Eigen: Eigen::MatrixBase< Derived > Class Template Reference

Searching...

No Matches

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

Detailed Description

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

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

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

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

Template Parameters

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

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

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

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

See also: The class hierarchy

Inheritance diagram for Eigen::MatrixBase< Derived >:

Public Member Functions
const MatrixFunctionReturnValue< Derived >	acosh () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .

const AdjointReturnType	adjoint () const

void	adjointInPlace ()

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

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

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

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

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

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

ArrayWrapper< Derived >	array ()

const ArrayWrapper< const Derived >	array () const

const DiagonalWrapper< const Derived >	asDiagonal () const

const MatrixFunctionReturnValue< Derived >	asinh () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic sine use ArrayBase::asinh .

const SkewSymmetricWrapper< const Derived >	asSkewSymmetric () const

const MatrixFunctionReturnValue< Derived >	atanh () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh .

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

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

template<typename CustomBinaryOp, typename OtherDerived>
const CwiseBinaryOp< CustomBinaryOp, const Derived, const OtherDerived >	binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const

RealScalar	blueNorm () const

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

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

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

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

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

const MatrixFunctionReturnValue< Derived >	cos () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise cosine use ArrayBase::cos .

const MatrixFunctionReturnValue< Derived >	cosh () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic cosine use ArrayBase::cosh .

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

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

const CwiseAbsReturnType	cwiseAbs () const

const CwiseAbs2ReturnType	cwiseAbs2 () const

const CwiseArgReturnType	cwiseArg () const

const CwiseCbrtReturnType	cwiseCbrt () const

template<typename OtherDerived>
const CwiseBinaryEqualReturnType< OtherDerived >	cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarEqualReturnType	cwiseEqual (const Scalar &s) const

template<typename OtherDerived>
const CwiseBinaryGreaterReturnType< OtherDerived >	cwiseGreater (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarGreaterReturnType	cwiseGreater (const Scalar &s) const

template<typename OtherDerived>
const CwiseBinaryGreaterOrEqualReturnType< OtherDerived >	cwiseGreaterOrEqual (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarGreaterOrEqualReturnType	cwiseGreaterOrEqual (const Scalar &s) const

const CwiseInverseReturnType	cwiseInverse () const

template<typename OtherDerived>
const CwiseBinaryLessReturnType< OtherDerived >	cwiseLess (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarLessReturnType	cwiseLess (const Scalar &s) const

template<typename OtherDerived>
const CwiseBinaryLessOrEqualReturnType< OtherDerived >	cwiseLessOrEqual (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarLessOrEqualReturnType	cwiseLessOrEqual (const Scalar &s) const

template<int NaNPropagation = PropagateFast, typename OtherDerived>
const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar, NaNPropagation >, const Derived, const OtherDerived >	cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const

template<int NaNPropagation = PropagateFast>
const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar, NaNPropagation >, const Derived, const ConstantReturnType >	cwiseMax (const Scalar &other) const

template<int NaNPropagation = PropagateFast, typename OtherDerived>
const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar, NaNPropagation >, const Derived, const OtherDerived >	cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const

template<int NaNPropagation = PropagateFast>
const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar, NaNPropagation >, const Derived, const ConstantReturnType >	cwiseMin (const Scalar &other) const

template<typename OtherDerived>
const CwiseBinaryNotEqualReturnType< OtherDerived >	cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const

const CwiseScalarNotEqualReturnType	cwiseNotEqual (const Scalar &s) const

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_product_op< Derived ::Scalar, OtherDerived ::Scalar >, const Derived, const OtherDerived >	cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const

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

const CwiseSignReturnType	cwiseSign () const

const CwiseSqrtReturnType	cwiseSqrt () const

const CwiseSquareReturnType	cwiseSquare () const

Scalar	determinant () const

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

DiagonalReturnType	diagonal ()

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

const ConstDiagonalReturnType	diagonal () const

Diagonal< Derived, DynamicIndex >	diagonal (Index index)

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

Index	diagonalSize () const

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

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

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

const MatrixExponentialReturnValue< Derived >	exp () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise exponential use ArrayBase::exp .

Derived &	forceAlignedAccess ()

const Derived &	forceAlignedAccess () const

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

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

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

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

const HNormalizedReturnType	hnormalized () const
	homogeneous normalization

HomogeneousReturnType	homogeneous () const

const HouseholderQR< PlainObject >	householderQr () const

RealScalar	hypotNorm () const

const Inverse< Derived >	inverse () const

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

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

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

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

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

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

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

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

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

const LDLT< PlainObject >	ldlt () const

const LLT< PlainObject >	llt () const

const MatrixLogarithmReturnValue< Derived >	log () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise logarithm use ArrayBase::log .

template<int p>
RealScalar	lpNorm () const

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

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

void	makeHouseholderInPlace (Scalar &tau, RealScalar &beta)

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

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

RealScalar	norm () const

void	normalize ()

const PlainObject	normalized () const

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

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_bitwise_and_op< Scalar >, const Derived, const OtherDerived >	operator& (const Eigen::MatrixBase< OtherDerived > &other) const

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_boolean_and_op< Scalar >, const Derived, const OtherDerived >	operator&& (const Eigen::MatrixBase< OtherDerived > &other) const

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

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

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

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

template<typename OtherDerived>
const CwiseBinaryOp< sum< Scalar >, const Derived, const OtherDerived >	operator+ (const Eigen::MatrixBase< OtherDerived > &other) const

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

template<typename OtherDerived>
const CwiseBinaryOp< difference< Scalar >, const Derived, const OtherDerived >	operator- (const Eigen::MatrixBase< OtherDerived > &other) const

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

Derived &	operator= (const MatrixBase &other)

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

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_bitwise_xor_op< Scalar >, const Derived, const OtherDerived >	operator^ (const Eigen::MatrixBase< OtherDerived > &other) const

RealScalar	operatorNorm () const
	Computes the L2 operator norm.

