Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > Class Template Reference

#include <SparseSelfAdjointView.h>

+ Inheritance diagram for DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >:

List of all members.

Public Types

enum  
enum  
enum  
enum  
typedef internal::remove_all
< ActualLhsType >::type 
_ActualLhsType
typedef internal::remove_all
< ActualRhsType >::type 
_ActualRhsType
typedef internal::remove_all
< LhsNested >::type 
_LhsNested
typedef internal::remove_all
< RhsNested >::type 
_RhsNested
typedef
LhsBlasTraits::DirectLinearAccessType 
ActualLhsType
typedef
RhsBlasTraits::DirectLinearAccessType 
ActualRhsType
typedef MatrixBase
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
Base
typedef Base::CoeffReturnType CoeffReturnType
typedef VectorwiseOp
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Vertical
ColwiseReturnType
typedef const VectorwiseOp
< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Vertical
ConstColwiseReturnType
typedef const Diagonal< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
ConstDiagonalReturnType
typedef const Reverse< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, BothDirections
ConstReverseReturnType
typedef const VectorwiseOp
< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Horizontal
ConstRowwiseReturnType
typedef const VectorBlock
< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
ConstSegmentReturnType
typedef Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
>::ColsAtCompileTime==1?SizeMinusOne:1,
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
>::ColsAtCompileTime==1?1:SizeMinusOne
ConstStartMinusOne
typedef const Transpose< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
ConstTransposeReturnType
typedef Diagonal
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
DiagonalReturnType
typedef
internal::add_const_on_value_type
< typename internal::eval
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::type >
::type 
EvalReturnType
typedef CoeffBasedProduct
< LhsNested, RhsNested, 0 > 
FullyLazyCoeffBaseProductType
typedef CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar >
, const ConstStartMinusOne
HNormalizedReturnType
typedef Homogeneous
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, HomogeneousReturnTypeDirection
HomogeneousReturnType
typedef internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Index 
Index
 The type of indices.
typedef internal::blas_traits
< _LhsNested
LhsBlasTraits
typedef Lhs::Nested LhsNested
typedef internal::traits< Lhs >
::Scalar 
LhsScalar
typedef
internal::packet_traits
< Scalar >::type 
PacketScalar
typedef Base::PlainObject PlainObject
 The plain matrix type corresponding to this expression.
typedef NumTraits< Scalar >::Real RealScalar
typedef Reverse
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, BothDirections
ReverseReturnType
typedef internal::blas_traits
< _RhsNested
RhsBlasTraits
typedef Rhs::Nested RhsNested
typedef internal::traits< Rhs >
::Scalar 
RhsScalar
typedef VectorwiseOp
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Horizontal
RowwiseReturnType
typedef internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
Scalar
typedef VectorBlock
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
SegmentReturnType
typedef
internal::stem_function
< Scalar >::type 
StemFunction
typedef internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
>::StorageKind 
StorageKind

