Eigen  5.0.1
 
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Public Member Functions | Static Public Member Functions | List of all members
Eigen::MatrixBase< Derived > Class Template Reference
Dense matrix and array manipulation » Reference » Core module

#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
Derivedis the derived type, e.g. a matrix type, or an expression, etc.

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

template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition MatrixBase.h:53

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="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .
 
constexpr 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)
 
constexpr ArrayWrapper< Derived > array ()
 
constexpr const ArrayWrapper< const Derived > array () const
 
constexpr const DiagonalWrapper< const Derived > asDiagonal () const
 
const MatrixFunctionReturnValue< Derived > asinh () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic sine use ArrayBase::asinh .
 
constexpr const SkewSymmetricWrapper< const Derived > asSkewSymmetric () const
 
const MatrixFunctionReturnValue< Derived > atanh () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic tangent 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>
constexpr const CwiseBinaryOp< CustomBinaryOp, const Derived, const OtherDerived > binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
 
RealScalar blueNorm () const
 
BunchKaufman< PlainObject > bunchKaufman () const
 
Matrix< Scalar, 3, 1 > canonicalEulerAngles (Index a0, Index a1, Index a2) const
 
template<typename PermutationIndexType>
ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType > colPivHouseholderQr () const
 
template<typename PermutationIndex>
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="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise cosine use ArrayBase::cos .
 
const MatrixFunctionReturnValue< Derived > cosh () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib 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 CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived > cwiseAbs () const
 
const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Derived > cwiseAbs2 () const
 
const CwiseUnaryOp< internal::scalar_arg_op< Scalar >, const Derived > cwiseArg () const
 
const CwiseUnaryOp< internal::scalar_cbrt_op< Scalar >, const Derived > cwiseCbrt () const
 
template<typename OtherDerived>
constexpr const CwiseBinaryEqualReturnType< OtherDerived > cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryGreaterReturnType< OtherDerived > cwiseGreater (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarGreaterReturnType cwiseGreater (const Scalar &s) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryGreaterOrEqualReturnType< OtherDerived > cwiseGreaterOrEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarGreaterOrEqualReturnType cwiseGreaterOrEqual (const Scalar &s) const
 
const CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const Derived > cwiseInverse () const
 
template<typename OtherDerived>
constexpr const CwiseBinaryLessReturnType< OtherDerived > cwiseLess (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarLessReturnType cwiseLess (const Scalar &s) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryLessOrEqualReturnType< OtherDerived > cwiseLessOrEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarLessOrEqualReturnType cwiseLessOrEqual (const Scalar &s) const
 
template<int NaNPropagation = PropagateFast, typename OtherDerived>
constexpr const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar, NaNPropagation >, const Derived, const OtherDerived > cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<int NaNPropagation = PropagateFast>
constexpr const CwiseBinaryOp< internal::scalar_max_op< Scalar, Scalar, NaNPropagation >, const Derived, const ConstantReturnType > cwiseMax (const Scalar &other) const
 
template<int NaNPropagation = PropagateFast, typename OtherDerived>
constexpr const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar, NaNPropagation >, const Derived, const OtherDerived > cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<int NaNPropagation = PropagateFast>
constexpr const CwiseBinaryOp< internal::scalar_min_op< Scalar, Scalar, NaNPropagation >, const Derived, const ConstantReturnType > cwiseMin (const Scalar &other) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryNotEqualReturnType< OtherDerived > cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
constexpr const CwiseScalarNotEqualReturnType cwiseNotEqual (const Scalar &s) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryOp< internal::scalar_product_op< Derived ::Scalar, OtherDerived ::Scalar >, const Derived, const OtherDerived > cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const Derived, const OtherDerived > cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
 
const CwiseUnaryOp< internal::scalar_sign_op< Scalar >, const Derived > cwiseSign () const
 
const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Derived > cwiseSqrt () const
 
const CwiseUnaryOp< internal::scalar_square_op< Scalar >, const Derived > cwiseSquare () const
 
Scalar determinant () const
 
template<int Index_>
constexpr Diagonal< Derived, Index_ > diagonal ()
 
constexpr DiagonalReturnType diagonal ()
 
template<int Index_>
constexpr const Diagonal< const Derived, Index_ > diagonal () const
 
constexpr const ConstDiagonalReturnType diagonal () const
 
constexpr Diagonal< Derived, DynamicIndex > diagonal (Index index)
 
constexpr const Diagonal< const Derived, DynamicIndex > diagonal (Index index) const
 
constexpr Index diagonalSize () const
 
template<int DiagIndex_ = 0>
constexpr DiagonalWrapper< Diagonal< Derived, DiagIndex_ > > diagonalView ()
 
template<int DiagIndex_ = 0>
constexpr DiagonalWrapper< Diagonal< const Derived, DiagIndex_ > > diagonalView () const
 
constexpr DiagonalWrapper< Diagonal< Derived, DynamicIndex > > diagonalView (Index index)
 
constexpr DiagonalWrapper< Diagonal< const Derived, DynamicIndex > > diagonalView (Index index) const
 
template<typename OtherDerived>
constexpr 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.
 
