Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | Related Functions
ProductBase< Derived, Lhs, Rhs > Class Template Reference

#include <ProductBase.h>

+ Inheritance diagram for ProductBase< Derived, Lhs, Rhs >:

List of all members.

Public Types

enum  { HomogeneousReturnTypeDirection }
enum  { SizeMinusOne }
enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime,
  MaxRowsAtCompileTime,
  MaxColsAtCompileTime,
  MaxSizeAtCompileTime,
  IsVectorAtCompileTime,
  Flags,
  IsRowMajor,
  InnerSizeAtCompileTime,
  CoeffReadCost,
  InnerStrideAtCompileTime,
  OuterStrideAtCompileTime
}
enum  { ThisConstantIsPrivateInPlainObjectBase }
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< Derived > Base
typedef Base::CoeffReturnType CoeffReturnType
typedef VectorwiseOp< Derived,
Vertical
ColwiseReturnType
typedef const VectorwiseOp
< const Derived, Vertical
ConstColwiseReturnType
typedef const Diagonal< const
Derived > 
ConstDiagonalReturnType
typedef const Reverse< const
Derived, BothDirections
ConstReverseReturnType
typedef const VectorwiseOp
< const Derived, Horizontal
ConstRowwiseReturnType
typedef const VectorBlock
< const Derived > 
ConstSegmentReturnType
typedef Block< const Derived,
internal::traits< Derived >
::ColsAtCompileTime==1?SizeMinusOne:1,
internal::traits< Derived >
::ColsAtCompileTime==1?1:SizeMinusOne
ConstStartMinusOne
typedef const Transpose< const
Derived > 
ConstTransposeReturnType
typedef Diagonal< Derived > DiagonalReturnType
typedef
internal::add_const_on_value_type
< typename internal::eval
< Derived >::type >::type 
EvalReturnType
typedef CoeffBasedProduct
< LhsNested, RhsNested, 0 > 
FullyLazyCoeffBaseProductType
typedef CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Derived >::Scalar >, const
ConstStartMinusOne
HNormalizedReturnType
typedef Homogeneous< Derived,
HomogeneousReturnTypeDirection
HomogeneousReturnType
typedef internal::traits
< Derived >::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< Derived,
BothDirections
ReverseReturnType
typedef internal::blas_traits
< _RhsNested
RhsBlasTraits
typedef Rhs::Nested RhsNested
typedef internal::traits< Rhs >
::Scalar 
RhsScalar
typedef VectorwiseOp< Derived,
Horizontal
RowwiseReturnType
typedef internal::traits
< Derived >::Scalar 
Scalar
typedef VectorBlock< Derived > SegmentReturnType
typedef
internal::stem_function
< Scalar >::type 
StemFunction
typedef internal::traits
< Derived >::StorageKind 
StorageKind

