), normalized()

Definition at line 143 of file Dot.h.

 {
   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);
 }

◆ normalized()

template<typename Derived >

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

inline

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

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also: norm(), normalize()

Definition at line 122 of file Dot.h.

 {
   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;
 }

◆ operator!=()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

See also: isApprox(), operator==

Definition at line 303 of file MatrixBase.h.

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

cwiseNotEqual

const CwiseBinaryNotEqualReturnType< OtherDerived > cwiseNotEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

Definition: MatrixCwiseBinaryOps.h:70

◆ operator*() [1/3]

template<typename Derived >

template<typename DiagonalDerived >

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

inline

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

Definition at line 23 of file DiagonalProduct.h.

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

◆ operator*() [2/3]

template<typename Derived >

template<typename OtherDerived >

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

inline

Implementation of matrix base methods

Returns: the matrix product of *this and other.

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

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

Definition at line 401 of file GeneralProduct.h.

 {
   // 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());
 }

◆ operator*() [3/3]

template<typename Derived >

template<typename SkewDerived >

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

inline

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

Definition at line 369 of file SkewSymmetricMatrix3.h.

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

◆ operator*=()

template<typename Derived >

template<typename OtherDerived >

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

inline

Implementation of matrix base methods replaces *this by *this * other.

Returns: a reference to *this

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566

Definition at line 519 of file MatrixBase.h.

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

◆ operator+=() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

Definition at line 497 of file MatrixBase.h.

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

◆ operator+=() [2/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by *this + other.

Returns: a reference to *this

Definition at line 177 of file CwiseBinaryOp.h.

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

◆ operator-=() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inlineprotected

Definition at line 500 of file MatrixBase.h.

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

◆ operator-=() [2/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by *this - other.

Returns: a reference to *this

Definition at line 164 of file CwiseBinaryOp.h.

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

◆ operator=() [1/4]

template<typename Derived >

template<typename OtherDerived >

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

inline

Definition at line 66 of file Assign.h.

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

◆ operator=() [2/4]

template<typename Derived >

template<typename OtherDerived >

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

inline

Definition at line 75 of file Assign.h.

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

◆ operator=() [3/4]

template<typename Derived >

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

inline

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

Definition at line 57 of file Assign.h.

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

◆ operator=() [4/4]

template<typename Derived >

template<typename OtherDerived >

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

inline

Definition at line 84 of file Assign.h.

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

◆ operator==()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

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

See also: isApprox(), operator!=

Definition at line 295 of file MatrixBase.h.

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

cwiseEqual

const CwiseBinaryEqualReturnType< OtherDerived > cwiseEqual(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

Definition: MatrixCwiseBinaryOps.h:50

◆ operatorNorm()

template<typename Derived >

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

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

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

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

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

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

Example:

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

Output:

The operator norm of the 3x3 matrix of ones is 3

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

Definition at line 122 of file MatrixBaseEigenvalues.h.

 {
   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()
                  );
 }

◆ partialPivLu() [1/2]

template<typename Derived >

template<typename PermutationIndex = DefaultPermutationIndex>

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

inline

◆ partialPivLu() [2/2]

template<typename Derived >

template<typename PermutationIndex >

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

inline

This is defined in the LU module.

#include <Eigen/LU>

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

See also: class PartialPivLU

Definition at line 600 of file PartialPivLU.h.

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

◆ pow() [1/2]

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

Returns: an expression of the matrix power to p of *this.

◆ pow() [2/2]

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

Returns: an expression of the matrix power to p of *this.

◆ selfadjointView() [1/4]

template<typename Derived >

template<unsigned int UpLo>

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:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the symmetric matrix extracted from the upper part of m:
 7  6 -3
 6  9  6
-3  6 -5
Here is the symmetric matrix extracted from the lower part of m:
 7 -2  6
-2  9 -6
 6 -6 -5

See also: class SelfAdjointView

Definition at line 358 of file SelfAdjointView.h.

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

◆ selfadjointView() [3/4]

template<typename Derived >

template<unsigned int UpLo>

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

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

Definition at line 341 of file SelfAdjointView.h.

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

◆ setIdentity() [1/2]

template<typename Derived >

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

inline

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

Example:

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

Output:

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

Definition at line 902 of file CwiseNullaryOp.h.

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

◆ setIdentity() [2/2]

template<typename Derived >

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

inline

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

Parameters

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

Example:

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

Output:

1 0 0
0 1 0
0 0 1

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

Definition at line 918 of file CwiseNullaryOp.h.

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

◆ setUnit() [1/2]

template<typename Derived >

Derived & Eigen::MatrixBase< Derived >::setUnit ( Index i )

inline

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

Parameters

i	index of the unique coefficient to be set to 1

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 1001 of file CwiseNullaryOp.h.

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

◆ setUnit() [2/2]

template<typename Derived >

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

inline

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

Parameters

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 1020 of file CwiseNullaryOp.h.

