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

Inheritance diagram for MatrixBase< Derived >:

Classes
struct	ConstDiagonalIndexReturnType
struct	ConstSelfAdjointViewReturnType
struct	ConstTriangularViewReturnType
struct	DiagonalIndexReturnType
struct	SelfAdjointViewReturnType
struct	TriangularViewReturnType
Public Types
enum	{ RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor, InnerSizeAtCompileTime, CoeffReadCost, InnerStrideAtCompileTime, OuterStrideAtCompileTime }
enum	{ ThisConstantIsPrivateInPlainObjectBase }
enum	{ HomogeneousReturnTypeDirection }
enum	{ SizeMinusOne }
typedef DenseCoeffsBase< Derived >	Base
typedef Base::CoeffReturnType	CoeffReturnType
typedef VectorwiseOp< Derived, Vertical >	ColwiseReturnType
typedef const VectorwiseOp < const Derived, Vertical >	ConstColwiseReturnType
typedef const Diagonal< const Derived >	ConstDiagonalReturnType
typedef const Reverse< const Derived, BothDirections >	ConstReverseReturnType
typedef const VectorwiseOp < const Derived, Horizontal >	ConstRowwiseReturnType
typedef const VectorBlock < const Derived >	ConstSegmentReturnType
typedef Block< const Derived, internal::traits< Derived > ::ColsAtCompileTime==1?SizeMinusOne:1, internal::traits< Derived > ::ColsAtCompileTime==1?1:SizeMinusOne >	ConstStartMinusOne
typedef const Transpose< const Derived >	ConstTransposeReturnType
typedef Diagonal< Derived >	DiagonalReturnType
typedef internal::add_const_on_value_type < typename internal::eval < Derived >::type >::type	EvalReturnType
typedef CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const ConstStartMinusOne >	HNormalizedReturnType
typedef Homogeneous< Derived, HomogeneousReturnTypeDirection >	HomogeneousReturnType
typedef internal::traits < Derived >::Index	Index
	The type of indices.
typedef internal::packet_traits < Scalar >::type	PacketScalar
typedef Matrix< typename internal::traits< Derived > ::Scalar, internal::traits < Derived >::RowsAtCompileTime, internal::traits< Derived > ::ColsAtCompileTime, AutoAlign\|(internal::traits < Derived >::Flags &RowMajorBit?RowMajor:ColMajor), internal::traits< Derived > ::MaxRowsAtCompileTime, internal::traits< Derived > ::MaxColsAtCompileTime >	PlainObject
	The plain matrix type corresponding to this expression.
typedef NumTraits< Scalar >::Real	RealScalar
typedef Reverse< Derived, BothDirections >	ReverseReturnType
typedef VectorwiseOp< Derived, Horizontal >	RowwiseReturnType
typedef internal::traits < Derived >::Scalar	Scalar
typedef VectorBlock< Derived >	SegmentReturnType
typedef internal::stem_function < Scalar >::type	StemFunction
typedef internal::traits < Derived >::StorageKind	StorageKind
Public Member Functions
const AdjointReturnType	adjoint () const
void	adjointInPlace ()
bool	all (void) const
bool	any (void) const
template<typename EssentialPart >
void	applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename EssentialPart >
void	applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename 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 PermutationWrapper < const Derived >	asPermutation () const
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp < CustomBinaryOp, const Derived, const OtherDerived >	binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
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
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
RealScalar	blueNorm () const
Block< Derived >	bottomLeftCorner (Index cRows, Index cCols)
const Block< const Derived >	bottomLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomLeftCorner ()
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	bottomLeftCorner () const
Block< Derived >	bottomRightCorner (Index cRows, Index cCols)
const Block< const Derived >	bottomRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols >	bottomRightCorner ()
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	bottomRightCorner () const
RowsBlockXpr	bottomRows (Index n)
ConstRowsBlockXpr	bottomRows (Index n) const
template<int N>
NRowsBlockXpr< N >::Type	bottomRows ()
template<int N>
ConstNRowsBlockXpr< N >::Type	bottomRows () const
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
ColXpr	col (Index i)
ConstColXpr	col (Index i) const
const ColPivHouseholderQR < PlainObject >	colPivHouseholderQr () const
ConstColwiseReturnType	colwise () const
ColwiseReturnType	colwise ()
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
ConjugateReturnType	conjugate () const
const MatrixFunctionReturnValue < Derived >	cos () const
const MatrixFunctionReturnValue < Derived >	cosh () const
Index	count () 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
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const Derived >	cwiseAbs () const
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const Derived >	cwiseAbs2 () const
template<typename OtherDerived >
const	CwiseBinaryOp (operator-)(const Eigen
template<typename OtherDerived >
const	CwiseBinaryOp (operator+)(const Eigen
template<typename OtherDerived >
const CwiseBinaryOp < std::equal_to< Scalar > , const Derived, const OtherDerived >	cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < std::binder1st < std::equal_to< Scalar > >, const Derived >	cwiseEqual (const Scalar &s) const
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const Derived >	cwiseInverse () const
template<typename OtherDerived >
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const OtherDerived >	cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const ConstantReturnType >	cwiseMax (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Derived, const OtherDerived >	cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Derived, const ConstantReturnType >	cwiseMin (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp < std::not_equal_to< Scalar > , const Derived, const OtherDerived >	cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp < internal::scalar_product_op < typename internal::traits < Derived >::Scalar, typename internal::traits< OtherDerived > ::Scalar >, const Derived, const OtherDerived >	cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const Derived, const OtherDerived >	cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const Derived >	cwiseSqrt () const