Public Member Functions

template<typename Dest >
void addTo (Dest &dst) const
const AdjointReturnType adjoint () const
void adjointInPlace ()
bool all (void) const
bool any (void) const
template<typename EssentialPart >
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename EssentialPart >
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename OtherDerived >
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
template<typename OtherScalar >
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherDerived >
void applyOnTheRight (const EigenBase< OtherDerived > &other)
template<typename OtherScalar >
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
ArrayWrapper< Derived > array ()
const ArrayWrapper< const Derived > array () const
const DiagonalWrapper< const
Derived > 
asDiagonal () const
const PermutationWrapper
< const Derived > 
asPermutation () const
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp
< CustomBinaryOp, const
Derived, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
Block< Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows,
BlockCols > 
block (Index startRow, Index startCol)
template<int BlockRows, int BlockCols>
const Block< const Derived,
BlockRows, BlockCols > 
block (Index startRow, Index startCol) const
RealScalar blueNorm () const
Block< Derived > bottomLeftCorner (Index cRows, Index cCols)
const Block< const Derived > bottomLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner ()
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomLeftCorner () const
Block< Derived > bottomRightCorner (Index cRows, Index cCols)
const Block< const Derived > bottomRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner ()
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomRightCorner () const
RowsBlockXpr bottomRows (Index n)
ConstRowsBlockXpr bottomRows (Index n) const
template<int N>
NRowsBlockXpr< N >::Type bottomRows ()
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows () const
template<typename NewType >
internal::cast_return_type
< Derived, const CwiseUnaryOp
< internal::scalar_cast_op
< typename internal::traits
< Derived >::Scalar, NewType >
, const Derived > >::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 ()
template<typename ResultType >
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
template<typename ResultType >
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
ConjugateReturnType conjugate () const
const
MatrixFunctionReturnValue
< Derived > 
cos () const
const
MatrixFunctionReturnValue
< Derived > 
cosh () const
Index count () const
template<typename OtherDerived >
cross_product_return_type
< OtherDerived >::type 
cross (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const Derived > 
cwiseAbs () const
const CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const Derived > 
cwiseAbs2 () const
template<typename OtherDerived >
const CwiseBinaryOp
< std::equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< std::binder1st
< std::equal_to< Scalar >
>, const Derived > 
cwiseEqual (const Scalar &s) const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const Derived > 
cwiseInverse () const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Derived,
const ConstantReturnType > 
cwiseMax (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Derived,
const ConstantReturnType > 
cwiseMin (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const Derived > 
cwiseSqrt () const
Scalar determinant () const
const Diagonal< const
FullyLazyCoeffBaseProductType, 0 > 
diagonal () const
template<int Index>
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
template<typename OtherDerived >
internal::scalar_product_traits
< typename internal::traits
< Derived >::Scalar, typename
internal::traits< OtherDerived >
::Scalar >::ReturnType 
dot (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const EIGEN_CWISE_PRODUCT_RETURN_TYPE (Derived, OtherDerived) cwiseProduct(const Eigen
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix.
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
EvalReturnType eval () const
template<typename Dest >
void evalTo (Dest &dst) const
const
MatrixExponentialReturnValue
< Derived > 
exp () const
void fill (const Scalar &value)
template<unsigned int Added, unsigned int Removed>
const Flagged< Derived, Added,
Removed > 
flagged () const
const ForceAlignedAccess< Derived > forceAlignedAccess () const
ForceAlignedAccess< Derived > forceAlignedAccess ()
template<bool Enable>
internal::add_const_on_value_type
< typename
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type >::type 
forceAlignedAccessIf () const
template<bool Enable>
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type 
forceAlignedAccessIf ()
const WithFormat< Derived > format (const IOFormat &fmt) const
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
const FullPivLU< PlainObjectfullPivLu () const
SegmentReturnType head (Index size)
DenseBase::ConstSegmentReturnType head (Index size) const
template<int Size>
FixedSegmentReturnType< Size >
::Type 
head ()
template<int Size>
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
< Derived > 
inverse () const
template<typename OtherDerived >
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
template<typename Derived >
bool isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const
bool isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
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
template<typename OtherDerived >
const LazyProductReturnType
< Derived, OtherDerived >
::Type 
lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObjectldlt () const
ColsBlockXpr leftCols (Index n)
ConstColsBlockXpr leftCols (Index n) const
template<int N>
NColsBlockXpr< N >::Type leftCols ()
template<int N>
ConstNColsBlockXpr< N >::Type leftCols () const
const _LhsNestedlhs () const
const LLT< PlainObjectllt () const
const
MatrixLogarithmReturnValue
< Derived > 
log () const
template<int p>
RealScalar lpNorm () const
const PartialPivLU< PlainObjectlu () const
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
MatrixBase< Derived > & matrix ()
const MatrixBase< Derived > & matrix () const
const
MatrixFunctionReturnValue
< Derived > 
matrixFunction (StemFunction f) const
internal::traits< Derived >::Scalar maxCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
Scalar mean () const
ColsBlockXpr middleCols (Index startCol, Index numCols)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
template<int N>