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_bitwise_or_op< Scalar >, const Derived, const OtherDerived >	operator\| (const Eigen::MatrixBase< OtherDerived > &other) const

template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_boolean_or_op< Scalar >, const Derived, const OtherDerived >	operator\|\| (const Eigen::MatrixBase< OtherDerived > &other) const

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

const MatrixPowerReturnValue< Derived >	pow (const RealScalar &p) const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to `p` use ArrayBase::pow .

const MatrixComplexPowerReturnValue< Derived >	pow (const std::complex< RealScalar > &p) const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to `p` use ArrayBase::pow .

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

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

Derived &	setIdentity ()

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

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

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

const MatrixFunctionReturnValue< Derived >	sin () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise sine use ArrayBase::sin .

const MatrixFunctionReturnValue< Derived >	sinh () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic sine use ArrayBase::sinh .

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

const MatrixSquareRootReturnValue< Derived >	sqrt () const
	This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise square root use ArrayBase::sqrt .

RealScalar	squaredNorm () const

RealScalar	stableNorm () const

void	stableNormalize ()

const PlainObject	stableNormalized () const

Scalar	trace () const

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

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

PlainObject	unitOrthogonal (void) const

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

bool	allFinite () const

bool	any () const

iterator	begin ()

const_iterator	begin () const

template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol)

template<int NRows, int NCols>
const ConstFixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol) const
	This is the const version of block<>(Index, Index). *‍/.

template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol, Index blockRows, Index blockCols)

template<int NRows, int NCols>
const ConstFixedBlockXpr< NRows, NCols >::Type	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
	This is the const version of block<>(Index, Index, Index, Index).

template<typename NRowsType, typename NColsType>
FixedBlockXpr<...,... >::Type	block (Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols)

template<typename NRowsType, typename NColsType>
const ConstFixedBlockXpr<...,... >::Type	block (Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols) const
	This is the const version of block(Index,Index,NRowsType,NColsType)

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner ()

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner () const
	This is the const version of bottomLeftCorner<int, int>().

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomLeftCorner (Index cRows, Index cCols) const
	This is the const version of bottomLeftCorner<int, int>(Index, Index).

template<typename NRowsType, typename NColsType>
FixedBlockXpr<...,... >::Type	bottomLeftCorner (NRowsType cRows, NColsType cCols)

template<typename NRowsType, typename NColsType>
ConstFixedBlockXpr<...,... >::Type	bottomLeftCorner (NRowsType cRows, NColsType cCols) const
	This is the const version of bottomLeftCorner(NRowsType, NColsType).

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	bottomRightCorner ()

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomRightCorner () const
	This is the const version of bottomRightCorner<int, int>().

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	bottomRightCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	bottomRightCorner (Index cRows, Index cCols) const
	This is the const version of bottomRightCorner<int, int>(Index, Index).

template<typename NRowsType, typename NColsType>
FixedBlockXpr<...,... >::Type	bottomRightCorner (NRowsType cRows, NColsType cCols)

template<typename NRowsType, typename NColsType>
const ConstFixedBlockXpr<...,... >::Type	bottomRightCorner (NRowsType cRows, NColsType cCols) const
	This is the const version of bottomRightCorner(NRowsType, NColsType).

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

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

template<typename NRowsType>
NRowsBlockXpr<... >::Type	bottomRows (NRowsType n)

template<typename NRowsType>
const ConstNRowsBlockXpr<... >::Type	bottomRows (NRowsType n) const
	This is the const version of bottomRows(NRowsType).

template<typename NewType>
CastXpr< NewType >::Type	cast () const

const_iterator	cbegin () const

const_iterator	cend () const

ColXpr	col (Index i)

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

ColwiseReturnType	colwise ()

ConstColwiseReturnType	colwise () const

ConjugateReturnType	conjugate () const

template<bool Cond>
std::conditional_t< Cond, ConjugateReturnType, const Derived & >	conjugateIf () const

Index	count () const

iterator	end ()

const_iterator	end () const

EvalReturnType	eval () const

void	fill (const Scalar &value)

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

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

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

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

template<typename NType>
FixedSegmentReturnType<... >::Type	head (NType n)

template<typename NType>
const ConstFixedSegmentReturnType<... >::Type	head (NType n) const
	This is the const version of head(NType).

NonConstImagReturnType	imag ()

const ImagReturnType	imag () const

EIGEN_CONSTEXPR Index	innerSize () const

InnerVectorReturnType	innerVector (Index outer)

const ConstInnerVectorReturnType	innerVector (Index outer) const

InnerVectorsReturnType	innerVectors (Index outerStart, Index outerSize)

const ConstInnerVectorsReturnType	innerVectors (Index outerStart, Index outerSize) const

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

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

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

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

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

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

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

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

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

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

template<typename NColsType>
NColsBlockXpr<... >::Type	leftCols (NColsType n)

template<typename NColsType>
const ConstNColsBlockXpr<... >::Type	leftCols (NColsType n) const
	This is the const version of leftCols(NColsType).

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

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

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

Scalar	mean () const

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

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

template<typename NColsType>
NColsBlockXpr<... >::Type	middleCols (Index startCol, NColsType numCols)

template<typename NColsType>
const ConstNColsBlockXpr<... >::Type	middleCols (Index startCol, NColsType numCols) const
	This is the const version of middleCols(Index,NColsType).

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

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

template<typename NRowsType>
NRowsBlockXpr<... >::Type	middleRows (Index startRow, NRowsType n)

template<typename NRowsType>
const ConstNRowsBlockXpr<... >::Type	middleRows (Index startRow, NRowsType n) const
	This is the const version of middleRows(Index,NRowsType).

