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Eigen::MatrixBase< Derived > Class Template Reference

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

#include <MatrixBase.h>

Inheritance diagram for Eigen::MatrixBase< Derived >:
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Classes

struct  ConstDiagonalIndexReturnType
 
struct  ConstSelfAdjointViewReturnType
 
struct  ConstTriangularViewReturnType
 
struct  cross_product_return_type
 
struct  DiagonalIndexReturnType
 
struct  SelfAdjointViewReturnType
 
struct  TriangularViewReturnType
 

Public Types

enum  { SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1 }
 
typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type AdjointReturnType
 
typedef DenseBase< Derived > Base
 
typedef Block< const CwiseNullaryOp< internal::scalar_identity_op< Scalar >, SquareMatrixType >, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTimeBasisReturnType
 
typedef Base::CoeffReturnType CoeffReturnType
 
typedef Base::ColXpr ColXpr
 
typedef internal::conditional< NumTraits< Scalar >::IsComplex, const CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, const Derived >, const Derived & >::type ConjugateReturnType
 
typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, Derived > ConstantReturnType
 
typedef internal::add_const< Diagonal< const Derived > >::type ConstDiagonalReturnType
 
typedef Block< const Derived, internal::traits< Derived >::ColsAtCompileTime==1?SizeMinusOne:1, internal::traits< Derived >::ColsAtCompileTime==1?1:SizeMinusOneConstStartMinusOne
 
typedef Base::ConstTransposeReturnType ConstTransposeReturnType
 
typedef Diagonal< Derived > DiagonalReturnType
 
typedef Matrix< std::complex< RealScalar >, internal::traits< Derived >::ColsAtCompileTime, 1, ColMajorEigenvaluesReturnType
 
typedef CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< Derived >::Scalar >, const ConstStartMinusOneHNormalizedReturnType
 
typedef CwiseNullaryOp< internal::scalar_identity_op< Scalar >, Derived > IdentityReturnType
 
typedef CwiseUnaryOp< internal::scalar_imag_op< Scalar >, const Derived > ImagReturnType
 
typedef internal::traits< Derived >::Index Index
 
typedef CwiseUnaryView< internal::scalar_imag_ref_op< Scalar >, Derived > NonConstImagReturnType
 
typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryView< internal::scalar_real_ref_op< Scalar >, Derived >, Derived & >::type NonConstRealReturnType
 
typedef internal::packet_traits< Scalar >::type PacketScalar
 
typedef 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 >::MaxColsAtCompileTimePlainObject
 The plain matrix type corresponding to this expression. More...
 
typedef internal::conditional< NumTraits< Scalar >::IsComplex, const CwiseUnaryOp< internal::scalar_real_op< Scalar >, const Derived >, const Derived & >::type RealReturnType
 
typedef NumTraits< Scalar >::Real RealScalar
 
typedef Base::RowXpr RowXpr
 
typedef internal::traits< Derived >::Scalar Scalar
 
typedef CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const Derived > ScalarMultipleReturnType
 
typedef CwiseUnaryOp< internal::scalar_quotient1_op< Scalar >, const Derived > ScalarQuotient1ReturnType
 
typedef Matrix< Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime)> SquareMatrixType
 
typedef internal::stem_function< Scalar >::type StemFunction
 
typedef MatrixBase StorageBaseType
 
typedef internal::traits< Derived >::StorageKind StorageKind
 
- Public Types inherited from Eigen::DenseBase< Derived >
enum  {
  RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
  MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags = internal::traits<Derived>::Flags,
  IsRowMajor = int(Flags) & RowMajorBit, InnerSizeAtCompileTime, CoeffReadCost = internal::traits<Derived>::CoeffReadCost, InnerStrideAtCompileTime = internal::inner_stride_at_compile_time<Derived>::ret,
  OuterStrideAtCompileTime = internal::outer_stride_at_compile_time<Derived>::ret
}
 
enum  { ThisConstantIsPrivateInPlainObjectBase }
 
typedef DenseCoeffsBase< Derived > Base
 
typedef Base::CoeffReturnType CoeffReturnType
 
typedef Block< Derived, internal::traits< Derived >::RowsAtCompileTime, Dynamic,!IsRowMajorColsBlockXpr
 
typedef VectorwiseOp< Derived, VerticalColwiseReturnType
 
typedef Block< Derived, internal::traits< Derived >::RowsAtCompileTime, 1,!IsRowMajorColXpr
 
typedef CwiseNullaryOp< internal::scalar_constant_op< Scalar >, Derived > ConstantReturnType
 
typedef const Block< const Derived, internal::traits< Derived >::RowsAtCompileTime, Dynamic,!IsRowMajorConstColsBlockXpr
 
typedef const VectorwiseOp< const Derived, VerticalConstColwiseReturnType
 
typedef const Block< const Derived, internal::traits< Derived >::RowsAtCompileTime, 1,!IsRowMajorConstColXpr
 
typedef const Reverse< const Derived, BothDirectionsConstReverseReturnType
 
typedef const Block< const Derived, Dynamic, internal::traits< Derived >::ColsAtCompileTime, IsRowMajorConstRowsBlockXpr
 
typedef const VectorwiseOp< const Derived, HorizontalConstRowwiseReturnType
 
typedef const Block< const Derived, 1, internal::traits< Derived >::ColsAtCompileTime, IsRowMajorConstRowXpr
 
typedef const VectorBlock< const Derived > ConstSegmentReturnType
 
typedef internal::add_const< Transpose< const Derived > >::type ConstTransposeReturnType
 
typedef Matrix< typename NumTraits< typename internal::traits< Derived >::Scalar >::Real, internal::traits< Derived >::ColsAtCompileTime, 1 > EigenvaluesReturnType
 
typedef internal::add_const_on_value_type< typename internal::eval< Derived >::type >::type EvalReturnType
 
typedef internal::traits< Derived >::Index Index
 The type of indices. More...
 