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
 
const MatrixExponentialReturnValue< Derived > exp () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise exponential use ArrayBase::exp .
 
template<typename PermutationIndex>
FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndex > fullPivHouseholderQr () const
 
template<typename PermutationIndex>
FullPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex > fullPivLu () const
 
const HNormalizedReturnType hnormalized () const
 homogeneous normalization
 
HomogeneousReturnType homogeneous () const
 
HouseholderQR< PlainObject > householderQr () const
 
RealScalar hypotNorm () 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
 
LDLT< PlainObject > ldlt () const
 
LLT< PlainObject > llt () const
 
const MatrixLogarithmReturnValue< Derived > log () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise logarithm use ArrayBase::log .
 
template<int p>
RealScalar lpNorm () const
 
template<typename PermutationIndex>
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 contrib 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>
constexpr const CwiseBinaryOp< internal::scalar_bitwise_and_op< Scalar >, const Derived, const OtherDerived > operator& (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
constexpr 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< internal::scalar_sum_op< Scalar, typename OtherDerived::Scalar >, const Derived, const OtherDerived > operator+ (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
EIGEN_ALWAYS_INLINE Derived & operator+= (const MatrixBase< OtherDerived > &other)
 
template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_difference_op< Scalar, typename OtherDerived::Scalar >, const Derived, const OtherDerived > operator- (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
EIGEN_ALWAYS_INLINE Derived & operator-= (const MatrixBase< OtherDerived > &other)
 
constexpr Derived & operator= (const MatrixBase &other)
 
template<typename OtherDerived>
bool operator== (const MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
constexpr 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>
constexpr const CwiseBinaryOp< internal::scalar_bitwise_or_op< Scalar >, const Derived, const OtherDerived > operator| (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived>
constexpr const CwiseBinaryOp< internal::scalar_boolean_or_op< Scalar >, const Derived, const OtherDerived > operator|| (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename PermutationIndex>
PartialPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex > partialPivLu () const
 
const MatrixComplexPowerReturnValue< Derived > pow (const internal::make_complex_t< Scalar > &p) const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow .
 
const MatrixPowerReturnValue< Derived > pow (const RealScalar &p) const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow .
 
template<typename PermutationIndexType>
RandColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType > randColPivHouseholderQr () const
 
template<typename PermutationIndex>
RandCompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject, PermutationIndex > randCompleteOrthogonalDecomposition () const
 
template<unsigned int UpLo>
constexpr MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView ()
 
template<unsigned int UpLo>
constexpr 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="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise sine use ArrayBase::sin .
 
const MatrixFunctionReturnValue< Derived > sinh () const
 This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib 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="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise square root use ArrayBase::sqrt .
 
constexpr RealScalar squaredNorm () const
 
RealScalar stableNorm () const
 
void stableNormalize ()
 
const PlainObject stableNormalized () const
 
Scalar trace () const
 
template<unsigned int Mode>
constexpr MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView ()
 
template<unsigned int Mode>
constexpr 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>
constexpr FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol)
 
template<int NRows, int NCols>
constexpr 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>
constexpr FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
template<int NRows, int NCols>
constexpr 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>
constexpr FixedBlockXpr<...,... >::Type block (Index startRow, Index startCol, NRowsType blockRows, NColsType blockCols)
 
template<typename NRowsType, typename NColsType>
constexpr 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>
constexpr FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner ()
 
template<int CRows, int CCols>
constexpr 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>
constexpr FixedBlockXpr<...,... >::Type bottomLeftCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType, typename NColsType>
constexpr ConstFixedBlockXpr<...,... >::Type bottomLeftCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of bottomLeftCorner(NRowsType, NColsType).
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type bottomRightCorner ()
 
template<int CRows, int CCols>
constexpr const ConstFixedBlockXpr< CRows, CCols >::Type bottomRightCorner () const
 This is the const version of bottomRightCorner<int, int>().
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type bottomRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
constexpr 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>
constexpr FixedBlockXpr<...,... >::Type bottomRightCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType, typename NColsType>
constexpr const ConstFixedBlockXpr<...,... >::Type bottomRightCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of bottomRightCorner(NRowsType, NColsType).
 
template<int N>
constexpr NRowsBlockXpr< N >::Type bottomRows (Index n=N)
 
template<int N>
constexpr ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
 This is the const version of bottomRows<int>().
 
template<typename NRowsType>
constexpr NRowsBlockXpr<... >::Type bottomRows (NRowsType n)
 
template<typename NRowsType>
constexpr const ConstNRowsBlockXpr<... >::Type bottomRows (NRowsType n) const
 This is the const version of bottomRows(NRowsType).
 
template<typename NewType>
constexpr CastXpr< NewType >::Type cast () const
 
const_iterator cbegin () const
 
const_iterator cend () const
 
constexpr ColXpr col (Index i)
 
constexpr ConstColXpr col (Index i) const
 This is the const version of col().
 