Scalar	determinant () const
DiagonalReturnType	diagonal ()
const ConstDiagonalReturnType	diagonal () const
template<int Index>
DiagonalIndexReturnType< Index > ::Type	diagonal ()
template<int Index>
ConstDiagonalIndexReturnType < Index >::Type	diagonal () const
DiagonalIndexReturnType < Dynamic >::Type	diagonal (Index index)
ConstDiagonalIndexReturnType < Dynamic >::Type	diagonal (Index index) const
Index	diagonalSize () 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
EigenvaluesReturnType	eigenvalues () const
	Computes the eigenvalues of a matrix.
Matrix< Scalar, 3, 1 >	eulerAngles (Index a0, Index a1, Index a2) const
EvalReturnType	eval () const
template<typename Dest >
void	evalTo (Dest &) const
const MatrixExponentialReturnValue < Derived >	exp () const
void	fill (const Scalar &value)
template<unsigned int Added, unsigned int Removed>
const Flagged< Derived, Added, Removed >	flagged () const
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 ()
const WithFormat< Derived >	format (const IOFormat &fmt) const
const FullPivHouseholderQR < PlainObject >	fullPivHouseholderQr () const
const FullPivLU< PlainObject >	fullPivLu () const
SegmentReturnType	head (Index size)
DenseBase::ConstSegmentReturnType	head (Index size) const
template<int Size>
FixedSegmentReturnType< Size > ::Type	head ()
template<int Size>
ConstFixedSegmentReturnType < Size >::Type	head () const
const HNormalizedReturnType	hnormalized () const
HomogeneousReturnType	homogeneous () const
const HouseholderQR< PlainObject >	householderQr () const
RealScalar	hypotNorm () const
const ImagReturnType	imag () const
NonConstImagReturnType	imag ()
Index	innerSize () const
const internal::inverse_impl < Derived >	inverse () const
template<typename OtherDerived >
bool	isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename Derived >
bool	isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const
bool	isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool	isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool	isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool	isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObject >	jacobiSvd (unsigned int computationOptions=0) const
template<typename OtherDerived >
const LazyProductReturnType < Derived, OtherDerived > ::Type	lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObject >	ldlt () const
ColsBlockXpr	leftCols (Index n)
ConstColsBlockXpr	leftCols (Index n) const
template<int N>
NColsBlockXpr< N >::Type	leftCols ()
template<int N>
ConstNColsBlockXpr< N >::Type	leftCols () const
const LLT< PlainObject >	llt () const
const MatrixLogarithmReturnValue < Derived >	log () const
template<int p>
RealScalar	lpNorm () const
const PartialPivLU< PlainObject >	lu () const
template<typename EssentialPart >
void	makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
MatrixBase< Derived > &	matrix ()
const MatrixBase< Derived > &	matrix () const
const MatrixFunctionReturnValue < Derived >	matrixFunction (StemFunction f) const
internal::traits< Derived >::Scalar	maxCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar	maxCoeff (IndexType row, IndexType col) const
template<typename IndexType >
internal::traits< Derived >::Scalar	maxCoeff (IndexType *index) const
Scalar	mean () const
ColsBlockXpr	middleCols (Index startCol, Index numCols)
ConstColsBlockXpr	middleCols (Index startCol, Index numCols) const
template<int N>
NColsBlockXpr< N >::Type	middleCols (Index startCol)
template<int N>
ConstNColsBlockXpr< N >::Type	middleCols (Index startCol) const
RowsBlockXpr	middleRows (Index startRow, Index numRows)
ConstRowsBlockXpr	middleRows (Index startRow, Index numRows) const
template<int N>
NRowsBlockXpr< N >::Type	middleRows (Index startRow)
template<int N>
ConstNRowsBlockXpr< N >::Type	middleRows (Index startRow) const
internal::traits< Derived >::Scalar	minCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar	minCoeff (IndexType row, IndexType col) const
template<typename IndexType >
internal::traits< Derived >::Scalar	minCoeff (IndexType *index) const
const NestByValue< Derived >	nestByValue () const
NoAlias< Derived, Eigen::MatrixBase >	noalias ()
Index	nonZeros () const
RealScalar	norm () const
void	normalize ()
const PlainObject	normalized () const
template<typename OtherDerived >
bool	operator!= (const MatrixBase< OtherDerived > &other) const
const ScalarMultipleReturnType	operator* (const Scalar &scalar) const
const ScalarMultipleReturnType	operator* (const RealScalar &scalar) const
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Derived >	operator* (const std::complex< Scalar > &scalar) const
template<typename OtherDerived >
const ProductReturnType < Derived, OtherDerived > ::Type	operator* (const MatrixBase< OtherDerived > &other) const
template<typename DiagonalDerived >
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight >	operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
ScalarMultipleReturnType	operator* (const UniformScaling< Scalar > &s) const
template<typename OtherDerived >
Derived &	operator*= (const EigenBase< OtherDerived > &other)
Derived &	operator*= (const Scalar &other)
template<typename OtherDerived >
Derived &	operator+= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Derived &	operator+= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < Derived >::Scalar >, const Derived >	operator- () const
template<typename OtherDerived >
Derived &	operator-= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Derived &	operator-= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const Derived >	operator/ (const Scalar &scalar) const
Derived &	operator/= (const Scalar &other)
CommaInitializer< Derived >	operator<< (const Scalar &s)
template<typename OtherDerived >