NColsBlockXpr< N >::Type middleCols (Index startCol)
template<int N>
ConstNColsBlockXpr< N >::Type middleCols (Index startCol) const
RowsBlockXpr middleRows (Index startRow, Index numRows)
ConstRowsBlockXpr middleRows (Index startRow, Index numRows) const
template<int N>
NRowsBlockXpr< N >::Type middleRows (Index startRow)
template<int N>
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow) const
internal::traits< Derived >::Scalar minCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
const NestByValue< Derived > nestByValue () const
NoAlias< Derived,
Eigen::MatrixBase
noalias ()
Index nonZeros () const
RealScalar norm () const
void normalize ()
const PlainObject normalized () const
 operator const PlainObject & () const
template<typename OtherDerived >
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 Derived > 
operator* (const std::complex< Scalar > &scalar) const
template<typename OtherDerived >
const ProductReturnType
< Derived, OtherDerived >
::Type 
operator* (const MatrixBase< OtherDerived > &other) const
template<typename DiagonalDerived >
const DiagonalProduct< Derived,
DiagonalDerived, OnTheRight
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
ScalarMultipleReturnType operator* (const UniformScaling< Scalar > &s) const
template<typename OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
Derived & operator*= (const Scalar &other)
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Derived & operator+= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_opposite_op
< typename internal::traits
< Derived >::Scalar >, const
Derived > 
operator- () const
template<typename OtherDerived >
Derived & operator-= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Derived & operator-= (const EigenBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Derived >::Scalar >, const
Derived > 
operator/ (const Scalar &scalar) const
Derived & operator/= (const Scalar &other)
CommaInitializer< Derived > operator<< (const Scalar &s)
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
RealScalar operatorNorm () const
 Computes the L2 operator norm.
Index outerSize () const
const PartialPivLU< PlainObjectpartialPivLu () const
Scalar prod () const
 ProductBase (const Lhs &lhs, const Rhs &rhs)
RealReturnType real () const
NonConstRealReturnType real ()
template<int RowFactor, int ColFactor>
const Replicate< Derived,
RowFactor, ColFactor > 
replicate () const
const Replicate< Derived,
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
template<int N>
NColsBlockXpr< N >::Type rightCols ()
template<int N>
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 &dst, Scalar alpha) const
SegmentReturnType segment (Index start, Index size)
DenseBase::ConstSegmentReturnType segment (Index start, Index size) const
template<int Size>
FixedSegmentReturnType< Size >
::Type 
segment (Index start)
template<int Size>
ConstFixedSegmentReturnType
< Size >::Type 
segment (Index start) const
template<typename ThenDerived , typename ElseDerived >
const Select< Derived,
ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
template<typename ThenDerived >
const Select< Derived,
ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const
template<typename ElseDerived >
const Select< Derived,
typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
template<unsigned int UpLo>
SelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView ()
template<unsigned int UpLo>
ConstSelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView () const
Derived & setConstant (const Scalar &value)
Derived & setIdentity ()
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
Derived & setOnes ()
Derived & setRandom ()
Derived & setZero ()
const
MatrixFunctionReturnValue
< Derived > 
sin () const
const
MatrixFunctionReturnValue
< Derived > 
sinh () const
const SparseView< Derived > sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const
const
MatrixSquareRootReturnValue
< Derived > 
sqrt () const
RealScalar squaredNorm () const
RealScalar stableNorm () const
template<typename Dest >
void subTo (Dest &dst) const
Scalar sum () const
template<typename OtherDerived >
void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
template<typename OtherDerived >
void swap (PlainObjectBase< OtherDerived > &other)
SegmentReturnType tail (Index size)
DenseBase::ConstSegmentReturnType tail (Index size) const
template<int Size>
FixedSegmentReturnType< Size >
::Type 
tail ()
template<int Size>
ConstFixedSegmentReturnType
< Size >::Type 
tail () const
Block< Derived > topLeftCorner (Index cRows, Index cCols)
const Block< const Derived > topLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner ()
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topLeftCorner () const
Block< Derived > topRightCorner (Index cRows, Index cCols)
const Block< const Derived > topRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner ()
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topRightCorner () const
RowsBlockXpr topRows (Index n)
ConstRowsBlockXpr topRows (Index n) const
template<int N>
NRowsBlockXpr< N >::Type topRows ()
template<int N>
ConstNRowsBlockXpr< N >::Type topRows () const
Scalar trace () const
Eigen::Transpose< Derived > transpose ()
ConstTransposeReturnType transpose () const
void transposeInPlace ()
template<unsigned int Mode>
TriangularViewReturnType< Mode >
::Type 
triangularView ()
template<unsigned int Mode>
ConstTriangularViewReturnType
< Mode >::Type 
triangularView () const
template<typename CustomUnaryOp >
const CwiseUnaryOp
< CustomUnaryOp, const Derived > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
template<typename CustomViewOp >
const CwiseUnaryView
< CustomViewOp, const Derived > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
PlainObject unitOrthogonal (void) const
CoeffReturnType value () const
template<typename Visitor >
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)
 Sets a linearly space vector.
static const
RandomAccessLinSpacedReturnType 
LinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
static const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index size, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
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 >, Derived > 
Random (Index rows, Index cols)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Derived > 
Random (Index size)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Derived > 
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