ColwiseReturnType colwise ()
 
ConstColwiseReturnType colwise () const
 
constexpr ConjugateReturnType conjugate () const
 
template<bool Cond>
constexpr 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>
constexpr FixedSegmentReturnType< N >::Type head (Index n=N)
 
template<int N>
constexpr ConstFixedSegmentReturnType< N >::Type head (Index n=N) const
 This is the const version of head<int>().
 
template<typename NType>
constexpr FixedSegmentReturnType<... >::Type head (NType n)
 
template<typename NType>
constexpr const ConstFixedSegmentReturnType<... >::Type head (NType n) const
 This is the const version of head(NType).
 
constexpr NonConstImagReturnType imag ()
 
constexpr const ImagReturnType imag () const
 
constexpr Index innerSize () const
 
constexpr InnerVectorReturnType innerVector (Index outer)
 
constexpr const ConstInnerVectorReturnType innerVector (Index outer) const
 
constexpr InnerVectorsReturnType innerVectors (Index outerStart, Index outerSize)
 
constexpr const ConstInnerVectorsReturnType innerVectors (Index outerStart, Index outerSize) const
 
template<typename OtherDerived>
constexpr 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>
constexpr bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename Derived>
constexpr 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 constexpr Derived & lazyAssign (const DenseBase< OtherDerived > &other)
 
template<int N>
constexpr NColsBlockXpr< N >::Type leftCols (Index n=N)
 
template<int N>
constexpr ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
 This is the const version of leftCols<int>().
 
template<typename NColsType>
constexpr NColsBlockXpr<... >::Type leftCols (NColsType n)
 
template<typename NColsType>
constexpr const ConstNColsBlockXpr<... >::Type leftCols (NColsType n) const
 This is the const version of leftCols(NColsType).
 
template<int NaNPropagation = PropagateFast>
internal::traits< Derived >::Scalar maxCoeff () const
 
template<int NaNPropagation = PropagateFast, typename IndexType>
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
 
template<int NaNPropagation = PropagateFast, typename IndexType>
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
 
Scalar mean () const
 
template<int N>
constexpr NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
 
template<int N>
constexpr ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
 This is the const version of middleCols<int>().
 
template<typename NColsType>
constexpr NColsBlockXpr<... >::Type middleCols (Index startCol, NColsType numCols)
 
template<typename NColsType>
constexpr const ConstNColsBlockXpr<... >::Type middleCols (Index startCol, NColsType numCols) const
 This is the const version of middleCols(Index,NColsType).
 
template<int N>
constexpr NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
 
template<int N>
constexpr ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
 This is the const version of middleRows<int>().
 
template<typename NRowsType>
constexpr NRowsBlockXpr<... >::Type middleRows (Index startRow, NRowsType n)
 
template<typename NRowsType>
constexpr const ConstNRowsBlockXpr<... >::Type middleRows (Index startRow, NRowsType n) const
 This is the const version of middleRows(Index,NRowsType).
 
template<int NaNPropagation = PropagateFast>
internal::traits< Derived >::Scalar minCoeff () const
 
template<int NaNPropagation = PropagateFast, typename IndexType>
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
 
template<int NaNPropagation = PropagateFast, typename IndexType>
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
 
constexpr 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)
 
constexpr const NegativeReturnType operator- () const
 
template<typename OtherDerived>
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
 
CommaInitializer< Derived > operator<< (const Scalar &s)
 
constexpr Derived & operator= (const DenseBase &other)
 
template<typename OtherDerived>
constexpr Derived & operator= (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived>
constexpr Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
 
constexpr Index outerSize () const
 
Scalar prod () const
 
constexpr NonConstRealReturnType real ()
 
constexpr RealReturnType real () const
 
RealViewReturnType realView ()
 
ConstRealViewReturnType realView () const
 This is the const version of realView().
 
