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

#include <MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:

Classes
struct	ConstDiagonalIndexReturnType

struct	ConstSelfAdjointViewReturnType

struct	ConstTriangularViewReturnType

struct	cross_product_return_type

struct	DiagonalIndexReturnType

struct	SelfAdjointViewReturnType

struct	TriangularViewReturnType

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

typedef MatrixBase	StorageBaseType

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

typedef internal::traits< Derived >::Index	Index

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

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

typedef NumTraits< Scalar >::Real	RealScalar

typedef DenseBase< Derived >	Base

typedef Base::CoeffReturnType	CoeffReturnType

typedef Base::ConstTransposeReturnType	ConstTransposeReturnType

typedef Base::RowXpr	RowXpr

typedef Base::ColXpr	ColXpr

typedef Matrix< Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime)>	SquareMatrixType
	type of the equivalent square matrix

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 >	PlainObject
	The plain matrix type corresponding to this expression. More...

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

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

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

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

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

typedef CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const Derived >	ScalarMultipleReturnType

typedef CwiseUnaryOp< internal::scalar_quotient1_op< Scalar >, const Derived >	ScalarQuotient1ReturnType

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

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

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

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

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

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

typedef Diagonal< Derived >	DiagonalReturnType

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

typedef Diagonal< Derived, DynamicIndex >	DiagonalDynamicIndexReturnType

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

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

typedef CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< Derived >::Scalar >, const ConstStartMinusOne >	HNormalizedReturnType

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

Public Types inherited from Eigen::DenseBase< Derived >
enum	{ RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime, MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags = internal::traits<Derived>::Flags, IsRowMajor = int(Flags) & RowMajorBit, InnerSizeAtCompileTime, CoeffReadCost = internal::traits<Derived>::CoeffReadCost, InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret, OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret }

enum	{ ThisConstantIsPrivateInPlainObjectBase }

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

typedef internal::traits< Derived >::Index	Index
	The type of indices. More...

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

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

typedef NumTraits< Scalar >::Real	RealScalar

typedef internal::special_scalar_op_base< Derived, Scalar, RealScalar, DenseCoeffsBase< Derived > >	Base

typedef Base::CoeffReturnType	CoeffReturnType

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

typedef CwiseNullaryOp< internal::linspaced_op< Scalar, false >, Derived >	SequentialLinSpacedReturnType

typedef CwiseNullaryOp< internal::linspaced_op< Scalar, true >, Derived >	RandomAccessLinSpacedReturnType

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

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

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

typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType

typedef const VectorwiseOp< const Derived, Horizontal >	ConstRowwiseReturnType

typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType

typedef const VectorwiseOp< const Derived, Vertical >	ConstColwiseReturnType

typedef Replicate< Derived, Dynamic, Dynamic >	ReplicateReturnType

typedef Reverse< Derived, BothDirections >	ReverseReturnType

typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType

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

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

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

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

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

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

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

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

typedef VectorBlock< Derived >	SegmentReturnType

typedef const VectorBlock< const Derived >	ConstSegmentReturnType

Public Member Functions
Index	diagonalSize () const

const CwiseUnaryOp< internal::scalar_opposite_op< typename internal::traits< Derived >::Scalar >, const Derived >	operator- () const

const ScalarMultipleReturnType	operator* (const Scalar &scalar) const

const CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< Derived >::Scalar >, const Derived >	operator/ (const Scalar &scalar) const

const CwiseUnaryOp< internal::scalar_multiple2_op< Scalar, std::complex< Scalar > >, const Derived >	operator* (const std::complex< Scalar > &scalar) const
	Overloaded for efficient real matrix times complex scalar value.

template<typename NewType >
internal::cast_return_type< Derived, const CwiseUnaryOp< internal::scalar_cast_op< typename internal::traits< Derived >::Scalar, NewType >, const Derived > >::type	cast () const

ConjugateReturnType	conjugate () const

RealReturnType	real () const

const ImagReturnType	imag () const

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

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

NonConstRealReturnType	real ()

NonConstImagReturnType	imag ()

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

EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived >	cwiseAbs () const

EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Derived >	cwiseAbs2 () const

const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Derived >	cwiseSqrt () const

const CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const Derived >	cwiseInverse () const

template<typename OtherDerived >
EIGEN_STRONG_INLINE const	EIGEN_CWISE_PRODUCT_RETURN_TYPE (Derived, OtherDerived) cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const

