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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;
}
*

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 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
 
BDCSVD< PlainObjectbdcSvd (unsigned int computationOptions=0) const
 
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp
< CustomBinaryOp, const
Derived, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
 
RealScalar blueNorm () const
 
template<typename NewType >
CastXpr< NewType >::Type cast () const
 
const ColPivHouseholderQR
< PlainObject
colPivHouseholderQr () const
 
const
CompleteOrthogonalDecomposition
< PlainObject
completeOrthogonalDecomposition () const
 
template<typename ResultType >
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
 
template<typename ResultType >
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
 
ConjugateReturnType conjugate () const
 
template<typename OtherDerived >
MatrixBase< Derived >::PlainObject cross (const MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
MatrixBase< Derived >::PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
 
const CwiseAbsReturnType cwiseAbs () const
 
const CwiseAbs2ReturnType cwiseAbs2 () const
 
const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
 
const CwiseInverseReturnType cwiseInverse () const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar, Scalar >, const
Derived, const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar, Scalar >, const
Derived, const
ConstantReturnType > 
cwiseMax (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, Scalar >, const
Derived, const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
 
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, Scalar >, const
Derived, const
ConstantReturnType > 
cwiseMin (const Scalar &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
 
const CwiseSignReturnType cwiseSign () const
 
const CwiseSqrtReturnType cwiseSqrt () const
 
Scalar determinant () const
 
DiagonalReturnType diagonal ()
 
ConstDiagonalReturnType diagonal () const
 
DiagonalDynamicIndexReturnType diagonal (Index index)
 
ConstDiagonalDynamicIndexReturnType diagonal (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 Derived & forceAlignedAccess () const
 
Derived & forceAlignedAccess ()
 
template<bool Enable>
internal::add_const_on_value_type
< typename
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type >::type 
forceAlignedAccessIf () const
 
template<bool Enable>
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type 
forceAlignedAccessIf ()
 
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
 
const FullPivLU< PlainObjectfullPivLu () const
 
const HNormalizedReturnType hnormalized () const
 homogeneous normalization More...
 
HomogeneousReturnType homogeneous () const
 
const HouseholderQR< PlainObjecthouseholderQr () const
 
RealScalar hypotNorm () const
 
const ImagReturnType imag () const
 
NonConstImagReturnType imag ()
 
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
 
template<int p>
MatrixBase< Derived >::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)
 
NoAlias< Derived,
Eigen::MatrixBase
noalias ()
 
RealScalar norm () const
 
void normalize ()
 
const PlainObject normalized () const
 
template<typename OtherDerived >
bool operator!= (const MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_and_op,
const Derived, const
OtherDerived > 
operator&& (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< Scalar, T >, Derived,
Constant< T > > 
operator* (const T &scalar) const
 
template<typename OtherDerived >
const Product< Derived,
OtherDerived > 
operator* (const MatrixBase< OtherDerived > &other) const
 
template<typename DiagonalDerived >
const Product< Derived,
DiagonalDerived, LazyProduct > 
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
 
template<typename OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
 
template<typename OtherDerived >
const CwiseBinaryOp< sum
< Scalar >, const Derived,
const OtherDerived > 
operator+ (const Eigen::MatrixBase< OtherDerived > &other) const
 
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
 
template<typename OtherDerived >
const CwiseBinaryOp
< difference< Scalar >, const
Derived, const OtherDerived > 
operator- (const Eigen::MatrixBase< OtherDerived > &other) const
 
const NegativeReturnType operator- () const
 
template<typename OtherDerived >
Derived & operator-= (const MatrixBase< OtherDerived > &other)
 
template<typename T >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar, T >, Derived,
Constant< T > > 
operator/ (const T &scalar) const
 
Derived & operator= (const MatrixBase &other)
 
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
 
RealScalar operatorNorm () const
 Computes the L2 operator norm. More...
 
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_or_op,
const Derived, const
OtherDerived > 
operator|| (const Eigen::MatrixBase< OtherDerived > &other) const
 
const PartialPivLU< PlainObjectpartialPivLu () const
 
RealReturnType real () const
 
NonConstRealReturnType real ()
 
Derived & setIdentity ()
 
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this. 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
 
template<typename CustomUnaryOp >
const CwiseUnaryOp
< CustomUnaryOp, const Derived > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise. More...
 
template<typename CustomViewOp >
const CwiseUnaryView
< CustomViewOp, const Derived > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
 
PlainObject unitOrthogonal (void) const
 
- Public Member Functions inherited from Eigen::DenseBase< Derived >
bool all () const
 
bool allFinite () const
 
bool any () const
 
BlockXpr block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
const ConstBlockXpr block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 This is the const version of block(Index,Index,Index,Index). */.
 