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<typename NRowsType, typename NColsType>
const Replicate< Derived, internal::get_fixed_value< NRowsType >::value, internal::get_fixed_value< NColsType >::value > replicate (NRowsType nRows, NColsType nCols) const
 
template<int Order = ColMajor>
constexpr Reshaped< Derived,... > reshaped ()
 
template<int Order = ColMajor>
constexpr const Reshaped< const Derived,... > reshaped () const
 This is the const version of reshaped().
 
template<int Order = ColMajor, typename NRowsType, typename NColsType>
constexpr Reshaped< Derived,... > reshaped (NRowsType nRows, NColsType nCols)
 
template<int Order = ColMajor, typename NRowsType, typename NColsType>
constexpr 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>
constexpr NColsBlockXpr< N >::Type rightCols (Index n=N)
 
template<int N>
constexpr ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
 This is the const version of rightCols<int>().
 
template<typename NColsType>
constexpr NColsBlockXpr<... >::Type rightCols (NColsType n)
 
template<typename NColsType>
constexpr const ConstNColsBlockXpr<... >::Type rightCols (NColsType n) const
 This is the const version of rightCols(NColsType).
 
constexpr RowXpr row (Index i)
 
constexpr ConstRowXpr row (Index i) const
 This is the const version of row().
 
RowwiseReturnType rowwise ()
 
ConstRowwiseReturnType rowwise () const
 
template<int N>
constexpr FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
 
template<int N>
constexpr ConstFixedSegmentReturnType< N >::Type segment (Index start, Index n=N) const
 This is the const version of segment<int>(Index).
 
template<typename NType>
constexpr FixedSegmentReturnType<... >::Type segment (Index start, NType n)
 
template<typename NType>
constexpr const ConstFixedSegmentReturnType<... >::Type segment (Index start, NType n) const
 This is the const version of segment(Index,NType).
 
template<typename ThenDerived, typename ElseDerived>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr std::conditional_t< Direction==Vertical, ColXpr, RowXpr > subVector (Index i)
 
template<DirectionType Direction>
constexpr std::conditional_t< Direction==Vertical, ConstColXpr, ConstRowXpr > subVector (Index i) const
 
template<DirectionType Direction>
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>
constexpr FixedSegmentReturnType< N >::Type tail (Index n=N)
 
template<int N>
constexpr ConstFixedSegmentReturnType< N >::Type tail (Index n=N) const
 This is the const version of tail<int>().
 
template<typename NType>
constexpr FixedSegmentReturnType<... >::Type tail (NType n)
 
template<typename NType>
constexpr const ConstFixedSegmentReturnType<... >::Type tail (NType n) const
 This is the const version of tail(NType).
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type topLeftCorner ()
 
template<int CRows, int CCols>
constexpr const ConstFixedBlockXpr< CRows, CCols >::Type topLeftCorner () const
 This is the const version of topLeftCorner<int, int>().
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type topLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
constexpr 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>
constexpr FixedBlockXpr<...,... >::Type topLeftCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType, typename NColsType>
constexpr const ConstFixedBlockXpr<...,... >::Type topLeftCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of topLeftCorner(Index, Index).
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type topRightCorner ()
 
template<int CRows, int CCols>
constexpr const ConstFixedBlockXpr< CRows, CCols >::Type topRightCorner () const
 This is the const version of topRightCorner<int, int>().
 
template<int CRows, int CCols>
constexpr FixedBlockXpr< CRows, CCols >::Type topRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
constexpr 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>
constexpr FixedBlockXpr<...,... >::Type topRightCorner (NRowsType cRows, NColsType cCols)
 
template<typename NRowsType, typename NColsType>
constexpr const ConstFixedBlockXpr<...,... >::Type topRightCorner (NRowsType cRows, NColsType cCols) const
 This is the const version of topRightCorner(NRowsType, NColsType).
 
template<int N>
constexpr NRowsBlockXpr< N >::Type topRows (Index n=N)
 
template<int N>
constexpr ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
 This is the const version of topRows<int>().
 
template<typename NRowsType>
constexpr NRowsBlockXpr<... >::Type topRows (NRowsType n)
 
template<typename NRowsType>
constexpr 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>
constexpr const CwiseUnaryOp< CustomUnaryOp, const Derived > unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
 
template<typename CustomViewOp>
constexpr CwiseUnaryView< CustomViewOp, Derived > unaryViewExpr (const CustomViewOp &func=CustomViewOp())
 
template<typename CustomViewOp>
constexpr 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 >
constexpr Index colStride () const noexcept
 
constexpr Index innerStride () const noexcept
 
constexpr Index outerStride () const noexcept
 
constexpr Index rowStride () const 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 const RandomAccessLinSpacedReturnType LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
 
static 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
 
using InnerIterator
 
typedef random_access_iterator_type iterator
 
using PlainArray
 
using PlainMatrix
 
using PlainObject
 The plain matrix or array type corresponding to this expression.
 
using Scalar
 
using StorageIndex
 The type used to store indices.
 