CommaInitializer< Derived >	operator<< (const DenseBase< OtherDerived > &other)
Derived &	operator= (const MatrixBase &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.
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.
Index	outerSize () const
const PartialPivLU< PlainObject >	partialPivLu () const
Scalar	prod () const
RealReturnType	real () const
NonConstRealReturnType	real ()
template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor >	replicate () const
const Replicate< Derived, Dynamic, Dynamic >	replicate (Index rowFacor, Index colFactor) const
void	resize (Index size)
void	resize (Index rows, Index cols)
ReverseReturnType	reverse ()
ConstReverseReturnType	reverse () const
void	reverseInPlace ()
ColsBlockXpr	rightCols (Index n)
ConstColsBlockXpr	rightCols (Index n) const
template<int N>
NColsBlockXpr< N >::Type	rightCols ()
template<int N>
ConstNColsBlockXpr< N >::Type	rightCols () const
RowXpr	row (Index i)
ConstRowXpr	row (Index i) const
ConstRowwiseReturnType	rowwise () const
RowwiseReturnType	rowwise ()
SegmentReturnType	segment (Index start, Index size)
DenseBase::ConstSegmentReturnType	segment (Index start, Index size) const
template<int Size>
FixedSegmentReturnType< Size > ::Type	segment (Index start)
template<int Size>
ConstFixedSegmentReturnType < Size >::Type	segment (Index start) const
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, typename ThenDerived::Scalar elseScalar) const
template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived >	select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
template<unsigned int UpLo>
SelfAdjointViewReturnType < UpLo >::Type	selfadjointView ()
template<unsigned int UpLo>
ConstSelfAdjointViewReturnType < UpLo >::Type	selfadjointView () const
Derived &	setConstant (const Scalar &value)
Derived &	setIdentity ()
Derived &	setIdentity (Index rows, Index cols)
	Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
Derived &	setLinSpaced (Index size, const Scalar &low, const Scalar &high)
	Sets a linearly space vector.
Derived &	setLinSpaced (const Scalar &low, const Scalar &high)
Derived &	setOnes ()
Derived &	setRandom ()
Derived &	setZero ()
const MatrixFunctionReturnValue < Derived >	sin () const
const MatrixFunctionReturnValue < Derived >	sinh () const
const SparseView< Derived >	sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const
const MatrixSquareRootReturnValue < Derived >	sqrt () const
RealScalar	squaredNorm () const
RealScalar	stableNorm () const
Scalar	sum () const
template<typename OtherDerived >
void	swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
template<typename OtherDerived >
void	swap (PlainObjectBase< OtherDerived > &other)
SegmentReturnType	tail (Index size)
DenseBase::ConstSegmentReturnType	tail (Index size) const
template<int Size>
FixedSegmentReturnType< Size > ::Type	tail ()
template<int Size>
ConstFixedSegmentReturnType < Size >::Type	tail () const
Block< Derived >	topLeftCorner (Index cRows, Index cCols)
const Block< const Derived >	topLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topLeftCorner ()
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	topLeftCorner () const
Block< Derived >	topRightCorner (Index cRows, Index cCols)
const Block< const Derived >	topRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols >	topRightCorner ()
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols >	topRightCorner () const
RowsBlockXpr	topRows (Index n)
ConstRowsBlockXpr	topRows (Index n) const
template<int N>
NRowsBlockXpr< N >::Type	topRows ()
template<int N>
ConstNRowsBlockXpr< N >::Type	topRows () const
Scalar	trace () const
Eigen::Transpose< Derived >	transpose ()
ConstTransposeReturnType	transpose () const
void	transposeInPlace ()
template<unsigned int Mode>
TriangularViewReturnType< Mode > ::Type	triangularView ()
template<unsigned int Mode>
ConstTriangularViewReturnType < Mode >::Type	triangularView () const
template<typename CustomUnaryOp >
const CwiseUnaryOp < CustomUnaryOp, const Derived >	unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
	Apply a unary operator coefficient-wise.
template<typename CustomViewOp >
const CwiseUnaryView < CustomViewOp, const Derived >	unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
PlainObject	unitOrthogonal (void) const
CoeffReturnType	value () const
template<typename Visitor >
void	visit (Visitor &func) const
Static Public Member Functions
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 IdentityReturnType	Identity ()
static const IdentityReturnType	Identity (Index rows, Index cols)
static const SequentialLinSpacedReturnType	LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
	Sets a linearly space vector.
static const RandomAccessLinSpacedReturnType	LinSpaced (Index size, const Scalar &low, const Scalar &high)
	Sets a linearly space vector.
static const SequentialLinSpacedReturnType	LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static const RandomAccessLinSpacedReturnType	LinSpaced (const Scalar &low, const Scalar &high)
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	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 ()
static const BasisReturnType	Unit (Index size, Index i)
static const BasisReturnType	Unit (Index i)
static const BasisReturnType	UnitW ()
static const BasisReturnType	UnitX ()
static const BasisReturnType	UnitY ()
static const BasisReturnType	UnitZ ()
static const ConstantReturnType	Zero (Index rows, Index cols)
static const ConstantReturnType	Zero (Index size)
static const ConstantReturnType	Zero ()
Protected Member Functions
template<typename OtherDerived >
void	checkTransposeAliasing (const OtherDerived &other) const
	MatrixBase ()
template<typename OtherDerived >
Derived &	operator+= (const ArrayBase< OtherDerived > &)
template<typename OtherDerived >
Derived &	operator-= (const ArrayBase< OtherDerived > &)
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)
Related Functions
(Note that these are not member functions.)
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