Public Member Functions

void addTo (Dest &dst) const
const AdjointReturnType adjoint () const
void adjointInPlace ()
bool all (void) const
bool any (void) const
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
void applyOnTheRight (const EigenBase< OtherDerived > &other)
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
ArrayWrapper
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
array ()
const ArrayWrapper< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
array () const
const DiagonalWrapper< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
asDiagonal () const
const PermutationWrapper
< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
asPermutation () const
const CwiseBinaryOp
< CustomBinaryOp, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, BlockRows,
BlockCols > 
block (Index startRow, Index startCol)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, BlockRows,
BlockCols > 
block (Index startRow, Index startCol) const
RealScalar blueNorm () const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
bottomLeftCorner (Index cRows, Index cCols)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
bottomLeftCorner (Index cRows, Index cCols) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
bottomLeftCorner ()
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
bottomLeftCorner () const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
bottomRightCorner (Index cRows, Index cCols)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
bottomRightCorner (Index cRows, Index cCols) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
bottomRightCorner ()
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
bottomRightCorner () const
RowsBlockXpr bottomRows (Index n)
ConstRowsBlockXpr bottomRows (Index n) const
NRowsBlockXpr< N >::Type bottomRows ()
ConstNRowsBlockXpr< N >::Type bottomRows () const
internal::cast_return_type
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
CwiseUnaryOp
< internal::scalar_cast_op
< typename internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar,
NewType >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > >::type 
cast () const
Base::CoeffReturnType coeff (Index row, Index col) const
Base::CoeffReturnType coeff (Index i) const
const ScalarcoeffRef (Index row, Index col) const
const ScalarcoeffRef (Index i) const
ColXpr col (Index i)
ConstColXpr col (Index i) const
const ColPivHouseholderQR
< PlainObject
colPivHouseholderQr () const
Index cols () const
ConstColwiseReturnType colwise () const
ColwiseReturnType colwise ()
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
ConjugateReturnType conjugate () const
const
MatrixFunctionReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cos () const
const
MatrixFunctionReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cosh () const
Index count () const
cross_product_return_type
< OtherDerived >::type 
cross (const MatrixBase< OtherDerived > &other) const
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cwiseAbs () const
const CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cwiseAbs2 () const
const CwiseBinaryOp
< std::equal_to< Scalar >
, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< std::binder1st
< std::equal_to< Scalar >
>, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cwiseEqual (const Scalar &s) const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cwiseInverse () const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
ConstantReturnType > 
cwiseMax (const Scalar &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
ConstantReturnType > 
cwiseMin (const Scalar &other) const
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, const
OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
cwiseSqrt () const
 DenseTimeSparseSelfAdjointProduct (const Lhs &lhs, const Rhs &rhs)
Scalar determinant () const
const Diagonal< const
FullyLazyCoeffBaseProductType, 0 > 
diagonal () const
const Diagonal
< FullyLazyCoeffBaseProductType,
Index
diagonal () const
const Diagonal
< FullyLazyCoeffBaseProductType,
Dynamic
diagonal (Index index) const
DiagonalReturnType diagonal ()
DiagonalIndexReturnType
< Dynamic >::Type 
diagonal (Index index)
Index diagonalSize () const
internal::scalar_product_traits
< typename internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar,
typename internal::traits
< OtherDerived >::Scalar >
::ReturnType 
dot (const MatrixBase< OtherDerived > &other) const
const EIGEN_CWISE_PRODUCT_RETURN_TYPE (DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, OtherDerived) cwiseProduct(const Eigen
EigenvaluesReturnType eigenvalues () const
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
EvalReturnType eval () const
void evalTo (Dest &dst) const
const
MatrixExponentialReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
exp () const
void fill (const Scalar &value)
const Flagged
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Added,
Removed > 
flagged () const
const ForceAlignedAccess
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
forceAlignedAccess () const
ForceAlignedAccess
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
forceAlignedAccess ()
internal::add_const_on_value_type
< typename
internal::conditional< Enable,
ForceAlignedAccess
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
>, DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & >::type >
::type 
forceAlignedAccessIf () const
internal::conditional< Enable,
ForceAlignedAccess
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
>, DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & >::type 
forceAlignedAccessIf ()
const WithFormat
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
format (const IOFormat &fmt) const
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
const FullPivLU< PlainObjectfullPivLu () const
SegmentReturnType head (Index size)
DenseBase::ConstSegmentReturnType head (Index size) const
FixedSegmentReturnType< Size >
::Type 
head ()
ConstFixedSegmentReturnType
< Size >::Type 
head () const
const HNormalizedReturnType hnormalized () const
HomogeneousReturnType homogeneous () const
const HouseholderQR< PlainObjecthouseholderQr () const
RealScalar hypotNorm () const
const ImagReturnType imag () const
NonConstImagReturnType imag ()
Index innerSize () const
const internal::inverse_impl
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
inverse () const
bool isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
const LazyProductReturnType
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, OtherDerived >::Type 
lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObjectldlt () const
ColsBlockXpr leftCols (Index n)
ConstColsBlockXpr leftCols (Index n) const
NColsBlockXpr< N >::Type leftCols ()
ConstNColsBlockXpr< N >::Type leftCols () const
const _LhsNestedlhs () const
const LLT< PlainObjectllt () const
const
MatrixLogarithmReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
log () const
RealScalar lpNorm () const
const PartialPivLU< PlainObjectlu () const
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
MatrixBase
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > & 
matrix ()
const MatrixBase
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > & 
matrix () const
const
MatrixFunctionReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
matrixFunction (StemFunction f) const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
maxCoeff () const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
maxCoeff (IndexType *row, IndexType *col) const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
maxCoeff (IndexType *index) const
Scalar mean () const
ColsBlockXpr middleCols (Index startCol, Index numCols)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
NColsBlockXpr< N >::Type middleCols (Index startCol)
ConstNColsBlockXpr< N >::Type middleCols (Index startCol) const
RowsBlockXpr middleRows (Index startRow, Index numRows)
ConstRowsBlockXpr middleRows (Index startRow, Index numRows) const
NRowsBlockXpr< N >::Type middleRows (Index startRow)
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow) const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
minCoeff () const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
minCoeff (IndexType *row, IndexType *col) const
internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar 
minCoeff (IndexType *index) const
const NestByValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
nestByValue () const
NoAlias
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, Eigen::MatrixBase
noalias ()
Index nonZeros () const
RealScalar norm () const
void normalize ()
const PlainObject normalized () const
 operator const PlainObject & () const
bool operator!= (const MatrixBase< OtherDerived > &other) const
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
const ScalarMultipleReturnType operator* (const RealScalar &scalar) const
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
operator* (const std::complex< Scalar > &scalar) const
const ProductReturnType
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, OtherDerived >::Type 
operator* (const MatrixBase< OtherDerived > &other) const
const DiagonalProduct
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, DiagonalDerived, OnTheRight
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
ScalarMultipleReturnType operator* (const UniformScaling< Scalar > &s) const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator*= (const EigenBase< OtherDerived > &other)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator*= (const Scalar &other)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator+= (const MatrixBase< OtherDerived > &other)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator+= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_opposite_op
< typename internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar >
, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
operator- () const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator-= (const MatrixBase< OtherDerived > &other)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator-= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > >::Scalar >
, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
operator/ (const Scalar &scalar) const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator/= (const Scalar &other)
CommaInitializer
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
operator<< (const Scalar &s)
CommaInitializer
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
operator<< (const DenseBase< OtherDerived > &other)
bool operator== (const MatrixBase< OtherDerived > &other) const
RealScalar operatorNorm () const
Index outerSize () const
const PartialPivLU< PlainObjectpartialPivLu () const
Scalar prod () const
RealReturnType real () const
NonConstRealReturnType real ()
const Replicate
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, RowFactor,
ColFactor > 
replicate () const
const Replicate
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, Dynamic,
Dynamic
replicate (Index rowFacor, Index colFactor) const
void resize (Index size)
void resize (Index rows, Index cols)
ReverseReturnType reverse ()
ConstReverseReturnType reverse () const
void reverseInPlace ()
const _RhsNestedrhs () const
ColsBlockXpr rightCols (Index n)
ConstColsBlockXpr rightCols (Index n) const
NColsBlockXpr< N >::Type rightCols ()
ConstNColsBlockXpr< N >::Type rightCols () const
RowXpr row (Index i)
ConstRowXpr row (Index i) const
Index rows () const
ConstRowwiseReturnType rowwise () const
RowwiseReturnType rowwise ()
template<typename Dest >
void scaleAndAddTo (Dest &, Scalar) const
SegmentReturnType segment (Index start, Index size)
DenseBase::ConstSegmentReturnType segment (Index start, Index size) const
FixedSegmentReturnType< Size >
::Type 
segment (Index start)
ConstFixedSegmentReturnType
< Size >::Type 
segment (Index start) const
const Select
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
const Select
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >
, ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const
const Select
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
SelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView ()
ConstSelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView () const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setConstant (const Scalar &value)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setIdentity ()
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setIdentity (Index rows, Index cols)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setLinSpaced (Index size, const Scalar &low, const Scalar &high)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setLinSpaced (const Scalar &low, const Scalar &high)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setOnes ()
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setRandom ()
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
setZero ()
const
MatrixFunctionReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
sin () const
const
MatrixFunctionReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
sinh () const
const SparseView
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const
const
MatrixSquareRootReturnValue
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
sqrt () const
RealScalar squaredNorm () const
RealScalar stableNorm () const
void subTo (Dest &dst) const
Scalar sum () const
void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
void swap (PlainObjectBase< OtherDerived > &other)
SegmentReturnType tail (Index size)
DenseBase::ConstSegmentReturnType tail (Index size) const
FixedSegmentReturnType< Size >
::Type 
tail ()
ConstFixedSegmentReturnType
< Size >::Type 
tail () const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
topLeftCorner (Index cRows, Index cCols)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
topLeftCorner (Index cRows, Index cCols) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
topLeftCorner ()
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
topLeftCorner () const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
topRightCorner (Index cRows, Index cCols)
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
topRightCorner (Index cRows, Index cCols) const
Block
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
topRightCorner ()
const Block< const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo >, CRows,
CCols > 
topRightCorner () const
RowsBlockXpr topRows (Index n)
ConstRowsBlockXpr topRows (Index n) const
NRowsBlockXpr< N >::Type topRows ()
ConstNRowsBlockXpr< N >::Type topRows () const
Scalar trace () const
Eigen::Transpose
< DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
transpose ()
ConstTransposeReturnType transpose () const
void transposeInPlace ()
TriangularViewReturnType< Mode >
::Type 
triangularView ()
ConstTriangularViewReturnType
< Mode >::Type 
triangularView () const
const CwiseUnaryOp
< CustomUnaryOp, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
const CwiseUnaryView
< CustomViewOp, const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
PlainObject unitOrthogonal (void) const
CoeffReturnType value () const
void visit (Visitor &func) const

Static Public Member Functions

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 IdentityReturnType Identity ()
static const IdentityReturnType Identity (Index rows, Index cols)
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)
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
static const CwiseNullaryOp
< CustomNullaryOp,
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
static const CwiseNullaryOp
< CustomNullaryOp,
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
NullaryExpr (Index size, const CustomNullaryOp &func)
static const CwiseNullaryOp
< CustomNullaryOp,
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
NullaryExpr (const CustomNullaryOp &func)
static const ConstantReturnType Ones (Index rows, Index cols)
static const ConstantReturnType Ones (Index size)
static const ConstantReturnType Ones ()
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >
, DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
Random (Index rows, Index cols)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >
, DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
Random (Index size)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >
, DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > > 
Random ()
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 const ConstantReturnType Zero (Index rows, Index cols)
static const ConstantReturnType Zero (Index size)
static const ConstantReturnType Zero ()

Protected Member Functions

void checkTransposeAliasing (const OtherDerived &other) const
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator+= (const ArrayBase< OtherDerived > &)
DenseTimeSparseSelfAdjointProduct
< Lhs, Rhs, UpLo > & 
operator-= (const ArrayBase< OtherDerived > &)