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

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

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

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

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

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

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

const CwiseScalarEqualReturnType	cwiseEqual (const Scalar &s) const

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

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

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

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

template<typename ProductDerived , typename Lhs , typename Rhs >
Derived &	lazyAssign (const ProductBase< ProductDerived, Lhs, Rhs > &other)

template<typename MatrixPower , typename Lhs , typename Rhs >
Derived &	lazyAssign (const MatrixPowerProduct< MatrixPower, Lhs, Rhs > &other)

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

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

template<typename OtherDerived >
const ProductReturnType< Derived, OtherDerived >::Type	operator* (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived >
const LazyProductReturnType< Derived, OtherDerived >::Type	lazyProduct (const MatrixBase< OtherDerived > &other) const

template<typename OtherDerived >
Derived &	operator*= (const EigenBase< OtherDerived > &other)
	replaces `this` by `this` * other. More...

template<typename OtherDerived >
void	applyOnTheLeft (const EigenBase< OtherDerived > &other)
	replaces `this` by other* * `*this`. More...

template<typename OtherDerived >
void	applyOnTheRight (const EigenBase< OtherDerived > &other)
	replaces `this` by `this` * other. More...

template<typename DiagonalDerived >
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight >	operator* (const DiagonalBase< DiagonalDerived > &diagonal) const

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

RealScalar	squaredNorm () const

RealScalar	norm () const

RealScalar	stableNorm () const

RealScalar	blueNorm () const

RealScalar	hypotNorm () const

const PlainObject	normalized () const

void	normalize ()
	Normalizes the vector, i.e. More...

const AdjointReturnType	adjoint () const

void	adjointInPlace ()
	This is the "in place" version of adjoint(): it replaces `*this` by its own transpose. More...

DiagonalReturnType	diagonal ()

ConstDiagonalReturnType	diagonal () const
	This is the const version of diagonal(). More...

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

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

DiagonalDynamicIndexReturnType	diagonal (Index index)

ConstDiagonalDynamicIndexReturnType	diagonal (Index index) const
	This is the const version of diagonal(Index). More...

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

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

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

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

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

const DiagonalWrapper< const Derived >	asDiagonal () const

const PermutationWrapper< const Derived >	asPermutation () const

Derived &	setIdentity ()
	Writes the identity expression (not necessarily square) into *this. More...

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

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

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

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

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

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

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

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

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

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

const ForceAlignedAccess< Derived >	forceAlignedAccess () const

ForceAlignedAccess< Derived >	forceAlignedAccess ()

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

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

Scalar	trace () const

template<int p>
RealScalar	lpNorm () const

MatrixBase< Derived > &	matrix ()

const MatrixBase< Derived > &	matrix () const

ArrayWrapper< Derived >	array ()

const ArrayWrapper< const Derived >	array () const

const FullPivLU< PlainObject >	fullPivLu () const

const PartialPivLU< PlainObject >	partialPivLu () const

const internal::inverse_impl< Derived >	inverse () const

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

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

Scalar	determinant () const

const LLT< PlainObject >	llt () const

const LDLT< PlainObject >	ldlt () const

const HouseholderQR< PlainObject >	householderQr () const

const ColPivHouseholderQR< PlainObject >	colPivHouseholderQr () const

const FullPivHouseholderQR< PlainObject >	fullPivHouseholderQr () const

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

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

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

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

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

PlainObject	unitOrthogonal (void) const

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

const HNormalizedReturnType	hnormalized () const

void	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: \( v^T = [1 essential^T] \). More...

template<typename EssentialPart >
void	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: \( v^T = [1 essential^T] \). More...

template<typename EssentialPart >
void	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. More...

template<typename EssentialPart >
void	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. More...

template<typename OtherScalar >
void	applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
	Applies the rotation in the plane j to the rows p and q of `this`, i.e., it computes B = J B, with \( B = \left ( \begin{array}{cc} \text{this.row}(p) \\ \text{this.row}(q) \end{array} \right ) \). More...

template<typename OtherScalar >
void	applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
	Applies the rotation in the plane j to the columns p and q of `this`, i.e., it computes B = B J with \( B = \left ( \begin{array}{cc} \text{this.col}(p) & \text{this.col}(q) \end{array} \right ) \). More...

