Eigen  3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)
Eigen::MatrixBase< Derived > Class Template Reference

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;
}
Scalar & x()
Definition: DenseCoeffsBase.h:437
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:52

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 unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh . More...
 
const AdjointReturnType adjoint () const
 
void adjointInPlace ()
 
template<typename EssentialPart >
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
 
template<typename EssentialPart >
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
 
template<typename OtherDerived >
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
 
template<typename OtherScalar >
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
 
template<typename OtherDerived >
void applyOnTheRight (const EigenBase< OtherDerived > &other)
 
template<typename OtherScalar >
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
 
ArrayWrapper< Derived > array ()
 
const ArrayWrapper< const Derived > array () const
 
const DiagonalWrapper< const Derived > asDiagonal () const
 
const MatrixFunctionReturnValue< Derived > asinh () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh . More...
 
const MatrixFunctionReturnValue< Derived > atanh () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh . More...
 
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
 
RealScalar blueNorm () const
 
const ColPivHouseholderQR< PlainObjectcolPivHouseholderQr () const
 
const CompleteOrthogonalDecomposition< PlainObjectcompleteOrthogonalDecomposition () 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 unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos . More...
 
const MatrixFunctionReturnValue< Derived > cosh () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh . More...
 
template<typename OtherDerived >
PlainObject cross (const MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
 
Scalar determinant () const
 
DiagonalReturnType diagonal ()
 
const ConstDiagonalReturnType diagonal () const
 
Diagonal< Derived, DynamicIndexdiagonal (Index index)
 
const Diagonal< const Derived, DynamicIndexdiagonal (Index index) const
 
Index diagonalSize () const
 
template<typename OtherDerived >
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot (const MatrixBase< OtherDerived > &other) const
 
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix. More...
 
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
 
const MatrixExponentialReturnValue< Derived > exp () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp . More...
 
Derived & forceAlignedAccess ()
 
const Derived & forceAlignedAccess () const
 
template<bool Enable>
std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > forceAlignedAccessIf ()
 
template<bool Enable>
add_const_on_value_type_t< std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > > forceAlignedAccessIf () const
 
const FullPivHouseholderQR< PlainObjectfullPivHouseholderQr () const
 
const FullPivLU< PlainObjectfullPivLu () const
 
const HNormalizedReturnType hnormalized () const
 homogeneous normalization More...
 
HomogeneousReturnType homogeneous () const
 
const HouseholderQR< PlainObjecthouseholderQr () const
 
RealScalar hypotNorm () const
 
const Inverse< Derived > inverse () const
 
bool isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
bool isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<int Options>
JacobiSVD< typename MatrixBase< Derived >::PlainObject, Options > jacobiSvd () const
 
template<typename OtherDerived >
const Product< Derived, OtherDerived, LazyProduct > lazyProduct (const MatrixBase< OtherDerived > &other) const
 
const LDLT< PlainObjectldlt () const
 
const LLT< PlainObjectllt () const
 
const MatrixLogarithmReturnValue< Derived > log () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log . More...
 
template<int p>
RealScalar lpNorm () const
 
const PartialPivLU< PlainObjectlu () const
 
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
 
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
 
const MatrixFunctionReturnValue< Derived > matrixFunction (StemFunction f) const
 Helper function for the unsupported MatrixFunctions module.
 
NoAlias< Derived, Eigen::MatrixBasenoalias ()
 
RealScalar norm () const
 
void normalize ()
 
const PlainObject normalized () const
 
template<typename OtherDerived >
bool operator!= (const 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 OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator-= (const MatrixBase< OtherDerived > &other)
 
Derived & operator= (const MatrixBase &other)
 
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
 
RealScalar operatorNorm () const
 Computes the L2 operator norm. More...
 
const PartialPivLU< PlainObjectpartialPivLu () const
 
const MatrixPowerReturnValue< Derived > pow (const RealScalar &p) const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow . More...
 
const MatrixComplexPowerReturnValue< Derived > pow (const std::complex< RealScalar > &p) const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow . More...
 
template<unsigned int UpLo>
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView ()
 
template<unsigned int UpLo>
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView () const
 
Derived & setIdentity ()
 
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this. More...
 