Protected Attributes

LhsNested m_lhs
PlainObject m_result
RhsNested m_rhs

Member Typedef Documentation

typedef internal::remove_all<ActualLhsType>::type _ActualLhsType
inherited
typedef internal::remove_all<ActualRhsType>::type _ActualRhsType
inherited
typedef internal::remove_all<LhsNested>::type _LhsNested
inherited
typedef internal::remove_all<RhsNested>::type _RhsNested
inherited
typedef LhsBlasTraits::DirectLinearAccessType ActualLhsType
inherited
typedef RhsBlasTraits::DirectLinearAccessType ActualRhsType
inherited
typedef MatrixBase<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > Base
inherited
typedef Base::CoeffReturnType CoeffReturnType
inherited
typedef const VectorwiseOp<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , Vertical> ConstColwiseReturnType
inherited
typedef const Diagonal<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > ConstDiagonalReturnType
inherited
typedef const Reverse<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , BothDirections> ConstReverseReturnType
inherited
typedef const VectorwiseOp<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , Horizontal> ConstRowwiseReturnType
inherited
typedef const VectorBlock<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > ConstSegmentReturnType
inherited
typedef Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne
inherited
typedef const Transpose<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > ConstTransposeReturnType
inherited
typedef Diagonal<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > DiagonalReturnType
inherited
typedef internal::add_const_on_value_type<typename internal::eval<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::type>::type EvalReturnType
inherited
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar>, const ConstStartMinusOne > HNormalizedReturnType
inherited
typedef internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Index Index
inherited

The type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also:
Preprocessor directives.
typedef internal::blas_traits<_LhsNested> LhsBlasTraits
inherited
typedef Lhs::Nested LhsNested
inherited
typedef internal::traits<Lhs>::Scalar LhsScalar
inherited
typedef internal::packet_traits<Scalar>::type PacketScalar
inherited
typedef Base::PlainObject PlainObject
inherited

The plain matrix type corresponding to this expression.

This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.

Reimplemented from MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

typedef NumTraits<Scalar>::Real RealScalar
inherited
typedef internal::blas_traits<_RhsNested> RhsBlasTraits
inherited
typedef Rhs::Nested RhsNested
inherited
typedef internal::traits<Rhs>::Scalar RhsScalar
inherited
typedef internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar Scalar
inherited
typedef VectorBlock<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > SegmentReturnType
inherited
typedef internal::stem_function<Scalar>::type StemFunction
inherited
typedef internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::StorageKind StorageKind
inherited

Member Enumeration Documentation

anonymous enum
inherited
anonymous enum
inherited
anonymous enum
inherited
anonymous enum
inherited

Constructor & Destructor Documentation

DenseTimeSparseSelfAdjointProduct ( const Lhs &  lhs,
const Rhs &  rhs 
)
inline

Member Function Documentation

void addTo ( Dest &  dst) const
inlineinherited
const AdjointReturnType adjoint ( ) const
inherited
Returns:
an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

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

Output:

Here is the 2x2 complex matrix m:
 (-0.211,0.68) (-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
void adjointInPlace ( )
inherited

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.
See also:
transpose(), adjoint(), transposeInPlace()
bool all ( void  ) const
inherited
Returns:
true if all coefficients are true

Example:

Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());
Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();
// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:
cout << "Is (" << p0.transpose() << ") inside the box: "
<< ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;
cout << "Is (" << p1.transpose() << ") inside the box: "
<< ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;

Output:

Is (  0.68 -0.211  0.566) inside the box: 0
Is (0.597 0.823 0.605) inside the box: 1
See also:
any(), Cwise::operator<()
bool any ( void  ) const
inherited
Returns:
true if at least one coefficient is true
See also:
all()
void applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)
inherited

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()
void applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)
inherited

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()
void applyOnTheLeft ( const EigenBase< OtherDerived > &  other)
inherited

replaces *this by *this * other.

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

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()
void applyOnTheRight ( const EigenBase< OtherDerived > &  other)
inherited

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

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

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

See also:
class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()
ArrayWrapper<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > array ( )
inlineinherited
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
const ArrayWrapper<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > array ( ) const
inlineinherited
const DiagonalWrapper<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > asDiagonal ( ) const
inherited
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()
const PermutationWrapper<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > asPermutation ( ) const
inherited
const CwiseBinaryOp<CustomBinaryOp, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const
inlineinherited
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-=()
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+=()
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**)
{
Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
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()
Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inlineinherited
Returns:
a dynamic-size expression of a block in *this.
Parameters:
startRowthe first row in the block
startColthe first column in the block
blockRowsthe number of rows in the block
blockColsthe number of columns in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
m.block(1, 1, 2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6 1
-3 0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, block(Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

This is the const version of block(Index,Index,Index,Index).

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
)
inlineinherited
Returns:
a fixed-size expression of a block in *this.

The template parameters BlockRows and BlockCols are the number of rows and columns in the block.

Parameters:
startRowthe first row in the block
startColthe first column in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
m.block<2,2>(1,1).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6 1
-3 0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note:
since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:
m.template block<3,3>(1,1);
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const
inlineinherited

This is the const version of block<>(Index, Index).

RealScalar blueNorm ( ) const
inherited
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()
Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns:
a dynamic-size expression of a bottom-left corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
cout << m.bottomLeftCorner(2, 2) << endl;
m.bottomLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomLeftCorner(Index, Index).

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> bottomLeftCorner ( )
inlineinherited
Returns:
an expression of a fixed-size bottom-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
cout << m.bottomLeftCorner<2,2>() << endl;
m.bottomLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> bottomLeftCorner ( ) const
inlineinherited

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

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > bottomRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns:
a dynamic-size expression of a bottom-right corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner(2, 2):" << endl;
cout << m.bottomRightCorner(2, 2) << endl;
m.bottomRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomRightCorner(Index, Index).

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> bottomRightCorner ( )
inlineinherited
Returns:
an expression of a fixed-size bottom-right corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,2>():" << endl;
cout << m.bottomRightCorner<2,2>() << endl;
m.bottomRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> bottomRightCorner ( ) const
inlineinherited

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

RowsBlockXpr bottomRows ( Index  n)
inlineinherited
Returns:
a block consisting of the bottom rows of *this.
Parameters:
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows(2):" << endl;
cout << a.bottomRows(2) << endl;
a.bottomRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstRowsBlockXpr bottomRows ( Index  n) const
inlineinherited

This is the const version of bottomRows(Index).

NRowsBlockXpr<N>::Type bottomRows ( )
inlineinherited
Returns:
a block consisting of the bottom rows of *this.
Template Parameters:
Nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows<2>():" << endl;
cout << a.bottomRows<2>() << endl;
a.bottomRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type bottomRows ( ) const
inlineinherited

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

internal::cast_return_type<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar, NewType>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > >::type cast ( ) const
inlineinherited
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
void checkTransposeAliasing ( const OtherDerived &  other) const
protectedinherited
Base::CoeffReturnType coeff ( Index  row,
Index  col 
) const
inlineinherited
Base::CoeffReturnType coeff ( Index  i) const
inlineinherited
const Scalar& coeffRef ( Index  row,
Index  col 
) const
inlineinherited
const Scalar& coeffRef ( Index  i) const
inlineinherited
ColXpr col ( Index  i)
inlineinherited
Returns:
an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

Matrix3d m = Matrix3d::Identity();
m.col(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 4 0
0 5 0
0 6 1
See also:
row(), class Block
ConstColXpr col ( Index  i) const
inlineinherited

This is the const version of col().

const ColPivHouseholderQR<PlainObject> colPivHouseholderQr ( ) const
inherited
Returns:
the column-pivoting Householder QR decomposition of *this.
See also:
class ColPivHouseholderQR
Index cols ( void  ) const
inlineinherited
ConstColwiseReturnType colwise ( ) const
inherited
Returns:
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl;
cout << "Here is the maximum absolute value of each column:"
<< endl << m.cwiseAbs().colwise().maxCoeff() << 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
Here is the sum of each column:
  1.04  0.815 -0.238
Here is the maximum absolute value of each column:
 0.68 0.823 0.536
See also:
rowwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
ColwiseReturnType colwise ( )
inherited
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
rowwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
void computeInverseAndDetWithCheck ( ResultType &  inverse,
typename ResultType::Scalar &  determinant,
bool invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const
inherited