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

const MatrixExponentialReturnValue< Derived >	exp () const

const MatrixFunctionReturnValue< Derived >	matrixFunction (StemFunction f) const

const MatrixFunctionReturnValue< Derived >	cosh () const

const MatrixFunctionReturnValue< Derived >	sinh () const

const MatrixFunctionReturnValue< Derived >	cos () const

const MatrixFunctionReturnValue< Derived >	sin () const

const MatrixSquareRootReturnValue< Derived >	sqrt () const

const MatrixLogarithmReturnValue< Derived >	log () const

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

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

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

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

template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator-= (const MatrixBase< OtherDerived > &other)
	replaces `this` by `this` - other. More...

template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator+= (const MatrixBase< OtherDerived > &other)
	replaces `this` by `this` + other. More...

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

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

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

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

template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type	triangularView () const
	This is the const version of MatrixBase::triangularView()

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

template<typename Derived >
MatrixBase< Derived >::ScalarMultipleReturnType	operator* (const UniformScaling< Scalar > &s) const
	Concatenates a linear transformation matrix and a uniform scaling.

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

Index	outerSize () const

Index	innerSize () const

void	resize (Index newSize)
	Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). More...

void	resize (Index nbRows, Index nbCols)
	Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). More...

template<typename OtherDerived >
Derived &	operator= (const DenseBase< OtherDerived > &other)
	Copies other into *this. More...

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

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

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

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

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

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

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

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

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

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

Eigen::Transpose< Derived >	transpose ()

ConstTransposeReturnType	transpose () const
	This is the const version of transpose(). More...

void	transposeInPlace ()
	This is the "in place" version of transpose(): it replaces `*this` by its own transpose. More...

void	fill (const Scalar &value)
	Alias for setConstant(): sets all coefficients in this expression to val. More...

Derived &	setConstant (const Scalar &value)
	Sets all coefficients in this expression to value. More...

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

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

Derived &	setZero ()
	Sets all coefficients in this expression to zero. More...

Derived &	setOnes ()
	Sets all coefficients in this expression to one. More...

Derived &	setRandom ()
	Sets all coefficients in this expression to random values. More...

template<typename OtherDerived >
bool	isApprox (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 OtherDerived >
bool	isMuchSmallerThan (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
	This is just an alias for isApproxToConstant(). More...

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

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

bool	hasNaN () const

bool	allFinite () const

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

Derived &	operator/= (const Scalar &other)

EIGEN_STRONG_INLINE EvalReturnType	eval () const

template<typename OtherDerived >
void	swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
	swaps this with the expression other*.

template<typename OtherDerived >
void	swap (PlainObjectBase< OtherDerived > &other)
	swaps this with the matrix or array other*.

const NestByValue< Derived >	nestByValue () const

const ForceAlignedAccess< Derived >	forceAlignedAccess () const

ForceAlignedAccess< Derived >	forceAlignedAccess ()

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

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

Scalar	sum () const

Scalar	mean () const

Scalar	trace () const

Scalar	prod () const

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

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

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

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

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

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

template<typename BinaryOp >
internal::result_of< BinaryOp(typename internal::traits< Derived >::Scalar)>::type	redux (const BinaryOp &func) const

template<typename Visitor >
void	visit (Visitor &func) const
	Applies the visitor visitor to the whole coefficients of the matrix or vector. More...

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

CoeffReturnType	value () const

bool	all (void) const

bool	any (void) const

Index	count () const

ConstRowwiseReturnType	rowwise () const

RowwiseReturnType	rowwise ()

ConstColwiseReturnType	colwise () const

ColwiseReturnType	colwise ()

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

template<typename ThenDerived >
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType >	select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const
	Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value. More...

template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived >	select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
	Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value. More...

template<int p>
RealScalar	lpNorm () const

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

const ReplicateReturnType	replicate (Index rowFacor, Index colFactor) const

ReverseReturnType	reverse ()

ConstReverseReturnType	reverse () const
	This is the const version of reverse(). More...

void	reverseInPlace ()
	This is the "in place" version of reverse: it reverses `*this`. More...

Block< Derived >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)

const Block< const Derived >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
	This is the const version of block(Index,Index,Index,Index). More...