Derived & setUnit (Index i)
 Set the coefficients of *this to the i-th unit (basis) vector. More...
 
Derived & setUnit (Index newSize, Index i)
 Resizes to the given newSize, and writes the i-th unit (basis) vector into *this. More...
 
const MatrixFunctionReturnValue< Derived > sin () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin . More...
 
const MatrixFunctionReturnValue< Derived > sinh () const
 This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh . More...
 
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 unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt . More...
 
RealScalar squaredNorm () const
 
RealScalar stableNorm () const
 
void stableNormalize ()
 
const PlainObject stableNormalized () const
 
Scalar trace () const
 
template<unsigned int Mode>
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView ()
 
template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView () const
 
PlainObject unitOrthogonal (void) const
 
- Public Member Functions inherited from Eigen::DenseBase< Derived >
bool all () const
 
bool allFinite () const
 
bool any () const
 
iterator begin ()
 
const_iterator begin () const
 
const_iterator cbegin () const
 
const_iterator cend () const
 
ColwiseReturnType colwise ()
 
ConstColwiseReturnType colwise () 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
 
bool hasNaN () const
 
EIGEN_CONSTEXPR Index innerSize () const
 
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename Derived >
bool isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const
 
bool isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
EIGEN_DEPRECATED Derived & lazyAssign (const DenseBase< OtherDerived > &other)
 
template<int NaNPropagation>
internal::traits< Derived >::Scalar maxCoeff () const
 
template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
 
template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
 
Scalar mean () const
 
template<int NaNPropagation>
internal::traits< Derived >::Scalar minCoeff () const
 
template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
 
template<int NaNPropagation, typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
 
const NestByValue< Derived > nestByValue () const
 
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
 
CommaInitializer< Derived > operator<< (const Scalar &s)
 
Derived & operator= (const DenseBase &other)
 
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this. More...
 
EIGEN_CONSTEXPR Index outerSize () const
 
Scalar prod () const
 
template<typename Func >
internal::traits< Derived >::Scalar redux (const Func &func) const
 
template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor > replicate () const
 
const Replicate< Derived, Dynamic, Dynamicreplicate (Index rowFactor, Index colFactor) const
 
void resize (Index newSize)
 
void resize (Index rows, Index cols)
 
ReverseReturnType reverse ()
 
ConstReverseReturnType reverse () const
 
void reverseInPlace ()
 
RowwiseReturnType rowwise ()
 
ConstRowwiseReturnType rowwise () const
 
template<typename ThenDerived , typename ElseDerived >
const Select< Derived, ThenDerived, ElseDerived > select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
 
template<typename ThenDerived >
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const
 
template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
 
Derived & setConstant (const Scalar &value)
 
Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector. More...
 
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector. More...
 
Derived & setOnes ()
 
Derived & setRandom ()
 
Derived & setZero ()
 
Scalar sum () const
 
template<typename OtherDerived >
void swap (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
void swap (PlainObjectBase< OtherDerived > &other)
 
TransposeReturnType transpose ()
 
const ConstTransposeReturnType transpose () const
 
void transposeInPlace ()
 
CoeffReturnType value () const
 
template<typename Visitor >
void visit (Visitor &func) const
 
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index colStride () const EIGEN_NOEXCEPT
 
Derived & derived ()
 
const Derived & derived () const
 
EIGEN_CONSTEXPR Index innerStride () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index outerStride () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index rowStride () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
 
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, WriteAccessors >
Scalar & coeffRef (Index index)
 
Scalar & coeffRef (Index row, Index col)
 
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
Derived & derived ()
 
const Derived & derived () const
 
Scalar & operator() (Index index)
 
Scalar & operator() (Index row, Index col)
 
Scalar & operator[] (Index index)
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
 
Scalar & w ()
 
Scalar & x ()
 
Scalar & y ()
 
Scalar & z ()
 
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
CoeffReturnType coeff (Index index) const
 
CoeffReturnType coeff (Index row, Index col) const
 
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
Derived & derived ()
 
const Derived & derived () const
 
CoeffReturnType operator() (Index index) const
 
CoeffReturnType operator() (Index row, Index col) const
 
CoeffReturnType operator[] (Index index) const
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
 
CoeffReturnType w () const
 
CoeffReturnType x () const
 
CoeffReturnType y () const
 
CoeffReturnType z () const
 
- Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
Derived & derived ()
 
const Derived & derived () const
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
 

Static Public Member Functions

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

Additional Inherited Members

- Public Types inherited from Eigen::DenseBase< Derived >
enum  {
  RowsAtCompileTime ,
  ColsAtCompileTime ,
  SizeAtCompileTime ,
  MaxRowsAtCompileTime ,
  MaxColsAtCompileTime ,
  MaxSizeAtCompileTime ,
  IsVectorAtCompileTime ,
  NumDimensions ,
  Flags ,
  IsRowMajor ,
  InnerSizeAtCompileTime ,
  InnerStrideAtCompileTime ,
  OuterStrideAtCompileTime
}
 
typedef random_access_iterator_type const_iterator
 
typedef random_access_iterator_type iterator
 
typedef Array< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTimePlainArray
 
typedef Matrix< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTimePlainMatrix
 
typedef std::conditional_t< internal::is_same< typename internal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArrayPlainObject
 The plain matrix or array type corresponding to this expression. More...
 
typedef internal::traits< Derived >::Scalar Scalar
 
typedef internal::traits< Derived >::StorageIndex StorageIndex
 The type used to store indices. More...
 
typedef Scalar value_type
 
- Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
 The interface type of indices. More...
 
- Protected Member Functions inherited from Eigen::DenseBase< Derived >
 DenseBase ()
 

Member Function Documentation

◆ acosh()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .

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

◆ adjoint()

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

Example:

cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
static const RandomReturnType Random()
Definition: Random.h:114
Matrix< std::complex< float >, 2, 2 > Matrix2cf
2×2 matrix of type std::complex<float>.
Definition: Matrix.h:502

Output:

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

◆ 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

replaces *this by other * *this.

Example:

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;
Matrix< float, 3, 3 > Matrix3f
3×3 matrix of type float.
Definition: Matrix.h:500

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()

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

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

Example:

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

◆ array() [1/2]

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

◆ array() [2/2]

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

◆ asDiagonal()

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

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

Example:

cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;
const DiagonalWrapper< const Derived > asDiagonal() const
Definition: DiagonalMatrix.h:327
Matrix< int, 3, 1 > Vector3i
3×1 vector of type int.
Definition: Matrix.h:499
Matrix< int, 3, 3 > Matrix3i
3×3 matrix of type int.
Definition: Matrix.h:499

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 unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh .

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

◆ atanh()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh .

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

◆ bdcSvd() [1/2]

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

This is defined in the SVD module.

#include <Eigen/SVD>
Returns
the singular value decomposition of *this computed by Divide & Conquer algorithm
See also
class BDCSVD

◆ bdcSvd() [2/2]

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

This is defined in the SVD module.

#include <Eigen/SVD>
Returns
the singular value decomposition of *this computed by Divide & Conquer algorithm
See also
class BDCSVD

◆ blueNorm()

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

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

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

◆ colPivHouseholderQr()

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

◆ completeOrthogonalDecomposition()

template<typename Derived >
const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition
inline
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:

cout << "Here is the matrix m:" << endl << m << endl;
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;
}
const Inverse< Derived > inverse() const
Definition: InverseImpl.h:350
Scalar determinant() const
Definition: Determinant.h:110
Matrix< double, 3, 3 > Matrix3d
3×3 matrix of type double.
Definition: Matrix.h:501

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its determinant is 0.209
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also
inverse(), computeInverseWithCheck()

◆ 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:

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

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also
inverse(), computeInverseAndDetWithCheck()

◆ cos()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos .

Returns
an expression of the matrix cosine of *this.

◆ cosh()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh .

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

◆ determinant()

template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant
inline

This is defined in the LU module.

#include <Eigen/LU>
Returns
the determinant of this matrix

◆ diagonal() [1/4]

template<typename Derived >
Diagonal< Derived, Index_ > Eigen::MatrixBase< Derived >::diagonal
inline
Returns
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here are the coefficients on the main diagonal of m:
 7
 9
-5
See also
class Diagonal
Returns
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

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

Example:

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;
TransposeReturnType transpose()
Definition: Transpose.h:184
Matrix< int, 4, 4 > Matrix4i
4×4 matrix of type int.
Definition: Matrix.h:499

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also
MatrixBase::diagonal(), class Diagonal

◆ diagonal() [2/4]

template<typename Derived >
const Diagonal< const Derived, Index_ > Eigen::MatrixBase< Derived >::diagonal
inline

This is the const version of diagonal().

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

◆ diagonal() [3/4]

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also
MatrixBase::diagonal(), class Diagonal

◆ diagonal() [4/4]

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

This is the const version of diagonal(Index).

◆ diagonalSize()

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

◆ dot()

template<typename Derived >
template<typename OtherDerived >
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType Eigen::MatrixBase< Derived >::dot ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
the dot product of *this with other.

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

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

◆ eigenvalues()

template<typename Derived >
MatrixBase< Derived >::EigenvaluesReturnType Eigen::MatrixBase< Derived >::eigenvalues
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:

VectorXcd eivals = ones.eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
static const ConstantReturnType Ones()
Definition: CwiseNullaryOp.h:672
Matrix< std::complex< double >, Dynamic, 1 > VectorXcd
Dynamic×1 vector of type std::complex<double>.
Definition: Matrix.h:503
Matrix< double, Dynamic, Dynamic > MatrixXd
Dynamic×Dynamic matrix of type double.
Definition: Matrix.h:501

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 unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp .

Returns
an expression of the matrix exponential of *this.

◆ forceAlignedAccess() [1/2]

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

◆ forceAlignedAccess() [2/2]

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

◆ forceAlignedAccessIf() [1/2]

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

◆ forceAlignedAccessIf() [2/2]

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

◆ fullPivHouseholderQr()

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

◆ fullPivLu()

template<typename Derived >
const FullPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::fullPivLu
inline

This is defined in the LU module.

#include <Eigen/LU>
Returns
the full-pivoting LU decomposition of *this.
See also
class FullPivLU

◆ householderQr()

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

◆ hypotNorm()

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

◆ Identity() [1/2]

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

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

Example:

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

Output:

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

◆ Identity() [2/2]

template<typename Derived >
const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( Index  rows,
Index  cols 
)
inlinestatic
Returns
an expression of the identity matrix (not necessarily square).

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

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

Example:

cout << MatrixXd::Identity(4, 3) << endl;
static const IdentityReturnType Identity()
Definition: CwiseNullaryOp.h:801

Output:

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

◆ inverse()

template<typename Derived >
const Inverse< Derived > Eigen::MatrixBase< Derived >::inverse
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:
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << endl;
Output:
Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also
computeInverseAndDetWithCheck()

◆ 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:

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:

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

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1
See also
class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()

◆ isLowerTriangular()

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

◆ isOrthogonal()

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

Example:

Vector3d v(1,0,0);
Vector3d w(1e-4,0,1);
cout << "Here's the vector v:" << endl << v << endl;
cout << "Here's the vector w:" << endl << w << endl;
cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl;
cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;
Scalar & w()
Definition: DenseCoeffsBase.h:463
Matrix< double, 3, 1 > Vector3d
3×1 vector of type double.
Definition: Matrix.h:501

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

◆ 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:

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

Output:

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

◆ isUpperTriangular()

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

◆ jacobiSvd()

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

This is defined in the SVD module.

#include <Eigen/SVD>
Returns
the singular value decomposition of *this computed by two-sided Jacobi transformations.
See also
class JacobiSVD

◆ lazyProduct()

template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived, LazyProduct > Eigen::MatrixBase< Derived >::lazyProduct ( const MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the matrix product of *this and other without implicit evaluation.