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol)
 
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol) const
 This is the const version of block<>(Index, Index). */.
 
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 This is the const version of block<>(Index, Index, Index, Index). */.
 
BlockXpr bottomLeftCorner (Index cRows, Index cCols)
 
const ConstBlockXpr bottomLeftCorner (Index cRows, Index cCols) const
 This is the const version of bottomLeftCorner(Index, Index).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner () const
 This is the const version of bottomLeftCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner (Index cRows, Index cCols) const
 This is the const version of bottomLeftCorner<int, int>(Index, Index).
 
BlockXpr bottomRightCorner (Index cRows, Index cCols)
 
const ConstBlockXpr bottomRightCorner (Index cRows, Index cCols) const
 This is the const version of bottomRightCorner(Index, Index).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner () const
 This is the const version of bottomRightCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner (Index cRows, Index cCols) const
 This is the const version of bottomRightCorner<int, int>(Index, Index).
 
RowsBlockXpr bottomRows (Index n)
 
ConstRowsBlockXpr bottomRows (Index n) const
 This is the const version of bottomRows(Index).
 
template<int N>
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
 This is the const version of bottomRows<int>().
 
ColXpr col (Index i)
 
ConstColXpr col (Index i) const
 This is the const version of col(). */.
 
ConstColwiseReturnType colwise () const
 
ColwiseReturnType colwise ()
 
Index count () 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
 
SegmentReturnType head (Index n)
 
ConstSegmentReturnType head (Index n) const
 This is the const version of head(Index).
 
template<int N>
FixedSegmentReturnType< N >::Type head (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
 This is the const version of head<int>().
 
Index innerSize () const
 
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename Derived >
bool isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const
 
template<typename OtherDerived >
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
template<typename OtherDerived >
Derived & lazyAssign (const DenseBase< OtherDerived > &other)
 
ColsBlockXpr leftCols (Index n)
 
ConstColsBlockXpr leftCols (Index n) const
 This is the const version of leftCols(Index).
 
template<int N>
NColsBlockXpr< N >::Type leftCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
 This is the const version of leftCols<int>().
 
internal::traits< Derived >::Scalar maxCoeff () const
 
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
 
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
 
Scalar mean () const
 
ColsBlockXpr middleCols (Index startCol, Index numCols)
 
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
 This is the const version of middleCols(Index,Index).
 
template<int N>
NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
 This is the const version of middleCols<int>().
 
RowsBlockXpr middleRows (Index startRow, Index n)
 
ConstRowsBlockXpr middleRows (Index startRow, Index n) const
 This is the const version of middleRows(Index,Index).
 
template<int N>
NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
 This is the const version of middleRows<int>().
 
internal::traits< Derived >::Scalar minCoeff () const
 
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
 
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
 
const NestByValue< Derived > nestByValue () const
 
Index nonZeros () const
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, typename
DenseBase< Derived >
::PlainObject
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, typename
DenseBase< Derived >
::PlainObject
NullaryExpr (Index size, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, typename
DenseBase< Derived >
::PlainObject
NullaryExpr (const CustomNullaryOp &func)
 
CommaInitializer< Derived > operator<< (const Scalar &s)
 
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
 
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
 
Derived & operator= (const DenseBase &other)
 
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this. More...
 
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, Dynamic
replicate (Index rowFactor, Index colFactor) const
 
void resize (Index newSize)
 
void resize (Index rows, Index cols)
 
ReverseReturnType reverse ()
 
ConstReverseReturnType reverse () const
 
void reverseInPlace ()
 
ColsBlockXpr rightCols (Index n)
 
ConstColsBlockXpr rightCols (Index n) const
 This is the const version of rightCols(Index).
 
template<int N>
NColsBlockXpr< N >::Type rightCols (Index n=N)
 
template<int N>
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
 This is the const version of rightCols<int>().
 
RowXpr row (Index i)
 
ConstRowXpr row (Index i) const
 This is the const version of row(). */.
 