Block< Derived >	topRightCorner (Index cRows, Index cCols)

const Block< const Derived >	topRightCorner (Index cRows, Index cCols) const
	This is the const version of topRightCorner(Index, Index). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topRightCorner ()

template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	topRightCorner () const
	This is the const version of topRightCorner<int, int>(). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topRightCorner (Index cRows, Index cCols)

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

Block< Derived >	topLeftCorner (Index cRows, Index cCols)

const Block< const Derived >	topLeftCorner (Index cRows, Index cCols) const
	This is the const version of topLeftCorner(Index, Index). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topLeftCorner ()

template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	topLeftCorner () const
	This is the const version of topLeftCorner<int, int>(). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topLeftCorner (Index cRows, Index cCols)

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

Block< Derived >	bottomRightCorner (Index cRows, Index cCols)

const Block< const Derived >	bottomRightCorner (Index cRows, Index cCols) const
	This is the const version of bottomRightCorner(Index, Index). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomRightCorner ()

template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	bottomRightCorner () const
	This is the const version of bottomRightCorner<int, int>(). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomRightCorner (Index cRows, Index cCols)

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

Block< Derived >	bottomLeftCorner (Index cRows, Index cCols)

const Block< const Derived >	bottomLeftCorner (Index cRows, Index cCols) const
	This is the const version of bottomLeftCorner(Index, Index). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomLeftCorner ()

template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	bottomLeftCorner () const
	This is the const version of bottomLeftCorner<int, int>(). More...

template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomLeftCorner (Index cRows, Index cCols)

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

RowsBlockXpr	topRows (Index n)

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

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

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

RowsBlockXpr	bottomRows (Index n)

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

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

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

RowsBlockXpr	middleRows (Index startRow, Index n)

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

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

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

ColsBlockXpr	leftCols (Index n)

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

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

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

ColsBlockXpr	rightCols (Index n)

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

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

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

ColsBlockXpr	middleCols (Index startCol, Index numCols)

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

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

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

template<int BlockRows, int BlockCols>
Block< Derived, BlockRows, BlockCols >	block (Index startRow, Index startCol)

template<int BlockRows, int BlockCols>
const Block< const Derived, BlockRows, BlockCols >	block (Index startRow, Index startCol) const
	This is the const version of block<>(Index, Index). More...

template<int BlockRows, int BlockCols>
Block< Derived, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)

template<int BlockRows, int BlockCols>
const Block< const Derived, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
	This is the const version of block<>(Index, Index, Index, Index). More...

ColXpr	col (Index i)

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

RowXpr	row (Index i)

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

SegmentReturnType	segment (Index start, Index n)

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

SegmentReturnType	head (Index n)

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

SegmentReturnType	tail (Index n)

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

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

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

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

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

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

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

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

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

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

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

template<typename CustomNullaryOp >
EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, Derived >	NullaryExpr (Index size, const CustomNullaryOp &func)

template<typename CustomNullaryOp >
EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, Derived >	NullaryExpr (const CustomNullaryOp &func)

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

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

Public Member Functions inherited from Eigen::internal::special_scalar_op_base< Derived, internal::traits< Derived >::Scalar, NumTraits< internal::traits< Derived >::Scalar >::Real, DenseCoeffsBase< Derived > >
void	operator* () const

Static Public Member Functions
static const IdentityReturnType	Identity ()

static const IdentityReturnType	Identity (Index rows, Index cols)

static const BasisReturnType	Unit (Index size, Index i)

static const BasisReturnType	Unit (Index i)

static const BasisReturnType	UnitX ()

static const BasisReturnType	UnitY ()

static const BasisReturnType	UnitZ ()

static const BasisReturnType	UnitW ()

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

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

static const ConstantReturnType	Constant (const Scalar &value)

static const SequentialLinSpacedReturnType	LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
	Sets a linearly space vector. More...

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

static const SequentialLinSpacedReturnType	LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
	Sets a linearly space vector. More...

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

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

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

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

static const ConstantReturnType	Zero (Index rows, Index cols)

static const ConstantReturnType	Zero (Index size)

static const ConstantReturnType	Zero ()

static const ConstantReturnType	Ones (Index rows, Index cols)

static const ConstantReturnType	Ones (Index size)

static const ConstantReturnType	Ones ()

static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Derived >	Random (Index rows, Index cols)

static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Derived >	Random (Index size)

static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Derived >	Random ()

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

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

Protected Member Functions inherited from Eigen::DenseBase< Derived >
template<typename OtherDerived >
void	checkTransposeAliasing (const OtherDerived &other) const

	DenseBase ()
	Default constructor. More...

Friends
const ScalarMultipleReturnType	operator* (const Scalar &scalar, const StorageBaseType &matrix)

const CwiseUnaryOp< internal::scalar_multiple2_op< Scalar, std::complex< Scalar > >, const Derived >	operator* (const std::complex< Scalar > &scalar, const StorageBaseType &matrix)

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 Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN.

See also: The class hierarchy

Member Typedef Documentation

§ PlainObject

template<typename Derived>

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

The plain matrix type corresponding to this expression.

This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.