using value_type
 
- Protected Member Functions inherited from Eigen::DenseBase< Derived >
constexpr DenseBase ()=default
 
- Related Symbols inherited from Eigen::DenseBase< 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="contrib/group__MatrixFunctions__Module.html"> contrib 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
constexpr
Returns
an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
Eigen::Matrix2cf
Matrix< std::complex< float >, 2, 2 > Matrix2cf
2×2 matrix of type std::complex<float>.
Definition Matrix.h:490

Output: 

Here is the 2x2 complex matrix m:
 (0.68,-0.211) (0.823,-0.605)
 (0.566,0.597)  (-0.33,0.536)
Here is the adjoint of m:
  (0.68,0.211) (0.566,-0.597)
 (0.823,0.605) (-0.33,-0.536)
Warning
If you want to replace a matrix by its own adjoint, do NOT do this:
m = m.adjoint(); // bug!!! caused by aliasing effect
Instead, use the adjointInPlace() method:
m.adjointInPlace();
which gives Eigen good opportunities for optimization, or alternatively you can also do:
m = m.adjoint().eval();
See also
adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op

◆ adjointInPlace()

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

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

m.adjointInPlace();

has the same effect on m as doing

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

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

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

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

◆ applyHouseholderOnTheLeft()

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

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

On input:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea 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 \( H = I - tau v v^*\) with \( v^T = [1 essential^T] \) from the right to a vector or matrix.

On input:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->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

Calling A.applyOnTheLeft(B) replaces A by the matrix product \( B A \).

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
Eigen::Matrix3f
Matrix< float, 3, 3 > Matrix3f
3×3 matrix of type float.
Definition Matrix.h:488

Output: 

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

◆ 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

Calling A.applyOnTheRight(B) replaces A by the matrix product \( A B \). It is equivalent to MatrixBase::operator*=().

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
Matrix3f A = Matrix3f::Random(3, 3), B;
B << 0, 1, 0, 0, 0, 1, 1, 0, 0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B); // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output: 

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

◆ 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 ( )
inlineconstexpr
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
inlineconstexpr
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
constexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
cout << Matrix3i(Vector3i(2, 5, 6).asDiagonal()) << endl;
Eigen::MatrixBase::asDiagonal
constexpr const DiagonalWrapper< const Derived > asDiagonal() const
Definition DiagonalMatrix.h:428
Eigen::Matrix3i
Matrix< int, 3, 3 > Matrix3i
3×3 matrix of type int.
Definition Matrix.h:487
Eigen::Vector3i
Matrix< int, 3, 1 > Vector3i
3×1 vector of type int.
Definition Matrix.h:487

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

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

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

◆ asSkewSymmetric()

template<typename Derived>
const SkewSymmetricWrapper< const Derived > Eigen::MatrixBase< Derived >::asSkewSymmetric ( ) const
constexpr
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

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

Returns
an expression of the matrix inverse hyperbolic tangent 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
inlineconstexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
#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;
}
Eigen::DenseBase::operator()
IndexedView_or_Block operator()(const RowIndices &rowIndices, const ColIndices &colIndices)
Eigen::DenseBase::Scalar
typename internal::traits< Derived >::Scalar Scalar
Definition DenseBase.h:63
Eigen::Matrix4d
Matrix< double, 4, 4 > Matrix4d
4×4 matrix of type double.
Definition Matrix.h:489

Output: 

(-0.211,-0.408)    (0.108,0.54)   (0.435,0.899)  (-0.198,-0.96)
 (0.597,0.0486)   (0.258,0.783)  (0.214,-0.828) (-0.782,-0.874)
 (-0.605,0.946) (0.0268,-0.295)  (-0.514,0.326)  (-0.563,0.941)
  (0.536,0.543)   (0.832,0.838)  (0.608,-0.302)   (0.678,0.702)
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 Blue's algorithm, with Anderson's Algorithm 978 correction for denormalized values. Blue, A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978; Anderson, ACM TOMS, Vol 44, Issue 1, 2017.

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

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

◆ bunchKaufman()

template<typename Derived>
BunchKaufman< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::bunchKaufman ( ) const
inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns
the Bunch-Kaufman factorization of *this
See also
SelfAdjointView::bunchKaufman()

◆ colPivHouseholderQr()

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

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
}
Eigen::MatrixBase::inverse
Inverse< Derived > inverse() const
Definition InverseImpl.h:280
Eigen::MatrixBase::determinant
Scalar determinant() const
Definition Determinant.h:88
Eigen::Matrix3d
Matrix< double, 3, 3 > Matrix3d
3×3 matrix of type double.
Definition Matrix.h:489

Output: 