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

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

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

const NestByValue< Derived >	nestByValue () const

template<typename Indices>
IndexedView_or_VectorBlock	operator() (const Indices &indices)

template<typename RowIndices, typename ColIndices>
IndexedView_or_Block	operator() (const RowIndices &rowIndices, const ColIndices &colIndices)

const NegativeReturnType	operator- () const

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

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

Derived &	operator= (const DenseBase &other)

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

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

EIGEN_CONSTEXPR Index	outerSize () const

Scalar	prod () const

NonConstRealReturnType	real ()

RealReturnType	real () const

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

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

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

template<int Order = ColMajor>
Reshaped< Derived,... >	reshaped ()

template<int Order = ColMajor>
const Reshaped< const Derived,... >	reshaped () const
	This is the const version of reshaped().

template<int Order = ColMajor, typename NRowsType, typename NColsType>
Reshaped< Derived,... >	reshaped (NRowsType nRows, NColsType nCols)

template<int Order = ColMajor, typename NRowsType, typename NColsType>
const Reshaped< const Derived,... >	reshaped (NRowsType nRows, NColsType nCols) const
	This is the const version of reshaped(NRowsType,NColsType).

void	resize (Index newSize)

void	resize (Index rows, Index cols)

ReverseReturnType	reverse ()

ConstReverseReturnType	reverse () const

void	reverseInPlace ()

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

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

template<typename NColsType>
NColsBlockXpr<... >::Type	rightCols (NColsType n)

template<typename NColsType>
const ConstNColsBlockXpr<... >::Type	rightCols (NColsType n) const
	This is the const version of rightCols(NColsType).

RowXpr	row (Index i)

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

RowwiseReturnType	rowwise ()

ConstRowwiseReturnType	rowwise () const

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

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

template<typename NType>
FixedSegmentReturnType<... >::Type	segment (Index start, NType n)

template<typename NType>
const ConstFixedSegmentReturnType<... >::Type	segment (Index start, NType n) const
	This is the const version of segment(Index,NType).

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

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

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

Derived &	setConstant (const Scalar &value)

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

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

Derived &	setOnes ()

Derived &	setRandom ()

Derived &	setZero ()

template<DirectionType Direction>
std::conditional_t< Direction==Vertical, ColXpr, RowXpr >	subVector (Index i)

template<DirectionType Direction>
std::conditional_t< Direction==Vertical, ConstColXpr, ConstRowXpr >	subVector (Index i) const

template<DirectionType Direction>
EIGEN_CONSTEXPR Index	subVectors () const

Scalar	sum () const

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

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

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

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

template<typename NType>
FixedSegmentReturnType<... >::Type	tail (NType n)

template<typename NType>
const ConstFixedSegmentReturnType<... >::Type	tail (NType n) const
	This is the const version of tail(Index).

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	topLeftCorner ()

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topLeftCorner () const
	This is the const version of topLeftCorner<int, int>().

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	topLeftCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topLeftCorner (Index cRows, Index cCols) const
	This is the const version of topLeftCorner<int, int>(Index, Index).

template<typename NRowsType, typename NColsType>
FixedBlockXpr<...,... >::Type	topLeftCorner (NRowsType cRows, NColsType cCols)

template<typename NRowsType, typename NColsType>
const ConstFixedBlockXpr<...,... >::Type	topLeftCorner (NRowsType cRows, NColsType cCols) const
	This is the const version of topLeftCorner(Index, Index).

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	topRightCorner ()

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topRightCorner () const
	This is the const version of topRightCorner<int, int>().

template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type	topRightCorner (Index cRows, Index cCols)

template<int CRows, int CCols>
const ConstFixedBlockXpr< CRows, CCols >::Type	topRightCorner (Index cRows, Index cCols) const
	This is the const version of topRightCorner<int, int>(Index, Index).

template<typename NRowsType, typename NColsType>
FixedBlockXpr<...,... >::Type	topRightCorner (NRowsType cRows, NColsType cCols)

template<typename NRowsType, typename NColsType>
const ConstFixedBlockXpr<...,... >::Type	topRightCorner (NRowsType cRows, NColsType cCols) const
	This is the const version of topRightCorner(NRowsType, NColsType).

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

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

template<typename NRowsType>
NRowsBlockXpr<... >::Type	topRows (NRowsType n)

template<typename NRowsType>
const ConstNRowsBlockXpr<... >::Type	topRows (NRowsType n) const
	This is the const version of topRows(NRowsType).

TransposeReturnType	transpose ()

const ConstTransposeReturnType	transpose () const

void	transposeInPlace ()

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

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

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

CoeffReturnType	value () const

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

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

EIGEN_CONSTEXPR Index	innerStride () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	outerStride () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	rowStride () const EIGEN_NOEXCEPT

Static Public Member Functions
static const IdentityReturnType	Identity ()

static const IdentityReturnType	Identity (Index rows, Index cols)

static const BasisReturnType	Unit (Index i)

static const BasisReturnType	Unit (Index size, Index i)

static const BasisReturnType	UnitW ()

static const BasisReturnType	UnitX ()

static const BasisReturnType	UnitY ()

static const BasisReturnType	UnitZ ()

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

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

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

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

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

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

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

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

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

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

static const ConstantReturnType	Ones ()

static const ConstantReturnType	Ones (Index rows, Index cols)

static const ConstantReturnType	Ones (Index size)

static const RandomReturnType	Random ()

static const RandomReturnType	Random (Index rows, Index cols)

static const RandomReturnType	Random (Index size)

static const ZeroReturnType	Zero ()

static const ZeroReturnType	Zero (Index rows, Index cols)

static const ZeroReturnType	Zero (Index size)

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

typedef random_access_iterator_type	const_iterator

typedef Eigen::InnerIterator< Derived >	InnerIterator

typedef random_access_iterator_type	iterator

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

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

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

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

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

typedef Scalar	value_type

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

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

Member Function Documentation

◆ acosh()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .

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

◆ adjoint()

template<typename Derived>

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

inline

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

Example:

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

Output:

Here is the 2x2 complex matrix m:
  (0.924,-0.824)   (0.146,-0.237)
(-0.199,-0.0532)    (0.334,0.634)
Here is the adjoint of m:
  (0.924,0.824) (-0.199,0.0532)
  (0.146,0.237)  (0.334,-0.634)

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

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

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

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

◆ adjointInPlace()

template<typename Derived>

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

inline

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

m.adjointInPlace();

has the same effect on m as doing

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

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

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

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

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

◆ applyHouseholderOnTheLeft()

template<typename Derived>

template<typename EssentialPart>

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

Apply the elementary reflector H given by with from the left to a vector or matrix.

On input:

Parameters

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

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

◆ applyHouseholderOnTheRight()

template<typename Derived>

template<typename EssentialPart>

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

Apply the elementary reflector H given by with from the right to a vector or matrix.

On input:

Parameters

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

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

◆ applyOnTheLeft() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

replaces *this by other * *this.

Example:

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

Output:

At start, A = 
 -0.824  -0.199   0.634
  0.924  -0.237   0.334
-0.0532   0.146  -0.779
After applyOnTheLeft, A = 
  0.924  -0.237   0.334
-0.0532   0.146  -0.779
 -0.824  -0.199   0.634

◆ applyOnTheLeft() [2/2]

template<typename Derived>

template<typename OtherScalar>

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

inline

This is defined in the Jacobi module.

#include <Eigen/Jacobi>

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

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

◆ applyOnTheRight() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

Example:

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

Output:

At start, A = 
 -0.824  -0.199   0.634
  0.924  -0.237   0.334
-0.0532   0.146  -0.779
After A *= B, A = 
  0.634  -0.824  -0.199
  0.334   0.924  -0.237
 -0.779 -0.0532   0.146
After applyOnTheRight, A = 
 -0.199   0.634  -0.824
 -0.237   0.334   0.924
  0.146  -0.779 -0.0532

◆ applyOnTheRight() [2/2]

template<typename Derived>

template<typename OtherScalar>

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

inline

This is defined in the Jacobi module.

#include <Eigen/Jacobi>

Applies the rotation in the plane j to the 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()

◆ array() [1/2]

template<typename Derived>

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

inline

Returns: an Array expression of this matrix

See also: ArrayBase::matrix()

◆ array() [2/2]

template<typename Derived>

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

inline

Returns: a const Array expression of this matrix

See also: ArrayBase::matrix()

◆ asDiagonal()

template<typename Derived>

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

inline

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

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

Example:

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

Eigen::MatrixBase::asDiagonal

const DiagonalWrapper< const Derived > asDiagonal() const

Definition DiagonalMatrix.h:347

Eigen::Matrix3i

Matrix< int, 3, 3 > Matrix3i

3×3 matrix of type int.

Definition Matrix.h:477

Eigen::Vector3i

Matrix< int, 3, 1 > Vector3i

3×1 vector of type int.

Definition Matrix.h:477

Output:

2 0 0
0 5 0
0 0 6

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

◆ asinh()

template<typename Derived>

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

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

◆ asSkewSymmetric()

template<typename Derived>

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

inline

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

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

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

◆ atanh()

template<typename Derived>

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

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

◆ bdcSvd() [1/2]

template<typename Derived>

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

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

See also: class BDCSVD

◆ bdcSvd() [2/2]

template<typename Derived>

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

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

See also: class BDCSVD

◆ binaryExpr()

template<typename Derived>

template<typename CustomBinaryOp, typename OtherDerived>

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

inline

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

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

Here is an example illustrating the use of custom functors:

#include <Eigen/Core>
#include <iostream>
 
using Eigen::Matrix4d;
 
// define a custom template binary functor
template <typename Scalar>
struct MakeComplexOp {
  typedef std::complex<Scalar> result_type;
  result_type operator()(const Scalar& a, const Scalar& b) const { return result_type(a, b); }
};
 
int main(int, char**) {
  Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
  std::cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << std::endl;
  return 0;
}

Output:

  (0.696,-0.727)   (-0.47,-0.216)  (0.0241,-0.778)   (0.134,0.0072)
    (0.205,0.74)    (0.928,0.852)  (0.0723,-0.758)     (-0.16,0.22)
 (-0.415,-0.757)    (0.445,0.835)   (0.432,-0.711) (-0.00986,0.859)
   (0.334,0.741)  (-0.633,-0.834)  (-0.046,-0.467)  (-0.498,-0.316)

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

◆ blueNorm()

template<typename Derived>

NumTraits< typenameinternal::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()

◆ colPivHouseholderQr()

template<typename Derived>

template<typename PermutationIndexType>

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

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

See also: class ColPivHouseholderQR

◆ completeOrthogonalDecomposition()

template<typename Derived>

template<typename PermutationIndex>

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

Returns: the complete orthogonal decomposition of *this.

See also: class CompleteOrthogonalDecomposition

◆ computeInverseAndDetWithCheck()

template<typename Derived>

template<typename ResultType>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse and determinant, with invertibility check.

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

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

Parameters

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

Example:

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

Output:

Here is the matrix m:
 0.696  0.334  0.445
 0.205  -0.47 -0.633
-0.415  0.928 0.0241
Its determinant is 0.485
It is invertible, and its inverse is:
    1.19    0.835 -0.00499
   0.531    0.416      1.1
-0.00911    -1.62   -0.816

See also: inverse(), computeInverseWithCheck()

◆ computeInverseWithCheck()

template<typename Derived>

template<typename ResultType>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse, with invertibility check.

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

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

Parameters

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

Example:

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

Output:

Here is the matrix m:
 0.696  0.334  0.445
 0.205  -0.47 -0.633
-0.415  0.928 0.0241
It is invertible, and its inverse is:
    1.19    0.835 -0.00499
   0.531    0.416      1.1
-0.00911    -1.62   -0.816

See also: inverse(), computeInverseAndDetWithCheck()

◆ cos()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise cosine use ArrayBase::cos .