typedef DenseCoeffsBase<Derived> Base [inherited]

typedef Base::CoeffReturnType CoeffReturnType [inherited]

typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType [inherited]

typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType [inherited]

typedef const Diagonal<const Derived> ConstDiagonalReturnType

typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType [inherited]

typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType [inherited]

typedef const VectorBlock<const Derived> ConstSegmentReturnType [inherited]

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

typedef const Transpose<const Derived> ConstTransposeReturnType [inherited]

typedef Diagonal<Derived> DiagonalReturnType

typedef internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType [inherited]

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

typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType

typedef internal::traits<Derived>::Index Index [inherited]

The type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also:: Preprocessor directives.

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

typedef internal::packet_traits<Scalar>::type PacketScalar [inherited]

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

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.

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&.

typedef NumTraits<Scalar>::Real RealScalar [inherited]

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

typedef Reverse<Derived, BothDirections> ReverseReturnType [inherited]

typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType [inherited]

typedef internal::traits<Derived>::Scalar Scalar [inherited]

Reimplemented in ScaledProduct< NestedProduct >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

typedef VectorBlock<Derived> SegmentReturnType [inherited]

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

typedef internal::traits<Derived>::StorageKind StorageKind [inherited]

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

Member Enumeration Documentation

anonymous enum [inherited]

Enumerator:

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

anonymous enum [inherited]

Enumerator:

ThisConstantIsPrivateInPlainObjectBase

anonymous enum

Enumerator:

HomogeneousReturnTypeDirection

anonymous enum

Enumerator:

SizeMinusOne

Constructor & Destructor Documentation

MatrixBase ( ) [inline, protected]

Member Function Documentation

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

void 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.

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

bool all ( void ) const [inline, inherited]

Returns:: true if all coefficients are true

Example:

Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());
Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();
// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:
cout << "Is (" << p0.transpose() << ") inside the box: "
     << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;
cout << "Is (" << p1.transpose() << ") inside the box: "
     << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;

Output:

Is (  0.68 -0.211  0.566) inside the box: 0
Is (0.597 0.823 0.605) inside the box: 1

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

bool any ( void ) const [inline, inherited]

Returns:: true if at least one coefficient is true

See also:: all()

void applyHouseholderOnTheLeft	(	const EssentialPart &	essential,
		const Scalar &	tau,
		Scalar *	workspace
	)

void applyHouseholderOnTheRight	(	const EssentialPart &	essential,
		const Scalar &	tau,
		Scalar *	workspace
	)

void applyOnTheLeft ( const EigenBase< OtherDerived > & other ) [inline]

replaces *this by *this * other.

void applyOnTheLeft	(	Index	p,
		Index	q,
		const JacobiRotation< OtherScalar > &	j
	)		`[inline]`

This is defined in the Jacobi module.

 #include <Eigen/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()

void applyOnTheRight ( const EigenBase< OtherDerived > & other ) [inline]

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

ArrayWrapper<Derived> array ( ) [inline]

Returns:: an Array expression of this matrix

See also:: ArrayBase::matrix()

const ArrayWrapper<const Derived> array ( ) const [inline]

const DiagonalWrapper< const Derived > asDiagonal ( ) const [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;

Output:

2 0 0
0 5 0
0 0 6

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

const PermutationWrapper< const Derived > asPermutation ( ) const

const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> binaryExpr	(	const Eigen::MatrixBase< OtherDerived > &	other,
		const CustomBinaryOp &	func = `CustomBinaryOp()`
	)		const `[inline]`

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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template binary functor
template<typename Scalar> struct MakeComplexOp {
  EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)
  typedef complex<Scalar> result_type;
  complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
  cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;
  return 0;
}

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)

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

Block<Derived> block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		`[inline, inherited]`

Returns:: a dynamic-size expression of a block in *this.

Parameters:

startRow	the first row in the block
startCol	the first column in the block
blockRows	the number of rows in the block
blockCols	the number of columns in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
m.block(1, 1, 2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6 1
-3 0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9

Note:: Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See also:: class Block, block(Index,Index)

Referenced by main().

const Block<const Derived> block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		const `[inline, inherited]`

This is the const version of block(Index,Index,Index,Index).

Block<Derived, BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol
	)		`[inline, inherited]`

Returns:: a fixed-size expression of a block in *this.

The template parameters BlockRows and BlockCols are the number of rows and columns in the block.

Parameters:

startRow	the first row in the block
startCol	the first column in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
m.block<2,2>(1,1).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6 1
-3 0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9

Note:

since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:

 m.template block<3,3>(1,1);

See also:: class Block, block(Index,Index,Index,Index)

const Block<const Derived, BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol
	)		const `[inline, inherited]`

This is the const version of block<>(Index, Index).