typedef internal::packet_traits< Scalar >::type PacketScalar
 
typedef CwiseNullaryOp< internal::linspaced_op< Scalar, true >, Derived > RandomAccessLinSpacedReturnType
 
typedef NumTraits< Scalar >::Real RealScalar
 
typedef Reverse< Derived, BothDirectionsReverseReturnType
 
typedef Block< Derived, Dynamic, internal::traits< Derived >::ColsAtCompileTime, IsRowMajorRowsBlockXpr
 
typedef VectorwiseOp< Derived, HorizontalRowwiseReturnType
 
typedef Block< Derived, 1, internal::traits< Derived >::ColsAtCompileTime, IsRowMajorRowXpr
 
typedef internal::traits< Derived >::Scalar Scalar
 
typedef VectorBlock< Derived > SegmentReturnType
 
typedef CwiseNullaryOp< internal::linspaced_op< Scalar, false >, Derived > SequentialLinSpacedReturnType
 
typedef internal::traits< Derived >::StorageKind StorageKind
 

Public Member Functions

const AdjointReturnType adjoint () const
 
void adjointInPlace ()
 
template<typename EssentialPart >
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
 
template<typename EssentialPart >
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
 
template<typename OtherDerived >
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
 
template<typename OtherScalar >
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
 
template<typename OtherDerived >
void applyOnTheRight (const EigenBase< OtherDerived > &other)
 
template<typename OtherScalar >
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
 
ArrayWrapper< Derived > array ()
 
const ArrayWrapper< const Derived > array () const
 
const DiagonalWrapper< const Derived > asDiagonal () const
 
const PermutationWrapper< const Derived > asPermutation () const
 
template<typename CustomBinaryOp , typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp< CustomBinaryOp, const Derived, const OtherDerived > binaryExpr (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
 
RealScalar blueNorm () 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
 
const ColPivHouseholderQR< PlainObjectcolPivHouseholderQr () const
 
template<typename ResultType >
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
 
template<typename ResultType >
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
 
ConjugateReturnType conjugate () const
 
const MatrixFunctionReturnValue< Derived > cos () const
 
const MatrixFunctionReturnValue< Derived > cosh () const
 
template<typename OtherDerived >
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross (const MatrixBase< OtherDerived > &other) 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
 
EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived > cwiseAbs () const
 
EIGEN_STRONG_INLINE const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Derived > cwiseAbs2 () const
 
template<typename OtherDerived >
const CwiseBinaryOp< std::equal_to< Scalar >, const Derived, const OtherDerived > cwiseEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< 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 >
EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_max_op< Scalar >, const Derived, const OtherDerived > cwiseMax (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
 
EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_max_op< Scalar >, const Derived, const ConstantReturnTypecwiseMax (const Scalar &other) const
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_min_op< Scalar >, const Derived, const OtherDerived > cwiseMin (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
 
EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_min_op< Scalar >, const Derived, const ConstantReturnTypecwiseMin (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp< std::not_equal_to< Scalar >, const Derived, const OtherDerived > cwiseNotEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const Derived, const OtherDerived > cwiseQuotient (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
 
const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Derived > cwiseSqrt () const
 
Scalar determinant () const
 
DiagonalReturnType diagonal ()
 
ConstDiagonalReturnType diagonal () const
 
template<int Index>
DiagonalIndexReturnType< Index >::Type diagonal ()
 
template<int Index>
ConstDiagonalIndexReturnType< Index >::Type diagonal () const
 
DiagonalIndexReturnType< DynamicIndex >::Type diagonal (Index index)
 
ConstDiagonalIndexReturnType< DynamicIndex >::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
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE (Derived, OtherDerived) cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
 
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix. More...
 
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
 
const MatrixExponentialReturnValue< Derived > exp () 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 FullPivHouseholderQR< PlainObjectfullPivHouseholderQr () const
 
const FullPivLU< PlainObjectfullPivLu () const
 
const HNormalizedReturnType hnormalized () const
 
const HouseholderQR< PlainObjecthouseholderQr () const
 
RealScalar hypotNorm () const
 
const ImagReturnType imag () const
 
NonConstImagReturnType imag ()
 
const internal::inverse_impl< Derived > inverse () const
 
bool isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
bool isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
 
template<typename ProductDerived , typename Lhs , typename Rhs >
Derived & lazyAssign (const ProductBase< ProductDerived, Lhs, Rhs > &other)
 
template<typename MatrixPower , typename Lhs , typename Rhs >
Derived & lazyAssign (const MatrixPowerProduct< MatrixPower, Lhs, Rhs > &other)
 
template<typename OtherDerived >
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct (const MatrixBase< OtherDerived > &other) const
 
const LDLT< PlainObjectldlt () const
 
const LLT< PlainObjectllt () const
 
const MatrixLogarithmReturnValue< Derived > log () const
 
template<int p>
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm () const
 
template<int p>
RealScalar lpNorm () 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
 
NoAlias< Derived, Eigen::MatrixBasenoalias ()
 
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 CwiseUnaryOp< internal::scalar_multiple2_op< Scalar, std::complex< Scalar > >, const Derived > operator* (const std::complex< Scalar > &scalar) const
 
template<typename Derived >
MatrixBase< Derived >::ScalarMultipleReturnType operator* (const UniformScaling< Scalar > &s) const
 
template<typename OtherDerived >
const ProductReturnType< Derived, OtherDerived >::Type operator* (const MatrixBase< OtherDerived > &other) const
 
template<typename DiagonalDerived >
const DiagonalProduct< Derived, DiagonalDerived, OnTheRightoperator* (const DiagonalBase< DiagonalDerived > &diagonal) const
 
template<typename OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & operator+= (const MatrixBase< 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 >
EIGEN_STRONG_INLINE Derived & operator-= (const MatrixBase< OtherDerived > &other)
 
const CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< Derived >::Scalar >, const Derived > operator/ (const Scalar &scalar) const
 
Derived & operator= (const MatrixBase &other)
 
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator= (const ReturnByValue< OtherDerived > &other)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & operator= (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & operator= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & operator= (const ReturnByValue< OtherDerived > &other)
 
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
 
RealScalar operatorNorm () const
 Computes the L2 operator norm. More...
 