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

◆ cosh()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic cosine use ArrayBase::cosh .

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

◆ cwiseAbs()

template<typename Derived>

const CwiseAbsReturnType Eigen::MatrixBase< Derived >::cwiseAbs ( ) const

inline

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

Example:

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

Output:

2 4 6
5 1 0

See also: cwiseAbs2()

◆ cwiseAbs2()

template<typename Derived>

const CwiseAbs2ReturnType Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const

inline

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

Example:

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

Output:

 4 16 36
25  1  0

See also: cwiseAbs()

◆ cwiseArg()

template<typename Derived>

const CwiseArgReturnType Eigen::MatrixBase< Derived >::cwiseArg ( ) const

inline

Returns: an expression of the coefficient-wise phase angle of *this

Example:

MatrixXcf v = MatrixXcf::Random(2, 3);
cout << v << endl << endl;
cout << v.cwiseArg() << endl;

Output:

  (0.924,-0.824)   (0.146,-0.237)   (0.633,-0.779)
(-0.199,-0.0532)    (0.334,0.634)   (0.982,-0.573)

-0.728  -1.02 -0.889
 -2.88   1.09 -0.528

◆ cwiseCbrt()

template<typename Derived>

const CwiseCbrtReturnType Eigen::MatrixBase< Derived >::cwiseCbrt ( ) const

inline

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

See also: cwiseSqrt(), cwiseSquare(), cwisePow()

◆ cwiseEqual() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

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

Example:

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

Output:

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

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

◆ cwiseEqual() [2/2]

template<typename Derived>

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

inline

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

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

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

◆ cwiseGreater() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

◆ cwiseGreater() [2/2]

template<typename Derived>

const CwiseScalarGreaterReturnType Eigen::MatrixBase< Derived >::cwiseGreater ( const Scalar & s ) const

inline

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

◆ cwiseGreaterOrEqual() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

◆ cwiseGreaterOrEqual() [2/2]

template<typename Derived>

const CwiseScalarGreaterOrEqualReturnType Eigen::MatrixBase< Derived >::cwiseGreaterOrEqual ( const Scalar & s ) const

inline

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

◆ cwiseInverse()

template<typename Derived>

const CwiseInverseReturnType Eigen::MatrixBase< Derived >::cwiseInverse ( ) const

inline

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

Example:

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

Output:

  0.5     2     1
0.333     4     1

See also: cwiseProduct()

◆ cwiseLess() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

◆ cwiseLess() [2/2]

template<typename Derived>

const CwiseScalarLessReturnType Eigen::MatrixBase< Derived >::cwiseLess ( const Scalar & s ) const

inline

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

◆ cwiseLessOrEqual() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

◆ cwiseLessOrEqual() [2/2]

template<typename Derived>

const CwiseScalarLessOrEqualReturnType Eigen::MatrixBase< Derived >::cwiseLessOrEqual ( const Scalar & s ) const

inline

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

◆ cwiseMax() [1/2]

template<typename Derived>

template<int NaNPropagation = PropagateFast, typename OtherDerived>

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

inline

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

Example:

Vector3d v(2, 3, 4), w(4, 2, 3);

cout << v.cwiseMax(w) << endl;

Eigen::Vector3d

Matrix< double, 3, 1 > Vector3d

3×1 vector of type double.

Definition Matrix.h:479

Output:

4
3
4

See also: class CwiseBinaryOp, min()

◆ cwiseMax() [2/2]

template<typename Derived>

template<int NaNPropagation = PropagateFast>

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

inline

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

See also: class CwiseBinaryOp, min()

◆ cwiseMin() [1/2]

template<typename Derived>

template<int NaNPropagation = PropagateFast, typename OtherDerived>

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

inline

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

Example:

Vector3d v(2, 3, 4), w(4, 2, 3);

cout << v.cwiseMin(w) << endl;

Output:

2
2
3

See also: class CwiseBinaryOp, max()

◆ cwiseMin() [2/2]

template<typename Derived>

template<int NaNPropagation = PropagateFast>

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

inline

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

See also: class CwiseBinaryOp, min()

◆ cwiseNotEqual() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

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

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

Example:

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

Output:

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

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

◆ cwiseNotEqual() [2/2]

template<typename Derived>

const CwiseScalarNotEqualReturnType Eigen::MatrixBase< Derived >::cwiseNotEqual ( 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

◆ cwiseProduct()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_product_op< Derived ::Scalar, OtherDerived ::Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::cwiseProduct ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

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

Example:

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

Output:

a:
 1804289383   719885386 -1364114958
 -465790871 -1550966999  2044897763
 -189735855 -1122281286  1365180540
b:
  304089172   336465782  1101513929
   35005211 -1868760786  1315634022
-1852781081    -2309581  -778350579
c:
-1900151348  1274064924  1451757314
 1178627603 -1395361186  1323254130
  982755863  -343432946  1494074956

See also: class CwiseBinaryOp, cwiseAbs2

◆ cwiseQuotient()

template<typename Derived>

template<typename OtherDerived>

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

inline

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

Example:

Vector3d v(2, 3, 4), w(4, 2, 3);

cout << v.cwiseQuotient(w) << endl;

Output:

 0.5
 1.5
1.33

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

◆ cwiseSign()

template<typename Derived>

const CwiseSignReturnType Eigen::MatrixBase< Derived >::cwiseSign ( ) const

inline

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

Example:

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

Output:

 1 -1  1
-1  1  0

◆ cwiseSqrt()

template<typename Derived>

const CwiseSqrtReturnType Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const

inline

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

Example:

Vector3d v(1, 2, 4);

cout << v.cwiseSqrt() << endl;

Output:

   1
1.41
   2

See also: cwisePow(), cwiseSquare(), cwiseCbrt()

◆ cwiseSquare()

template<typename Derived>

const CwiseSquareReturnType Eigen::MatrixBase< Derived >::cwiseSquare ( ) const

inline

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

See also: cwisePow(), cwiseSqrt(), cwiseCbrt()

◆ determinant()

template<typename Derived>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Returns: the determinant of this matrix

◆ diagonal() [1/6]

template<typename Derived>

template<int Index_>

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

inline

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
 1804289383 -1550966999  1365180540   336465782
 -465790871 -1122281286   304089172 -1868760786
 -189735855 -1364114958    35005211    -2309581
  719885386  2044897763 -1852781081  1101513929
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
-1550966999   304089172    -2309581
-189735855 2044897763

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

◆ diagonal() [2/6]

template<typename Derived>

MatrixBase< Derived >::DiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( )

inline

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

*this is not required to be square.