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

◆ sin()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin .

Returns: an expression of the matrix sine of *this.

◆ sinh()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh .

Returns: an expression of the matrix hyperbolic sine of *this.

◆ sqrt()

template<typename Derived >

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt .

Returns: an expression of the matrix square root of *this.

◆ squaredNorm()

template<typename Derived >

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

inline

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

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

Definition at line 94 of file Dot.h.

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

◆ stableNorm()

template<typename Derived >

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

inline

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

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

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

Definition at line 215 of file StableNorm.h.

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

◆ stableNormalize()

template<typename Derived >

void Eigen::MatrixBase< Derived >::stableNormalize

inline

Normalizes the vector while avoid underflow and overflow

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

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

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

Definition at line 189 of file Dot.h.

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

◆ stableNormalized()

template<typename Derived >

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

inline

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

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

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

Definition at line 165 of file Dot.h.

 {
   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;
 }

◆ trace()

template<typename Derived >

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

inline

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

*this can be any matrix, not necessarily square.

See also: diagonal(), sum()

Definition at line 595 of file Redux.h.

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

◆ triangularView() [1/4]

template<typename Derived >

template<unsigned int Mode>

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 ( )

Implementation of TriangularView methods Implementation of MatrixBase methods

Returns: an expression of a triangular view extracted from the current matrix

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

Example:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the upper-triangular matrix extracted from m:
 7  6 -3
 0  9  6
 0  0 -5
Here is the strictly-upper-triangular matrix extracted from m:
 0  6 -3
 0  0  6
 0  0  0
Here is the unit-lower-triangular matrix extracted from m:
 1  0  0
-2  1  0
 6 -6  1

See also: class TriangularView

Definition at line 646 of file TriangularMatrix.h.

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

◆ triangularView() [3/4]

template<typename Derived >

template<unsigned int Mode>

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()

Definition at line 656 of file TriangularMatrix.h.

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

◆ Unit() [1/2]

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

This variant is for fixed-size vector only.

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

Definition at line 946 of file CwiseNullaryOp.h.

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

◆ Unit() [2/2]

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 931 of file CwiseNullaryOp.h.

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

◆ UnitW()

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 989 of file CwiseNullaryOp.h.

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

◆ UnitX()

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 959 of file CwiseNullaryOp.h.

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

◆ UnitY()

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 969 of file CwiseNullaryOp.h.

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

◆ UnitZ()

template<typename Derived >

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

inlinestatic

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

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Definition at line 979 of file CwiseNullaryOp.h.

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

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ ConstDiagonalReturnType

◆ ConstStartMinusOne

◆ DiagonalReturnType

◆ HomogeneousReturnType

◆ PlainObject

◆ StemFunction

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ MatrixBase() [1/3]

◆ MatrixBase() [2/3]

◆ MatrixBase() [3/3]

Member Function Documentation

◆ acosh()

◆ adjoint()

◆ adjointInPlace()

◆ applyHouseholderOnTheLeft()

◆ applyHouseholderOnTheRight()

◆ applyOnTheLeft() [1/2]

◆ applyOnTheLeft() [2/2]

◆ applyOnTheRight()

◆ array() [1/2]

◆ array() [2/2]

◆ asDiagonal()

◆ asinh()

◆ asPermutation()

◆ asSkewSymmetric()

◆ atanh()

◆ bdcSvd() [1/4]

◆ bdcSvd() [2/4]

◆ bdcSvd() [3/4]

◆ bdcSvd() [4/4]

◆ blueNorm()

◆ colPivHouseholderQr() [1/2]

◆ colPivHouseholderQr() [2/2]

◆ completeOrthogonalDecomposition() [1/2]

◆ completeOrthogonalDecomposition() [2/2]

◆ computeInverseAndDetWithCheck()

◆ computeInverseWithCheck()

◆ cos()

◆ cosh()

◆ cross()

◆ cwiseProduct()

◆ determinant()

◆ diagonal() [1/6]

◆ diagonal() [2/6]

◆ diagonal() [3/6]

◆ diagonal() [4/6]

◆ diagonal() [5/6]

◆ diagonal() [6/6]

◆ diagonalSize()

◆ dot()

◆ EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE()

◆ eigenvalues()

◆ exp()

◆ forceAlignedAccess() [1/2]

◆ forceAlignedAccess() [2/2]

◆ forceAlignedAccessIf() [1/4]

◆ forceAlignedAccessIf() [2/4]

◆ forceAlignedAccessIf() [3/4]

◆ forceAlignedAccessIf() [4/4]

◆ fullPivHouseholderQr() [1/2]

◆ fullPivHouseholderQr() [2/2]

◆ fullPivLu() [1/2]

◆ fullPivLu() [2/2]

◆ householderQr()

◆ hypotNorm()

◆ Identity() [1/2]

◆ Identity() [2/2]

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