const PartialPivLU< PlainObjectpartialPivLu () const
 
const MatrixPowerReturnValue< Derived > pow (const RealScalar &p) const
 
RealReturnType real () const
 
NonConstRealReturnType real ()
 
template<unsigned int UpLo>
SelfAdjointViewReturnType< UpLo >::Type selfadjointView ()
 
template<unsigned int UpLo>
ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView () const
 
template<unsigned int UpLo>
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView () const
 
template<unsigned int UpLo>
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView ()
 
Derived & setIdentity ()
 
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this. More...
 
const MatrixFunctionReturnValue< Derived > sin () const
 
const MatrixFunctionReturnValue< Derived > sinh () const
 
const SparseView< Derived > sparseView (const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const
 
const MatrixSquareRootReturnValue< Derived > sqrt () const
 
RealScalar squaredNorm () const
 
RealScalar stableNorm () const
 
Scalar trace () const
 
template<unsigned int Mode>
TriangularViewReturnType< Mode >::Type triangularView ()
 
template<unsigned int Mode>
ConstTriangularViewReturnType< Mode >::Type triangularView () const
 
template<unsigned int Mode>
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView ()
 
template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView () const
 
template<typename CustomUnaryOp >
const CwiseUnaryOp< CustomUnaryOp, const Derived > unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise. More...
 
template<typename CustomViewOp >
const CwiseUnaryView< CustomViewOp, const Derived > unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
 
PlainObject unitOrthogonal (void) const
 
- Public Member Functions inherited from Eigen::DenseBase< Derived >
bool all (void) const
 
bool allFinite () const
 
bool any (void) 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
 
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows, BlockCols > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
template<int BlockRows, int BlockCols>
const Block< const Derived, BlockRows, BlockCols > block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 
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
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomLeftCorner (Index cRows, Index cCols) const
 
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
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > bottomRightCorner (Index cRows, Index cCols) const
 
RowsBlockXpr bottomRows (Index n)
 
ConstRowsBlockXpr bottomRows (Index n) const
 
template<int N>
NRowsBlockXpr< N >::Type bottomRows ()
 
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows () const
 
ColXpr col (Index i)
 
ConstColXpr col (Index i) const
 
ConstColwiseReturnType colwise () const
 
ColwiseReturnType colwise ()
 
Index count () const
 
EIGEN_STRONG_INLINE EvalReturnType eval () const
 
template<typename Dest >
void evalTo (Dest &) 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>
const internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf () const
 
template<bool Enable>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf ()
 
const WithFormat< Derived > format (const IOFormat &fmt) const
 
bool hasNaN () const
 
SegmentReturnType head (Index vecSize)
 
ConstSegmentReturnType head (Index vecSize) const
 
template<int Size>
FixedSegmentReturnType< Size >::Type head ()
 
template<int Size>
ConstFixedSegmentReturnType< Size >::Type head () const
 
Index innerSize () const
 
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename Derived >
bool isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const
 
bool isMuchSmallerThan (const RealScalar &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
Derived & lazyAssign (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & lazyAssign (const DenseBase< OtherDerived > &other)
 
ColsBlockXpr leftCols (Index n)
 
ConstColsBlockXpr leftCols (Index n) const
 
template<int N>
NColsBlockXpr< N >::Type leftCols ()
 
template<int N>
ConstNColsBlockXpr< N >::Type leftCols () const
 
template<int p>
RealScalar lpNorm () 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
 
Index nonZeros () const
 
template<typename CustomNullaryOp >
EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (Index size, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
EIGEN_STRONG_INLINE const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (const CustomNullaryOp &func)
 
Derived & operator*= (const Scalar &other)
 
template<typename OtherDerived >
Derived & operator+= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator-= (const EigenBase< OtherDerived > &other)
 
Derived & operator/= (const Scalar &other)
 
CommaInitializer< Derived > operator<< (const Scalar &s)
 
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
 
Derived & operator= (const DenseBase &other)
 
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this. More...
 
template<typename OtherDerived >
Derived & operator= (const ReturnByValue< OtherDerived > &func)
 
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & operator= (const DenseBase< OtherDerived > &other)
 
Index outerSize () const
 
Scalar prod () const
 
template<typename Func >
EIGEN_STRONG_INLINE internal::result_of< Func(typename internal::traits< Derived >::Scalar)>::type redux (const Func &func) const
 
template<typename BinaryOp >
internal::result_of< BinaryOp(typename internal::traits< Derived >::Scalar)>::type redux (const BinaryOp &func) const
 
template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor > replicate () const
 
const Replicate< Derived, Dynamic, Dynamicreplicate (Index rowFacor, Index colFactor) const
 
void resize (Index newSize)
 
void resize (Index nbRows, Index nbCols)
 
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 vecSize)
 
ConstSegmentReturnType segment (Index start, Index vecSize) 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, const typename ThenDerived::Scalar &elseScalar) const
 
template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
 
Derived & setConstant (const Scalar &value)
 
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
Derived & setOnes ()
 
Derived & setRandom ()
 
Derived & setZero ()
 
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 vecSize)
 
ConstSegmentReturnType tail (Index vecSize) 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
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topLeftCorner (Index cRows, Index cCols) const
 
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
 
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const Block< const Derived, CRows, CCols > topRightCorner (Index cRows, Index cCols) const
 
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 ()
 
CoeffReturnType value () const
 
template<typename Visitor >
void visit (Visitor &func) const
 
- Public Member Functions inherited from Eigen::internal::special_scalar_op_base< Derived, internal::traits< Derived >::Scalar, NumTraits< internal::traits< Derived >::Scalar >::Real >
void operator* () const
 

Static Public Member Functions

static const IdentityReturnType Identity ()
 
static const IdentityReturnType Identity (Index rows, Index cols)
 
static const BasisReturnType Unit (Index size, Index i)
 
static const BasisReturnType Unit (Index i)
 
static const BasisReturnType UnitW ()
 
static const BasisReturnType UnitX ()
 
static const BasisReturnType UnitY ()
 
static const BasisReturnType UnitZ ()
 
- Static Public Member Functions inherited from Eigen::DenseBase< Derived >
static const ConstantReturnType Constant (Index rows, Index cols, const Scalar &value)
 
static const ConstantReturnType Constant (Index size, const Scalar &value)
 
static const ConstantReturnType Constant (const Scalar &value)
 
static const SequentialLinSpacedReturnType LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static const RandomAccessLinSpacedReturnType LinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static const SequentialLinSpacedReturnType LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static const RandomAccessLinSpacedReturnType LinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
template<typename CustomNullaryOp >
static const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
static const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (Index size, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
static const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr (const CustomNullaryOp &func)
 
static const ConstantReturnType 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 ConstantReturnType Zero (Index rows, Index cols)
 
static const ConstantReturnType Zero (Index size)
 
static const ConstantReturnType Zero ()
 

Protected Member Functions

 MatrixBase ()
 
template<typename OtherDerived >
Derived & operator+= (const ArrayBase< OtherDerived > &)
 
template<typename OtherDerived >
Derived & operator-= (const ArrayBase< OtherDerived > &)
 
- Protected Member Functions inherited from Eigen::DenseBase< Derived >
template<typename OtherDerived >
void checkTransposeAliasing (const OtherDerived &other) const
 
 DenseBase ()
 

Private Member Functions

 MatrixBase (int)
 
 MatrixBase (int, int)
 
template<typename OtherDerived >
 MatrixBase (const MatrixBase< 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)
 

Additional Inherited Members

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
Derivedis 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 TopicCustomizingEigen by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN.

See also
TopicClassHierarchy

Definition at line 48 of file MatrixBase.h.

Member Typedef Documentation

Definition at line 124 of file MatrixBase.h.

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

Definition at line 60 of file MatrixBase.h.

Definition at line 132 of file MatrixBase.h.

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

Definition at line 85 of file MatrixBase.h.

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

Definition at line 88 of file MatrixBase.h.

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

Definition at line 24 of file MatrixBase.h.

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

Definition at line 119 of file MatrixBase.h.

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

Definition at line 218 of file MatrixBase.h.

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

Definition at line 421 of file MatrixBase.h.

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

Definition at line 86 of file MatrixBase.h.

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

Definition at line 216 of file MatrixBase.h.

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

Definition at line 126 of file MatrixBase.h.

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

Definition at line 423 of file MatrixBase.h.

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

Definition at line 128 of file MatrixBase.h.

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

Definition at line 36 of file MatrixBase.h.

template<typename Derived>
typedef internal::traits<Derived>::Index Eigen::MatrixBase< Derived >::Index

Definition at line 55 of file MatrixBase.h.

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

Definition at line 38 of file MatrixBase.h.

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

Definition at line 34 of file MatrixBase.h.

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

Definition at line 57 of file MatrixBase.h.

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&.

Definition at line 115 of file MatrixBase.h.

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

Definition at line 29 of file MatrixBase.h.

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

Definition at line 58 of file MatrixBase.h.

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

Definition at line 87 of file MatrixBase.h.

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

Definition at line 56 of file MatrixBase.h.

template<typename Derived>
typedef CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::ScalarMultipleReturnType

Definition at line 17 of file MatrixBase.h.

template<typename Derived>
typedef CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::ScalarQuotient1ReturnType

Definition at line 19 of file MatrixBase.h.

type of the equivalent square matrix

Definition at line 96 of file MatrixBase.h.

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

Definition at line 451 of file MatrixBase.h.

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

Definition at line 53 of file MatrixBase.h.

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

Definition at line 54 of file MatrixBase.h.

Member Enumeration Documentation

template<typename Derived>
anonymous enum
Enumerator
SizeMinusOne 

Definition at line 416 of file MatrixBase.h.

Constructor & Destructor Documentation

template<typename Derived>
Eigen::MatrixBase< Derived >::MatrixBase ( )
inlineprotected

Definition at line 498 of file MatrixBase.h.

template<typename Derived>
Eigen::MatrixBase< Derived >::MatrixBase ( int  )
explicitprivate
template<typename Derived>
Eigen::MatrixBase< Derived >::MatrixBase ( int  ,
int   
)
private
template<typename Derived>
template<typename OtherDerived >
Eigen::MatrixBase< Derived >::MatrixBase ( const MatrixBase< OtherDerived > &  )
explicitprivate

Member Function Documentation

template<typename Derived >
const MatrixBase< Derived >::AdjointReturnType Eigen::MatrixBase< Derived >::adjoint ( ) const
inline
Returns
an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

Output:

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

Definition at line 237 of file Transpose.h.

template<typename Derived >
void Eigen::MatrixBase< Derived >::adjointInPlace ( )
inline

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

m.adjointInPlace();

has the same effect on m as doing

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

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

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

Note
if the matrix is not square, then *this must be a resizable matrix.
See also
transpose(), adjoint(), transposeInPlace()

Definition at line 321 of file Transpose.h.

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

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

On input:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()

Definition at line 112 of file Householder.h.

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

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

On input:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()

Definition at line 149 of file Householder.h.

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

replaces *this by *this * other.

Definition at line 154 of file EigenBase.h.

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

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

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

Definition at line 277 of file Jacobi.h.

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

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

Definition at line 146 of file EigenBase.h.

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

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

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

Definition at line 292 of file Jacobi.h.

template<typename Derived>
ArrayWrapper<Derived> Eigen::MatrixBase< Derived >::array ( )
inline
Returns
an Array expression of this matrix
See also
ArrayBase::matrix()

Definition at line 322 of file MatrixBase.h.

template<typename Derived>
const ArrayWrapper<const Derived> Eigen::MatrixBase< Derived >::array ( ) const
inline

Definition at line 323 of file MatrixBase.h.

template<typename Derived >
const DiagonalWrapper< const Derived > Eigen::MatrixBase< Derived >::asDiagonal ( ) const
inline
Returns
a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients

Example:

Output:

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

Definition at line 278 of file DiagonalMatrix.h.

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

Definition at line 681 of file PermutationMatrix.h.

template<typename Derived>
template<typename CustomBinaryOp , typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::binaryExpr ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const
inline
Returns
an expression of the difference of *this and other
Note
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See also
class CwiseBinaryOp, operator-=()
Returns
an expression of the sum of *this and other
Note
If you want to add a given scalar to all coefficients, see Cwise::operator+().
See also
class CwiseBinaryOp, operator+=()
Returns
an expression of a custom coefficient-wise operator func of *this and other

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

Here is an example illustrating the use of custom functors:

Output:

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

Definition at line 43 of file MatrixBase.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::blueNorm ( ) const
inline
Returns
the l2 norm of *this using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

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

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

Definition at line 171 of file StableNorm.h.

template<typename Derived>
template<typename NewType >
internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type Eigen::MatrixBase< Derived >::cast ( ) const
inline
Returns
an expression of *this with the Scalar type casted to NewScalar.

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

See also
class CwiseUnaryOp

Definition at line 93 of file MatrixBase.h.

template<typename Derived >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::colPivHouseholderQr ( ) const
Returns
the column-pivoting Householder QR decomposition of *this.
See also
class ColPivHouseholderQR

Definition at line 572 of file ColPivHouseholderQR.h.

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

Computation of matrix inverse and determinant, with invertibility check.

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

Parameters
inverseReference to the matrix in which to store the inverse.
determinantReference to the variable in which to store the determinant.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

Output:

See also
inverse(), computeInverseWithCheck()

Definition at line 347 of file Inverse.h.

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

Computation of matrix inverse, with invertibility check.

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

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

Example:

Output:

See also
inverse(), computeInverseAndDetWithCheck()

Definition at line 386 of file Inverse.h.

template<typename Derived>
ConjugateReturnType Eigen::MatrixBase< Derived >::conjugate ( ) const
inline
Returns
an expression of the complex conjugate of *this.
See also
adjoint()

Definition at line 102 of file MatrixBase.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase< Derived >::cos ( ) const
template<typename Derived>
const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase< Derived >::cosh ( ) const
template<typename Derived>
template<typename OtherDerived >
MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type Eigen::MatrixBase< Derived >::cross ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
the cross product of *this and other

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

See also
MatrixBase::cross3()

Definition at line 26 of file OrthoMethods.h.

template<typename Derived>
template<typename OtherDerived >
cross_product_return_type<OtherDerived>::type Eigen::MatrixBase< Derived >::cross ( const MatrixBase< OtherDerived > &  other) const
template<typename Derived >
template<typename OtherDerived >
MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::cross3 ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
the cross product of *this and other using only the x, y, and z coefficients

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

See also
MatrixBase::cross()

Definition at line 74 of file OrthoMethods.h.

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseAbs ( ) const
inline
Returns
an expression of the coefficient-wise absolute value of *this

Example:

Output:

See also
cwiseAbs2()

Definition at line 22 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const
inline
Returns
an expression of the coefficient-wise squared absolute value of *this

Example:

Output:

See also
cwiseAbs()

Definition at line 32 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise == operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

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

Definition at line 42 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const Derived> Eigen::MatrixBase< Derived >::cwiseEqual ( const Scalar s) const
inline
Returns
an expression of the coefficient-wise == operator of *this and a scalar s
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().
See also
cwiseEqual(const MatrixBase<OtherDerived> &) const

Definition at line 64 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseInverse ( ) const
inline
Returns
an expression of the coefficient-wise inverse of *this.

Example:

Output:

See also
cwiseProduct()

Definition at line 52 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMax ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise max of *this and other

Example:

Output:

See also
class CwiseBinaryOp, min()

Definition at line 99 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMax ( const Scalar other) const
inline
Returns
an expression of the coefficient-wise max of *this and scalar other
See also
class CwiseBinaryOp, min()

Definition at line 109 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMin ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise min of *this and other

Example:

Output:

See also
class CwiseBinaryOp, max()

Definition at line 75 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMin ( const Scalar other) const
inline
Returns
an expression of the coefficient-wise min of *this and scalar other
See also
class CwiseBinaryOp, min()

Definition at line 85 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseNotEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise != operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

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

Definition at line 61 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseQuotient ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise quotient of *this and other

Example:

Output:

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

Definition at line 124 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const
inline
Returns
an expression of the coefficient-wise square root of *this.

Example:

Output:

See also
cwisePow(), cwiseSquare()

Definition at line 42 of file MatrixBase.h.

template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant ( ) const
inline
Returns
the determinant of this matrix

Definition at line 92 of file Determinant.h.

template<typename Derived >
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type Eigen::MatrixBase< Derived >::diagonal ( )
inline
Returns
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

Output:

See also
class Diagonal
Returns
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

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

Example:

Output:

See also
MatrixBase::diagonal(), class Diagonal

Definition at line 168 of file Diagonal.h.

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

This is the const version of diagonal().

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

Definition at line 176 of file Diagonal.h.

template<typename Derived>
template<int Index>
DiagonalIndexReturnType<Index>::Type Eigen::MatrixBase< Derived >::diagonal ( )
template<typename Derived>
template<int Index>
ConstDiagonalIndexReturnType<Index>::Type Eigen::MatrixBase< Derived >::diagonal ( ) const
template<typename Derived >
MatrixBase< Derived >::template DiagonalIndexReturnType< DynamicIndex >::Type Eigen::MatrixBase< Derived >::diagonal ( Index  index)
inline
Returns
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

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

Example:

Output:

See also
MatrixBase::diagonal(), class Diagonal

Definition at line 194 of file Diagonal.h.

template<typename Derived >
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< DynamicIndex >::Type Eigen::MatrixBase< Derived >::diagonal ( Index  index) const
inline

This is the const version of diagonal(Index).

Definition at line 202 of file Diagonal.h.

template<typename Derived>
Index Eigen::MatrixBase< Derived >::diagonalSize ( ) const
inline
Returns
the size of the main diagonal, which is min(rows(),cols()).
See also
rows(), cols(), SizeAtCompileTime.

Definition at line 101 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType Eigen::MatrixBase< Derived >::dot ( const MatrixBase< OtherDerived > &  other) const
Returns
the dot product of *this with other.
Note
If the scalar type is complex numbers, then this function returns the hermitian (sesquilinear) dot product, conjugate-linear in the first variable and linear in the second variable.
See also
squaredNorm(), norm()

Definition at line 63 of file Dot.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const Eigen::MatrixBase< Derived >::EIGEN_CWISE_PRODUCT_RETURN_TYPE ( Derived  ,
OtherDerived   
) const
inline
Returns
an expression of the Schur product (coefficient wise product) of *this and other

Example:

Output:

See also
class CwiseBinaryOp, cwiseAbs2

Definition at line 22 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::EigenvaluesReturnType Eigen::MatrixBase< Derived >::eigenvalues ( ) const
inline

Computes the eigenvalues of a matrix.

Returns
Column vector containing the eigenvalues.

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

Output:

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

Definition at line 67 of file MatrixBaseEigenvalues.h.

template<typename Derived>
const MatrixExponentialReturnValue<Derived> Eigen::MatrixBase< Derived >::exp ( ) const
template<typename Derived >
const ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess ( ) const
inline
Returns
an expression of *this with forced aligned access
See also
forceAlignedAccessIf(),class ForceAlignedAccess

Definition at line 107 of file ForceAlignedAccess.h.

template<typename Derived >
ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess ( )
inline
Returns
an expression of *this with forced aligned access
See also
forceAlignedAccessIf(), class ForceAlignedAccess

Definition at line 117 of file ForceAlignedAccess.h.

template<typename Derived >
template<bool Enable>
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( ) const
inline
Returns
an expression of *this with forced aligned access if Enable is true.
See also
forceAlignedAccess(), class ForceAlignedAccess

Definition at line 128 of file ForceAlignedAccess.h.

template<typename Derived >
template<bool Enable>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( )
inline
Returns
an expression of *this with forced aligned access if Enable is true.
See also
forceAlignedAccess(), class ForceAlignedAccess

Definition at line 139 of file ForceAlignedAccess.h.

template<typename Derived >
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::fullPivHouseholderQr ( ) const
Returns
the full-pivoting Householder QR decomposition of *this.
See also
class FullPivHouseholderQR

Definition at line 616 of file FullPivHouseholderQR.h.

template<typename Derived >
const FullPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::fullPivLu ( ) const
inline
Returns
the full-pivoting LU decomposition of *this.
See also
class FullPivLU

Definition at line 735 of file FullPivLU.h.

template<typename Derived >
const MatrixBase< Derived >::HNormalizedReturnType Eigen::MatrixBase< Derived >::hnormalized ( ) const
inline
Returns
an expression of the homogeneous normalized vector of *this

Example:

Output:

See also
VectorwiseOp::hnormalized()

Definition at line 158 of file Homogeneous.h.

template<typename Derived >
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::householderQr ( ) const
Returns
the Householder QR decomposition of *this.
See also
class HouseholderQR

Definition at line 367 of file HouseholderQR.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::hypotNorm ( ) const
inline
Returns
the l2 norm of *this avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
See also
norm(), stableNorm()

Definition at line 183 of file StableNorm.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( )
static
Returns
an expression of the identity matrix (not necessarily square).

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

Example:

Output:

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

Definition at line 700 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( Index  nbRows,
Index  nbCols 
)
static
Returns
an expression of the identity matrix (not necessarily square).

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

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

Example:

Output:

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

Definition at line 683 of file CwiseNullaryOp.h.

template<typename Derived>
const ImagReturnType Eigen::MatrixBase< Derived >::imag ( ) const
inline
Returns
an read-only expression of the imaginary part of *this.
See also
real()

Definition at line 117 of file MatrixBase.h.

template<typename Derived>
NonConstImagReturnType Eigen::MatrixBase< Derived >::imag ( )
inline
Returns
a non const expression of the imaginary part of *this.
See also
real()

Definition at line 173 of file MatrixBase.h.

template<typename Derived >
const internal::inverse_impl< Derived > Eigen::MatrixBase< Derived >::inverse ( ) const
inline
Returns
the matrix inverse of this matrix.

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

Note
This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following: Example:
Output:
See also
computeInverseAndDetWithCheck()

Definition at line 320 of file Inverse.h.

template<typename Derived >
bool Eigen::MatrixBase< Derived >::isDiagonal ( const RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
Returns
true if *this is approximately equal to a diagonal matrix, within the precision given by prec.

Example:

Output:

See also
asDiagonal()

Definition at line 292 of file DiagonalMatrix.h.

template<typename Derived >
bool Eigen::MatrixBase< Derived >::isIdentity ( const RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
Returns
true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.

Example:

Output:

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

Definition at line 717 of file CwiseNullaryOp.h.

template<typename Derived >
bool Eigen::MatrixBase< Derived >::isLowerTriangular ( const RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
Returns
true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
See also
isUpperTriangular()

Definition at line 808 of file TriangularMatrix.h.

template<typename Derived >
template<typename OtherDerived >
bool Eigen::MatrixBase< Derived >::isOrthogonal ( const MatrixBase< OtherDerived > &  other,
const RealScalar prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns
true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

Output:

 

Definition at line 228 of file Dot.h.

template<typename Derived >
bool Eigen::MatrixBase< Derived >::isUnitary ( const RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
Returns
true if *this is approximately an unitary matrix, within the precision given by prec. In the case where the Scalar type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
Note
This can be used to check whether a family of vectors forms an orthonormal basis. Indeed, m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.

Example:

Output:

 

Definition at line 247 of file Dot.h.

template<typename Derived >
bool Eigen::MatrixBase< Derived >::isUpperTriangular ( const RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
Returns
true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
See also
isLowerTriangular()

Definition at line 782 of file TriangularMatrix.h.

template<typename Derived >
JacobiSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::jacobiSvd ( unsigned int  computationOptions = 0) const
Returns
the singular value decomposition of *this computed by two-sided Jacobi transformations.
See also
class JacobiSVD

Definition at line 872 of file JacobiSVD.h.

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

Definition at line 270 of file ProductBase.h.

template<typename Derived>
template<typename MatrixPower , typename Lhs , typename Rhs >
Derived& Eigen::MatrixBase< Derived >::lazyAssign ( const MatrixPowerProduct< MatrixPower, Lhs, Rhs > &  other)
template<typename Derived >
template<typename OtherDerived >
const LazyProductReturnType< Derived, OtherDerived >::Type Eigen::MatrixBase< Derived >::lazyProduct ( const MatrixBase< OtherDerived > &  other) const
Returns
an expression of the matrix product of *this and other without implicit evaluation.

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

Warning
This version of the matrix product can be much much slower. So use it only if you know what you are doing and that you measured a true speed improvement.
See also
operator*(const MatrixBase&)

Definition at line 612 of file GeneralProduct.h.

template<typename Derived >
const LDLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::ldlt ( ) const
inline
Returns
the Cholesky decomposition with full pivoting without square root of *this

Definition at line 593 of file LDLT.h.

template<typename Derived >
const LLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::llt ( ) const
inline
Returns
the LLT decomposition of *this

Definition at line 473 of file LLT.h.

template<typename Derived>
const MatrixLogarithmReturnValue<Derived> Eigen::MatrixBase< Derived >::log ( ) const
template<typename Derived>
template<int p>
NumTraits<typename internal::traits<Derived>::Scalar>::Real Eigen::MatrixBase< Derived >::lpNorm ( ) const
inline
Returns
the $ \ell^p $ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values of the coefficients of *this. If p is the special value Eigen::Infinity, this function returns the $ \ell^\infty $ norm, that is the maximum of the absolute values of the coefficients of *this.
See also
norm()

Definition at line 212 of file Dot.h.

template<typename Derived>
template<int p>
RealScalar Eigen::MatrixBase< Derived >::lpNorm ( ) const
template<typename Derived >
template<typename EssentialPart >
void Eigen::MatrixBase< Derived >::makeHouseholder ( EssentialPart &  essential,
Scalar tau,
RealScalar beta 
) const

Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $

On output:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
betathe result of H * *this
See also
MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

Definition at line 65 of file Householder.h.

template<typename Derived >
void Eigen::MatrixBase< Derived >::makeHouseholderInPlace ( Scalar tau,
RealScalar beta 
)

Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $

The essential part of the vector v is stored in *this.

On output:

Parameters
tauthe scaling factor of the Householder transformation
betathe result of H * *this
See also
MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

Definition at line 42 of file Householder.h.

template<typename Derived>
MatrixBase<Derived>& Eigen::MatrixBase< Derived >::matrix ( )
inline

Definition at line 317 of file MatrixBase.h.

template<typename Derived>
const MatrixBase<Derived>& Eigen::MatrixBase< Derived >::matrix ( ) const
inline

Definition at line 318 of file MatrixBase.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase< Derived >::matrixFunction ( StemFunction  f) const
template<typename Derived >
NoAlias< Derived, MatrixBase > Eigen::MatrixBase< Derived >::noalias ( )
Returns
a pseudo expression of *this with an operator= assuming no aliasing between *this and the source expression.

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

Here are some examples where noalias is usefull:

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

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

A.noalias() = A * B;

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

A = A * B;
See also
class NoAlias

Definition at line 127 of file NoAlias.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm ( ) const
inline
Returns
, for vectors, the l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.
See also
dot(), squaredNorm()

Definition at line 125 of file Dot.h.

template<typename Derived >
void Eigen::MatrixBase< Derived >::normalize ( )
inline

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

See also
norm(), normalized()

Definition at line 154 of file Dot.h.

template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::normalized ( ) const
inline
Returns
an expression of the quotient of *this by its own norm.
See also
norm(), normalize()

Definition at line 139 of file Dot.h.

template<typename Derived>
template<typename OtherDerived >
bool Eigen::MatrixBase< Derived >::operator!= ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
true if at least one pair of coefficients of *this and other are not exactly equal to each other.
Warning
When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
See also
isApprox(), operator==

Definition at line 301 of file MatrixBase.h.

template<typename Derived>
const ScalarMultipleReturnType Eigen::MatrixBase< Derived >::operator* ( const Scalar scalar) const
inline
Returns
an expression of *this scaled by the scalar factor scalar

Definition at line 50 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> Eigen::MatrixBase< Derived >::operator* ( const std::complex< Scalar > &  scalar) const
inline

Overloaded for efficient real matrix times complex scalar value

Definition at line 70 of file MatrixBase.h.

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

Concatenates a linear transformation matrix and a uniform scaling

Definition at line 111 of file Geometry/Scaling.h.

template<typename Derived >
template<typename OtherDerived >
const ProductReturnType< Derived, OtherDerived >::Type Eigen::MatrixBase< Derived >::operator* ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
the matrix product of *this and other.
Note
If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
See also
lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()

Definition at line 571 of file GeneralProduct.h.

template<typename Derived >
template<typename DiagonalDerived >
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > Eigen::MatrixBase< Derived >::operator* ( const DiagonalBase< DiagonalDerived > &  a_diagonal) const
inline
Returns
the diagonal matrix product of *this by the diagonal matrix diagonal.

Definition at line 123 of file DiagonalProduct.h.

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

replaces *this by *this * other.

Returns
a reference to *this

Definition at line 136 of file EigenBase.h.

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

replaces *this by *this + other.

Returns
a reference to *this

Definition at line 220 of file CwiseBinaryOp.h.

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

Definition at line 506 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> Eigen::MatrixBase< Derived >::operator- ( ) const
inline
Returns
an expression of the opposite of *this

Definition at line 45 of file MatrixBase.h.

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

replaces *this by *this - other.

Returns
a reference to *this

Definition at line 206 of file CwiseBinaryOp.h.

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

Definition at line 509 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> Eigen::MatrixBase< Derived >::operator/ ( const Scalar scalar) const
inline
Returns
an expression of *this divided by the scalar value scalar

Definition at line 62 of file MatrixBase.h.