ConstRowwiseReturnType rowwise () const
 
RowwiseReturnType rowwise ()
 
SegmentReturnType segment (Index start, Index n)
 
ConstSegmentReturnType segment (Index start, Index n) const
 This is the const version of segment(Index,Index).
 
template<int N>
FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
segment (Index start, Index n=N) const
 This is the const version of segment<int>(Index).
 
template<typename ThenDerived , typename ElseDerived >
const Select< Derived,
ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
 
template<typename ThenDerived >
const Select< Derived,
ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const
 
template<typename ElseDerived >
const Select< Derived,
typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
 
Derived & setConstant (const Scalar &value)
 
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector. More...
 
Derived & setLinSpaced (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)
 
SegmentReturnType tail (Index n)
 
ConstSegmentReturnType tail (Index n) const
 This is the const version of tail(Index).
 
template<int N>
FixedSegmentReturnType< N >::Type tail (Index n=N)
 
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
 This is the const version of tail<int>.
 
BlockXpr topLeftCorner (Index cRows, Index cCols)
 
const ConstBlockXpr topLeftCorner (Index cRows, Index cCols) const
 This is the const version of topLeftCorner(Index, Index).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner () const
 This is the const version of topLeftCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner (Index cRows, Index cCols) const
 This is the const version of topLeftCorner<int, int>(Index, Index).
 
BlockXpr topRightCorner (Index cRows, Index cCols)
 
const ConstBlockXpr topRightCorner (Index cRows, Index cCols) const
 This is the const version of topRightCorner(Index, Index).
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner ()
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner () const
 This is the const version of topRightCorner<int, int>().
 
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner (Index cRows, Index cCols)
 
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner (Index cRows, Index cCols) const
 This is the const version of topRightCorner<int, int>(Index, Index).
 
RowsBlockXpr topRows (Index n)
 
ConstRowsBlockXpr topRows (Index n) const
 This is the const version of topRows(Index).
 
template<int N>
NRowsBlockXpr< N >::Type topRows (Index n=N)
 
template<int N>
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
 This is the const version of topRows<int>().
 
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 >
Index colStride () const
 
Index innerStride () const
 
Index outerStride () const
 
Index rowStride () const
 
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, WriteAccessors >
Scalar & coeffRef (Index row, Index col)
 
Scalar & coeffRef (Index index)
 
Scalar & operator() (Index row, Index col)
 
Scalar & operator() (Index index)
 
Scalar & operator[] (Index index)
 
Scalar & w ()
 
Scalar & x ()
 
Scalar & y ()
 
Scalar & z ()
 
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
CoeffReturnType coeff (Index row, Index col) const
 
CoeffReturnType coeff (Index index) const
 
CoeffReturnType operator() (Index row, Index col) const
 
CoeffReturnType operator() (Index index) const
 
CoeffReturnType operator[] (Index index) const
 
CoeffReturnType w () const
 
CoeffReturnType x () const
 
CoeffReturnType y () const
 
CoeffReturnType z () const
 
- Public Member Functions inherited from Eigen::EigenBase< Derived >
Index cols () const
 
Derived & derived ()
 
const Derived & derived () const
 
Index rows () const
 
Index size () const
 

Static Public Member Functions

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

Friends

template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< T, Scalar >, Constant< T >
, Derived > 
operator* (const T &scalar, const StorageBaseType &expr)
 

Additional Inherited Members

- Public Types inherited from Eigen::DenseBase< Derived >
enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime,
  MaxRowsAtCompileTime,
  MaxColsAtCompileTime,
  MaxSizeAtCompileTime,
  IsVectorAtCompileTime,
  Flags,
  IsRowMajor
}
 
typedef Array< typename
internal::traits< Derived >
::Scalar, internal::traits
< Derived >::RowsAtCompileTime,
internal::traits< Derived >
::ColsAtCompileTime, AutoAlign|(internal::traits
< Derived >::Flags
&RowMajorBit?RowMajor:ColMajor),
internal::traits< Derived >
::MaxRowsAtCompileTime,
internal::traits< Derived >
::MaxColsAtCompileTime
PlainArray
 
typedef Matrix< typename
internal::traits< Derived >
::Scalar, internal::traits
< Derived >::RowsAtCompileTime,
internal::traits< Derived >
::ColsAtCompileTime, AutoAlign|(internal::traits
< Derived >::Flags
&RowMajorBit?RowMajor:ColMajor),
internal::traits< Derived >
::MaxRowsAtCompileTime,
internal::traits< Derived >
::MaxColsAtCompileTime
PlainMatrix
 
typedef internal::conditional
< internal::is_same< typename
internal::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 ()
 

Member Function Documentation

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

Example:

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

Output:

Here is the 2x2 complex matrix m:
 (-0.211,0.68) (-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
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()
template<typename Derived >
template<typename EssentialPart >
void Eigen::MatrixBase< Derived >::applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

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

On input:

Parameters
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See Also
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()
template<typename Derived >
template<typename EssentialPart >
void Eigen::MatrixBase< Derived >::applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

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

On input:

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

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

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

Example:

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

Output:

2 0 0
0 5 0
0 0 6
See Also
class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
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
See Also
class BDCSVD
template<typename Derived>
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const
inline
Returns
an expression of a custom coefficient-wise operator func of *this and other

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

Here is an example illustrating the use of custom functors:

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

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)
See Also
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::blueNorm ( ) const
inline
Returns
the l2 norm of *this using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

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

See Also
norm(), stableNorm(), hypotNorm()
template<typename Derived>
template<typename NewType >
CastXpr<NewType>::Type Eigen::MatrixBase< Derived >::cast ( ) const
inline
Returns
an expression of *this with the Scalar type casted to NewScalar.

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

See Also
class CwiseUnaryOp
template<typename Derived >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::colPivHouseholderQr ( ) const
inline
Returns
the column-pivoting Householder QR decomposition of *this.
See Also
class ColPivHouseholderQR
template<typename Derived >
const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition ( ) const
inline
Returns
the complete orthogonal decomposition of *this.
See Also
class CompleteOrthogonalDecomposition
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.

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;
}

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()
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.

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()
template<typename Derived>
ConjugateReturnType Eigen::MatrixBase< Derived >::conjugate ( ) const
inline
Returns
an expression of the complex conjugate of *this.
See Also
Math functions, MatrixBase::adjoint()
template<typename Derived>
const CwiseAbsReturnType Eigen::MatrixBase< Derived >::cwiseAbs ( ) const
inline
Returns
an expression of the coefficient-wise absolute value of *this

Example:

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

Output:

2 4 6
5 1 0
See Also
cwiseAbs2()
template<typename Derived>
const CwiseAbs2ReturnType Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const
inline
Returns
an expression of the coefficient-wise squared absolute value of *this

Example:

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

Output:

 4 16 36
25  1  0
See Also
cwiseAbs()
template<typename Derived>
const CwiseScalarEqualReturnType Eigen::MatrixBase< Derived >::cwiseEqual ( const Scalar s) const
inline
Returns
an expression of the coefficient-wise == operator of *this and a scalar s
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().
See Also
cwiseEqual(const MatrixBase<OtherDerived> &) const
template<typename Derived>
const CwiseInverseReturnType Eigen::MatrixBase< Derived >::cwiseInverse ( ) const
inline
Returns
an expression of the coefficient-wise inverse of *this.

Example:

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

Output:

  0.5     2     1
0.333     4     1
See Also
cwiseProduct()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise max of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMax(w) << endl;

Output:

4
3
4
See Also
class CwiseBinaryOp, min()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMax ( const Scalar other) const
inline
Returns
an expression of the coefficient-wise max of *this and scalar other
See Also
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise min of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMin(w) << endl;

Output:

2
2
3
See Also
class CwiseBinaryOp, max()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMin ( const Scalar other) const
inline
Returns
an expression of the coefficient-wise min of *this and scalar other
See Also
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseNotEqual ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise != operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

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

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1
See Also
cwiseEqual(), isApprox(), isMuchSmallerThan()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise quotient of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseQuotient(w) << endl;

Output:

 0.5
 1.5
1.33
See Also
class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
template<typename Derived>
const CwiseSignReturnType Eigen::MatrixBase< Derived >::cwiseSign ( ) const
inline
Returns
an expression of the coefficient-wise signum of *this.

Example:

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

Output:

 1 -1  1
-1  1  0
template<typename Derived>
const CwiseSqrtReturnType Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const
inline
Returns
an expression of the coefficient-wise square root of *this.

Example:

Vector3d v(1,2,4);
cout << v.cwiseSqrt() << endl;

Output:

   1
1.41
   2
See Also
cwisePow(), cwiseSquare()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant ( ) const
inline

This is defined in the LU module.

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

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;

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

This is the const version of diagonal().

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

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:

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
template<typename Derived >
MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType Eigen::MatrixBase< Derived >::diagonal ( Index  index) const
inline

This is the const version of diagonal(Index).

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

Computes the eigenvalues of a matrix.