Example:

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

Output:

Here is the matrix m:
 1804289383   719885386 -1364114958
 -465790871 -1550966999  2044897763
 -189735855 -1122281286  1365180540
Here are the coefficients on the main diagonal of m:
 1804289383
-1550966999
 1365180540

See also: class Diagonal

◆ diagonal() [3/6]

template<typename Derived>

template<int Index_>

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

inline

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

◆ diagonal() [4/6]

template<typename Derived>

const MatrixBase< Derived >::ConstDiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( ) const

inline

This is the const version of diagonal().

◆ diagonal() [5/6]

template<typename Derived>

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

inline

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
 1804289383 -1550966999  1365180540   336465782
 -465790871 -1122281286   304089172 -1868760786
 -189735855 -1364114958    35005211    -2309581
  719885386  2044897763 -1852781081  1101513929
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
-1550966999   304089172    -2309581
-189735855 2044897763

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

◆ diagonal() [6/6]

template<typename Derived>

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

inline

This is the const version of diagonal(Index).

◆ diagonalSize()

template<typename Derived>

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

inline

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

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

◆ dot()

template<typename Derived>

template<typename OtherDerived>

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

inline

Returns: the dot product of *this with other.

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

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

See also: squaredNorm(), norm()

◆ eigenvalues()

template<typename Derived>

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

inline

Computes the eigenvalues of a matrix.

Returns: Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

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

Output:

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

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

◆ exp()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise exponential use ArrayBase::exp .

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

◆ forceAlignedAccess() [1/2]

template<typename Derived>

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(), class ForceAlignedAccess

◆ forceAlignedAccess() [2/2]

template<typename Derived>

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

inline

Returns: an expression of *this with forced aligned access

See also: forceAlignedAccessIf(),class ForceAlignedAccess

◆ forceAlignedAccessIf() [1/2]

template<typename Derived>

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

◆ forceAlignedAccessIf() [2/2]

template<typename Derived>

template<bool Enable>

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

inline

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

See also: forceAlignedAccess(), class ForceAlignedAccess

◆ fullPivHouseholderQr()

template<typename Derived>

template<typename PermutationIndex>

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

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

See also: class FullPivHouseholderQR

◆ fullPivLu()

template<typename Derived>

template<typename PermutationIndex>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

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

See also: class FullPivLU

◆ householderQr()

template<typename Derived>

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

inline

Returns: the Householder QR decomposition of *this.

See also: class HouseholderQR

◆ hypotNorm()

template<typename Derived>

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

inline

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

See also: norm(), stableNorm()

◆ Identity() [1/2]

template<typename Derived>

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

inlinestatic

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

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

Example:

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

Output:

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

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

◆ Identity() [2/2]

template<typename Derived>

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

inlinestatic

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

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

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

Example:

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

Output:

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

◆ inverse()

template<typename Derived>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Returns: the matrix inverse of this matrix.

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

Note

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

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

Example:

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

Output:

Here is the matrix m:
 0.696  0.334  0.445
 0.205  -0.47 -0.633
-0.415  0.928 0.0241
Its inverse is:
    1.19    0.835 -0.00499
   0.531    0.416      1.1
-0.00911    -1.62   -0.816

See also: computeInverseAndDetWithCheck()

◆ isDiagonal()

template<typename Derived>

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

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

Example:

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

Output:

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

See also: asDiagonal()

◆ isIdentity()

template<typename Derived>

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

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

Example:

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

Output:

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

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

◆ isLowerTriangular()

template<typename Derived>

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

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

See also: isUpperTriangular()

◆ isOrthogonal()

template<typename Derived>

template<typename OtherDerived>

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

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

Example:

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

Output:

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

◆ isSkewSymmetric()

template<typename Derived>

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

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

◆ isUnitary()

template<typename Derived>

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

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

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

Example:

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

Output:

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

◆ isUpperTriangular()

template<typename Derived>

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

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

See also: isLowerTriangular()

◆ jacobiSvd()

template<typename Derived>

template<int Options>

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

This is defined in the SVD module.

#include <Eigen/SVD>

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

See also: class JacobiSVD

◆ lazyProduct()

template<typename Derived>

template<typename OtherDerived>

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

inline

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

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

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

See also: operator*(const MatrixBase&)

◆ ldlt()

template<typename Derived>

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

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

See also: SelfAdjointView::ldlt()

◆ llt()

template<typename Derived>

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

inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>

Returns: the LLT decomposition of *this

See also: SelfAdjointView::llt()

◆ log()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise logarithm use ArrayBase::log .

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

◆ lpNorm()

template<typename Derived>

template<int p>

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

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

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

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

See also: norm()

◆ lu()

template<typename Derived>

template<typename PermutationIndex>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

Synonym of partialPivLu().