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

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

◆ ldlt()

template<typename Derived >
const LDLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::ldlt
inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns
the Cholesky decomposition with full pivoting without square root of *this
See also
SelfAdjointView::ldlt()

◆ llt()

template<typename Derived >
const LLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::llt
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 unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log .

Returns
an expression of the matrix logarithm of *this.

◆ lpNorm()

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

◆ normalize()

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

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

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

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

◆ normalized()

template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::normalized
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*() [1/2]

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*() [2/2]

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*=()

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:

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

replaces *this by *this + other.

Returns
a reference to *this

◆ operator-=()

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

replaces *this by *this - other.

Returns
a reference to *this

◆ operator=()

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

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

◆ operator==()

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

◆ operatorNorm()

template<typename Derived >
MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::operatorNorm
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:

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()

◆ partialPivLu()

template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::partialPivLu
inline

This is defined in the LU module.

#include <Eigen/LU>
Returns
the partial-pivoting LU decomposition of *this.
See also
class PartialPivLU

◆ pow() [1/2]

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

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

◆ pow() [2/2]

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

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

◆ selfadjointView() [1/2]

template<typename Derived >
template<unsigned int UpLo>
MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase< Derived >::selfadjointView ( )
Returns
an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix

The parameter UpLo can be either Upper or Lower

Example:

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;
@ Lower
Definition: Constants.h:211
@ Upper
Definition: Constants.h:213

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the symmetric matrix extracted from the upper part of m:
 7  6 -3
 6  9  6
-3  6 -5
Here is the symmetric matrix extracted from the lower part of m:
 7 -2  6
-2  9 -6
 6 -6 -5
See also
class SelfAdjointView

◆ selfadjointView() [2/2]

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

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

◆ setIdentity() [1/2]

template<typename Derived >
Derived & Eigen::MatrixBase< Derived >::setIdentity
inline

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

Example:

m.block<3,3>(1,0).setIdentity();
cout << m << endl;
static const ConstantReturnType Zero()
Definition: CwiseNullaryOp.h:516
Derived & setIdentity()
Definition: CwiseNullaryOp.h:875

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:

m.setIdentity(3, 3);
cout << m << endl;
Matrix< float, Dynamic, Dynamic > MatrixXf
Dynamic×Dynamic matrix of type float.
Definition: Matrix.h:500

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 unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin .

Returns
an expression of the matrix sine of *this.

◆ sinh()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh .

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

◆ sqrt()

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

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt .

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

◆ squaredNorm()

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

◆ stableNorm()

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

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

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

◆ stableNormalize()

template<typename Derived >
void Eigen::MatrixBase< Derived >::stableNormalize
inline

Normalizes the vector while avoid underflow and overflow

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

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

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

◆ stableNormalized()

template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::stableNormalized
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
inline
Returns
the trace of *this, i.e. the sum of the coefficients on the main diagonal.

*this can be any matrix, not necessarily square.

See also
diagonal(), sum()

◆ triangularView() [1/2]

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

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

Example:

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)
@ StrictlyUpper
Definition: Constants.h:225
@ UnitLower
Definition: Constants.h:219

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the upper-triangular matrix extracted from m:
 7  6 -3
 0  9  6
 0  0 -5
Here is the strictly-upper-triangular matrix extracted from m:
 0  6 -3
 0  0  6
 0  0  0
Here is the unit-lower-triangular matrix extracted from m:
 1  0  0
-2  1  0
 6 -6  1
See also
class TriangularView

◆ triangularView() [2/2]

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

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

◆ Unit() [1/2]

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

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

This variant is for fixed-size vector only.

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

◆ Unit() [2/2]

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

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

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

◆ UnitW()

template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitW
inlinestatic
Returns
an expression of the W axis unit vector (0,0,0,1)

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

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

◆ UnitX()

template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitX
inlinestatic
Returns
an expression of the X axis unit vector (1{,0}^*)

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

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

◆ UnitY()

template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitY
inlinestatic
Returns
an expression of the Y axis unit vector (0,1{,0}^*)

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

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

◆ UnitZ()

template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitZ
inlinestatic
Returns
an expression of the Z axis unit vector (0,0,1{,0}^*)

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

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

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