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 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:

Matrix3d m = Matrix3d::Random();
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()
void computeInverseWithCheck ( ResultType &  inverse,
bool invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const
inherited

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:

Matrix3d m = Matrix3d::Random();
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()
ConjugateReturnType conjugate ( ) const
inlineinherited
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()
static const ConstantReturnType Constant ( Index  rows,
Index  cols,
const Scalar value 
)
staticinherited
Returns:
an expression of a constant matrix of value value

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase 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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
static const ConstantReturnType Constant ( Index  size,
const Scalar value 
)
staticinherited
Returns:
an expression of a constant matrix of value value

The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
static const ConstantReturnType Constant ( const Scalar value)
staticinherited
Returns:
an expression of a constant matrix of value value

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

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
const MatrixFunctionReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cos ( ) const
inherited
const MatrixFunctionReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cosh ( ) const
inherited
Index count ( ) const
inherited
Returns:
the number of coefficients which evaluate to true
See also:
all(), any()
cross_product_return_type<OtherDerived>::type cross ( const MatrixBase< OtherDerived > &  other) const
inherited

This is defined in the Geometry module.

#include <Eigen/Geometry>
Returns:
the cross product of *this and other

Here is a very good explanation of cross-product: http://xkcd.com/199/

See also:
MatrixBase::cross3()
PlainObject cross3 ( const MatrixBase< OtherDerived > &  other) const
inherited

This is defined in the Geometry module.

#include <Eigen/Geometry>
Returns:
the cross product of *this and other using only the x, y, and z coefficients

The size of *this and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.

See also:
MatrixBase::cross()
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cwiseAbs ( ) const
inlineinherited
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()
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cwiseAbs2 ( ) const
inlineinherited
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()
const CwiseBinaryOp<std::equal_to<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> cwiseEqual ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns:
an expression of the coefficient-wise == operator of *this and other
Warning:
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

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

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3
See also:
cwiseNotEqual(), isApprox(), isMuchSmallerThan()
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cwiseEqual ( const Scalar s) const
inlineinherited
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
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cwiseInverse ( ) const
inlineinherited
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()
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
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()
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const ConstantReturnType> cwiseMax ( const Scalar other) const
inlineinherited
Returns:
an expression of the coefficient-wise max of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
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()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const ConstantReturnType> cwiseMin ( const Scalar other) const
inlineinherited
Returns:
an expression of the coefficient-wise min of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<std::not_equal_to<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> cwiseNotEqual ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
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()
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , const OtherDerived> cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
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()
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > cwiseSqrt ( ) const
inlineinherited
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()
Scalar determinant ( ) const
inherited

This is defined in the LU module.

#include <Eigen/LU>
Returns:
the determinant of this matrix
const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal ( ) const
inlineinherited

This is the const version of diagonal().

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

Reimplemented from MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal ( ) const
inlineinherited

This is the const version of diagonal().

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

Reimplemented from MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal ( Index  index) const
inlineinherited

This is the const version of diagonal(Index).

Reimplemented from MatrixBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

DiagonalReturnType diagonal ( )
inherited
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:
 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:

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:
 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
DiagonalIndexReturnType<Dynamic>::Type diagonal ( Index  index)
inherited
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:
 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
Index diagonalSize ( ) const
inlineinherited
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.
internal::scalar_product_traits<typename internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType dot ( const MatrixBase< OtherDerived > &  other) const
inherited
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()
const EIGEN_CWISE_PRODUCT_RETURN_TYPE ( DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >  ,
OtherDerived   
) const
inlineinherited
Returns:
an expression of the Schur product (coefficient wise product) of *this and other

Example:

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

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25
See also:
class CwiseBinaryOp, cwiseAbs2
EigenvaluesReturnType eigenvalues ( ) const
inherited

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:
(-2.98e-17,0)
(3,0)
(1.81e-32,0)
See also:
EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()
Matrix<Scalar,3,1> eulerAngles ( Index  a0,
Index  a1,
Index  a2 
) const
inherited

This is defined in the Geometry module.

#include <Eigen/Geometry>
Returns:
the Euler-angles of the rotation matrix *this using the convention defined by the triplet (a0,a1,a2)

Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:

Vector3f ea = mat.eulerAngles(2, 0, 2);

"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:

mat == AngleAxisf(ea[0], Vector3f::UnitZ())
* AngleAxisf(ea[1], Vector3f::UnitX())
* AngleAxisf(ea[2], Vector3f::UnitZ());

This corresponds to the right-multiply conventions (with right hand side frames).

EvalReturnType eval ( ) const
inlineinherited
Returns:
the matrix or vector obtained by evaluating this expression.

Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.

void evalTo ( Dest &  dst) const
inlineinherited
const MatrixExponentialReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > exp ( ) const
inherited
void fill ( const Scalar value)
inherited

Alias for setConstant(): sets all coefficients in this expression to value.

See also:
setConstant(), Constant(), class CwiseNullaryOp
const Flagged<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , Added, Removed> flagged ( ) const
inherited
Returns:
an expression of *this with added and removed flags

This is mostly for internal use.

See also:
class Flagged
const ForceAlignedAccess<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > forceAlignedAccess ( ) const
inlineinherited
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(),class ForceAlignedAccess

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

ForceAlignedAccess<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > forceAlignedAccess ( )
inlineinherited
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(), class ForceAlignedAccess

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >,DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > &>::type>::type forceAlignedAccessIf ( ) const
inlineinherited
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

internal::conditional<Enable,ForceAlignedAccess<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >,DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > &>::type forceAlignedAccessIf ( )
inlineinherited
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

const WithFormat<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > format ( const IOFormat fmt) const
inlineinherited
Returns:
a WithFormat proxy object allowing to print a matrix the with given format fmt.

See class IOFormat for some examples.

See also:
class IOFormat, class WithFormat
const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr ( ) const
inherited
Returns:
the full-pivoting Householder QR decomposition of *this.
See also:
class FullPivHouseholderQR
const FullPivLU<PlainObject> fullPivLu ( ) const
inherited

This is defined in the LU module.

#include <Eigen/LU>
Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU
SegmentReturnType head ( Index  size)
inherited
Returns:
a dynamic-size expression of the first coefficients of *this.

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.

Parameters:
sizethe number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head(2) << endl;
v.head(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, block(Index,Index)
DenseBase::ConstSegmentReturnType head ( Index  size) const
inherited

This is the const version of head(Index).

FixedSegmentReturnType<Size>::Type head ( )
inherited
Returns:
a fixed-size expression of the first coefficients of *this.

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.

The template parameter Size is the number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
v.head<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
See also:
class Block
ConstFixedSegmentReturnType<Size>::Type head ( ) const
inherited

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

const HNormalizedReturnType hnormalized ( ) const
inherited

This is defined in the Geometry module.

#include <Eigen/Geometry>
Returns:
an expression of the homogeneous normalized vector of *this

Example:

Output:

See also:
VectorwiseOp::hnormalized()
HomogeneousReturnType homogeneous ( ) const
inherited

This is defined in the Geometry module.

#include <Eigen/Geometry>
Returns:
an expression of the equivalent homogeneous 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.