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

See also: class PartialPivLU

◆ makeHouseholder()

template<typename Derived>

template<typename EssentialPart>

void Eigen::MatrixBase< Derived >::makeHouseholder	(	EssentialPart &	essential,
		Scalar &	tau,
		RealScalar &	beta ) const

Computes the elementary reflector H such that: where the transformation H is: and the vector v is:

On output:

Parameters

essential	the essential part of the vector `v`
tau	the scaling factor of the Householder transformation
beta	the result of H * `*this`

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

◆ makeHouseholderInPlace()

template<typename Derived>

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

Computes the elementary reflector H such that: where the transformation H is: and the vector v is:

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

On output:

Parameters

tau	the scaling factor of the Householder transformation
beta	the result of H * `*this`

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

◆ noalias()

template<typename Derived>

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

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

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

Here are some examples where noalias is useful:

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

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

A.noalias() = A * B;

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

A = A * B;

See also: class NoAlias

◆ norm()

template<typename Derived>

NumTraits< typenameinternal::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: lpNorm(), dot(), squaredNorm()

◆ normalize()

template<typename Derived>

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

inline

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

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

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

See also: norm(), normalized()

◆ normalized()

template<typename Derived>

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

inline

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

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

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

See also: norm(), normalize()

◆ operator!=()

template<typename Derived>

template<typename OtherDerived>

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

inline

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

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

See also: isApprox(), operator==

◆ operator&()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_bitwise_and_op< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator& ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

Returns: an expression of the bitwise and operator of *this and other

See also: operator|(), operator^()

◆ operator&&()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_boolean_and_op< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator&& ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

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

Template Parameters

T	is the scalar type of scalar. It must be compatible with the scalar type of the given expression.

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

Template Parameters

T	is the scalar type of scalar. It must be compatible with the scalar type of the given expression.

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

Example:

Array3d v(-1, 2, 1), w(-3, 2, 3);

cout << ((v < w) && (v < 0)) << endl;

Output:

0
0
0

See also: operator||(), select()

◆ operator*() [1/3]

template<typename Derived>

template<typename DiagonalDerived>

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

inline

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

◆ operator*() [2/3]

template<typename Derived>

template<typename OtherDerived>

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

inline

Returns: the matrix product of *this and other.

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

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

◆ operator*() [3/3]

template<typename Derived>

template<typename SkewDerived>

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

inline

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

◆ operator*=()

template<typename Derived>

template<typename OtherDerived>

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

inline

replaces *this by *this * other.

Returns: a reference to *this

Example:

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

Output:

At start, A = 
 -0.824  -0.199   0.634
  0.924  -0.237   0.334
-0.0532   0.146  -0.779
After A *= B, A = 
  0.634  -0.824  -0.199
  0.334   0.924  -0.237
 -0.779 -0.0532   0.146
After applyOnTheRight, A = 
 -0.199   0.634  -0.824
 -0.237   0.334   0.924
  0.146  -0.779 -0.0532

◆ operator+()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< sum< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator+ ( const Eigen::MatrixBase< OtherDerived > & other ) const

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+=()

◆ operator+=()

template<typename Derived>

template<typename OtherDerived>

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

inline

replaces *this by *this + other.

Returns: a reference to *this

◆ operator-()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< difference< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator- ( const Eigen::MatrixBase< OtherDerived > & other ) const

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

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

See also: class CwiseBinaryOp, operator-=()

◆ operator-=()

template<typename Derived>

template<typename OtherDerived>

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

inline

replaces *this by *this - other.

Returns: a reference to *this

◆ operator=()

template<typename Derived>

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

inline

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

◆ operator==()

template<typename Derived>

template<typename OtherDerived>

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

inline

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

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

See also: isApprox(), operator!=

◆ operator^()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_bitwise_xor_op< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator^ ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

Returns: an expression of the bitwise xor operator of *this and other

See also: operator&(), operator|()

◆ operatorNorm()

template<typename Derived>

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

inline

Computes the L2 operator norm.

Returns: Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix 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 .

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

Example:

MatrixXd ones = MatrixXd::Ones(3, 3);

cout << "The operator norm of the 3x3 matrix of ones is " << ones.operatorNorm() << endl;

Output:

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

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

◆ operator|()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_bitwise_or_op< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator| ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

Returns: an expression of the bitwise boolean or operator of *this and other

See also: operator&(), operator^()

◆ operator||()

template<typename Derived>

template<typename OtherDerived>

const CwiseBinaryOp< internal::scalar_boolean_or_op< Scalar >, const Derived, const OtherDerived > Eigen::MatrixBase< Derived >::operator|| ( const Eigen::MatrixBase< OtherDerived > & other ) const

inline

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

Example:

Array3d v(-1, 2, 1), w(-3, 2, 3);

cout << ((v < w) || (v < 0)) << endl;

Output:

1
0
1

See also: operator&&(), select()

◆ partialPivLu()

template<typename Derived>

template<typename PermutationIndex>

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

inline

This is defined in the LU module.

#include <Eigen/LU>

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

See also: class PartialPivLU

◆ pow() [1/2]

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow .

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

◆ pow() [2/2]

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow .

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

◆ selfadjointView() [1/2]

template<typename Derived>

template<unsigned int UpLo>

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

Returns: an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix

The parameter UpLo can be either Upper or Lower

Example:

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

Output:

Here is the matrix m:
 1804289383   719885386 -1364114958
 -465790871 -1550966999  2044897763
 -189735855 -1122281286  1365180540
Here is the symmetric matrix extracted from the upper part of m:
 1804289383   719885386 -1364114958
  719885386 -1550966999  2044897763
-1364114958  2044897763  1365180540
Here is the symmetric matrix extracted from the lower part of m:
 1804289383  -465790871  -189735855
 -465790871 -1550966999 -1122281286
 -189735855 -1122281286  1365180540

See also: class SelfAdjointView

◆ selfadjointView() [2/2]

template<typename Derived>

template<unsigned int UpLo>

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

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

◆ setIdentity() [1/2]

template<typename Derived>

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

inline

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

Example:

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

Output:

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

◆ setIdentity() [2/2]

template<typename Derived>

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

inline

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

Parameters

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

Example:

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

Output:

1 0 0
0 1 0
0 0 1

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

◆ setUnit() [1/2]

template<typename Derived>

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

inline

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

Parameters

i	index of the unique coefficient to be set to 1

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

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

◆ setUnit() [2/2]

template<typename Derived>

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

inline

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

Parameters

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

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

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

◆ sin()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise sine use ArrayBase::sin .