Returns
Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

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

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

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

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

Output:

The eigenvalues of the 3x3 matrix of ones are:
(-5.31e-17,0)
        (3,0)
        (0,0)
See Also
EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()
template<typename Derived >
const ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess ( ) const
inline
Returns
an expression of *this with forced aligned access
See Also
forceAlignedAccessIf(),class ForceAlignedAccess
template<typename Derived >
ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess ( )
inline
Returns
an expression of *this with forced aligned access
See Also
forceAlignedAccessIf(), class ForceAlignedAccess
template<typename Derived>
template<bool Enable>
internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type>::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( ) const
inline
Returns
an expression of *this with forced aligned access if Enable is true.
See Also
forceAlignedAccess(), class ForceAlignedAccess
template<typename Derived>
template<bool Enable>
internal::conditional<Enable,ForceAlignedAccess<Derived>,Derived&>::type Eigen::MatrixBase< Derived >::forceAlignedAccessIf ( )
inline
Returns
an expression of *this with forced aligned access if Enable is true.
See Also
forceAlignedAccess(), class ForceAlignedAccess
template<typename Derived >
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::fullPivHouseholderQr ( ) const
inline
Returns
the full-pivoting Householder QR decomposition of *this.
See Also
class FullPivHouseholderQR
template<typename Derived >
const FullPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::fullPivLu ( ) const
inline

This is defined in the LU module.

#include <Eigen/LU>
Returns
the full-pivoting LU decomposition of *this.
See Also
class FullPivLU
template<typename Derived >
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::householderQr ( ) const
inline
Returns
the Householder QR decomposition of *this.
See Also
class HouseholderQR
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::hypotNorm ( ) const
inline
Returns
the l2 norm of *this avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
See Also
norm(), stableNorm()
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()
template<typename Derived >
const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( Index  rows,
Index  cols 
)
inlinestatic
Returns
an expression of the identity matrix (not necessarily square).

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

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

Example:

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

Output:

1 0 0
0 1 0
0 0 1
0 0 0
See Also
Identity(), setIdentity(), isIdentity()
template<typename Derived>
const ImagReturnType Eigen::MatrixBase< Derived >::imag ( ) const
inline
Returns
an read-only expression of the imaginary part of *this.
See Also
real()
template<typename Derived>
NonConstImagReturnType Eigen::MatrixBase< Derived >::imag ( )
inline
Returns
a non const expression of the imaginary part of *this.
See Also
real()
template<typename Derived >
const Inverse< Derived > Eigen::MatrixBase< Derived >::inverse ( ) const
inline

This is defined in the LU module.

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

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

Note
This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following: 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()
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()
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()
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()
template<typename Derived >
template<typename OtherDerived >
bool Eigen::MatrixBase< Derived >::isOrthogonal ( const MatrixBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns
true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

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

Output:

Here's the vector v:
1
0
0
Here's the vector w:
0.0001
     0
     1
v.isOrthogonal(w) returns: 0
v.isOrthogonal(w,1e-3) returns: 1
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
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()
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.
See Also
class JacobiSVD
template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived, LazyProduct > Eigen::MatrixBase< Derived >::lazyProduct ( const MatrixBase< OtherDerived > &  other) const
Returns
an expression of the matrix product of *this and other without implicit evaluation.

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

Warning
This version of the matrix product can be much much slower. So use it only if you know what you are doing and that you measured a true speed improvement.
See Also
operator*(const MatrixBase&)
template<typename Derived >
const LDLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::ldlt ( ) const
inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns
the Cholesky decomposition with full pivoting without square root of *this
See Also
SelfAdjointView::ldlt()
template<typename Derived >
const LLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::llt ( ) const
inline

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns
the LLT decomposition of *this
See Also
SelfAdjointView::llt()
template<typename Derived>
template<int p>
MatrixBase<Derived>::RealScalar Eigen::MatrixBase< Derived >::lpNorm ( ) const
Returns
the coefficient-wise $ \ell^p $ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values of the coefficients of *this. If p is the special value Eigen::Infinity, this function returns the $ \ell^\infty $ norm, that is the maximum of the absolute values of the coefficients of *this.

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

Note
For matrices, this function does not compute the operator-norm. That is, if *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and $\infty$-norm matrix operator norms using partial reductions .
See Also
norm()
template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::lu ( ) const
inline

This is defined in the LU module.

#include <Eigen/LU>

Synonym of partialPivLu().

Returns
the partial-pivoting LU decomposition of *this.
See Also
class PartialPivLU
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()
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()
template<typename Derived >
NoAlias< Derived, MatrixBase > Eigen::MatrixBase< Derived >::noalias ( )
Returns
a pseudo expression of *this with an operator= assuming no aliasing between *this and the source expression.