Example:

Output:

See also:
class Homogeneous
const HouseholderQR<PlainObject> householderQr ( ) const
inherited
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR
RealScalar hypotNorm ( ) const
inherited
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()
static const IdentityReturnType Identity ( )
staticinherited
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()
static const IdentityReturnType Identity ( Index  rows,
Index  cols 
)
staticinherited
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()
const ImagReturnType imag ( ) const
inlineinherited
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()
NonConstImagReturnType imag ( )
inlineinherited
Returns:
a non const expression of the imaginary part of *this.
See also:
real()
Index innerSize ( ) const
inlineinherited
Returns:
the inner size.
Note:
For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension with respect to the storage order, i.e., the number of rows for a column-major matrix, and the number of columns for a row-major matrix.
const internal::inverse_impl<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > inverse ( ) const
inherited

This is defined in the LU module.

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

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

Note:
This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following:
  • for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
  • for the general case, use class FullPivLU.
Example:
Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << endl;
Output:
Here is the matrix m:
  0.68  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()
bool isApprox ( const DenseBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
Returns:
true if *this is approximately equal to other, within the precision determined by prec.
Note:
The fuzzy compares are done multiplicatively. Two vectors $ v $ and $ w $ are considered to be approximately equal within precision $ p $ if

\[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \]

For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm L2 norm).
Because of the multiplicativeness of this comparison, one can't use this function to check whether *this is approximately equal to the zero matrix or vector. Indeed, isApprox(zero) returns false unless *this itself is exactly the zero matrix or vector. If you want to test whether *this is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.
See also:
internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
bool isApproxToConstant ( const Scalar value,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
Returns:
true if all coefficients in this matrix are approximately equal to value, to within precision prec
bool isConstant ( const Scalar value,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited

This is just an alias for isApproxToConstant().

Returns:
true if all coefficients in this matrix are approximately equal to value, to within precision prec
bool isDiagonal ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to a diagonal matrix, within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
1e+04     0     1
    0 1e+04     0
    0     0 1e+04
m.isDiagonal() returns: 0
m.isDiagonal(1e-3) returns: 1
See also:
asDiagonal()
bool isIdentity ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
bool isLowerTriangular ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
See also:
isUpperTriangular()
bool isMuchSmallerThan ( const RealScalar other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
bool isMuchSmallerThan ( const DenseBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
Returns:
true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.
Note:
The fuzzy compares are done multiplicatively. A vector $ v $ is considered to be much smaller than a vector $ w $ within precision $ p $ if

\[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \]

For matrices, the comparison is done using the Hilbert-Schmidt norm.
See also:
isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
bool isOnes ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to the matrix where all coefficients are equal to 1, within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
1 1 1
1 1 1
1 1 1
m.isOnes() returns: 0
m.isOnes(1e-3) returns: 1
See also:
class CwiseNullaryOp, Ones()
bool isOrthogonal ( const MatrixBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
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
bool isUnitary ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
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
bool isUpperTriangular ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
See also:
isLowerTriangular()
bool isZero ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns:
true if *this is approximately equal to the zero matrix, within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
     0      0 0.0001
     0      0      0
     0      0      0
m.isZero() returns: 0
m.isZero(1e-3) returns: 1
See also:
class CwiseNullaryOp, Zero()
JacobiSVD<PlainObject> jacobiSvd ( unsigned int  computationOptions = 0) const
inherited

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
const LazyProductReturnType<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,OtherDerived>::Type lazyProduct ( const MatrixBase< OtherDerived > &  other) const
inherited
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&)
const LDLT<PlainObject> ldlt ( ) const
inherited

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns:
the Cholesky decomposition with full pivoting without square root of *this
ColsBlockXpr leftCols ( Index  n)
inlineinherited
Returns:
a block consisting of the left columns of *this.
Parameters:
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols(2):" << endl;
cout << a.leftCols(2) << endl;
a.leftCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstColsBlockXpr leftCols ( Index  n) const
inlineinherited

This is the const version of leftCols(Index).

NColsBlockXpr<N>::Type leftCols ( )
inlineinherited
Returns:
a block consisting of the left columns of *this.
Template Parameters:
Nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols<2>():" << endl;
cout << a.leftCols<2>() << endl;
a.leftCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstNColsBlockXpr<N>::Type leftCols ( ) const
inlineinherited

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

const _LhsNested& lhs ( ) const
inlineinherited
static const SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
Index  size,
const Scalar low,
const Scalar high 
)
staticinherited

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.

When size is set to 1, a vector of length 1 containing 'high' is returned.

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 << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See also:
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp
static const RandomAccessLinSpacedReturnType LinSpaced ( Index  size,
const Scalar low,
const Scalar high 
)
staticinherited

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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 << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See also:
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp
static const SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
const Scalar low,
const Scalar high 
)
staticinherited

Special version for fixed size types which does not require the size parameter.

static const RandomAccessLinSpacedReturnType LinSpaced ( const Scalar low,
const Scalar high 
)
staticinherited

Special version for fixed size types which does not require the size parameter.

const LLT<PlainObject> llt ( ) const
inherited

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns:
the LLT decomposition of *this
const MatrixLogarithmReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > log ( ) const
inherited
RealScalar lpNorm ( ) const
inherited
Returns:
the $ \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.
See also:
norm()

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

const PartialPivLU<PlainObject> lu ( ) const
inherited

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
void makeHouseholder ( EssentialPart &  essential,
Scalar tau,
RealScalar beta 
) const
inherited

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()
void makeHouseholderInPlace ( Scalar tau,
RealScalar beta 
)
inherited

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()
MatrixBase<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >& matrix ( )
inlineinherited
const MatrixBase<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >& matrix ( ) const
inlineinherited
const MatrixFunctionReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > matrixFunction ( StemFunction  f) const
inherited
internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar maxCoeff ( ) const
inherited
Returns:
the maximum of all coefficients of *this
internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar maxCoeff ( IndexType *  row,
IndexType *  col 
) const
inherited
Returns:
the maximum of all coefficients of *this and puts in *row and *col its location.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar maxCoeff ( IndexType *  index) const
inherited
Returns:
the maximum of all coefficients of *this and puts in *index its location.
See also:
DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
Scalar mean ( ) const
inherited
Returns:
the mean of all coefficients of *this
See also:
trace(), prod(), sum()
ColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
)
inlineinherited
Returns:
a block consisting of a range of columns of *this.
Parameters:
startColthe index of the first column in the block
numColsthe number of columns in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
ConstColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) const
inlineinherited

This is the const version of middleCols(Index,Index).

NColsBlockXpr<N>::Type middleCols ( Index  startCol)
inlineinherited
Returns:
a block consisting of a range of columns of *this.
Template Parameters:
Nthe number of columns in the block
Parameters:
startColthe index of the first column in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol) const
inlineinherited

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

RowsBlockXpr middleRows ( Index  startRow,
Index  numRows 
)
inlineinherited
Returns:
a block consisting of a range of rows of *this.
Parameters:
startRowthe index of the first row in the block
numRowsthe number of rows in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
ConstRowsBlockXpr middleRows ( Index  startRow,
Index  numRows 
) const
inlineinherited

This is the const version of middleRows(Index,Index).

NRowsBlockXpr<N>::Type middleRows ( Index  startRow)
inlineinherited
Returns:
a block consisting of a range of rows of *this.
Template Parameters:
Nthe number of rows in the block
Parameters:
startRowthe index of the first row in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type middleRows ( Index  startRow) const
inlineinherited

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

internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar minCoeff ( ) const
inherited
Returns:
the minimum of all coefficients of *this
internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar minCoeff ( IndexType *  row,
IndexType *  col 
) const
inherited
Returns:
the minimum of all coefficients of *this and puts in *row and *col its location.
See also:
DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar minCoeff ( IndexType *  index) const
inherited
Returns:
the minimum of all coefficients of *this and puts in *index its location.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
const NestByValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > nestByValue ( ) const
inlineinherited
Returns:
an expression of the temporary version of *this.
NoAlias<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,Eigen::MatrixBase > noalias ( )
inherited
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
Index nonZeros ( ) const
inlineinherited
Returns:
the number of nonzero coefficients which is in practice the number of stored coefficients.
RealScalar norm ( ) const
inherited
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:
dot(), squaredNorm()
void normalize ( void  )
inherited

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.

See also:
norm(), normalized()
const PlainObject normalized ( ) const
inherited
Returns:
an expression of the quotient of *this 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.

See also:
norm(), normalize()
static const CwiseNullaryOp<CustomNullaryOp, DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
)
staticinherited
Returns:
an expression of a matrix defined by a custom functor func

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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
static const CwiseNullaryOp<CustomNullaryOp, DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
)
staticinherited
Returns:
an expression of a matrix defined by a custom functor func

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
static const CwiseNullaryOp<CustomNullaryOp, DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > NullaryExpr ( const CustomNullaryOp &  func)
staticinherited
Returns:
an expression of a matrix defined by a custom functor func

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

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
static const ConstantReturnType Ones ( Index  rows,
Index  cols 
)
staticinherited
Returns:
an expression of a matrix where all coefficients equal one.

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 Ones() should be used instead.

Example:

cout << MatrixXi::Ones(2,3) << endl;

Output:

1 1 1
1 1 1
See also:
Ones(), Ones(Index), isOnes(), class Ones
static const ConstantReturnType Ones ( Index  size)
staticinherited
Returns:
an expression of a vector where all coefficients equal one.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.

Example:

cout << 6 * RowVectorXi::Ones(4) << endl;
cout << VectorXf::Ones(2) << endl;

Output:

6 6 6 6
1
1
See also:
Ones(), Ones(Index,Index), isOnes(), class Ones
static const ConstantReturnType Ones ( )
staticinherited
Returns:
an expression of a fixed-size matrix or vector where all coefficients equal one.

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

Example:

cout << Matrix2d::Ones() << endl;
cout << 6 * RowVector4i::Ones() << endl;

Output:

1 1
1 1
6 6 6 6
See also:
Ones(Index), Ones(Index,Index), isOnes(), class Ones
operator const PlainObject & ( ) const
inlineinherited
bool operator!= ( const MatrixBase< OtherDerived > &  other) const
inlineinherited
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==
const ScalarMultipleReturnType operator* ( const Scalar scalar) const
inlineinherited
Returns:
an expression of *this scaled by the scalar factor scalar
const ScalarMultipleReturnType operator* ( const RealScalar scalar) const
inherited
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > operator* ( const std::complex< Scalar > &  scalar) const
inlineinherited

Overloaded for efficient real matrix times complex scalar value

const ProductReturnType<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,OtherDerived>::Type operator* ( const MatrixBase< OtherDerived > &  other) const
inherited
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*()
const DiagonalProduct<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , DiagonalDerived, OnTheRight> operator* ( const DiagonalBase< DiagonalDerived > &  diagonal) const
inherited
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.
ScalarMultipleReturnType operator* ( const UniformScaling< Scalar > &  s) const
inherited

Concatenates a linear transformation matrix and a uniform scaling

DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator*= ( const EigenBase< OtherDerived > &  other)
inherited

replaces *this by *this * other.

Returns:
a reference to *this
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator*= ( const Scalar other)
inlineinherited
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator+= ( const MatrixBase< OtherDerived > &  other)
inherited

replaces *this by *this + other.

Returns:
a reference to *this
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator+= ( const EigenBase< OtherDerived > &  other)
inherited
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator+= ( const ArrayBase< OtherDerived > &  )
inlineprotectedinherited
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > operator- ( ) const
inlineinherited
Returns:
an expression of the opposite of *this
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator-= ( const MatrixBase< OtherDerived > &  other)
inherited

replaces *this by *this - other.

Returns:
a reference to *this
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator-= ( const EigenBase< OtherDerived > &  other)
inherited
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator-= ( const ArrayBase< OtherDerived > &  )
inlineprotectedinherited
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >::Scalar>, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > operator/ ( const Scalar scalar) const
inlineinherited
Returns:
an expression of *this divided by the scalar value scalar
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & operator/= ( const Scalar other)
inlineinherited
CommaInitializer<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > operator<< ( const Scalar s)
inherited

Convenient operator to set the coefficients of a matrix.

The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.

Example:

m1 << 1, 2, 3,
4, 5, 6,
7, 8, 9;
cout << m1 << endl << endl;
Matrix3i m2 = Matrix3i::Identity();
m2.block(0,0, 2,2) << 10, 11, 12, 13;
cout << m2 << endl << endl;
v1 << 14, 15;
m2 << v1.transpose(), 16,
v1, m1.block(1,1,2,2);
cout << m2 << endl;

Output:

1 2 3
4 5 6
7 8 9

10 11  0
12 13  0
 0  0  1

14 15 16
14  5  6
15  8  9
See also:
CommaInitializer::finished(), class CommaInitializer
CommaInitializer<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > operator<< ( const DenseBase< OtherDerived > &  other)
inherited
See also:
operator<<(const Scalar&)
bool operator== ( const MatrixBase< OtherDerived > &  other) const
inlineinherited
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!=
RealScalar operatorNorm ( ) const
inherited

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()
Index outerSize ( ) const
inlineinherited
Returns:
true if either the number of rows or the number of columns is equal to 1. In other words, this function returns
rows()==1 || cols()==1
See also:
rows(), cols(), IsVectorAtCompileTime.
Returns:
the outer size.
Note:
For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension with respect to the storage order, i.e., the number of columns for a column-major matrix, and the number of rows for a row-major matrix.
const PartialPivLU<PlainObject> partialPivLu ( ) const
inherited

This is defined in the LU module.

#include <Eigen/LU>
Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU
Scalar prod ( ) const
inherited
Returns:
the product of all coefficients of *this

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the product of all the coefficients:" << endl << m.prod() << 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
Here is the product of all the coefficients:
0.0019
See also:
sum(), mean(), trace()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > Random ( Index  rows,
Index  cols 
)
staticinherited
Returns:
a random matrix expression

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 Random() should be used instead.

Example:

cout << MatrixXi::Random(2,3) << endl;

Output:

 7  6  9
-2  6 -6

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See also:
MatrixBase::setRandom(), MatrixBase::Random(Index), MatrixBase::Random()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > Random ( Index  size)
staticinherited
Returns:
a random vector expression

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.

Example:

cout << VectorXi::Random(2) << endl;

Output:

7
-2

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See also:
MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > Random ( )
staticinherited
Returns:
a fixed-size random matrix or vector expression

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

Example:

cout << 100 * Matrix2i::Random() << endl;

Output:

700 600
-200 600

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See also:
MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random(Index)
RealReturnType real ( ) const
inlineinherited
Returns:
a read-only expression of the real part of *this.
See also:
imag()
NonConstRealReturnType real ( )
inlineinherited
Returns:
a non const expression of the real part of *this.
See also:
imag()
const Replicate<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,RowFactor,ColFactor> replicate ( ) const
inherited
Returns:
an expression of the replication of *this

Example:

MatrixXi m = MatrixXi::Random(2,3);
cout << "Here is the matrix m:" << endl << m << endl;
cout << "m.replicate<3,2>() = ..." << endl;
cout << m.replicate<3,2>() << endl;

Output:

Here is the matrix m:
 7  6  9
-2  6 -6
m.replicate<3,2>() = ...
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
See also:
VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
const Replicate<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,Dynamic,Dynamic> replicate ( Index  rowFacor,
Index  colFactor 
) const
inherited
Returns:
an expression of the replication of *this

Example:

Vector3i v = Vector3i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "v.replicate(2,5) = ..." << endl;
cout << v.replicate(2,5) << endl;

Output:

Here is the vector v:
7
-2
6
v.replicate(2,5) = ...
 7  7  7  7  7
-2 -2 -2 -2 -2
 6  6  6  6  6
 7  7  7  7  7
-2 -2 -2 -2 -2
 6  6  6  6  6
See also:
VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
void resize ( Index  size)
inlineinherited

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

void resize ( Index  rows,
Index  cols 
)
inlineinherited

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

ReverseReturnType reverse ( )
inherited
Returns:
an expression of the reverse of *this.

Example:

MatrixXi m = MatrixXi::Random(3,4);
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the reverse of m:" << endl << m.reverse() << endl;
cout << "Here is the coefficient (1,0) in the reverse of m:" << endl
<< m.reverse()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 4." << endl;
m.reverse()(1,0) = 4;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  6 -3  1
-2  9  6  0
 6 -6 -5  3
Here is the reverse of m:
 3 -5 -6  6
 0  6  9 -2
 1 -3  6  7
Here is the coefficient (1,0) in the reverse of m:
0
Let us overwrite this coefficient with the value 4.
Now the matrix m is:
 7  6 -3  1
-2  9  6  4
 6 -6 -5  3
ConstReverseReturnType reverse ( ) const
inherited

This is the const version of reverse().

void reverseInPlace ( )
inherited

This is the "in place" version of reverse: it reverses *this.

In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:

  • less error prone: doing the same operation with .reverse() requires special care:
    m = m.reverse().eval();
  • this API allows to avoid creating a temporary (the current implementation creates a temporary, but that could be avoided using swap)
  • it allows future optimizations (cache friendliness, etc.)
See also:
reverse()
const _RhsNested& rhs ( ) const
inlineinherited
ColsBlockXpr rightCols ( Index  n)
inlineinherited
Returns:
a block consisting of the right columns of *this.
Parameters:
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols(2):" << endl;
cout << a.rightCols(2) << endl;
a.rightCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstColsBlockXpr rightCols ( Index  n) const
inlineinherited

This is the const version of rightCols(Index).

NColsBlockXpr<N>::Type rightCols ( )
inlineinherited
Returns:
a block consisting of the right columns of *this.
Template Parameters:
Nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols<2>():" << endl;
cout << a.rightCols<2>() << endl;
a.rightCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols<2>():
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstNColsBlockXpr<N>::Type rightCols ( ) const
inlineinherited

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

RowXpr row ( Index  i)
inlineinherited
Returns:
an expression of the i-th row of *this. Note that the numbering starts at 0.

Example:

Matrix3d m = Matrix3d::Identity();
m.row(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 0 0
4 5 6
0 0 1
See also:
col(), class Block
ConstRowXpr row ( Index  i) const
inlineinherited

This is the const version of row().

Index rows ( void  ) const
inlineinherited
ConstRowwiseReturnType rowwise ( ) const
inherited
Returns:
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl;
cout << "Here is the maximum absolute value of each row:"
<< endl << m.cwiseAbs().rowwise().maxCoeff() << 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
Here is the sum of each row:
0.948
1.15
-0.483
Here is the maximum absolute value of each row:
0.68
0.823
0.605
See also:
colwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
RowwiseReturnType rowwise ( )
inherited
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
colwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
void scaleAndAddTo ( Dest &  ,
Scalar   
) const
inline
SegmentReturnType segment ( Index  start,
Index  size 
)
inherited
Returns:
a dynamic-size expression of a segment (i.e. a vector block) in *this.

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.

Parameters:
startthe first coefficient in the segment
sizethe number of coefficients in the segment

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl;
v.segment(1, 2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment(1, 2):
-2 6
Now the vector v is:
7 0 0 6
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, segment(Index)
DenseBase::ConstSegmentReturnType segment ( Index  start,
Index  size 
) const
inherited

This is the const version of segment(Index,Index).

FixedSegmentReturnType<Size>::Type segment ( Index  start)
inherited
Returns:
a fixed-size expression of a segment (i.e. a vector block) in *this

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.

The template parameter Size is the number of coefficients in the block

Parameters:
startthe index of the first element of the sub-vector

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl;
v.segment<2>(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment<2>(1):
-2 6
Now the vector v is:
 7 -2  0  0
See also:
class Block
ConstFixedSegmentReturnType<Size>::Type segment ( Index  start) const
inherited

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

const Select<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,ThenDerived,ElseDerived> select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const
inherited
Returns:
a matrix where each coefficient (i,j) is equal to thenMatrix(i,j) if *this(i,j), and elseMatrix(i,j) otherwise.

Example:

MatrixXi m(3, 3);
m << 1, 2, 3,
4, 5, 6,
7, 8, 9;
m = (m.array() >= 5).select(-m, m);
cout << m << endl;

Output:

 1  2  3
 4 -5 -6
-7 -8 -9
See also:
class Select
const Select<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > ,ThenDerived, typename ThenDerived::ConstantReturnType> select ( const DenseBase< ThenDerived > &  thenMatrix,
typename ThenDerived::Scalar  elseScalar 
) const
inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.

See also:
DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
const Select<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , typename ElseDerived::ConstantReturnType, ElseDerived > select ( typename ElseDerived::Scalar  thenScalar,
const DenseBase< ElseDerived > &  elseMatrix 
) const
inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.

See also:
DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
SelfAdjointViewReturnType<UpLo>::Type selfadjointView ( )
inherited
ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView ( ) const
inherited
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setConstant ( const Scalar value)
inherited

Sets all coefficients in this expression to value.

See also:
fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setIdentity ( )
inherited

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

Example:

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

Output:

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()
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setIdentity ( Index  rows,
Index  cols 
)
inherited

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()
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setLinSpaced ( Index  size,
const Scalar low,
const Scalar high 
)
inherited

Sets a linearly space vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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:

VectorXf v;
v.setLinSpaced(5,0.5f,1.5f).transpose();
cout << v << endl;

Output:

0.5
0.75
1
1.25
1.5
See also:
CwiseNullaryOp
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setLinSpaced ( const Scalar low,
const Scalar high 
)
inherited

Sets a linearly space vector.

The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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:
setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setOnes ( )
inherited

Sets all coefficients in this expression to one.

Example:

Matrix4i m = Matrix4i::Random();
m.row(1).setOnes();
cout << m << endl;

Output:

 7  9 -5 -3
 1  1  1  1
 6 -3  0  9
 6  6  3  9
See also:
class CwiseNullaryOp, Ones()
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setRandom ( )
inherited

Sets all coefficients in this expression to random values.

Example:

Matrix4i m = Matrix4i::Zero();
m.col(1).setRandom();
cout << m << endl;

Output:

 0  7  0  0
 0 -2  0  0
 0  6  0  0
 0  6  0  0
See also:
class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > & setZero ( )
inherited

Sets all coefficients in this expression to zero.

Example:

Matrix4i m = Matrix4i::Random();
m.row(1).setZero();
cout << m << endl;

Output:

 7  9 -5 -3
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class CwiseNullaryOp, Zero()
const MatrixFunctionReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > sin ( ) const
inherited
const MatrixFunctionReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > sinh ( ) const
inherited
const SparseView<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > sparseView ( const Scalar m_reference = Scalar(0),
typename NumTraits< Scalar >::Real  m_epsilon = NumTraits<Scalar>::dummy_precision() 
) const
inherited
const MatrixSquareRootReturnValue<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > sqrt ( ) const
inherited
RealScalar squaredNorm ( ) const
inherited
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()
RealScalar stableNorm ( ) const
inherited
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()
void subTo ( Dest &  dst) const
inlineinherited
Scalar sum ( ) const
inherited
Returns:
the sum of all coefficients of *this
See also:
trace(), prod(), mean()
void swap ( const DenseBase< OtherDerived > &  other,
int  = OtherDerived::ThisConstantIsPrivateInPlainObjectBase 
)
inlineinherited

swaps *this with the expression other.

void swap ( PlainObjectBase< OtherDerived > &  other)
inlineinherited

swaps *this with the matrix or array other.

SegmentReturnType tail ( Index  size)
inherited
Returns:
a dynamic-size expression of the last coefficients of *this.

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.

Parameters:
sizethe number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail(2) << endl;
v.tail(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, block(Index,Index)
DenseBase::ConstSegmentReturnType tail ( Index  size) const
inherited

This is the const version of tail(Index).

FixedSegmentReturnType<Size>::Type tail ( )
inherited
Returns:
a fixed-size expression of the last coefficients of *this.

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.

The template parameter Size is the number of coefficients in the block

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl;
v.tail<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
See also:
class Block
ConstFixedSegmentReturnType<Size>::Type tail ( ) const
inherited

This is the const version of tail<int>.

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > topLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns:
a dynamic-size expression of a top-left corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner(2, 2):" << endl;
cout << m.topLeftCorner(2, 2) << endl;
m.topLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topLeftCorner(Index, Index).

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> topLeftCorner ( )
inlineinherited
Returns:
an expression of a fixed-size top-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,2>():" << endl;
cout << m.topLeftCorner<2,2>() << endl;
m.topLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,2>():
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> topLeftCorner ( ) const
inlineinherited

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

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > topRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns:
a dynamic-size expression of a top-right corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner(2, 2):" << endl;
cout << m.topRightCorner(2, 2) << endl;
m.topRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topRightCorner(Index, Index).

Block<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> topRightCorner ( )
inlineinherited
Returns:
an expression of a fixed-size top-right corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,2>():" << endl;
cout << m.topRightCorner<2,2>() << endl;
m.topRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,2>():
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > , CRows, CCols> topRightCorner ( ) const
inlineinherited

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

RowsBlockXpr topRows ( Index  n)
inlineinherited
Returns:
a block consisting of the top rows of *this.
Parameters:
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows(2):" << endl;
cout << a.topRows(2) << endl;
a.topRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstRowsBlockXpr topRows ( Index  n) const
inlineinherited

This is the const version of topRows(Index).

NRowsBlockXpr<N>::Type topRows ( )
inlineinherited
Returns:
a block consisting of the top rows of *this.
Template Parameters:
Nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows<2>():" << endl;
cout << a.topRows<2>() << endl;
a.topRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type topRows ( ) const
inlineinherited

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

Scalar trace ( ) const
inherited
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()

Reimplemented from DenseBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > >.

Eigen::Transpose<DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > transpose ( )
inherited
Returns:
an expression of the transpose of *this.

Example:

Matrix2i m = Matrix2i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the transpose of m:" << endl << m.transpose() << endl;
cout << "Here is the coefficient (1,0) in the transpose of m:" << endl
<< m.transpose()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 0." << endl;
m.transpose()(1,0) = 0;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
7 6
-2 6
Here is the transpose of m:
 7 -2
 6  6
Here is the coefficient (1,0) in the transpose of m:
6
Let us overwrite this coefficient with the value 0.
Now the matrix m is:
7 0
-2 6
Warning:
If you want to replace a matrix by its own transpose, do NOT do this:
m = m.transpose(); // bug!!! caused by aliasing effect
Instead, use the transposeInPlace() method:
m.transposeInPlace();
which gives Eigen good opportunities for optimization, or alternatively you can also do:
m = m.transpose().eval();
See also:
transposeInPlace(), adjoint()
ConstTransposeReturnType transpose ( ) const
inherited

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also:
transposeInPlace(), adjoint()
void transposeInPlace ( )
inherited

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

m.transposeInPlace();

has the same effect on m as doing

m = m.transpose().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 transpose. If you just need the transpose of a matrix, use transpose().

Note:
if the matrix is not square, then *this must be a resizable matrix.
See also:
transpose(), adjoint(), adjointInPlace()
TriangularViewReturnType<Mode>::Type triangularView ( )
inherited
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:

#ifndef _MSC_VER
#warning deprecated
#endif
/* deprecated
Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the upper-triangular matrix extracted from m:" << endl
<< m.part<Eigen::UpperTriangular>() << endl;
cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
<< m.part<Eigen::StrictlyUpperTriangular>() << endl;
cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
<< m.part<Eigen::UnitLowerTriangular>() << endl;
*/

Output:

See also:
class TriangularView
ConstTriangularViewReturnType<Mode>::Type triangularView ( ) const
inherited

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

const CwiseUnaryOp<CustomUnaryOp, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp()) const
inlineinherited

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**)
{
Matrix4d m1 = Matrix4d::Random();
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**)
{
Matrix4d m1 = Matrix4d::Random();
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:
class CwiseUnaryOp, class CwiseBinaryOp
const CwiseUnaryView<CustomViewOp, const DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo > > unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inlineinherited
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**)
{
Matrix4d m1 = Matrix4d::Random();
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:
class CwiseUnaryOp, class CwiseBinaryOp
static const BasisReturnType Unit ( Index  size,
Index  i 
)
staticinherited
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()
static const BasisReturnType Unit ( Index  i)
staticinherited
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()
PlainObject unitOrthogonal ( void  ) const
inherited
Returns:
a unit vector which is orthogonal to *this

The size of *this must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this, i.e., (-y,x).normalized().

See also:
cross()
static const BasisReturnType UnitW ( )
staticinherited
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()
static const BasisReturnType UnitX ( )
staticinherited
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()
static const BasisReturnType UnitY ( )
staticinherited
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()
static const BasisReturnType UnitZ ( )
staticinherited
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()
CoeffReturnType value ( ) const
inlineinherited
Returns:
the unique coefficient of a 1x1 expression
void visit ( Visitor &  func) const
inherited

Applies the visitor visitor to the whole coefficients of the matrix or vector.

The template parameter Visitor is the type of the visitor and provides the following interface:

struct MyVisitor {
// called for the first coefficient
void init(const Scalar& value, Index i, Index j);
// called for all other coefficients
void operator() (const Scalar& value, Index i, Index j);
};
Note:
compared to one or two for loops, visitors offer automatic unrolling for small fixed size matrix.
See also:
minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()
static const ConstantReturnType Zero ( Index  rows,
Index  cols 
)
staticinherited
Returns:
an expression of a zero matrix.

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 Zero() should be used instead.

Example:

cout << MatrixXi::Zero(2,3) << endl;

Output:

0 0 0
0 0 0
See also:
Zero(), Zero(Index)
static const ConstantReturnType Zero ( Index  size)
staticinherited
Returns:
an expression of a zero vector.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

Example:

cout << RowVectorXi::Zero(4) << endl;
cout << VectorXf::Zero(2) << endl;

Output:

0 0 0 0
0
0
See also:
Zero(), Zero(Index,Index)
static const ConstantReturnType Zero ( )
staticinherited
Returns:
an expression of a fixed-size zero matrix or vector.

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

Example:

cout << Matrix2d::Zero() << endl;
cout << RowVector4i::Zero() << endl;

Output:

0 0
0 0
0 0 0 0
See also:
Zero(Index), Zero(Index,Index)

Member Data Documentation

LhsNested m_lhs
protectedinherited
PlainObject m_result
mutableprotectedinherited
RhsNested m_rhs
protectedinherited

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