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

◆ sinh()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic sine use ArrayBase::sinh .

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

◆ sqrt()

template<typename Derived>

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

This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise square root use ArrayBase::sqrt .

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

◆ squaredNorm()

template<typename Derived>

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

inline

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

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

◆ stableNorm()

template<typename Derived>

NumTraits< typenameinternal::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()

◆ stableNormalize()

template<typename Derived>

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

inline

Normalizes the vector while avoid underflow and overflow

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

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

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

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

◆ stableNormalized()

template<typename Derived>

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

inline

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

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

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

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

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

◆ trace()

template<typename Derived>

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

inline

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

*this can be any matrix, not necessarily square.

See also: diagonal(), sum()

◆ triangularView() [1/2]

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:

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

Output:

Here is the matrix m:
 1804289383   719885386 -1364114958
 -465790871 -1550966999  2044897763
 -189735855 -1122281286  1365180540
Here is the upper-triangular matrix extracted from m:
 1804289383   719885386 -1364114958
          0 -1550966999  2044897763
          0           0  1365180540
Here is the strictly-upper-triangular matrix extracted from m:
          0   719885386 -1364114958
          0           0  2044897763
          0           0           0
Here is the unit-lower-triangular matrix extracted from m:
          1           0           0
 -465790871           1           0
 -189735855 -1122281286           1

See also: class TriangularView

◆ triangularView() [2/2]

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()

◆ Unit() [1/2]

template<typename Derived>

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

inlinestatic

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

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

This variant is for fixed-size vector only.

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

◆ Unit() [2/2]

template<typename Derived>

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

inlinestatic

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

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

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

◆ UnitW()

template<typename Derived>

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

inlinestatic

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

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

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

◆ UnitX()

template<typename Derived>

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

inlinestatic

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

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

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

◆ UnitY()

template<typename Derived>

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

inlinestatic

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

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

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

◆ UnitZ()

template<typename Derived>

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

inlinestatic

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

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

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

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

/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/MatrixBase.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/util/ForwardDeclarations.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Cholesky/LDLT.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Cholesky/LLT.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/Assign.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/CwiseBinaryOp.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/CwiseNullaryOp.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/Diagonal.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/DiagonalMatrix.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/DiagonalProduct.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/Dot.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/ForceAlignedAccess.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/GeneralProduct.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/NoAlias.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/PermutationMatrix.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/Redux.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/SelfAdjointView.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/SkewSymmetricMatrix3.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/StableNorm.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/Transpose.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Core/TriangularMatrix.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Geometry/EulerAngles.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Geometry/Homogeneous.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Geometry/OrthoMethods.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Householder/Householder.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/Jacobi/Jacobi.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/LU/Determinant.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/LU/FullPivLU.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/LU/InverseImpl.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/LU/PartialPivLU.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/QR/ColPivHouseholderQR.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/QR/CompleteOrthogonalDecomposition.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/QR/FullPivHouseholderQR.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/QR/HouseholderQR.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/SparseCore/SparseView.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/SVD/BDCSVD.h
/usr/local/google/home/cantonios/dev/eigen/Eigen/src/SVD/JacobiSVD.h

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ acosh()

◆ adjoint()

◆ adjointInPlace()

◆ applyHouseholderOnTheLeft()

◆ applyHouseholderOnTheRight()

◆ applyOnTheLeft() [1/2]

◆ applyOnTheLeft() [2/2]

◆ applyOnTheRight() [1/2]

◆ applyOnTheRight() [2/2]

◆ array() [1/2]

◆ array() [2/2]

◆ asDiagonal()

◆ asinh()

◆ asSkewSymmetric()

◆ atanh()

◆ bdcSvd() [1/2]

◆ bdcSvd() [2/2]

◆ binaryExpr()

◆ blueNorm()

◆ colPivHouseholderQr()

◆ completeOrthogonalDecomposition()

◆ computeInverseAndDetWithCheck()

◆ computeInverseWithCheck()

◆ cos()

◆ cosh()

◆ cwiseAbs()

◆ cwiseAbs2()

◆ cwiseArg()

◆ cwiseCbrt()

◆ cwiseEqual() [1/2]

◆ cwiseEqual() [2/2]

◆ cwiseGreater() [1/2]

◆ cwiseGreater() [2/2]

◆ cwiseGreaterOrEqual() [1/2]

◆ cwiseGreaterOrEqual() [2/2]

◆ cwiseInverse()

◆ cwiseLess() [1/2]

◆ cwiseLess() [2/2]

◆ cwiseLessOrEqual() [1/2]

◆ cwiseLessOrEqual() [2/2]

◆ cwiseMax() [1/2]

◆ cwiseMax() [2/2]

◆ cwiseMin() [1/2]

◆ cwiseMin() [2/2]

◆ cwiseNotEqual() [1/2]

◆ cwiseNotEqual() [2/2]

◆ cwiseProduct()

◆ cwiseQuotient()

◆ cwiseSign()

◆ cwiseSqrt()

◆ cwiseSquare()

◆ determinant()

◆ diagonal() [1/6]

◆ diagonal() [2/6]

◆ diagonal() [3/6]

◆ diagonal() [4/6]

◆ diagonal() [5/6]

◆ diagonal() [6/6]

◆ diagonalSize()

◆ dot()

◆ eigenvalues()

◆ exp()

◆ forceAlignedAccess() [1/2]

◆ forceAlignedAccess() [2/2]

◆ forceAlignedAccessIf() [1/2]

◆ forceAlignedAccessIf() [2/2]

◆ fullPivHouseholderQr()

◆ fullPivLu()

◆ householderQr()

◆ hypotNorm()

◆ Identity() [1/2]

◆ Identity() [2/2]

◆ inverse()

◆ isDiagonal()

◆ isIdentity()