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

Here are some examples where noalias is usefull:

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

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

* A.noalias() = A * B;
*

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

* A = A * B;
*
See Also
class NoAlias
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm ( ) const
inline
Returns
, for vectors, the l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.
See Also
lpNorm(), dot(), squaredNorm()
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()
template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::normalized ( ) const
inline
Returns
an expression of the quotient of *this by its own norm.
Warning
If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.

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

See Also
norm(), normalize()
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==
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator&& ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise boolean and operator of *this and other
Warning
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) && (v<0)) << endl;

Output:

0
0
0
See Also
operator||(), select()
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > Eigen::MatrixBase< Derived >::operator* ( const T &  scalar) const
Returns
an expression of *this scaled by the scalar factor scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
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*()
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.
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
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< sum <Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator+ ( const Eigen::MatrixBase< OtherDerived > &  other) const
Returns
an expression of the sum of *this and other
Note
If you want to add a given scalar to all coefficients, see Cwise::operator+().
See Also
class CwiseBinaryOp, operator+=()
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
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< difference <Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator- ( const Eigen::MatrixBase< OtherDerived > &  other) const
Returns
an expression of the difference of *this and other
Note
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See Also
class CwiseBinaryOp, operator-=()
template<typename Derived>
const NegativeReturnType Eigen::MatrixBase< Derived >::operator- ( ) const
inline
Returns
an expression of the opposite of *this
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
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > Eigen::MatrixBase< Derived >::operator/ ( const T &  scalar) const
Returns
an expression of *this divided by the scalar value scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
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)

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

Computes the L2 operator norm.

Returns
Operator norm of the matrix.

This is defined in the Eigenvalues module.

#include <Eigen/Eigenvalues>

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

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

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

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

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
<< ones.operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3
See Also
SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator|| ( const Eigen::MatrixBase< OtherDerived > &  other) const
inline
Returns
an expression of the coefficient-wise boolean or operator of *this and other
Warning
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) || (v<0)) << endl;

Output:

1
0
1
See Also
operator&&(), select()
template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::partialPivLu ( ) const
inline

This is defined in the LU module.

#include <Eigen/LU>
Returns
the partial-pivoting LU decomposition of *this.
See Also
class PartialPivLU
template<typename Derived>
RealReturnType Eigen::MatrixBase< Derived >::real ( ) const
inline
Returns
a read-only expression of the real part of *this.
See Also
imag()
template<typename Derived>
NonConstRealReturnType Eigen::MatrixBase< Derived >::real ( )
inline
Returns
a non const expression of the real part of *this.
See Also
imag()
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;

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()
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;

Output:

1 0 0
0 1 0
0 0 1
See Also
MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm ( ) const
inline
Returns
, for vectors, the squared l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this with itself.
See Also
dot(), norm(), lpNorm()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::stableNorm ( ) const
inline
Returns
the l2 norm of *this avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s 2 - compute $ s \Vert \frac{*this}{s} \Vert $ in a standard way

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

See Also
norm(), blueNorm(), hypotNorm()
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()
template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::stableNormalized ( ) const
inline
Returns
an expression of the quotient of *this by its own norm while avoiding underflow and overflow.

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

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

Warning
If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.
See Also
stableNorm(), stableNormalize(), normalized()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::trace ( ) const
inline
Returns
the trace of *this, i.e. the sum of the coefficients on the main diagonal.

*this can be any matrix, not necessarily square.

See Also
diagonal(), sum()
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)

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
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()

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

Apply a unary operator coefficient-wise.

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

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define function to be applied coefficient-wise
double ramp(double x)
{
if (x > 0)
return x;
else
return 0;
}
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
  0.68  0.823      0      0
     0      0  0.108 0.0268
 0.566      0      0  0.904
 0.597  0.536  0.258  0.832

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See Also
unaryViewExpr, binaryExpr, class CwiseUnaryOp
template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, const Derived> Eigen::MatrixBase< Derived >::unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inline
Returns
an expression of a custom coefficient-wise unary operator func of *this

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See Also
unaryExpr, binaryExpr class CwiseUnaryOp
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()
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()
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()
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()
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()
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()

Friends And Related Function Documentation

template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator* ( const T &  scalar,
const StorageBaseType &  expr 
)
friend
Returns
an expression of expr scaled by the scalar factor scalar
Template Parameters
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.

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