NumTraits< typename internal::traits< Derived >::Scalar >::Real 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()

Block<Derived> bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

Returns:: a dynamic-size expression of a bottom-left corner of *this.

Parameters:

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
cout << m.bottomLeftCorner(2, 2) << endl;
m.bottomLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9

See also:: class Block, block(Index,Index,Index,Index)

const Block<const Derived> bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

This is the const version of bottomLeftCorner(Index, Index).

Block<Derived, CRows, CCols> bottomLeftCorner ( ) [inline, inherited]

Returns:: an expression of a fixed-size bottom-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
cout << m.bottomLeftCorner<2,2>() << endl;
m.bottomLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9

See also:: class Block, block(Index,Index,Index,Index)

const Block<const Derived, CRows, CCols> bottomLeftCorner ( ) const [inline, inherited]

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

Block<Derived> bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

Returns:: a dynamic-size expression of a bottom-right corner of *this.

Parameters:

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner(2, 2):" << endl;
cout << m.bottomRightCorner(2, 2) << endl;
m.bottomRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0

See also:: class Block, block(Index,Index,Index,Index)

const Block<const Derived> bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

This is the const version of bottomRightCorner(Index, Index).

Block<Derived, CRows, CCols> bottomRightCorner ( ) [inline, inherited]

Returns:: an expression of a fixed-size bottom-right corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,2>():" << endl;
cout << m.bottomRightCorner<2,2>() << endl;
m.bottomRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0

See also:: class Block, block(Index,Index,Index,Index)

const Block<const Derived, CRows, CCols> bottomRightCorner ( ) const [inline, inherited]

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

RowsBlockXpr bottomRows ( Index n ) [inline, inherited]

Returns:: a block consisting of the bottom rows of *this.

Parameters:

n	the number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows(2):" << endl;
cout << a.bottomRows(2) << endl;
a.bottomRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0

See also:: class Block, block(Index,Index,Index,Index)

ConstRowsBlockXpr bottomRows ( Index n ) const [inline, inherited]

This is the const version of bottomRows(Index).

NRowsBlockXpr<N>::Type bottomRows ( ) [inline, inherited]

Returns:: a block consisting of the bottom rows of *this.

Template Parameters:

N	the number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows<2>():" << endl;
cout << a.bottomRows<2>() << endl;
a.bottomRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0

See also:: class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type bottomRows ( ) const [inline, inherited]

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

internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type 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

void checkTransposeAliasing ( const OtherDerived & other ) const [protected, inherited]

ColXpr col ( Index i ) [inline, inherited]

Returns:: an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

Matrix3d m = Matrix3d::Identity();
m.col(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 4 0
0 5 0
0 6 1

See also:: row(), class Block

Referenced by main().

ConstColXpr col ( Index i ) const [inline, inherited]

This is the const version of col().

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

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

See also:: class ColPivHouseholderQR

const DenseBase< Derived >::ConstColwiseReturnType colwise ( ) const [inline, inherited]

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

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl;
cout << "Here is the maximum absolute value of each column:"
     << endl << m.cwiseAbs().colwise().maxCoeff() << 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
Here is the sum of each column:
  1.04  0.815 -0.238
Here is the maximum absolute value of each column:
 0.68 0.823 0.536

See also:: rowwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting

Referenced by main().

DenseBase< Derived >::ColwiseReturnType colwise ( ) [inline, inherited]

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

See also:: rowwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting

void 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>

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 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;
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()

void 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.

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()

ConjugateReturnType conjugate ( ) const [inline]

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

See also:: adjoint()

const DenseBase< Derived >::ConstantReturnType Constant	(	Index	rows,
		Index	cols,
		const Scalar &	value
	)		`[inline, static, inherited]`

Returns:: an expression of a constant matrix of value value

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const DenseBase< Derived >::ConstantReturnType Constant	(	Index	size,
		const Scalar &	value
	)		`[inline, static, inherited]`

Returns:: an expression of a constant matrix of value value

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const DenseBase< Derived >::ConstantReturnType Constant ( const Scalar & value ) [inline, static, inherited]

Returns:: an expression of a constant matrix of value value

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const MatrixFunctionReturnValue<Derived> cos ( ) const

Referenced by main().

const MatrixFunctionReturnValue<Derived> cosh ( ) const

DenseBase< Derived >::Index count ( ) const [inline, inherited]

Returns:: the number of coefficients which evaluate to true

See also:: all(), any()

MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross ( const MatrixBase< OtherDerived > & other ) const [inline]

This is defined in the Geometry module.

 #include <Eigen/Geometry>

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()

MatrixBase< Derived >::PlainObject cross3 ( const MatrixBase< OtherDerived > & other ) const [inline]

This is defined in the Geometry module.