Here is the matrix m:
-0.211  0.536 0.0268
 0.597  0.108  0.832
-0.605  0.258  0.435
Its determinant is -0.368
It is invertible, and its inverse is:
 0.456  0.615  -1.21
  2.07  0.205 -0.521
-0.595  0.734  0.932
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
inverseReference to the matrix in which to store the inverse.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:
-0.211  0.536 0.0268
 0.597  0.108  0.832
-0.605  0.258  0.435
It is invertible, and its inverse is:
 0.456  0.615  -1.21
  2.07  0.205 -0.521
-0.595  0.734  0.932
See also
inverse(), computeInverseAndDetWithCheck()

◆ cos()

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

This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib 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="contrib/group__MatrixFunctions__Module.html"> contrib 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 CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseAbs ( ) const
Returns
an expression of the coefficient-wise absolute value of *this

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
MatrixXd m(2, 3);
m << 2, -4, 6, -5, 1, 0;
cout << m.cwiseAbs() << endl;
Eigen::MatrixXd
Matrix< double, Dynamic, Dynamic > MatrixXd
Dynamic×Dynamic matrix of type double.
Definition Matrix.h:489

Output: 

2 4 6
5 1 0
See also
cwiseAbs2()

◆ cwiseAbs2()

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

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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 CwiseUnaryOp< internal::scalar_arg_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseArg ( ) const
Returns
an expression of the coefficient-wise phase angle of *this

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
MatrixXcf v = MatrixXcf::Random(2, 3);
cout << v << endl << endl;
cout << v.cwiseArg() << endl;
Eigen::MatrixXcf
Matrix< std::complex< float >, Dynamic, Dynamic > MatrixXcf
Dynamic×Dynamic matrix of type std::complex<float>.
Definition Matrix.h:490

Output: 

  (0.68,-0.211)  (0.823,-0.605)  (-0.444,0.108)
  (0.566,0.597)   (-0.33,0.536) (-0.0452,0.258)

-0.301 -0.634    2.9
 0.812   2.12   1.74

◆ cwiseCbrt()

template<typename Derived>
const CwiseUnaryOp< internal::scalar_cbrt_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseCbrt ( ) const
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
inlineconstexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
Eigen::DenseBase::count
Index count() const
Definition Visitor.h:672
Eigen::MatrixXi
Matrix< int, Dynamic, Dynamic > MatrixXi
Dynamic×Dynamic matrix of type int.
Definition Matrix.h:487

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

◆ cwiseInverse()

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

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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
inlineconstexpr
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
inlineconstexpr
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
inlineconstexpr
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
inlineconstexpr
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
inlineconstexpr
Returns
an expression of the coefficient-wise max of *this and other

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:489

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

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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
inlineconstexpr
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
inlineconstexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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
inlineconstexpr
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
inlineconstexpr
Returns
an expression of the Schur product (coefficient wise product) of *this and other

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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 -1427598262 -1364114958
 -465790871 -1550966999  -102585885
 1957747793 -1122281286  -782303108
b:
-1843394476   336465782 -1045969719
   35005211   278722862  1315634022
-1852781081  2145174067  -778350579
c:
  247332300  1274064924  1451757314
 1178627603   752122462  1323254130
-1164727785  -343432946  -653408692
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
inlineconstexpr
Returns
an expression of the coefficient-wise quotient of *this and other

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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 CwiseUnaryOp< internal::scalar_sign_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseSign ( ) const
Returns
an expression of the coefficient-wise signum of *this.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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 CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const
Returns
an expression of the coefficient-wise square root of *this.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
Vector3d v(1, 2, 4);
cout << v.cwiseSqrt() << endl;

Output: 

   1
1.41
   2
See also
cwisePow(), cwiseSquare(), cwiseCbrt()

◆ cwiseSquare()

template<typename Derived>
const CwiseUnaryOp< internal::scalar_square_op< Scalar >, const Derived > Eigen::MatrixBase< Derived >::cwiseSquare ( ) const
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 ( )
constexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
Eigen::DenseBase::transpose
TransposeReturnType transpose()
Definition Transpose.h:165
Eigen::Matrix4i
Matrix< int, 4, 4 > Matrix4i
4×4 matrix of type int.
Definition Matrix.h:487

Output: 

Here is the matrix m:
 1804289383 -1550966999  -782303108   336465782
 -465790871 -1122281286 -1843394476   278722862
 1957747793 -1364114958    35005211  2145174067
-1427598262  -102585885 -1852781081 -1045969719
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
-1550966999 -1843394476  2145174067
1957747793 -102585885
See also
MatrixBase::diagonal(), class Diagonal

◆ diagonal() [2/6]

template<typename Derived>
MatrixBase< Derived >::DiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( )
constexpr
Returns
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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 -1427598262 -1364114958
 -465790871 -1550966999  -102585885
 1957747793 -1122281286  -782303108
Here are the coefficients on the main diagonal of m:
 1804289383
-1550966999
 -782303108
See also
class Diagonal

◆ diagonal() [3/6]

template<typename Derived>
template<int Index_>
const Diagonal< const Derived, Index_ > Eigen::MatrixBase< Derived >::diagonal ( ) const
constexpr

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

◆ diagonal() [4/6]

template<typename Derived>
const MatrixBase< Derived >::ConstDiagonalReturnType Eigen::MatrixBase< Derived >::diagonal ( ) const
constexpr

This is the const version of diagonal().