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

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

Definition at line 555 of file Assign.h.

template<typename Derived>
template<typename OtherDerived >
Derived& Eigen::MatrixBase< Derived >::operator= ( const DenseBase< OtherDerived > &  other)
template<typename Derived>
template<typename OtherDerived >
Derived& Eigen::MatrixBase< Derived >::operator= ( const EigenBase< OtherDerived > &  other)
template<typename Derived>
template<typename OtherDerived >
Derived& Eigen::MatrixBase< Derived >::operator= ( const ReturnByValue< OtherDerived > &  other)
template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived& Eigen::MatrixBase< Derived >::operator= ( const DenseBase< OtherDerived > &  other)

Definition at line 562 of file Assign.h.

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

Definition at line 569 of file Assign.h.

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

Definition at line 576 of file Assign.h.

template<typename Derived>
template<typename OtherDerived >
bool Eigen::MatrixBase< Derived >::operator== ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
true if each coefficients of *this and other are all exactly equal.
Warning
When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
See also
isApprox(), operator!=

Definition at line 293 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::operatorNorm ( ) const
inline

Computes the L2 operator norm.

Returns
Operator norm of the matrix.

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

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

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

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

Example:

Output:

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

Definition at line 122 of file MatrixBaseEigenvalues.h.

template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::partialPivLu ( ) const
inline
Returns
the partial-pivoting LU decomposition of *this.
See also
class PartialPivLU

Definition at line 477 of file PartialPivLU.h.

template<typename Derived>
const MatrixPowerReturnValue<Derived> Eigen::MatrixBase< Derived >::pow ( const RealScalar p) const
template<typename Derived>
RealReturnType Eigen::MatrixBase< Derived >::real ( ) const
inline
Returns
a read-only expression of the real part of *this.
See also
imag()

Definition at line 111 of file MatrixBase.h.

template<typename Derived>
NonConstRealReturnType Eigen::MatrixBase< Derived >::real ( )
inline
Returns
a non const expression of the real part of *this.
See also
imag()

Definition at line 167 of file MatrixBase.h.

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

Definition at line 299 of file SelfAdjointView.h.

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

Definition at line 307 of file SelfAdjointView.h.

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

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

Example:

Output:

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

Definition at line 772 of file CwiseNullaryOp.h.

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

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

Parameters
nbRowsthe new number of rows
nbColsthe new number of columns

Example:

Output:

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

Definition at line 788 of file CwiseNullaryOp.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase< Derived >::sin ( ) const
template<typename Derived>
const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase< Derived >::sinh ( ) const
template<typename Derived >
const SparseView< Derived > Eigen::MatrixBase< Derived >::sparseView ( const Scalar m_reference = Scalar(0),
const typename NumTraits< Scalar >::Real &  m_epsilon = NumTraits<Scalar>::dummy_precision() 
) const

Definition at line 91 of file SparseView.h.

template<typename Derived>
const MatrixSquareRootReturnValue<Derived> Eigen::MatrixBase< Derived >::sqrt ( ) const
template<typename Derived >
EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm ( ) const
Returns
, for vectors, the squared l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this with itself.
See also
dot(), norm()

Definition at line 113 of file Dot.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::stableNorm ( ) const
inline
Returns
the l2 norm of *this avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s 2 - compute $ s \Vert \frac{*this}{s} \Vert $ in a standard way

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

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

Definition at line 140 of file StableNorm.h.

template<typename Derived >
EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::trace ( ) const
Returns
the trace of *this, i.e. the sum of the coefficients on the main diagonal.

*this can be any matrix, not necessarily square.

See also
diagonal(), sum()

Definition at line 401 of file Redux.h.

template<typename Derived>
template<unsigned int Mode>
TriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView ( )
template<typename Derived>
template<unsigned int Mode>
ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView ( ) const
template<typename Derived>
template<unsigned int Mode>
MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type Eigen::MatrixBase< Derived >::triangularView ( )
Returns
an expression of a triangular view extracted from the current matrix

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

Example:

Output:

See also
class TriangularView

Definition at line 762 of file TriangularMatrix.h.

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

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

Definition at line 771 of file TriangularMatrix.h.

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

Apply a unary operator coefficient-wise.

Parameters
[in]funcFunctor implementing the unary operator
Template Parameters
CustomUnaryOpType of func
Returns
An expression of a custom coefficient-wise unary operator func of *this

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

Example:

Output:

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

Example:

Output:

See also
class CwiseUnaryOp, class CwiseBinaryOp

Definition at line 140 of file MatrixBase.h.

template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, const Derived> Eigen::MatrixBase< Derived >::unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inline
Returns
an expression of a custom coefficient-wise unary operator func of *this

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

Example:

Output:

See also
class CwiseUnaryOp, class CwiseBinaryOp

Definition at line 158 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  newSize,
Index  i 
)
static
Returns
an expression of the i-th unit (basis) vector.
See also
MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Definition at line 801 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  i)
static
Returns
an expression of the i-th unit (basis) vector.

This variant is for fixed-size vector only.

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

Definition at line 816 of file CwiseNullaryOp.h.

template<typename Derived >
MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::unitOrthogonal ( void  ) const
Returns
a unit vector which is orthogonal to *this

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

See also
cross()

Definition at line 210 of file OrthoMethods.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitW ( )
static
Returns
an expression of the W axis unit vector (0,0,0,1)
See also
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Definition at line 859 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitX ( )
static
Returns
an expression of the X axis unit vector (1{,0}^*)
See also
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Definition at line 829 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitY ( )
static
Returns
an expression of the Y axis unit vector (0,1{,0}^*)
See also
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Definition at line 839 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitZ ( )
static
Returns
an expression of the Z axis unit vector (0,0,1{,0}^*)
See also
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Definition at line 849 of file CwiseNullaryOp.h.

Friends And Related Function Documentation

template<typename Derived>
const ScalarMultipleReturnType operator* ( const Scalar scalar,
const StorageBaseType matrix 
)
friend

Definition at line 77 of file MatrixBase.h.

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

Definition at line 81 of file MatrixBase.h.


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


tuw_aruco
Author(s): Lukas Pfeifhofer
autogenerated on Mon Jun 10 2019 15:41:07