 Eigen  3.4.90 (git rev a4098ac676528a83cfb73d4d26ce1b42ec05f47c) 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
 Derived is the derived type, e.g. a matrix type, or an expression, etc.

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

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

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...

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...

BDCSVD< PlainObjectbdcSvd (unsigned int computationOptions=0) 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 ()

ConstDiagonalReturnType diagonal () const

DiagonalDynamicIndexReturnType diagonal (Index index)

ConstDiagonalDynamicIndexReturnType diagonal (Index index) const

Index diagonalSize () const

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

EigenvaluesReturnType eigenvalues () const
Computes the eigenvalues of a matrix. 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>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf ()

template<bool Enable>
internal::add_const_on_value_type< typenameinternal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type 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

JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) 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>

template<unsigned int UpLo>

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 ()

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) 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 internal::conditional< internal::is_same< typenameinternal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray >::type PlainObject
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 ()

## ◆ 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.

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

Example:

Matrix2cf m = Matrix2cf::Random();
cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
static const RandomReturnType Random()
Definition: Random.h:115

Output:

Here is the 2x2 complex matrix m:
(-1,-0.737) (0.0655,-0.562)
(0.511,-0.0827)  (-0.906,0.358)
Here is the adjoint of m:
(-1,0.737)  (0.511,0.0827)
(0.0655,0.562) (-0.906,-0.358)

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

template<typename Derived >
inline

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

has the same effect on m as doing

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.

## ◆ 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
 essential the essential part of the vector v tau the scaling factor of the Householder transformation workspace a pointer to working space with at least this->cols() entries
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
 essential the essential part of the vector v tau the scaling factor of the Householder transformation workspace a pointer to working space with at least this->rows() entries
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()

## ◆ applyOnTheLeft() [1/2]

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

replaces *this by other * *this.

Example:

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

Output:

At start, A =
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
After applyOnTheLeft, A =
-0.737  0.0655   0.358
0.511  -0.562   0.359
-1 -0.0827  -0.906


## ◆ 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 $$B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right )$$.

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:

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 =
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
After A *= B, A =
-0.906      -1 -0.0827
0.358  -0.737  0.0655
0.359   0.511  -0.562
After applyOnTheRight, A =
-0.0827  -0.906      -1
0.0655   0.358  -0.737
-0.562   0.359   0.511


## ◆ array() [1/2]

template<typename Derived >
 ArrayWrapper< Derived > Eigen::MatrixBase< Derived >::array ( )
inline
Returns
an Array expression of this matrix
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
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:325

Output:

2 0 0
0 5 0
0 0 6

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()

template<typename Derived >
 BDCSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::bdcSvd ( unsigned int computationOptions = 0 ) const
inline

This is defined in the SVD module.

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

## ◆ blueNorm()

template<typename Derived >
 NumTraits< typenameinternal::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.

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.
class ColPivHouseholderQR

## ◆ completeOrthogonalDecomposition()

template<typename Derived >
 const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition
inline
Returns
the complete orthogonal decomposition of *this.
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::dummy_precision() ) const
inline

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse and determinant, with invertibility check.

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

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

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

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
double determinant;
m.computeInverseAndDetWithCheck(inverse,determinant,invertible);
cout << "Its determinant is " << determinant << endl;
if(invertible) {
cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
}
else {
cout << "It is not invertible." << endl;
}
const Inverse< Derived > inverse() const
Definition: InverseImpl.h:350
Scalar determinant() const
Definition: Determinant.h:110

Output:

Here is the matrix m:
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
Its determinant is -0.606
It is invertible, and its inverse is:
-0.37  -0.889 -0.0491
-0.737  -0.172   -1.69
-0.628   0.997   0.209

inverse(), computeInverseWithCheck()

## ◆ computeInverseWithCheck()

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

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse, with invertibility check.

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

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

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

Example:

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

Output:

Here is the matrix m:
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
It is invertible, and its inverse is:
-0.37  -0.889 -0.0491
-0.737  -0.172   -1.69
-0.628   0.997   0.209

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

*this is not required to be square.

Example:

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:
-10  -1 -10
-8   1   4
5  -6   4
Here are the coefficients on the main diagonal of m:
-10
1
4

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

*this is not required to be square.

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

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
<< m.diagonal<1>().transpose() << endl
<< m.diagonal<-2>().transpose() << endl;
TransposeReturnType transpose()
Definition: Transpose.h:184

Output:

Here is the matrix m:
-10   1   4   7
-8  -6   9 -10
5 -10  -2  -9
-1   4   0   1
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
1  9 -9
5 4

MatrixBase::diagonal(), class Diagonal

## ◆ diagonal() [2/4]

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

*this is not required to be square.

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

Example:

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

Output:

Here is the matrix m:
-10   1   4   7
-8  -6   9 -10
5 -10  -2  -9
-1   4   0   1
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
1  9 -9
5 4

MatrixBase::diagonal(), class Diagonal

## ◆ diagonal() [4/4]

template<typename Derived >
 MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType 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()).
rows(), cols(), SizeAtCompileTime.

## ◆ dot()

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

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

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

Example:

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

Output:

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


## ◆ 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
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
forceAlignedAccessIf(),class ForceAlignedAccess

## ◆ forceAlignedAccessIf() [1/2]

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

## ◆ forceAlignedAccessIf() [2/2]

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

## ◆ householderQr()

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

## ◆ hypotNorm()

template<typename Derived >
 NumTraits< typenameinternal::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.
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

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

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:
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:
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
Its inverse is:
-0.37  -0.889 -0.0491
-0.737  -0.172   -1.69
-0.628   0.997   0.209

computeInverseAndDetWithCheck()

## ◆ isDiagonal()

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

Example:

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

Output:

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

asDiagonal()

## ◆ isIdentity()

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

Example:

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

Output:

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

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

## ◆ isLowerTriangular()

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

## ◆ isOrthogonal()

template<typename Derived >
template<typename OtherDerived >
 bool Eigen::MatrixBase< Derived >::isOrthogonal ( const MatrixBase< OtherDerived > & other, const RealScalar & prec = NumTraits::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

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

Example:

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

Output:

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


## ◆ isUpperTriangular()

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

## ◆ jacobiSvd()

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

This is defined in the SVD module.

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

## ◆ 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

## ◆ 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 .
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.
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
 essential the essential part of the vector v tau the scaling factor of the Householder transformation beta the result of H * *this
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
 tau the scaling factor of the Householder transformation beta the result of H * *this
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;
class NoAlias

## ◆ norm()

template<typename Derived >
 NumTraits< typenameinternal::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.
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.
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.

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()
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*().
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:

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 =
-1 -0.0827  -0.906
-0.737  0.0655   0.358
0.511  -0.562   0.359
After A *= B, A =
-0.906      -1 -0.0827
0.358  -0.737  0.0655
0.359   0.511  -0.562
After applyOnTheRight, A =
-0.0827  -0.906      -1
0.0655   0.358  -0.737
-0.562   0.359   0.511


## ◆ 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()
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:

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


## ◆ 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.
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.

template<typename Derived >
template<unsigned int UpLo>
Returns
an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix

The parameter UpLo can be either Upper or Lower

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the symmetric matrix extracted from the upper part of m:" << endl
cout << "Here is the symmetric matrix extracted from the lower part of m:" << endl
@ Lower
Definition: Constants.h:211
@ Upper
Definition: Constants.h:213

Output:

Here is the matrix m:
-10  -1 -10
-8   1   4
5  -6   4
Here is the symmetric matrix extracted from the upper part of m:
-10  -1 -10
-1   1   4
-10   4   4
Here is the symmetric matrix extracted from the lower part of m:
-10  -8   5
-8   1  -6
5  -6   4


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

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

## ◆ setIdentity() [1/2]

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

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

Example:

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

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

## ◆ setIdentity() [2/2]

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

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

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

Example:

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

Output:

1 0 0
0 1 0
0 0 1

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

## ◆ setUnit() [1/2]

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

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

Parameters
 i index of the unique coefficient to be set to 1

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

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

## ◆ setUnit() [2/2]

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

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

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

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

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< typenameinternal::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.
dot(), norm(), lpNorm()

## ◆ stableNorm()

template<typename Derived >
 NumTraits< typenameinternal::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.

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.
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.
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.

diagonal(), sum()

## ◆ triangularView() [1/2]

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

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

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the upper-triangular matrix extracted from m:" << endl
<< Matrix3i(m.triangularView<Eigen::Upper>()) << endl;
cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
<< Matrix3i(m.triangularView<Eigen::StrictlyUpper>()) << endl;
cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
<< Matrix3i(m.triangularView<Eigen::UnitLower>()) << endl;
// FIXME need to implement output for triangularViews (Bug 885)
@ StrictlyUpper
Definition: Constants.h:225
@ UnitLower
Definition: Constants.h:219

Output:

Here is the matrix m:
-10  -1 -10
-8   1   4
5  -6   4
Here is the upper-triangular matrix extracted from m:
-10  -1 -10
0   1   4
0   0   4
Here is the strictly-upper-triangular matrix extracted from m:
0  -1 -10
0   0   4
0   0   0
Here is the unit-lower-triangular matrix extracted from m:
1  0  0
-8  1  0
5 -6  1

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.

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.

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.

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.

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.

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.