Member Function Documentation

§ adjoint()

template<typename Derived >

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

inline

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

Example:

Output:

Warning: If you want to replace a matrix by its own adjoint, do NOT do this:
m = m.adjoint(); // bug!!! caused by aliasing effect
Instead, use the adjointInPlace() method:
m.adjointInPlace();
which gives Eigen good opportunities for optimization, or alternatively you can also do:
m = m.adjoint().eval();

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

§ adjointInPlace()

template<typename Derived >

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

inline

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

Thus, doing

m.adjointInPlace();

has the same effect on m as doing

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

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

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

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

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

§ applyHouseholderOnTheLeft()

template<typename Derived >

template<typename EssentialPart >

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

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

On input:

Parameters

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

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

§ applyHouseholderOnTheRight()

template<typename Derived >

template<typename EssentialPart >

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

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

On input:

Parameters

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

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

§ applyOnTheLeft() [1/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by other * *this.

Example:

Output:

§ applyOnTheLeft() [2/2]

template<typename Derived >

template<typename OtherScalar >

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

inline

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

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

§ applyOnTheRight()

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by *this * other.

It is equivalent to MatrixBase::operator*=().

Example:

Output:

§ array()

template<typename Derived>

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

inline

Returns: an Array expression of this matrix

See also: ArrayBase::matrix()

§ asDiagonal()

template<typename Derived >

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

inline

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

Example:

Output:

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

§ binaryExpr()

template<typename Derived>

template<typename CustomBinaryOp , typename OtherDerived >

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

inline

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

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

See also: class CwiseBinaryOp, operator-=()

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

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

See also: class CwiseBinaryOp, operator+=()

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

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

Here is an example illustrating the use of custom functors:

Output:

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

§ blueNorm()

template<typename Derived >

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

inline

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

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

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

§ cast()

template<typename Derived>

template<typename NewType >

internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type Eigen::MatrixBase< Derived >::cast ( ) const

inline

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

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

See also: class CwiseUnaryOp

§ colPivHouseholderQr()

template<typename Derived >

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

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

See also: class ColPivHouseholderQR

§ 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

Computation of matrix inverse and determinant, with invertibility check.

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

Parameters

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

Example:

Output:

See also: inverse(), computeInverseWithCheck()

§ 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

Computation of matrix inverse, with invertibility check.

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

Parameters

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

Example:

Output:

See also: inverse(), computeInverseAndDetWithCheck()

§ conjugate()

template<typename Derived>

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

inline

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

See also: adjoint()

§ cross()

template<typename Derived>

template<typename OtherDerived >

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

inline

Returns: the cross product of *this and other

Here is a very good explanation of cross-product: http://xkcd.com/199/

See also: MatrixBase::cross3()

§ cross3()

template<typename Derived >

template<typename OtherDerived >

MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::cross3 ( const MatrixBase< OtherDerived > & other ) const

inline

Returns: the cross product of *this and other using only the x, y, and z coefficients

The size of *this and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.

See also: MatrixBase::cross()

§ cwiseAbs()

template<typename Derived>

EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseAbs ( ) const

inline

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

Example:

Output:

See also: cwiseAbs2()

§ cwiseAbs2()

template<typename Derived>

EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const

inline

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

Example:

Output:

See also: cwiseAbs()

§ cwiseEqual() [1/2]

template<typename Derived>

template<typename OtherDerived >

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

inline

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

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

Example:

Output:

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

§ cwiseEqual() [2/2]

template<typename Derived>

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

inline

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

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

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

§ cwiseInverse()

template<typename Derived>

const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseInverse ( ) const

inline

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

Example:

Output:

See also: cwiseProduct()

§ cwiseMax() [1/2]

template<typename Derived>

template<typename OtherDerived >

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

inline

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

Example:

Output:

See also: class CwiseBinaryOp, min()

§ cwiseMax() [2/2]

template<typename Derived>

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

inline

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

See also: class CwiseBinaryOp, min()

§ cwiseMin() [1/2]

template<typename Derived>

template<typename OtherDerived >

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

inline

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

Example:

Output:

See also: class CwiseBinaryOp, max()

§ cwiseMin() [2/2]

template<typename Derived>

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

inline

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

See also: class CwiseBinaryOp, min()

§ cwiseNotEqual()

template<typename Derived>

template<typename OtherDerived >

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

inline

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

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

Example:

Output:

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

§ cwiseQuotient()

template<typename Derived>

template<typename OtherDerived >

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

inline

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

Example:

Output:

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

§ cwiseSqrt()

template<typename Derived>

const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const

inline

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

Example:

Output:

See also: cwisePow(), cwiseSquare()

§ determinant()

template<typename Derived >

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

inline

Returns: the determinant of this matrix

§ diagonal() [1/4]

template<typename Derived >

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

inline

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

*this is not required to be square.

Example:

Output:

See also: class Diagonal

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

*this is not required to be square.

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

Example:

Output:

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

§ diagonal() [2/4]

template<typename Derived >

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

inline

This is the const version of diagonal().

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

§ diagonal() [3/4]

template<typename Derived >

MatrixBase< Derived >::DiagonalDynamicIndexReturnType Eigen::MatrixBase< Derived >::diagonal ( Index index )

inline

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

*this is not required to be square.

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

Example:

Output:

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

§ diagonal() [4/4]

template<typename Derived >

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

inline

This is the const version of diagonal(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.

§ dot()

template<typename Derived >

template<typename OtherDerived >

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

Returns: the dot product of *this with other.

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

See also: squaredNorm(), norm()

§ EIGEN_CWISE_PRODUCT_RETURN_TYPE()

template<typename Derived>

template<typename OtherDerived >

EIGEN_STRONG_INLINE const Eigen::MatrixBase< Derived >::EIGEN_CWISE_PRODUCT_RETURN_TYPE	(	Derived	,
		OtherDerived
	)		const

inline

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

Example:

Output:

See also: class CwiseBinaryOp, cwiseAbs2

§ eigenvalues()

template<typename Derived >

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

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

Output:

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

§ forceAlignedAccess() [1/2]

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(),class ForceAlignedAccess

§ forceAlignedAccess() [2/2]

template<typename Derived >

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(), class ForceAlignedAccess

§ forceAlignedAccessIf() [1/2]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

§ forceAlignedAccessIf() [2/2]

template<typename Derived >

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

§ fullPivHouseholderQr()

template<typename Derived >

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

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

See also: class FullPivHouseholderQR

§ fullPivLu()

template<typename Derived >

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

inline

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

See also: class FullPivLU

§ hnormalized()

template<typename Derived >

const MatrixBase< Derived >::HNormalizedReturnType Eigen::MatrixBase< Derived >::hnormalized ( ) const

inline

Returns: an expression of the homogeneous normalized vector of *this

Example:

Output:

See also: VectorwiseOp::hnormalized()

§ householderQr()

template<typename Derived >

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

Returns: the Householder QR decomposition of *this.

See also: class HouseholderQR

§ hypotNorm()

template<typename Derived >

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

inline

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

See also: norm(), stableNorm()

§ Identity() [1/2]

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( )

static

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

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

Example:

Output:

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

§ Identity() [2/2]

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity	(	Index	nbRows,
		Index	nbCols
	)

static

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

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

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

Example:

Output:

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

§ imag() [1/2]

template<typename Derived>

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

inline

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

See also: real()

§ imag() [2/2]

template<typename Derived>

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

inline

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

See also: real()

§ inverse()

template<typename Derived >

const internal::inverse_impl< Derived > Eigen::MatrixBase< Derived >::inverse ( ) const

inline

Returns: the matrix inverse of this matrix.

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

Note

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

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

Example:

Output:

See also: computeInverseAndDetWithCheck()

§ isDiagonal()

template<typename Derived >

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

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

Example:

Output:

See also: asDiagonal()

§ isIdentity()

template<typename Derived >

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

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

Example:

Output:

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

§ isLowerTriangular()

template<typename Derived >

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

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

See also: isUpperTriangular()

§ isOrthogonal()

template<typename Derived >

template<typename OtherDerived >

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

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

Example:

Output:

§ isUnitary()

template<typename Derived >

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

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

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

Example:

Output:

§ isUpperTriangular()

template<typename Derived >

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

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

See also: isLowerTriangular()

§ jacobiSvd()

template<typename Derived >

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

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

See also: class JacobiSVD

§ lazyProduct()

template<typename Derived >

template<typename OtherDerived >

const LazyProductReturnType< Derived, OtherDerived >::Type Eigen::MatrixBase< Derived >::lazyProduct ( const MatrixBase< OtherDerived > & other ) const

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

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

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

See also: operator*(const MatrixBase&)

§ ldlt()

template<typename Derived >

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

inline

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

§ llt()

template<typename Derived >

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

inline

Returns: the LLT decomposition of *this

§ lpNorm()

template<typename Derived>

template<int p>

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

inline

Returns: the \( \ell^p \) 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.

See also: norm()

§ 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()

§ 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()

§ noalias()

template<typename Derived >

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

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

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

Here are some examples where noalias is usefull:

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

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

A.noalias() = A * B;

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

A = A * B;

See also: class NoAlias

§ norm()

template<typename Derived >

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

inline

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

See also: dot(), squaredNorm()

§ normalize()

template<typename Derived >

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

inline

Normalizes the vector, i.e.

divides it by its own norm.

See also: norm(), normalized()

§ normalized()

template<typename Derived >

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

inline

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

See also: norm(), normalize()

§ 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==

§ operator*() [1/3]

template<typename Derived>

const ScalarMultipleReturnType Eigen::MatrixBase< Derived >::operator* ( const Scalar & scalar ) const

inline

Returns: an expression of *this scaled by the scalar factor scalar

§ operator*() [2/3]

template<typename Derived >

template<typename OtherDerived >

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

inline

Returns: the matrix product of *this and other.

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

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

§ operator*() [3/3]

template<typename Derived >

template<typename DiagonalDerived >

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

inline

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

§ operator*=()

template<typename Derived >

template<typename OtherDerived >

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

inline

replaces *this by *this * other.

Returns: a reference to *this

Example:

Output:

§ operator+=()

template<typename Derived>

template<typename OtherDerived >

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

replaces *this by *this + other.

Returns: a reference to *this

§ operator-()

template<typename Derived>

const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> Eigen::MatrixBase< Derived >::operator- ( ) const

inline

Returns: an expression of the opposite of *this

§ operator-=()

template<typename Derived>

template<typename OtherDerived >

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

replaces *this by *this - other.

Returns: a reference to *this

§ operator/()

template<typename Derived>

const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> Eigen::MatrixBase< Derived >::operator/ ( const Scalar & scalar ) const

inline

Returns: an expression of *this divided by the scalar value scalar

§ 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!=

§ operatorNorm()

template<typename Derived >

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

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

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

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

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

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

Example:

Output:

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

§ partialPivLu()

template<typename Derived >

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

inline

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

See also: class PartialPivLU

§ real() [1/2]

template<typename Derived>

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

inline

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

See also: imag()

§ real() [2/2]

template<typename Derived>

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

inline

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

See also: imag()

§ setIdentity() [1/2]

template<typename Derived >

EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setIdentity ( )

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

Example:

Output:

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

§ setIdentity() [2/2]

template<typename Derived >

EIGEN_STRONG_INLINE Derived & Eigen::MatrixBase< Derived >::setIdentity	(	Index	nbRows,
		Index	nbCols
	)

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

Parameters

nbRows	the new number of rows
nbCols	the new number of columns

Example:

Output:

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

§ squaredNorm()

template<typename Derived >

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

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

See also: dot(), norm()

§ stableNorm()

template<typename Derived >

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

inline

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

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

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

§ trace()

template<typename Derived >

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

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

*this can be any matrix, not necessarily square.

See also: diagonal(), sum()

§ triangularView()

template<typename Derived>

template<unsigned int Mode>

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

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

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

Example:

Output:

See also: class TriangularView

§ unaryExpr()

template<typename Derived>

template<typename CustomUnaryOp >

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

inline

Apply a unary operator coefficient-wise.

Parameters

[in] func Functor implementing the unary operator

Template Parameters

CustomUnaryOp Type of func

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

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

Example:

Output:

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

Example:

Output:

See also: class CwiseUnaryOp, class CwiseBinaryOp

§ unaryViewExpr()

template<typename Derived>

template<typename CustomViewOp >

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

inline

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

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

Example:

Output:

See also: class CwiseUnaryOp, class CwiseBinaryOp

§ Unit() [1/2]

template<typename Derived >

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

static

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

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

§ Unit() [2/2]

template<typename Derived >

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

static

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

This variant is for fixed-size vector only.

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

§ unitOrthogonal()

template<typename Derived >

MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::unitOrthogonal ( void ) const

Returns: a unit vector which is orthogonal to *this

The size of *this must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this, i.e., (-y,x).normalized().