 #include <Eigen/Geometry>

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()

const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> cwiseAbs ( ) const [inline]

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

Example:

MatrixXd m(2,3);
m << 2, -4, 6,   
     -5, 1, 0;
cout << m.cwiseAbs() << endl;

Output:

2 4 6
5 1 0

See also:: cwiseAbs2()

const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> cwiseAbs2 ( ) const [inline]

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

Example:

MatrixXd m(2,3);
m << 2, -4, 6,   
     -5, 1, 0;
cout << m.cwiseAbs2() << endl;

Output:

 4 16 36
25  1  0

See also:: cwiseAbs()

const CwiseBinaryOp ( operator- ) 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-=()

const CwiseBinaryOp ( operator+ ) const [inline]

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+=()

const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> cwiseEqual ( const Eigen::MatrixBase< 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:

MatrixXi m(2,2);
m << 1, 0,
     1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are equal: " << count << endl;

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3

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

const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const 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

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

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

Example:

MatrixXd m(2,3);
m << 2, 0.5, 1,   
     3, 0.25, 1;
cout << m.cwiseInverse() << endl;

Output:

0.5 2 1
0.333 4 1

See also:: cwiseProduct()

const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> cwiseMax ( const Eigen::MatrixBase< OtherDerived > & other ) const [inline]

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

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMax(w) << endl;

Output:

4
3
4

See also:: class CwiseBinaryOp, min()

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

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

See also:: class CwiseBinaryOp, min()

const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> cwiseMin ( const Eigen::MatrixBase< OtherDerived > & other ) const [inline]

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

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMin(w) << endl;

Output:

2
2
3

See also:: class CwiseBinaryOp, max()

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

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

See also:: class CwiseBinaryOp, min()

const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> cwiseNotEqual ( const Eigen::MatrixBase< 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:

MatrixXi m(2,2);
m << 1, 0,
     1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are not equal: " << count << endl;

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1

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

const CwiseBinaryOp< internal::scalar_product_op< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >, const Derived , const OtherDerived > cwiseProduct ( const Eigen::MatrixBase< OtherDerived > & other ) const [inline]

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

Example:

Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random();
Matrix3i c = a.cwiseProduct(b);
cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;

Output:

See also:: class CwiseBinaryOp, cwiseAbs2

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > & other ) const [inline]

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

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseQuotient(w) << endl;

Output:

0.5
1.5
1.33

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

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

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

Example:

Vector3d v(1,2,4);
cout << v.cwiseSqrt() << endl;

Output:

1
1.41
2

See also:: cwisePow(), cwiseSquare()

internal::traits< Derived >::Scalar determinant ( ) const [inline]

This is defined in the LU module.

 #include <Eigen/LU>

Returns:: the determinant of this matrix

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

Referenced by main().

MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type diagonal ( ) const [inline]

This is the const version of diagonal().

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

DiagonalIndexReturnType<Index>::Type diagonal ( )

ConstDiagonalIndexReturnType<Index>::Type diagonal ( ) const

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

MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Dynamic >::Type diagonal ( Index index ) const [inline]

This is the const version of diagonal(Index).

Index diagonalSize ( ) const [inline]

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

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

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

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()

MatrixBase< Derived >::EigenvaluesReturnType eigenvalues ( ) const [inline]

Computes the eigenvalues of a matrix.

Returns:: Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

 #include <Eigen/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()

EvalReturnType eval ( ) const [inline, inherited]

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

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

void evalTo ( Dest & ) const [inline, inherited]

const MatrixExponentialReturnValue<Derived> exp ( ) const

void fill ( const Scalar & value ) [inline, inherited]

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

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

const Flagged< Derived, Added, Removed > flagged ( ) const [inline, inherited]

Returns:: an expression of *this with added and removed flags

This is mostly for internal use.

See also:: class Flagged

const ForceAlignedAccess< Derived > forceAlignedAccess ( ) const [inline]

Returns:: an expression of *this with forced aligned access

See also:: forceAlignedAccessIf(),class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

ForceAlignedAccess< Derived > forceAlignedAccess ( ) [inline]

Returns:: an expression of *this with forced aligned access

See also:: forceAlignedAccessIf(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf ( ) const [inline]

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

See also:: forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf ( ) [inline]

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

See also:: forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

const WithFormat< Derived > format ( const IOFormat & fmt ) const [inline, inherited]

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

See class IOFormat for some examples.

See also:: class IOFormat, class WithFormat

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

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

See also:: class FullPivHouseholderQR

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

DenseBase< Derived >::SegmentReturnType head ( Index size ) [inline, inherited]

Returns:: a dynamic-size expression of the first coefficients of *this.

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.

Parameters:

size	the number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head(2) << endl;
v.head(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6

Note:: Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See also:: class Block, block(Index,Index)

DenseBase< Derived >::ConstSegmentReturnType head ( Index size ) const [inline, inherited]

This is the const version of head(Index).

DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type head ( ) [inline, inherited]

Returns:: a fixed-size expression of the first coefficients of *this.

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.

The template parameter Size is the number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
v.head<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6

See also:: class Block

DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type head ( ) const [inline, inherited]

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

const MatrixBase< Derived >::HNormalizedReturnType hnormalized ( ) const [inline]

This is defined in the Geometry module.

 #include <Eigen/Geometry>

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

Example:

Output:

See also:: VectorwiseOp::hnormalized()

MatrixBase< Derived >::HomogeneousReturnType homogeneous ( ) const [inline]

This is defined in the Geometry module.

 #include <Eigen/Geometry>

Returns:: an expression of the equivalent homogeneous 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.

Example:

Output:

See also:: class Homogeneous

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

Returns:: the Householder QR decomposition of *this.