template<typename OtherDerived >
void checkTransposeAliasing (const OtherDerived &other) const
template<typename OtherDerived >
Derived & operator+= (const ArrayBase< OtherDerived > &)
template<typename OtherDerived >
Derived & operator-= (const ArrayBase< OtherDerived > &)

Protected Attributes

LhsNested m_lhs
PlainObject m_result
RhsNested m_rhs

Related Functions

(Note that these are not member functions.)

template<typename Derived >
std::ostream & operator<< (std::ostream &s, const DenseBase< Derived > &m)

Member Typedef Documentation

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<Derived> Base

Reimplemented from DenseBase< Derived >.

Reimplemented in ScaledProduct< NestedProduct >.

typedef Base::CoeffReturnType CoeffReturnType
inherited
typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType
inherited
typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType
inherited
typedef const Diagonal<const Derived> ConstDiagonalReturnType
inherited
typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType
inherited
typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType
inherited
typedef const VectorBlock<const Derived> ConstSegmentReturnType
inherited
typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne
inherited
typedef const Transpose<const Derived> ConstTransposeReturnType
inherited
typedef Diagonal<Derived> DiagonalReturnType
inherited
typedef internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType
inherited
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const ConstStartMinusOne > HNormalizedReturnType
inherited
typedef internal::traits<Derived>::Index Index
inherited

The type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also:
Preprocessor directives.

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

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

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< Derived >.

Reimplemented in ScaledProduct< NestedProduct >.

typedef NumTraits<Scalar>::Real RealScalar
inherited
typedef Reverse<Derived, BothDirections> ReverseReturnType
inherited
typedef internal::blas_traits<_RhsNested> RhsBlasTraits
typedef Rhs::Nested RhsNested
typedef internal::traits<Rhs>::Scalar RhsScalar
typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType
inherited
typedef internal::traits<Derived>::Scalar Scalar
inherited
typedef VectorBlock<Derived> SegmentReturnType
inherited
typedef internal::stem_function<Scalar>::type StemFunction
inherited
typedef internal::traits<Derived>::StorageKind StorageKind
inherited

Member Enumeration Documentation

anonymous enum
inherited
Enumerator:
HomogeneousReturnTypeDirection 
anonymous enum
inherited
Enumerator:
SizeMinusOne 
anonymous enum
inherited
Enumerator:
RowsAtCompileTime 

The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also:
MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime
ColsAtCompileTime 

The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also:
MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime
SizeAtCompileTime 

This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.

See also:
RowsAtCompileTime, ColsAtCompileTime
MaxRowsAtCompileTime 

This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
MaxColsAtCompileTime 

This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
MaxSizeAtCompileTime 

This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
IsVectorAtCompileTime 

This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row).

Flags 

This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags.

IsRowMajor 

True if this expression has row-major storage order.

InnerSizeAtCompileTime 
CoeffReadCost 

This is a rough measure of how expensive it is to read one coefficient from this expression.

InnerStrideAtCompileTime 
OuterStrideAtCompileTime 
anonymous enum
inherited
Enumerator:
ThisConstantIsPrivateInPlainObjectBase 

Constructor & Destructor Documentation

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

Member Function Documentation

void addTo ( Dest &  dst) const
inline

Reimplemented in ScaledProduct< NestedProduct >.

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

Example:

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

Output:

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

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()

References DenseBase< Derived >::eval().

bool all ( void  ) const
inlineinherited
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<()

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

bool any ( void  ) const
inlineinherited
Returns:
true if at least one coefficient is true
See also:
all()

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

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()

References row().

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()

References col().

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

replaces *this by *this * other.

References EigenBase< Derived >::derived().

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

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()

References Eigen::internal::apply_rotation_in_the_plane(), row(), and Eigen::internal::y.

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

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

References EigenBase< Derived >::derived().

ArrayWrapper<Derived> array ( )
inlineinherited
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
const ArrayWrapper<const Derived> array ( ) const
inlineinherited
const DiagonalWrapper< const Derived > asDiagonal ( ) const
inlineinherited
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()

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::fromPositionOrientationScale(), Transform< _Scalar, _Dim, _Mode, _Options >::prescale(), and Transform< _Scalar, _Dim, _Mode, _Options >::scale().

const PermutationWrapper< const Derived > asPermutation ( ) const
inherited
const CwiseBinaryOp<CustomBinaryOp, const Derived, 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**)
{
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<Derived> 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:

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)

Referenced by main().

const Block<const Derived> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

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

Block<Derived, 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:

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 Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const
inlineinherited

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

NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm ( ) const
inlineinherited
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()

References abs(), abs2(), eigen_assert, pow(), and sqrt().