◆ diagonal() [5/6]

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

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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  -782303108   336465782
 -465790871 -1122281286 -1843394476   278722862
 1957747793 -1364114958    35005211  2145174067
-1427598262  -102585885 -1852781081 -1045969719
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
-1550966999 -1843394476  2145174067
1957747793 -102585885
See also
MatrixBase::diagonal(), class Diagonal

◆ diagonal() [6/6]

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

This is the const version of diagonal(Index).

◆ diagonalSize()

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

◆ diagonalView() [1/4]

template<typename Derived>
template<int DiagIndex_>
DiagonalWrapper< Diagonal< Derived, DiagIndex_ > > Eigen::MatrixBase< Derived >::diagonalView ( )
constexpr
Returns
DiagonalWrapper.

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
Matrix3d m;
m << 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.diagonal().asDiagonal() returns: " << endl << m.diagonal().asDiagonal() << endl;
cout << "m.diagonalView() returns: " << endl << m.diagonalView() << endl;

Output: 

Here's the matrix m:
1.1 2.2 3.3
4.4 5.5 6.6
7.7 8.8 9.9
m.diagonal().asDiagonal() returns: 
1.1   0   0
  0 5.5   0
  0   0 9.9
m.diagonalView() returns: 
1.1   0   0
  0 5.5   0
  0   0 9.9
See also
diagonalView() This is the non-const version of diagonalView() with DiagIndex_ .

◆ diagonalView() [2/4]

template<typename Derived>
template<int DiagIndex_>
DiagonalWrapper< Diagonal< const Derived, DiagIndex_ > > Eigen::MatrixBase< Derived >::diagonalView ( ) const
constexpr

This is the const version of diagonalView() with DiagIndex_ .

◆ diagonalView() [3/4]

template<typename Derived>
DiagonalWrapper< Diagonal< Derived, DynamicIndex > > Eigen::MatrixBase< Derived >::diagonalView ( Index index)
constexpr

This is the non-const version of diagonalView() with dynamic index.

◆ diagonalView() [4/4]

template<typename Derived>
DiagonalWrapper< Diagonal< const Derived, DynamicIndex > > Eigen::MatrixBase< Derived >::diagonalView ( Index index) const
constexpr

This is the const version of diagonalView() with dynamic index.

◆ 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
inlineconstexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
MatrixXd ones = MatrixXd::Ones(3, 3);
VectorXcd eivals = ones.eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
Eigen::VectorXcd
Matrix< std::complex< double >, Dynamic, 1 > VectorXcd
Dynamic×1 vector of type std::complex<double>.
Definition Matrix.h:491

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="contrib/group__MatrixFunctions__Module.html"> contrib MatrixFunctions module. To compute the * coefficient-wise exponential use ArrayBase::exp .

Returns
an expression of the matrix exponential of *this.

◆ fullPivHouseholderQr()

template<typename Derived>
template<typename PermutationIndex>
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>
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>
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
cout << MatrixXd::Identity(4, 3) << endl;

Output: 

1 0 0
0 1 0
0 0 1
0 0 0
See also
Identity(), setIdentity(), isIdentity()

◆ inverse()

template<typename Derived>
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: Example:
// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:
-0.211  0.536 0.0268
 0.597  0.108  0.832
-0.605  0.258  0.435
Its inverse is:
 0.456  0.615  -1.21
  2.07  0.205 -0.521
-0.595  0.734  0.932
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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>
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>
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="contrib/group__MatrixFunctions__Module.html"> contrib 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>
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: \( H *this = [ beta 0 ... 0]^T \) where the transformation H is: \( H = I - tau v v^*\) and the vector v is: \( v^T = [1 essential^T] \)

On output:

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

◆ makeHouseholderInPlace()

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

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

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

On output:

Parameters
tauthe scaling factor of the Householder transformation
betathe 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 equal 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
inlineconstexpr
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
inlineconstexpr
Returns
an expression of *this scaled by the scalar factor scalar
Template Parameters
Tis 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
Tis 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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
Matrix3f A = Matrix3f::Random(3, 3), B;
B << 0, 1, 0, 0, 0, 1, 1, 0, 0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B); // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output: 

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

◆ operator+()

template<typename Derived>
template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_sum_op< Scalar, typename OtherDerived::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>
EIGEN_ALWAYS_INLINE Derived & Eigen::MatrixBase< Derived >::operator+= ( const MatrixBase< OtherDerived > & other)

replaces *this by *this + other.