See also:: class HouseholderQR

NumTraits< typename internal::traits< Derived >::Scalar >::Real 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()

const MatrixBase< Derived >::IdentityReturnType Identity ( ) [inline, 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:

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()

const MatrixBase< Derived >::IdentityReturnType Identity	(	Index	rows,
		Index	cols
	)		`[inline, static]`

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

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

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

Example:

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

Output:

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

const ImagReturnType imag ( ) const [inline]

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

See also:: real()

NonConstImagReturnType imag ( ) [inline]

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

See also:: real()

Index innerSize ( ) const [inline, inherited]

Returns:: the inner size.

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

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

bool isApprox	(	const DenseBase< OtherDerived > &	other,
		RealScalar	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const `[inherited]`

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

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

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

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

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

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

This is just an alias for isApproxToConstant().

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

bool isDiagonal ( 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()

bool isIdentity ( 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()

bool isLowerTriangular ( 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()

bool isMuchSmallerThan	(	const typename NumTraits< Scalar >::Real &	other,
		RealScalar	prec
	)		const `[inherited]`

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

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

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

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

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

bool isMuchSmallerThan	(	const DenseBase< OtherDerived > &	other,
		RealScalar	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const `[inherited]`

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

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

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

bool isOnes ( RealScalar prec = NumTraits<Scalar>::dummy_precision() ) const [inherited]

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

Example:

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

Output:

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

See also:: class CwiseNullaryOp, Ones()

bool isOrthogonal	(	const MatrixBase< OtherDerived > &	other,
		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

bool isUnitary ( 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

bool isUpperTriangular ( 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()

bool isZero ( RealScalar prec = NumTraits<Scalar>::dummy_precision() ) const [inherited]

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

Example:

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

Output:

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

See also:: class CwiseNullaryOp, Zero()

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

const LazyProductReturnType< Derived, OtherDerived >::Type 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&)

const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt ( ) const [inline]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky>

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

ColsBlockXpr leftCols ( Index n ) [inline, inherited]

Returns:: a block consisting of the left columns of *this.

Parameters:

n	the number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols(2):" << endl;
cout << a.leftCols(2) << endl;
a.leftCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9

See also:: class Block, block(Index,Index,Index,Index)

ConstColsBlockXpr leftCols ( Index n ) const [inline, inherited]

This is the const version of leftCols(Index).

NColsBlockXpr<N>::Type leftCols ( ) [inline, inherited]

Returns:: a block consisting of the left columns of *this.

Template Parameters:

N	the number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols<2>():" << endl;
cout << a.leftCols<2>() << endl;
a.leftCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9

See also:: class Block, block(Index,Index,Index,Index)

ConstNColsBlockXpr<N>::Type leftCols ( ) const [inline, inherited]

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

const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced	(	Sequential_t	,
		Index	size,
		const Scalar &	low,
		const Scalar &	high
	)		`[inline, static, inherited]`

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.

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 << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

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

const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced	(	Index	size,
		const Scalar &	low,
		const Scalar &	high
	)		`[inline, static, inherited]`

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high].

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 << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

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

const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced	(	Sequential_t	,
		const Scalar &	low,
		const Scalar &	high
	)		`[inline, static, inherited]`

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.

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 << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

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

Special version for fixed size types which does not require the size parameter.

const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced	(	const Scalar &	low,
		const Scalar &	high
	)		`[inline, static, inherited]`

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high].

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 << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

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

Special version for fixed size types which does not require the size parameter.

const LLT< typename MatrixBase< Derived >::PlainObject > llt ( ) const [inline]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky>

Returns:: the LLT decomposition of *this

const MatrixLogarithmReturnValue<Derived> log ( ) const

NumTraits< typename internal::traits< Derived >::Scalar >::Real 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()

Reimplemented from DenseBase< Derived >.

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

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] $

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()

void makeHouseholderInPlace	(	Scalar &	tau,
		RealScalar &	beta
	)

MatrixBase<Derived>& matrix ( ) [inline]

const MatrixBase<Derived>& matrix ( ) const [inline]

const MatrixFunctionReturnValue<Derived> matrixFunction ( StemFunction f ) const

internal::traits< Derived >::Scalar maxCoeff ( ) const [inline, inherited]

Returns:: the maximum of all coefficients of *this

internal::traits< Derived >::Scalar maxCoeff	(	IndexType *	row,
		IndexType *	col
	)		const `[inherited]`

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

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

internal::traits< Derived >::Scalar maxCoeff ( IndexType * index ) const [inherited]

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

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

internal::traits< Derived >::Scalar mean ( ) const [inline, inherited]

Returns:: the mean of all coefficients of *this

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

ColsBlockXpr middleCols	(	Index	startCol,
		Index	numCols
	)		`[inline, inherited]`

Returns:: a block consisting of a range of columns of *this.

Parameters:

startCol	the index of the first column in the block
numCols	the number of columns in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl;
    return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2

See also:: class Block, block(Index,Index,Index,Index)

ConstColsBlockXpr middleCols	(	Index	startCol,
		Index	numCols
	)		const `[inline, inherited]`

This is the const version of middleCols(Index,Index).

NColsBlockXpr<N>::Type middleCols ( Index startCol ) [inline, inherited]

Returns:: a block consisting of a range of columns of *this.

Template Parameters:

N	the number of columns in the block

Parameters:

startCol the index of the first column in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl;
    return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2

See also:: class Block, block(Index,Index,Index,Index)

ConstNColsBlockXpr<N>::Type middleCols ( Index startCol ) const [inline, inherited]

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

RowsBlockXpr middleRows	(	Index	startRow,
		Index	numRows
	)		`[inline, inherited]`

Returns:: a block consisting of a range of rows of *this.

Parameters:

startRow	the index of the first row in the block
numRows	the number of rows in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl;
    return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6

See also:: class Block, block(Index,Index,Index,Index)

ConstRowsBlockXpr middleRows	(	Index	startRow,
		Index	numRows
	)		const `[inline, inherited]`

This is the const version of middleRows(Index,Index).

NRowsBlockXpr<N>::Type middleRows ( Index startRow ) [inline, inherited]

Returns:: a block consisting of a range of rows of *this.

Template Parameters:

N	the number of rows in the block

Parameters:

startRow the index of the first row in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl;
    return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6

See also:: class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type middleRows ( Index startRow ) const [inline, inherited]

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

internal::traits< Derived >::Scalar minCoeff ( ) const [inline, inherited]

Returns:: the minimum of all coefficients of *this

internal::traits< Derived >::Scalar minCoeff	(	IndexType *	row,
		IndexType *	col
	)		const `[inherited]`

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

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

internal::traits< Derived >::Scalar minCoeff ( IndexType * index ) const [inherited]

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

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

const NestByValue< Derived > nestByValue ( ) const [inline, inherited]

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

NoAlias< Derived, MatrixBase > 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

Index nonZeros ( ) const [inline, inherited]

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

NumTraits< typename internal::traits< Derived >::Scalar >::Real 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()

void 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.

See also:: norm(), normalized()

const MatrixBase< Derived >::PlainObject normalized ( ) const [inline]

Returns:: an expression of the quotient of *this 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.

See also:: norm(), normalize()

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr	(	Index	rows,
		Index	cols,
		const CustomNullaryOp &	func
	)		`[inline, static, inherited]`

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

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr	(	Index	size,
		const CustomNullaryOp &	func
	)		`[inline, static, inherited]`

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

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( const CustomNullaryOp & func ) [inline, static, inherited]

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:: class CwiseNullaryOp

const DenseBase< Derived >::ConstantReturnType Ones	(	Index	rows,
		Index	cols
	)		`[inline, static, inherited]`

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

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

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

Example:

cout << MatrixXi::Ones(2,3) << endl;

Output:

1 1 1
1 1 1

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

const DenseBase< Derived >::ConstantReturnType Ones ( Index size ) [inline, static, inherited]

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

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

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

Example:

cout << 6 * RowVectorXi::Ones(4) << endl;
cout << VectorXf::Ones(2) << endl;

Output:

6 6 6 6
1
1

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

const DenseBase< Derived >::ConstantReturnType Ones ( ) [inline, static, inherited]

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

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

Example:

cout << Matrix2d::Ones() << endl;
cout << 6 * RowVector4i::Ones() << endl;

Output:

1 1
1 1
6 6 6 6

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

bool 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==

const ScalarMultipleReturnType operator* ( const Scalar & scalar ) const [inline]

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

const ScalarMultipleReturnType operator* ( const RealScalar & scalar ) const

const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> operator* ( const std::complex< Scalar > & scalar ) const [inline]

Overloaded for efficient real matrix times complex scalar value

const ProductReturnType< Derived, OtherDerived >::Type 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*()

const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* ( const DiagonalBase< DiagonalDerived > & diagonal ) const [inline]

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

MatrixBase< Derived >::ScalarMultipleReturnType operator* ( const UniformScaling< Scalar > & s ) const

Concatenates a linear transformation matrix and a uniform scaling

Derived & operator*= ( const EigenBase< OtherDerived > & other ) [inline]

replaces *this by *this * other.

Returns:: a reference to *this

Derived & operator*= ( const Scalar & other ) [inline, inherited]

Derived & operator+= ( const MatrixBase< OtherDerived > & other ) [inline]

replaces *this by *this + other.

Returns:: a reference to *this

Derived & operator+= ( const EigenBase< OtherDerived > & other ) [inherited]

Derived& operator+= ( const ArrayBase< OtherDerived > & ) [inline, protected]

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

Returns:: an expression of the opposite of *this

Derived & operator-= ( const MatrixBase< OtherDerived > & other ) [inline]

replaces *this by *this - other.

Returns:: a reference to *this

Derived & operator-= ( const EigenBase< OtherDerived > & other ) [inherited]

Derived& operator-= ( const ArrayBase< OtherDerived > & ) [inline, protected]

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

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

Derived & operator/= ( const Scalar & other ) [inline, inherited]

CommaInitializer< Derived > operator<< ( const Scalar & s ) [inline, inherited]

Convenient operator to set the coefficients of a matrix.

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

Example:

Matrix3i m1;
m1 << 1, 2, 3,
      4, 5, 6,
      7, 8, 9;
cout << m1 << endl << endl;
Matrix3i m2 = Matrix3i::Identity();
m2.block(0,0, 2,2) << 10, 11, 12, 13;
cout << m2 << endl << endl;
Vector2i v1;
v1 << 14, 15;
m2 << v1.transpose(), 16,
      v1, m1.block(1,1,2,2);
cout << m2 << endl;

Output:

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

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Detailed Description

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

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