Block<Derived> 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:

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 Derived> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

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

Block<Derived, 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:

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 Derived, CRows, CCols> bottomLeftCorner ( ) const
inlineinherited

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

Block<Derived> 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:

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 Derived> bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

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

Block<Derived, 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:

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 Derived, 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<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::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
inline
Base::CoeffReturnType coeff ( Index  i) const
inline
const Scalar& coeffRef ( Index  row,
Index  col 
) const
inline
const Scalar& coeffRef ( Index  i) const
inline
ColXpr col ( Index  i)
inlineinherited
Returns:
an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

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

Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), and main().

ConstColXpr col ( Index  i) const
inlineinherited

This is the const version of col().

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

Example:

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

Referenced by main(), and Eigen::umeyama().

DenseBase< Derived >::ColwiseReturnType colwise ( )
inlineinherited
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
inlineinherited

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:

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()

References eigen_assert.

void computeInverseWithCheck ( ResultType &  inverse,
bool invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const
inlineinherited

This is defined in the LU module.

#include <Eigen/LU>

Computation of matrix inverse, with invertibility check.

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

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

Example:

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

Output:

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

References eigen_assert.

ConjugateReturnType conjugate ( ) const
inlineinherited
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()
const DenseBase< Derived >::ConstantReturnType Constant ( Index  rows,
Index  cols,
const Scalar value 
)
inlinestaticinherited
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
const DenseBase< Derived >::ConstantReturnType Constant ( Index  size,
const Scalar value 
)
inlinestaticinherited
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
const DenseBase< Derived >::ConstantReturnType Constant ( const Scalar value)
inlinestaticinherited
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

References EIGEN_STATIC_ASSERT_FIXED_SIZE.

const MatrixFunctionReturnValue<Derived> cos ( ) const
inherited

Referenced by main().

const MatrixFunctionReturnValue<Derived> cosh ( ) const
inherited
DenseBase< Derived >::Index count ( ) const
inlineinherited
Returns:
the number of coefficients which evaluate to true
See also:
all(), any()
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross ( const MatrixBase< OtherDerived > &  other) const
inlineinherited

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()

References conj(), and EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE.

MatrixBase< Derived >::PlainObject cross3 ( const MatrixBase< OtherDerived > &  other) const
inlineinherited

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()

References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, and Eigen::Architecture::Target.

const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> 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 Derived> 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 Derived, 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 Derived> 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

Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator==().

const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> 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 Derived, 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 Derived, 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 Derived, 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 Derived, 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 Derived, 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()

Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator!=().

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, 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 Derived> 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()
internal::traits< Derived >::Scalar determinant ( ) const
inlineinherited

This is defined in the LU module.

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

This is the const version of diagonal().

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

Reimplemented from MatrixBase< Derived >.

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

This is the const version of diagonal().

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

Reimplemented from MatrixBase< Derived >.

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

This is the const version of diagonal(Index).

Reimplemented from MatrixBase< Derived >.

MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal ( )
inlineinherited
Returns:
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

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

Output:

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

*this is not required to be square.

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

Example:

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

Output:

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

Referenced by main(), AngleAxis< _Scalar >::toRotationMatrix(), and MatrixBase< Derived >::trace().

MatrixBase< Derived >::template DiagonalIndexReturnType< Dynamic >::Type diagonal ( Index  index)
inlineinherited
Returns:
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

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

Example:

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

Output:

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

References eigen_assert, EIGEN_CHECK_BINARY_COMPATIBILIY, EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const EIGEN_CWISE_PRODUCT_RETURN_TYPE ( Derived  ,
OtherDerived   
) const
inlineinherited
Returns:
an expression of the Schur product (coefficient wise product) of *this and other

Example:

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
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues ( ) const
inlineinherited

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()

References Eigen::internal::IsComplex.

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.

Referenced by MatrixBase< Derived >::adjointInPlace().

void evalTo ( Dest &  dst) const
inline

Reimplemented from DenseBase< Derived >.

Reimplemented in ScaledProduct< NestedProduct >.

const MatrixExponentialReturnValue<Derived> exp ( ) const
inherited
void fill ( const Scalar value)
inlineinherited

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

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

This is mostly for internal use.

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

Reimplemented from DenseBase< Derived >.

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

Reimplemented from DenseBase< Derived >.

internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::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< Derived >.

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

Reimplemented from DenseBase< Derived >.

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

This is defined in the LU module.

#include <Eigen/LU>
Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU
DenseBase< Derived >::SegmentReturnType head ( Index  size)
inlineinherited
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:

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)

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::ConstSegmentReturnType head ( Index  size) const
inlineinherited

This is the const version of head(Index).

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type head ( )
inlineinherited
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:

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type head ( ) const
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const MatrixBase< Derived >::HNormalizedReturnType hnormalized ( ) const
inlineinherited

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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

MatrixBase< Derived >::HomogeneousReturnType homogeneous ( ) const
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const HouseholderQR< typename MatrixBase< Derived >::PlainObject > householderQr ( ) const
inherited
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR
NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm ( ) const
inlineinherited
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()

References cwiseAbs().

const MatrixBase< Derived >::IdentityReturnType Identity ( )
inlinestaticinherited
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()

References EIGEN_STATIC_ASSERT_FIXED_SIZE.

const MatrixBase< Derived >::IdentityReturnType Identity ( Index  rows,
Index  cols 
)
inlinestaticinherited
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< Derived > inverse ( ) const
inlineinherited

This is defined in the LU module.

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

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

Note:
This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following: Example:
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << endl;
Output:
Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
computeInverseAndDetWithCheck()

References eigen_assert, and EIGEN_STATIC_ASSERT.

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse(), and Hyperplane< _Scalar, _AmbientDim, _Options >::transform().

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

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::isApprox().

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

References Eigen::internal::isApprox().

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:

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()

References abs(), and Eigen::internal::isMuchSmallerThan().

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:

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()

References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().

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()

References abs().

bool isMuchSmallerThan ( const typename NumTraits< Scalar >::Real &  other,
RealScalar  prec 
) const
inherited
Returns:
true if the norm of *this is much smaller than other, within the precision determined by prec.
Note:
The fuzzy compares are done multiplicatively. A vector $ v $ is considered to be much smaller than $ x $ within precision $ p $ if

\[ \Vert v \Vert \leqslant p\,\vert x\vert. \]

For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.

See also:
isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
bool isMuchSmallerThan ( const RealScalar other,
RealScalar  prec = NumTraitsScalar >::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:

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

References abs2().

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:

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

References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().

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()

References abs().

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:

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()

References Eigen::internal::isMuchSmallerThan().

JacobiSVD< typename MatrixBase< Derived >::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< Derived, 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&)

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt ( ) const
inlineinherited

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
inline
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
Index  size,
const Scalar low,
const Scalar high 
)
inlinestaticinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( Index  size,
const Scalar low,
const Scalar high 
)
inlinestaticinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
const Scalar low,
const Scalar high 
)
inlinestaticinherited

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

References EIGEN_STATIC_ASSERT_FIXED_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( const Scalar low,
const Scalar high 
)
inlinestaticinherited

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

References EIGEN_STATIC_ASSERT_FIXED_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const LLT< typename MatrixBase< Derived >::PlainObject > llt ( ) const
inlineinherited

This is defined in the Cholesky module.

#include <Eigen/Cholesky>
Returns:
the LLT decomposition of *this
const MatrixLogarithmReturnValue<Derived> log ( ) const
inherited
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm ( ) const
inlineinherited
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< Derived >.

const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu ( ) const
inlineinherited

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()

References abs2(), conj(), EIGEN_STATIC_ASSERT_VECTOR_ONLY, imag(), real(), and sqrt().

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<Derived>& matrix ( )
inlineinherited
const MatrixBase<Derived>& matrix ( ) const
inlineinherited
const MatrixFunctionReturnValue<Derived> matrixFunction ( StemFunction  f) const
inherited
internal::traits< Derived >::Scalar maxCoeff ( ) const
inlineinherited
Returns:
the maximum of all coefficients of *this
internal::traits< Derived >::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< Derived >::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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

internal::traits< Derived >::Scalar mean ( ) const
inlineinherited
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< Derived >::Scalar minCoeff ( ) const
inlineinherited
Returns:
the minimum of all coefficients of *this
internal::traits< Derived >::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< Derived >::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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const NestByValue< Derived > nestByValue ( ) const
inlineinherited
Returns:
an expression of the temporary version of *this.
NoAlias< Derived, 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.
NumTraits< typename internal::traits< Derived >::Scalar >::Real norm ( ) const
inlineinherited
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()

References sqrt().

void normalize ( )
inlineinherited

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 MatrixBase< Derived >::PlainObject normalized ( ) const
inlineinherited
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()

Referenced by QuaternionBase< Derived >::setFromTwoVectors().

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
)
inlinestaticinherited
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
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
)
inlinestaticinherited
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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( const CustomNullaryOp &  func)
inlinestaticinherited
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
const DenseBase< Derived >::ConstantReturnType Ones ( Index  rows,
Index  cols 
)
inlinestaticinherited
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
const DenseBase< Derived >::ConstantReturnType Ones ( Index  size)
inlinestaticinherited
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
const DenseBase< Derived >::ConstantReturnType Ones ( )
inlinestaticinherited
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
inline
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 Derived> operator* ( const std::complex< Scalar > &  scalar) const
inlineinherited

Overloaded for efficient real matrix times complex scalar value

const ProductReturnType< Derived, OtherDerived >::Type operator* ( const MatrixBase< OtherDerived > &  other) const
inlineinherited
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*()

References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* ( const DiagonalBase< DiagonalDerived > &  diagonal) const
inlineinherited
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.
MatrixBase< Derived >::ScalarMultipleReturnType operator* ( const UniformScaling< Scalar > &  s) const
inherited

Concatenates a linear transformation matrix and a uniform scaling

References UniformScaling< _Scalar >::factor().

Derived & operator*= ( const EigenBase< OtherDerived > &  other)
inlineinherited

replaces *this by *this * other.

Returns:
a reference to *this

References EigenBase< Derived >::derived().

Derived & operator*= ( const Scalar other)
inlineinherited
Derived & operator+= ( const MatrixBase< OtherDerived > &  other)
inlineinherited

replaces *this by *this + other.

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

replaces *this by *this - other.

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

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;
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< Derived > operator<< ( const DenseBase< OtherDerived > &  other)
inlineinherited
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!=
MatrixBase< Derived >::RealScalar operatorNorm ( ) const
inlineinherited

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()

References sqrt().

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< typename MatrixBase< Derived >::PlainObject > partialPivLu ( ) const
inlineinherited

This is defined in the LU module.

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

Example:

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()

References Eigen::Dynamic.

const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  rows,
Index  cols 
)
inlinestaticinherited
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()
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  size)
inlinestaticinherited
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()
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( )
inlinestaticinherited
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< Derived, RowFactor, ColFactor > replicate ( ) const
inlineinherited
Returns:
an expression of the replication of *this

Example:

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< Derived, Dynamic, Dynamic > replicate ( Index  rowFactor,
Index  colFactor 
) const
inlineinherited
Returns:
an expression of the replication of *this

Example:

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.

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

Referenced by TriangularBase< Derived >::evalToLazy(), and MatrixBase< Derived >::setIdentity().

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.

Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

DenseBase< Derived >::ReverseReturnType reverse ( )
inlineinherited
Returns:
an expression of the reverse of *this.

Example:

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

Referenced by DenseBase< Derived >::reverseInPlace().

const DenseBase< Derived >::ConstReverseReturnType reverse ( ) const
inlineinherited

This is the const version of reverse().

void reverseInPlace ( )
inlineinherited

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()

References DenseBase< Derived >::reverse().

const _RhsNested& rhs ( ) const
inline
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:

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

Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), main(), Translation< _Scalar, _Dim >::operator*(), and Transform< _Scalar, _Dim, _Mode, _Options >::pretranslate().

ConstRowXpr row ( Index  i) const
inlineinherited

This is the const version of row().

Index rows ( void  ) const
inline
const DenseBase< Derived >::ConstRowwiseReturnType rowwise ( ) const
inlineinherited
Returns:
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

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

Referenced by main(), and Eigen::umeyama().

DenseBase< Derived >::RowwiseReturnType rowwise ( )
inlineinherited
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 &  dst,
Scalar  alpha 
) const
inline
DenseBase< Derived >::SegmentReturnType segment ( Index  start,
Index  size 
)
inlineinherited
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:

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)

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::ConstSegmentReturnType segment ( Index  start,
Index  size 
) const
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type segment ( Index  start)
inlineinherited
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:

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type segment ( Index  start) const
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const Select< Derived, ThenDerived, ElseDerived > select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const
inlineinherited
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< Derived, 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< Derived, 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
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView ( )
inherited
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView ( ) const
inherited
Derived & setConstant ( const Scalar value)
inlineinherited

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()
Derived & setIdentity ( )
inlineinherited

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

Example:

m.block<3,3>(1,0).setIdentity();
cout << m << endl;

Output:

0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity().

Derived & setIdentity ( Index  rows,
Index  cols 
)
inlineinherited

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()

References DenseBase< Derived >::resize().

Derived & setLinSpaced ( Index  size,
const Scalar low,
const Scalar high 
)
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

Derived & setLinSpaced ( const Scalar low,
const Scalar high 
)
inlineinherited

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

Derived & setOnes ( )
inlineinherited

Sets all coefficients in this expression to one.

Example:

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()
Derived & setRandom ( )
inlineinherited

Sets all coefficients in this expression to random values.

Example:

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)
Derived & setZero ( )
inlineinherited

Sets all coefficients in this expression to zero.

Example:

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()

Referenced by SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::evalTo().

const MatrixFunctionReturnValue<Derived> sin ( ) const
inherited
const MatrixFunctionReturnValue<Derived> sinh ( ) const
inherited
const SparseView< Derived > sparseView ( const Scalar m_reference = Scalar(0),
typename NumTraits< Scalar >::Real  m_epsilon = NumTraits<Scalar>::dummy_precision() 
) const
inherited
const MatrixSquareRootReturnValue<Derived> sqrt ( ) const
inherited
NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm ( ) const
inlineinherited
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()

References real().

NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm ( ) const
inlineinherited
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()

References Eigen::AlignedBit, Eigen::DirectAccessBit, sqrt(), and Eigen::internal::stable_norm_kernel().

void subTo ( Dest &  dst) const
inline

Reimplemented in ScaledProduct< NestedProduct >.

internal::traits< Derived >::Scalar sum ( ) const
inlineinherited
Returns:
the sum of all coefficients of *this
See also:
trace(), prod(), mean()

References Eigen::Dynamic.

Referenced by main().

void swap ( const DenseBase< OtherDerived > &  other,
int  = OtherDerived::ThisConstantIsPrivateInPlainObjectBase 
)
inlineinherited

swaps *this with the expression other.

Referenced by TriangularBase< Derived >::evalTo().

void swap ( PlainObjectBase< OtherDerived > &  other)
inlineinherited

swaps *this with the matrix or array other.

DenseBase< Derived >::SegmentReturnType tail ( Index  size)
inlineinherited
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:

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)

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::ConstSegmentReturnType tail ( Index  size) const
inlineinherited

This is the const version of tail(Index).

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type tail ( )
inlineinherited
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:

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

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type tail ( ) const
inlineinherited

This is the const version of tail<int>.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

Block<Derived> 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:

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 Derived> topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

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

Block<Derived, 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:

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 Derived, CRows, CCols> topLeftCorner ( ) const
inlineinherited

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

Block<Derived> 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:

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 Derived> topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

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

Block<Derived, 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:

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 Derived, 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>().

internal::traits< Derived >::Scalar trace ( ) const
inlineinherited
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< Derived >.

References MatrixBase< Derived >::diagonal().

Transpose< Derived > transpose ( )
inlineinherited
Returns:
an expression of the transpose of *this.

Example:

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()

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse().

const DenseBase< Derived >::ConstTransposeReturnType transpose ( ) const
inlineinherited

This is the const version of transpose().

Make sure you read the warning for transpose() !

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

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()
MatrixBase< Derived >::template 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
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView ( ) const
inherited

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

const CwiseUnaryOp<CustomUnaryOp, const Derived> 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**)
{
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
return 0;
}

Output:

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

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

Example:

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

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also:
class CwiseUnaryOp, class CwiseBinaryOp
const CwiseUnaryView<CustomViewOp, const Derived> 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**)
{
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 MatrixBase< Derived >::BasisReturnType Unit ( Index  size,
Index  i 
)
inlinestaticinherited
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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const MatrixBase< Derived >::BasisReturnType Unit ( Index  i)
inlinestaticinherited
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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

MatrixBase< Derived >::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()

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

const MatrixBase< Derived >::BasisReturnType UnitW ( )
inlinestaticinherited
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()
const MatrixBase< Derived >::BasisReturnType UnitX ( )
inlinestaticinherited
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()
const MatrixBase< Derived >::BasisReturnType UnitY ( )
inlinestaticinherited
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()
const MatrixBase< Derived >::BasisReturnType UnitZ ( )
inlinestaticinherited
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

Referenced by SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::evalTo().

void visit ( Visitor &  visitor) 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()

References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.

const DenseBase< Derived >::ConstantReturnType Zero ( Index  rows,
Index  cols 
)
inlinestaticinherited
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)
const DenseBase< Derived >::ConstantReturnType Zero ( Index  size)
inlinestaticinherited
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)
const DenseBase< Derived >::ConstantReturnType Zero ( )
inlinestaticinherited
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)

Friends And Related Function Documentation

std::ostream & operator<< ( std::ostream &  s,
const DenseBase< Derived > &  m 
)
related

Outputs the matrix, to the given stream.

If you wish to print the matrix with a format different than the default, use DenseBase::format().

It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.

See also:
DenseBase::format()

References EIGEN_DEFAULT_IO_FORMAT, and Eigen::internal::print_matrix().


Member Data Documentation

LhsNested m_lhs
protected
PlainObject m_result
mutableprotected
RhsNested m_rhs
protected

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