See also: cross()

§ UnitW()

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitW ( )

static

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

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

§ UnitX()

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitX ( )

static

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

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

§ UnitY()

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitY ( )

static

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

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

§ UnitZ()

template<typename Derived >

EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitZ ( )

static

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

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

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

vendor/eigen/Eigen/src/Core/MatrixBase.h
vendor/eigen/Eigen/src/Cholesky/LDLT.h
vendor/eigen/Eigen/src/Cholesky/LLT.h
vendor/eigen/Eigen/src/Core/Assign.h
vendor/eigen/Eigen/src/Core/CwiseBinaryOp.h
vendor/eigen/Eigen/src/Core/CwiseNullaryOp.h
vendor/eigen/Eigen/src/Core/Diagonal.h
vendor/eigen/Eigen/src/Core/DiagonalMatrix.h
vendor/eigen/Eigen/src/Core/DiagonalProduct.h
vendor/eigen/Eigen/src/Core/Dot.h
vendor/eigen/Eigen/src/Core/ForceAlignedAccess.h
vendor/eigen/Eigen/src/Core/GeneralProduct.h
vendor/eigen/Eigen/src/Core/NoAlias.h
vendor/eigen/Eigen/src/Core/PermutationMatrix.h
vendor/eigen/Eigen/src/Core/ProductBase.h
vendor/eigen/Eigen/src/Core/Redux.h
vendor/eigen/Eigen/src/Core/SelfAdjointView.h
vendor/eigen/Eigen/src/Core/StableNorm.h
vendor/eigen/Eigen/src/Core/Transpose.h
vendor/eigen/Eigen/src/Core/TriangularMatrix.h
vendor/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
vendor/eigen/Eigen/src/Geometry/EulerAngles.h
vendor/eigen/Eigen/src/Geometry/Homogeneous.h
vendor/eigen/Eigen/src/Geometry/OrthoMethods.h
vendor/eigen/Eigen/src/Geometry/Scaling.h
vendor/eigen/Eigen/src/Householder/Householder.h
vendor/eigen/Eigen/src/Jacobi/Jacobi.h
vendor/eigen/Eigen/src/LU/Determinant.h
vendor/eigen/Eigen/src/LU/FullPivLU.h
vendor/eigen/Eigen/src/LU/Inverse.h
vendor/eigen/Eigen/src/LU/PartialPivLU.h
vendor/eigen/Eigen/src/QR/ColPivHouseholderQR.h
vendor/eigen/Eigen/src/QR/FullPivHouseholderQR.h
vendor/eigen/Eigen/src/QR/HouseholderQR.h
vendor/eigen/Eigen/src/SparseCore/SparseView.h
vendor/eigen/Eigen/src/SVD/JacobiSVD.h
vendor/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
vendor/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
vendor/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
vendor/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
vendor/eigen/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

§ PlainObject

Member Function Documentation

§ adjoint()

§ adjointInPlace()

§ applyHouseholderOnTheLeft()

§ applyHouseholderOnTheRight()

§ applyOnTheLeft() [1/2]

§ applyOnTheLeft() [2/2]

§ applyOnTheRight()

§ array()

§ asDiagonal()

§ binaryExpr()

§ blueNorm()

§ cast()

§ colPivHouseholderQr()

§ computeInverseAndDetWithCheck()

§ computeInverseWithCheck()

§ conjugate()

§ cross()

§ cross3()

§ cwiseAbs()

§ cwiseAbs2()

§ cwiseEqual() [1/2]

§ cwiseEqual() [2/2]

§ cwiseInverse()

§ cwiseMax() [1/2]

§ cwiseMax() [2/2]

§ cwiseMin() [1/2]

§ cwiseMin() [2/2]

§ cwiseNotEqual()

§ cwiseQuotient()

§ cwiseSqrt()

§ determinant()

§ diagonal() [1/4]

§ diagonal() [2/4]

§ diagonal() [3/4]

§ diagonal() [4/4]

§ diagonalSize()

§ dot()

§ EIGEN_CWISE_PRODUCT_RETURN_TYPE()

§ eigenvalues()

§ forceAlignedAccess() [1/2]

§ forceAlignedAccess() [2/2]

§ forceAlignedAccessIf() [1/2]

§ forceAlignedAccessIf() [2/2]

§ fullPivHouseholderQr()

§ fullPivLu()

§ hnormalized()

§ householderQr()

§ hypotNorm()

§ Identity() [1/2]

§ Identity() [2/2]

§ imag() [1/2]

§ imag() [2/2]

§ inverse()

§ isDiagonal()

§ isIdentity()

§ isLowerTriangular()

§ isOrthogonal()

§ isUnitary()

§ isUpperTriangular()

§ jacobiSvd()

§ lazyProduct()

§ ldlt()

§ llt()

§ lpNorm()

§ makeHouseholder()

§ makeHouseholderInPlace()

§ noalias()

§ norm()

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