Returns
a reference to *this

◆ operator-()

template<typename Derived>
template<typename OtherDerived>
const CwiseBinaryOp< internal::scalar_difference_op< Scalar, typename OtherDerived::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
Subtraction is not supported for bool coefficients. Cast to a signed integer type first.
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>
EIGEN_ALWAYS_INLINE Derived & Eigen::MatrixBase< Derived >::operator-= ( const MatrixBase< OtherDerived > & other)

replaces *this by *this - other.

Returns
a reference to *this

◆ operator=()

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

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
inlineconstexpr
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 \( A \) is defined to be

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

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

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

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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
inlineconstexpr
Returns
an expression of the bitwise 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
inlineconstexpr
Returns
an expression of the coefficient-wise boolean or operator of *this and other

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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>
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 MatrixComplexPowerReturnValue< Derived > Eigen::MatrixBase< Derived >::pow ( const internal::make_complex_t< Scalar > & p) const

This function requires the <a * href="contrib/group__MatrixFunctions__Module.html"> contrib 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 MatrixPowerReturnValue< Derived > Eigen::MatrixBase< Derived >::pow ( const RealScalar & p) const

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

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

◆ randColPivHouseholderQr()

template<typename Derived>
template<typename PermutationIndexType>
RandColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType > Eigen::MatrixBase< Derived >::randColPivHouseholderQr ( ) const
Returns
the randomized column-pivoted Householder QR decomposition of *this.
See also
class RandColPivHouseholderQR

◆ randCompleteOrthogonalDecomposition()

template<typename Derived>
template<typename PermutationIndex>
RandCompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject, PermutationIndex > Eigen::MatrixBase< Derived >::randCompleteOrthogonalDecomposition ( ) const
Returns
the randomized complete orthogonal decomposition of *this.
See also
class RandCompleteOrthogonalDecomposition

◆ selfadjointView() [1/2]

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

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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;
Eigen::Lower
@ Lower
Definition Constants.h:212
Eigen::Upper
@ Upper
Definition Constants.h:214

Output: 

Here is the matrix m:
 1804289383 -1427598262 -1364114958
 -465790871 -1550966999  -102585885
 1957747793 -1122281286  -782303108
Here is the symmetric matrix extracted from the upper part of m:
 1804289383 -1427598262 -1364114958
-1427598262 -1550966999  -102585885
-1364114958  -102585885  -782303108
Here is the symmetric matrix extracted from the lower part of m:
 1804289383  -465790871  1957747793
 -465790871 -1550966999 -1122281286
 1957747793 -1122281286  -782303108
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
constexpr

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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
Matrix4i m = Matrix4i::Zero();
m.block<3, 3>(1, 0).setIdentity();
cout << m << endl;
Eigen::MatrixBase::setIdentity
Derived & setIdentity()
Definition CwiseNullaryOp.h:812

Output: 

0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
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
rowsthe new number of rows
colsthe new number of columns

Example:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
MatrixXf m;
m.setIdentity(3, 3);
cout << m << endl;
Eigen::MatrixXf
Matrix< float, Dynamic, Dynamic > MatrixXf
Dynamic×Dynamic matrix of type float.
Definition Matrix.h:488

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
iindex 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
newSizethe new size of the vector
iindex 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="contrib/group__MatrixFunctions__Module.html"> contrib 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="contrib/group__MatrixFunctions__Module.html"> contrib 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="contrib/group__MatrixFunctions__Module.html"> contrib 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
inlineconstexpr
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 equal 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 uses a blockwise two-pass algorithm: 1 - find the absolute largest coefficient and choose a scale s (a nearby normal power of two for supported binary floating-point accumulators) 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 ( )
constexpr
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:

// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0
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)
Eigen::StrictlyUpper
@ StrictlyUpper
Definition Constants.h:226
Eigen::UnitLower
@ UnitLower
Definition Constants.h:220

Output: 

Here is the matrix m:
 1804289383 -1427598262 -1364114958
 -465790871 -1550966999  -102585885
 1957747793 -1122281286  -782303108
Here is the upper-triangular matrix extracted from m:
 1804289383 -1427598262 -1364114958
          0 -1550966999  -102585885
          0           0  -782303108
Here is the strictly-upper-triangular matrix extracted from m:
          0 -1427598262 -1364114958
          0           0  -102585885
          0           0           0
Here is the unit-lower-triangular matrix extracted from m:
          1           0           0
 -465790871           1           0
 1957747793 -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
constexpr

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: