#include <GeneralProduct.h>
Public Types | |
enum | { Side } |
enum | |
enum | |
enum | |
enum | |
typedef internal::remove_all < ActualLhsType >::type | _ActualLhsType |
typedef internal::remove_all < ActualRhsType >::type | _ActualRhsType |
typedef internal::remove_all < LhsNested >::type | _LhsNested |
typedef internal::remove_all < RhsNested >::type | _RhsNested |
typedef LhsBlasTraits::DirectLinearAccessType | ActualLhsType |
typedef RhsBlasTraits::DirectLinearAccessType | ActualRhsType |
typedef MatrixBase < GeneralProduct< Lhs, Rhs, GemvProduct > > | Base |
typedef Base::CoeffReturnType | CoeffReturnType |
typedef VectorwiseOp < GeneralProduct< Lhs, Rhs, GemvProduct >, Vertical > | ColwiseReturnType |
typedef const VectorwiseOp < const GeneralProduct< Lhs, Rhs, GemvProduct >, Vertical > | ConstColwiseReturnType |
typedef const Diagonal< const GeneralProduct< Lhs, Rhs, GemvProduct > > | ConstDiagonalReturnType |
typedef const Reverse< const GeneralProduct< Lhs, Rhs, GemvProduct >, BothDirections > | ConstReverseReturnType |
typedef const VectorwiseOp < const GeneralProduct< Lhs, Rhs, GemvProduct >, Horizontal > | ConstRowwiseReturnType |
typedef const VectorBlock < const GeneralProduct< Lhs, Rhs, GemvProduct > > | ConstSegmentReturnType |
typedef Block< const GeneralProduct< Lhs, Rhs, GemvProduct > , internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::ColsAtCompileTime==1?SizeMinusOne:1, internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::ColsAtCompileTime==1?1:SizeMinusOne > | ConstStartMinusOne |
typedef const Transpose< const GeneralProduct< Lhs, Rhs, GemvProduct > > | ConstTransposeReturnType |
typedef Diagonal < GeneralProduct< Lhs, Rhs, GemvProduct > > | DiagonalReturnType |
typedef internal::add_const_on_value_type < typename internal::eval < GeneralProduct< Lhs, Rhs, GemvProduct > >::type >::type | EvalReturnType |
typedef CoeffBasedProduct < LhsNested, RhsNested, 0 > | FullyLazyCoeffBaseProductType |
typedef CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar > , const ConstStartMinusOne > | HNormalizedReturnType |
typedef Homogeneous < GeneralProduct< Lhs, Rhs, GemvProduct > , HomogeneousReturnTypeDirection > | HomogeneousReturnType |
typedef internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Index | Index |
The type of indices. | |
typedef internal::blas_traits < _LhsNested > | LhsBlasTraits |
typedef Lhs::Nested | LhsNested |
typedef Lhs::Scalar | LhsScalar |
typedef internal::conditional < int(Side)==OnTheRight, _LhsNested, _RhsNested >::type | MatrixType |
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 < GeneralProduct< Lhs, Rhs, GemvProduct >, BothDirections > | ReverseReturnType |
typedef internal::blas_traits < _RhsNested > | RhsBlasTraits |
typedef Rhs::Nested | RhsNested |
typedef Rhs::Scalar | RhsScalar |
typedef VectorwiseOp < GeneralProduct< Lhs, Rhs, GemvProduct >, Horizontal > | RowwiseReturnType |
typedef internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | Scalar |
typedef VectorBlock < GeneralProduct< Lhs, Rhs, GemvProduct > > | SegmentReturnType |
typedef internal::stem_function < Scalar >::type | StemFunction |
typedef internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::StorageKind | StorageKind |
Public Member Functions | |
void | addTo (Dest &dst) const |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
bool | all (void) const |
bool | any (void) const |
void | applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
void | applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
ArrayWrapper< GeneralProduct < Lhs, Rhs, GemvProduct > > | array () |
const ArrayWrapper< const GeneralProduct< Lhs, Rhs, GemvProduct > > | array () const |
const DiagonalWrapper< const GeneralProduct< Lhs, Rhs, GemvProduct > > | asDiagonal () const |
const PermutationWrapper < const GeneralProduct< Lhs, Rhs, GemvProduct > > | asPermutation () const |
const CwiseBinaryOp < CustomBinaryOp, const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct >, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct >, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
RealScalar | blueNorm () const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct > > | bottomLeftCorner (Index cRows, Index cCols) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct > > | bottomLeftCorner (Index cRows, Index cCols) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | bottomLeftCorner () |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | bottomLeftCorner () const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct > > | bottomRightCorner (Index cRows, Index cCols) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct > > | bottomRightCorner (Index cRows, Index cCols) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | bottomRightCorner () |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | bottomRightCorner () const |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
NRowsBlockXpr< N >::Type | bottomRows () |
ConstNRowsBlockXpr< N >::Type | bottomRows () const |
internal::cast_return_type < GeneralProduct< Lhs, Rhs, GemvProduct >, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar, NewType >, const GeneralProduct< Lhs, Rhs, GemvProduct > > >::type | cast () const |
Base::CoeffReturnType | coeff (Index row, Index col) const |
Base::CoeffReturnType | coeff (Index i) const |
const Scalar & | coeffRef (Index row, Index col) const |
const Scalar & | coeffRef (Index i) const |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () const |
Index | cols () const |
ConstColwiseReturnType | colwise () const |
ColwiseReturnType | colwise () |
void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
ConjugateReturnType | conjugate () const |
const MatrixFunctionReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | cos () const |
const MatrixFunctionReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | cosh () const |
Index | count () const |
cross_product_return_type < OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | cwiseAbs () const |
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | cwiseAbs2 () const |
const CwiseBinaryOp < std::equal_to< Scalar > , const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < std::binder1st < std::equal_to< Scalar > >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | cwiseEqual (const Scalar &s) const |
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | cwiseInverse () const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct >, const ConstantReturnType > | cwiseMax (const Scalar &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct >, const ConstantReturnType > | cwiseMin (const Scalar &other) const |
const CwiseBinaryOp < std::not_equal_to< Scalar > , const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct >, const OtherDerived > | cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | cwiseSqrt () const |
Scalar | determinant () const |
const Diagonal< const FullyLazyCoeffBaseProductType, 0 > | diagonal () const |
const Diagonal < FullyLazyCoeffBaseProductType, Index > | diagonal () const |
const Diagonal < FullyLazyCoeffBaseProductType, Dynamic > | diagonal (Index index) const |
DiagonalReturnType | diagonal () |
DiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) |
Index | diagonalSize () const |
internal::scalar_product_traits < typename internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar, typename internal::traits < OtherDerived >::Scalar > ::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
const | EIGEN_CWISE_PRODUCT_RETURN_TYPE (GeneralProduct< Lhs, Rhs, GemvProduct >, OtherDerived) cwiseProduct(const Eigen |
EigenvaluesReturnType | eigenvalues () const |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
EvalReturnType | eval () const |
void | evalTo (Dest &dst) const |
const MatrixExponentialReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | exp () const |
void | fill (const Scalar &value) |
const Flagged< GeneralProduct < Lhs, Rhs, GemvProduct > , Added, Removed > | flagged () const |
const ForceAlignedAccess < GeneralProduct< Lhs, Rhs, GemvProduct > > | forceAlignedAccess () const |
ForceAlignedAccess < GeneralProduct< Lhs, Rhs, GemvProduct > > | forceAlignedAccess () |
internal::add_const_on_value_type < typename internal::conditional< Enable, ForceAlignedAccess < GeneralProduct< Lhs, Rhs, GemvProduct > >, GeneralProduct< Lhs, Rhs, GemvProduct > & >::type > ::type | forceAlignedAccessIf () const |
internal::conditional< Enable, ForceAlignedAccess < GeneralProduct< Lhs, Rhs, GemvProduct > >, GeneralProduct< Lhs, Rhs, GemvProduct > & >::type | forceAlignedAccessIf () |
const WithFormat < GeneralProduct< Lhs, Rhs, GemvProduct > > | format (const IOFormat &fmt) const |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
const FullPivLU< PlainObject > | fullPivLu () const |
GeneralProduct (const Lhs &lhs, const Rhs &rhs) | |
SegmentReturnType | head (Index size) |
DenseBase::ConstSegmentReturnType | head (Index size) const |
FixedSegmentReturnType< Size > ::Type | head () |
ConstFixedSegmentReturnType < Size >::Type | head () const |
const HNormalizedReturnType | hnormalized () const |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
const ImagReturnType | imag () const |
NonConstImagReturnType | imag () |
Index | innerSize () const |
const internal::inverse_impl < GeneralProduct< Lhs, Rhs, GemvProduct > > | inverse () const |
bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
JacobiSVD< PlainObject > | jacobiSvd (unsigned int computationOptions=0) const |
const LazyProductReturnType < GeneralProduct< Lhs, Rhs, GemvProduct >, OtherDerived > ::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
const LDLT< PlainObject > | ldlt () const |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
NColsBlockXpr< N >::Type | leftCols () |
ConstNColsBlockXpr< N >::Type | leftCols () const |
const _LhsNested & | lhs () const |
const LLT< PlainObject > | llt () const |
const MatrixLogarithmReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | log () const |
RealScalar | lpNorm () const |
const PartialPivLU< PlainObject > | lu () const |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
MatrixBase< GeneralProduct < Lhs, Rhs, GemvProduct > > & | matrix () |
const MatrixBase < GeneralProduct< Lhs, Rhs, GemvProduct > > & | matrix () const |
const MatrixFunctionReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | matrixFunction (StemFunction f) const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | maxCoeff () const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | maxCoeff (IndexType *index) const |
Scalar | mean () const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
NColsBlockXpr< N >::Type | middleCols (Index startCol) |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
RowsBlockXpr | middleRows (Index startRow, Index numRows) |
ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | minCoeff () const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar | minCoeff (IndexType *index) const |
const NestByValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | nestByValue () const |
NoAlias< GeneralProduct< Lhs, Rhs, GemvProduct > , Eigen::MatrixBase > | noalias () |
Index | nonZeros () const |
RealScalar | norm () const |
void | normalize () |
const PlainObject | normalized () const |
operator const PlainObject & () const | |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
const ScalarMultipleReturnType | operator* (const RealScalar &scalar) const |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | operator* (const std::complex< Scalar > &scalar) const |
const ProductReturnType < GeneralProduct< Lhs, Rhs, GemvProduct >, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
const DiagonalProduct < GeneralProduct< Lhs, Rhs, GemvProduct >, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator*= (const EigenBase< OtherDerived > &other) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator*= (const Scalar &other) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator+= (const MatrixBase< OtherDerived > &other) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator+= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar > , const GeneralProduct< Lhs, Rhs, GemvProduct > > | operator- () const |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator-= (const MatrixBase< OtherDerived > &other) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator-= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar > , const GeneralProduct< Lhs, Rhs, GemvProduct > > | operator/ (const Scalar &scalar) const |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator/= (const Scalar &other) |
CommaInitializer < GeneralProduct< Lhs, Rhs, GemvProduct > > | operator<< (const Scalar &s) |
CommaInitializer < GeneralProduct< Lhs, Rhs, GemvProduct > > | operator<< (const DenseBase< OtherDerived > &other) |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
RealScalar | operatorNorm () const |
Index | outerSize () const |
const PartialPivLU< PlainObject > | partialPivLu () const |
Scalar | prod () const |
RealReturnType | real () const |
NonConstRealReturnType | real () |
const Replicate < GeneralProduct< Lhs, Rhs, GemvProduct >, RowFactor, ColFactor > | replicate () const |
const Replicate < GeneralProduct< Lhs, Rhs, GemvProduct >, 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 _RhsNested & | rhs () const |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
NColsBlockXpr< N >::Type | rightCols () |
ConstNColsBlockXpr< N >::Type | rightCols () const |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
Index | rows () const |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
template<typename Dest > | |
void | scaleAndAddTo (Dest &dst, Scalar alpha) const |
SegmentReturnType | segment (Index start, Index size) |
DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
FixedSegmentReturnType< Size > ::Type | segment (Index start) |
ConstFixedSegmentReturnType < Size >::Type | segment (Index start) const |
const Select< GeneralProduct < Lhs, Rhs, GemvProduct > , ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
const Select< GeneralProduct < Lhs, Rhs, GemvProduct > , ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
const Select< GeneralProduct < Lhs, Rhs, GemvProduct > , typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
SelfAdjointViewReturnType < UpLo >::Type | selfadjointView () |
ConstSelfAdjointViewReturnType < UpLo >::Type | selfadjointView () const |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setConstant (const Scalar &value) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setIdentity () |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setIdentity (Index rows, Index cols) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setLinSpaced (const Scalar &low, const Scalar &high) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setOnes () |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setRandom () |
GeneralProduct< Lhs, Rhs, GemvProduct > & | setZero () |
const MatrixFunctionReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | sin () const |
const MatrixFunctionReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | sinh () const |
const SparseView < GeneralProduct< Lhs, Rhs, GemvProduct > > | sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const |
const MatrixSquareRootReturnValue < GeneralProduct< Lhs, Rhs, GemvProduct > > | sqrt () const |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () const |
void | subTo (Dest &dst) const |
Scalar | sum () const |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index size) |
DenseBase::ConstSegmentReturnType | tail (Index size) const |
FixedSegmentReturnType< Size > ::Type | tail () |
ConstFixedSegmentReturnType < Size >::Type | tail () const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct > > | topLeftCorner (Index cRows, Index cCols) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct > > | topLeftCorner (Index cRows, Index cCols) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | topLeftCorner () |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | topLeftCorner () const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct > > | topRightCorner (Index cRows, Index cCols) |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct > > | topRightCorner (Index cRows, Index cCols) const |
Block< GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | topRightCorner () |
const Block< const GeneralProduct< Lhs, Rhs, GemvProduct >, CRows, CCols > | topRightCorner () const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
NRowsBlockXpr< N >::Type | topRows () |
ConstNRowsBlockXpr< N >::Type | topRows () const |
Scalar | trace () const |
Eigen::Transpose < GeneralProduct< Lhs, Rhs, GemvProduct > > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
TriangularViewReturnType< Mode > ::Type | triangularView () |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
const CwiseUnaryOp < CustomUnaryOp, const GeneralProduct< Lhs, Rhs, GemvProduct > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. | |
const CwiseUnaryView < CustomViewOp, const GeneralProduct< Lhs, Rhs, GemvProduct > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
PlainObject | unitOrthogonal (void) const |
CoeffReturnType | value () const |
void | visit (Visitor &func) const |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
static const CwiseNullaryOp < CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
static const CwiseNullaryOp < CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > | NullaryExpr (Index size, const CustomNullaryOp &func) |
static const CwiseNullaryOp < CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > | 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 >, GeneralProduct < Lhs, Rhs, GemvProduct > > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, GeneralProduct < Lhs, Rhs, GemvProduct > > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, GeneralProduct < Lhs, Rhs, GemvProduct > > | Random () |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero () |
Protected Member Functions | |
void | checkTransposeAliasing (const OtherDerived &other) const |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator+= (const ArrayBase< OtherDerived > &) |
GeneralProduct< Lhs, Rhs, GemvProduct > & | operator-= (const ArrayBase< OtherDerived > &) |
Protected Attributes | |
LhsNested | m_lhs |
PlainObject | m_result |
RhsNested | m_rhs |
Friends | |
const ScalarMultipleReturnType | operator* (const Scalar &scalar, const StorageBaseType &matrix) |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const GeneralProduct< Lhs, Rhs, GemvProduct > > | operator* (const std::complex< Scalar > &scalar, const StorageBaseType &matrix) |
typedef internal::remove_all<ActualLhsType>::type _ActualLhsType [inherited] |
typedef internal::remove_all<ActualRhsType>::type _ActualRhsType [inherited] |
typedef internal::remove_all<LhsNested>::type _LhsNested [inherited] |
typedef internal::remove_all<RhsNested>::type _RhsNested [inherited] |
typedef LhsBlasTraits::DirectLinearAccessType ActualLhsType [inherited] |
typedef RhsBlasTraits::DirectLinearAccessType ActualRhsType [inherited] |
typedef MatrixBase<GeneralProduct< Lhs, Rhs, GemvProduct > > Base [inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
typedef Base::CoeffReturnType CoeffReturnType [inherited] |
typedef VectorwiseOp<GeneralProduct< Lhs, Rhs, GemvProduct > , Vertical> ColwiseReturnType [inherited] |
typedef const VectorwiseOp<const GeneralProduct< Lhs, Rhs, GemvProduct > , Vertical> ConstColwiseReturnType [inherited] |
typedef const Diagonal<const GeneralProduct< Lhs, Rhs, GemvProduct > > ConstDiagonalReturnType [inherited] |
typedef const Reverse<const GeneralProduct< Lhs, Rhs, GemvProduct > , BothDirections> ConstReverseReturnType [inherited] |
typedef const VectorwiseOp<const GeneralProduct< Lhs, Rhs, GemvProduct > , Horizontal> ConstRowwiseReturnType [inherited] |
typedef const VectorBlock<const GeneralProduct< Lhs, Rhs, GemvProduct > > ConstSegmentReturnType [inherited] |
typedef Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne [inherited] |
typedef const Transpose<const GeneralProduct< Lhs, Rhs, GemvProduct > > ConstTransposeReturnType [inherited] |
typedef Diagonal<GeneralProduct< Lhs, Rhs, GemvProduct > > DiagonalReturnType [inherited] |
typedef internal::add_const_on_value_type<typename internal::eval<GeneralProduct< Lhs, Rhs, GemvProduct > >::type>::type EvalReturnType [inherited] |
typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType [inherited] |
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar>, const ConstStartMinusOne > HNormalizedReturnType [inherited] |
typedef Homogeneous<GeneralProduct< Lhs, Rhs, GemvProduct > , HomogeneousReturnTypeDirection> HomogeneousReturnType [inherited] |
typedef internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Index Index [inherited] |
The type of indices.
To change this, #define
the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE
.
typedef internal::blas_traits<_LhsNested> LhsBlasTraits [inherited] |
typedef Lhs::Nested LhsNested [inherited] |
typedef Lhs::Scalar LhsScalar |
Reimplemented from ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >.
typedef internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType |
typedef internal::packet_traits<Scalar>::type PacketScalar [inherited] |
typedef Base::PlainObject PlainObject [inherited] |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
Reimplemented from MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
typedef NumTraits<Scalar>::Real RealScalar [inherited] |
typedef Reverse<GeneralProduct< Lhs, Rhs, GemvProduct > , BothDirections> ReverseReturnType [inherited] |
typedef internal::blas_traits<_RhsNested> RhsBlasTraits [inherited] |
typedef Rhs::Nested RhsNested [inherited] |
typedef Rhs::Scalar RhsScalar |
Reimplemented from ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >.
typedef VectorwiseOp<GeneralProduct< Lhs, Rhs, GemvProduct > , Horizontal> RowwiseReturnType [inherited] |
typedef internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar Scalar [inherited] |
typedef VectorBlock<GeneralProduct< Lhs, Rhs, GemvProduct > > SegmentReturnType [inherited] |
typedef internal::stem_function<Scalar>::type StemFunction [inherited] |
typedef internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::StorageKind StorageKind [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
GeneralProduct | ( | const Lhs & | lhs, |
const Rhs & | rhs | ||
) | [inline] |
void addTo | ( | Dest & | dst | ) | const [inline, inherited] |
const AdjointReturnType adjoint | ( | ) | const [inherited] |
Example:
Matrix2cf m = Matrix2cf::Random(); cout << "Here is the 2x2 complex matrix m:" << endl << m << endl; cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
Output:
Here is the 2x2 complex matrix m: (-0.211,0.68) (-0.605,0.823) (0.597,0.566) (0.536,-0.33) Here is the adjoint of m: (-0.211,-0.68) (0.597,-0.566) (-0.605,-0.823) (0.536,0.33)
m = m.adjoint(); // bug!!! caused by aliasing effect
m.adjointInPlace();
m = m.adjoint().eval();
void adjointInPlace | ( | ) | [inherited] |
This is the "in place" version of adjoint(): it replaces *this
by its own transpose. Thus, doing
m.adjointInPlace();
has the same effect on m as doing
m = m.adjoint().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
*this
must be a resizable matrix.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
void applyHouseholderOnTheLeft | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) | [inherited] |
Apply the elementary reflector H given by with
from the left to a vector or matrix.
On input:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
workspace | a pointer to working space with at least this->cols() * essential.size() entries |
void applyHouseholderOnTheRight | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) | [inherited] |
Apply the elementary reflector H given by with
from the right to a vector or matrix.
On input:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
workspace | a pointer to working space with at least this->cols() * essential.size() entries |
void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other.
void applyOnTheLeft | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) | [inherited] |
This is defined in the Jacobi module.
#include <Eigen/Jacobi>
Applies the rotation in the plane j to the rows p and q of *this
, i.e., it computes B = J * B, with .
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=()
void applyOnTheRight | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) | [inherited] |
Applies the rotation in the plane j to the columns p and q of *this
, i.e., it computes B = B * J with .
ArrayWrapper<GeneralProduct< Lhs, Rhs, GemvProduct > > array | ( | ) | [inline, inherited] |
const ArrayWrapper<const GeneralProduct< Lhs, Rhs, GemvProduct > > array | ( | ) | const [inline, inherited] |
const DiagonalWrapper<const GeneralProduct< Lhs, Rhs, GemvProduct > > asDiagonal | ( | ) | const [inherited] |
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
const PermutationWrapper<const GeneralProduct< Lhs, Rhs, GemvProduct > > asPermutation | ( | ) | const [inherited] |
const CwiseBinaryOp<CustomBinaryOp, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> binaryExpr | ( | const Eigen::MatrixBase< OtherDerived > & | other, |
const CustomBinaryOp & | func = CustomBinaryOp() |
||
) | const [inline, inherited] |
*this
and other *this
and other The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template binary functor template<typename Scalar> struct MakeComplexOp { EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp) typedef complex<Scalar> result_type; complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); } }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random(); cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl; return 0; }
Output:
(0.68,0.271) (0.823,-0.967) (-0.444,-0.687) (-0.27,0.998) (-0.211,0.435) (-0.605,-0.514) (0.108,-0.198) (0.0268,-0.563) (0.566,-0.717) (-0.33,-0.726) (-0.0452,-0.74) (0.904,0.0259) (0.597,0.214) (0.536,0.608) (0.258,-0.782) (0.832,0.678)
Block<GeneralProduct< Lhs, Rhs, GemvProduct > > block | ( | Index | startRow, |
Index | startCol, | ||
Index | blockRows, | ||
Index | blockCols | ||
) | [inline, inherited] |
startRow | the first row in the block |
startCol | the first column in the block |
blockRows | the number of rows in the block |
blockCols | the number of columns in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl; m.block(1, 1, 2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > > block | ( | Index | startRow, |
Index | startCol, | ||
Index | blockRows, | ||
Index | blockCols | ||
) | const [inline, inherited] |
This is the const version of block(Index,Index,Index,Index).
Block<GeneralProduct< Lhs, Rhs, GemvProduct > , BlockRows, BlockCols> block | ( | Index | startRow, |
Index | startCol | ||
) | [inline, inherited] |
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
startRow | the first row in the block |
startCol | the first column in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl; m.block<2,2>(1,1).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
m.template block<3,3>(1,1);
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , BlockRows, BlockCols> block | ( | Index | startRow, |
Index | startCol | ||
) | const [inline, inherited] |
This is the const version of block<>(Index, Index).
RealScalar blueNorm | ( | ) | const [inherited] |
*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.
Block<GeneralProduct< Lhs, Rhs, GemvProduct > > bottomLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner(2, 2):" << endl; cout << m.bottomLeftCorner(2, 2) << endl; m.bottomLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > > bottomLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomLeftCorner(Index, Index).
Block<GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> bottomLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner<2,2>():" << endl; cout << m.bottomLeftCorner<2,2>() << endl; m.bottomLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> bottomLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomLeftCorner<int, int>().
Block<GeneralProduct< Lhs, Rhs, GemvProduct > > bottomRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner(2, 2):" << endl; cout << m.bottomRightCorner(2, 2) << endl; m.bottomRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > > bottomRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomRightCorner(Index, Index).
Block<GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> bottomRightCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner<2,2>():" << endl; cout << m.bottomRightCorner<2,2>() << endl; m.bottomRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> bottomRightCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomRightCorner<int, int>().
RowsBlockXpr bottomRows | ( | Index | n | ) | [inline, inherited] |
n | the 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
ConstRowsBlockXpr bottomRows | ( | Index | n | ) | const [inline, inherited] |
This is the const version of bottomRows(Index).
NRowsBlockXpr<N>::Type bottomRows | ( | ) | [inline, inherited] |
N | the 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
ConstNRowsBlockXpr<N>::Type bottomRows | ( | ) | const [inline, inherited] |
This is the const version of bottomRows<int>().
internal::cast_return_type<GeneralProduct< Lhs, Rhs, GemvProduct > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar, NewType>, const GeneralProduct< Lhs, Rhs, GemvProduct > > >::type cast | ( | ) | const [inline, inherited] |
The template parameter NewScalar is the type we are casting the scalars to.
void checkTransposeAliasing | ( | const OtherDerived & | other | ) | const [protected, inherited] |
const ColPivHouseholderQR<PlainObject> colPivHouseholderQr | ( | ) | const [inherited] |
*this
.ConstColwiseReturnType colwise | ( | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl; cout << "Here is the maximum absolute value of each column:" << endl << m.cwiseAbs().colwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
ColwiseReturnType colwise | ( | ) | [inherited] |
void computeInverseAndDetWithCheck | ( | ResultType & | inverse, |
typename ResultType::Scalar & | determinant, | ||
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
determinant | Reference to the variable in which to store the inverse. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; 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
void computeInverseWithCheck | ( | ResultType & | inverse, |
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; m.computeInverseWithCheck(inverse,invertible); if(invertible) { cout << "It is invertible, and its inverse is:" << endl << inverse << endl; } else { cout << "It is not invertible." << endl; }
Output:
Here is the matrix m: 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
ConjugateReturnType conjugate | ( | ) | const [inline, inherited] |
*this
.static const ConstantReturnType Constant | ( | Index | rows, |
Index | cols, | ||
const Scalar & | value | ||
) | [static, inherited] |
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.
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.
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.
const MatrixFunctionReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > cos | ( | ) | const [inherited] |
const MatrixFunctionReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > cosh | ( | ) | const [inherited] |
cross_product_return_type<OtherDerived>::type cross | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other Here is a very good explanation of cross-product: http://xkcd.com/199/
PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other using only the x, y, and z coefficientsThe 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.
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > cwiseAbs | ( | ) | const [inline, inherited] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs() << endl;
Output:
2 4 6 5 1 0
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > cwiseAbs2 | ( | ) | const [inline, inherited] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs2() << endl;
Output:
4 16 36 25 1 0
const CwiseBinaryOp<std::equal_to<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> cwiseEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
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
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const GeneralProduct< Lhs, Rhs, GemvProduct > > cwiseEqual | ( | const Scalar & | s | ) | const [inline, inherited] |
*this
and a scalar s const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > cwiseInverse | ( | ) | const [inline, inherited] |
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
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> cwiseMax | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMax(w) << endl;
Output:
4 3 4
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const ConstantReturnType> cwiseMax | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> cwiseMin | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMin(w) << endl;
Output:
2 2 3
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const ConstantReturnType> cwiseMin | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<std::not_equal_to<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> cwiseNotEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
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
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > , const OtherDerived> cwiseQuotient | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseQuotient(w) << endl;
Output:
0.5 1.5 1.33
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > cwiseSqrt | ( | ) | const [inline, inherited] |
Example:
Vector3d v(1,2,4); cout << v.cwiseSqrt() << endl;
Output:
1 1.41 2
Scalar determinant | ( | ) | const [inherited] |
const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal | ( | ) | const [inline, inherited] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
Reimplemented from MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal | ( | ) | const [inline, inherited] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
Reimplemented from MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal | ( | Index | index | ) | const [inline, inherited] |
This is the const version of diagonal(Index).
Reimplemented from MatrixBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
DiagonalReturnType diagonal | ( | ) | [inherited] |
*this
*this
is not required to be square.
Example:
Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the main diagonal of m:" << endl << m.diagonal() << endl;
Output:
Here is the matrix m: 7 6 -3 -2 9 6 6 -6 -5 Here are the coefficients on the main diagonal of m: 7 9 -5
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal<1>().transpose() << endl << m.diagonal<-2>().transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal(1).transpose() << endl << m.diagonal(-2).transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
Index diagonalSize | ( | ) | const [inline, inherited] |
internal::scalar_product_traits<typename internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
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.
const EIGEN_CWISE_PRODUCT_RETURN_TYPE | ( | GeneralProduct< Lhs, Rhs, GemvProduct > | , |
OtherDerived | |||
) | const [inline, inherited] |
Example:
Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random(); Matrix3i c = a.cwiseProduct(b); cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;
Output:
a: 7 6 -3 -2 9 6 6 -6 -5 b: 1 -3 9 0 0 3 3 9 5 c: 7 -18 -27 0 0 18 18 -54 -25
EigenvaluesReturnType eigenvalues | ( | ) | const [inherited] |
Computes the eigenvalues of a matrix.
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)
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
using the convention defined by the triplet (a0,a1,a2)Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:
Vector3f ea = mat.eulerAngles(2, 0, 2);
"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:
mat == AngleAxisf(ea[0], Vector3f::UnitZ()) * AngleAxisf(ea[1], Vector3f::UnitX()) * AngleAxisf(ea[2], Vector3f::UnitZ());
This corresponds to the right-multiply conventions (with right hand side frames).
EvalReturnType eval | ( | ) | const [inline, inherited] |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
void evalTo | ( | Dest & | dst | ) | const [inline, inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
const MatrixExponentialReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > exp | ( | ) | const [inherited] |
Alias for setConstant(): sets all coefficients in this expression to value.
const Flagged<GeneralProduct< Lhs, Rhs, GemvProduct > , Added, Removed> flagged | ( | ) | const [inherited] |
This is mostly for internal use.
const ForceAlignedAccess<GeneralProduct< Lhs, Rhs, GemvProduct > > forceAlignedAccess | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
ForceAlignedAccess<GeneralProduct< Lhs, Rhs, GemvProduct > > forceAlignedAccess | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<GeneralProduct< Lhs, Rhs, GemvProduct > >,GeneralProduct< Lhs, Rhs, GemvProduct > &>::type>::type forceAlignedAccessIf | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
internal::conditional<Enable,ForceAlignedAccess<GeneralProduct< Lhs, Rhs, GemvProduct > >,GeneralProduct< Lhs, Rhs, GemvProduct > &>::type forceAlignedAccessIf | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
const WithFormat<GeneralProduct< Lhs, Rhs, GemvProduct > > format | ( | const IOFormat & | fmt | ) | const [inline, inherited] |
See class IOFormat for some examples.
const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr | ( | ) | const [inherited] |
*this
.const FullPivLU<PlainObject> fullPivLu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.SegmentReturnType head | ( | Index | size | ) | [inherited] |
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.
size | the number of coefficients in the block |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head(2) << endl; v.head(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
DenseBase::ConstSegmentReturnType head | ( | Index | size | ) | const [inherited] |
This is the const version of head(Index).
FixedSegmentReturnType<Size>::Type head | ( | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head<2>() << endl; v.head<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
ConstFixedSegmentReturnType<Size>::Type head | ( | ) | const [inherited] |
This is the const version of head<int>().
const HNormalizedReturnType hnormalized | ( | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
Example:
Output:
HomogeneousReturnType homogeneous | ( | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
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:
const HouseholderQR<PlainObject> householderQr | ( | ) | const [inherited] |
*this
.RealScalar hypotNorm | ( | ) | const [inherited] |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.static const IdentityReturnType Identity | ( | ) | [static, inherited] |
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
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
const ImagReturnType imag | ( | ) | const [inline, inherited] |
*this
.NonConstImagReturnType imag | ( | ) | [inline, inherited] |
*this
.const internal::inverse_impl<GeneralProduct< Lhs, Rhs, GemvProduct > > inverse | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Its inverse is:" << endl << m.inverse() << endl;
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
bool isApprox | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
true
if *this
is approximately equal to other, within the precision determined by prec.
*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.bool isApproxToConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
bool isConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is just an alias for isApproxToConstant().
bool isDiagonal | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = 10000 * Matrix3d::Identity(); m(0,2) = 1; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl; cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;
Output:
Here's the matrix m: 1e+04 0 1 0 1e+04 0 0 0 1e+04 m.isDiagonal() returns: 0 m.isDiagonal(1e-3) returns: 1
bool isIdentity | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isIdentity() returns: " << m.isIdentity() << endl; cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isIdentity() returns: 0 m.isIdentity(1e-3) returns: 1
bool isLowerTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
bool isMuchSmallerThan | ( | const RealScalar & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
bool isMuchSmallerThan | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
bool isOnes | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Ones(); m(0,2) += 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isOnes() returns: " << m.isOnes() << endl; cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
bool isOrthogonal | ( | const MatrixBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
Example:
Vector3d v(1,0,0); Vector3d w(1e-4,0,1); cout << "Here's the vector v:" << endl << v << endl; cout << "Here's the vector w:" << endl << w << endl; cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl; cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;
Output:
Here's the vector v: 1 0 0 Here's the vector w: 0.0001 0 1 v.isOrthogonal(w) returns: 0 v.isOrthogonal(w,1e-3) returns: 1
bool isUnitary | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isUnitary() returns: " << m.isUnitary() << endl; cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isUnitary() returns: 0 m.isUnitary(1e-3) returns: 1
bool isUpperTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
bool isZero | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Zero(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isZero() returns: " << m.isZero() << endl; cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;
Output:
Here's the matrix m: 0 0 0.0001 0 0 0 0 0 0 m.isZero() returns: 0 m.isZero(1e-3) returns: 1
JacobiSVD<PlainObject> jacobiSvd | ( | unsigned int | computationOptions = 0 | ) | const [inherited] |
This is defined in the SVD module.
#include <Eigen/SVD>
*this
computed by two-sided Jacobi transformations.const LazyProductReturnType<GeneralProduct< Lhs, Rhs, GemvProduct > ,OtherDerived>::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
*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.
const LDLT<PlainObject> ldlt | ( | ) | const [inherited] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
n | the 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
This is the const version of leftCols(Index).
NColsBlockXpr<N>::Type leftCols | ( | ) | [inline, inherited] |
N | the 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
ConstNColsBlockXpr<N>::Type leftCols | ( | ) | const [inline, inherited] |
This is the const version of leftCols<int>().
const _LhsNested& lhs | ( | ) | const [inline, inherited] |
static const SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
Index | size, | ||
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
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
static const RandomAccessLinSpacedReturnType LinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
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
static const SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
static const RandomAccessLinSpacedReturnType LinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [static, inherited] |
const LLT<PlainObject> llt | ( | ) | const [inherited] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
const MatrixLogarithmReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > log | ( | ) | const [inherited] |
RealScalar lpNorm | ( | ) | const [inherited] |
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
const PartialPivLU<PlainObject> lu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Synonym of partialPivLu().
*this
.void makeHouseholder | ( | EssentialPart & | essential, |
Scalar & | tau, | ||
RealScalar & | beta | ||
) | const [inherited] |
Computes the elementary reflector H such that: where the transformation H is:
and the vector v is:
On output:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
beta | the result of H * *this |
void makeHouseholderInPlace | ( | Scalar & | tau, |
RealScalar & | beta | ||
) | [inherited] |
Computes the elementary reflector H such that: where the transformation H is:
and the vector v is:
The essential part of the vector v
is stored in *this.
On output:
tau | the scaling factor of the Householder transformation |
beta | the result of H * *this |
MatrixBase<GeneralProduct< Lhs, Rhs, GemvProduct > >& matrix | ( | ) | [inline, inherited] |
const MatrixBase<GeneralProduct< Lhs, Rhs, GemvProduct > >& matrix | ( | ) | const [inline, inherited] |
const MatrixFunctionReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > matrixFunction | ( | StemFunction | f | ) | const [inherited] |
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar maxCoeff | ( | ) | const [inherited] |
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar maxCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const [inherited] |
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar maxCoeff | ( | IndexType * | index | ) | const [inherited] |
ColsBlockXpr middleCols | ( | Index | startCol, |
Index | numCols | ||
) | [inline, inherited] |
startCol | the index of the first column in the block |
numCols | the 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
ConstColsBlockXpr middleCols | ( | Index | startCol, |
Index | numCols | ||
) | const [inline, inherited] |
This is the const version of middleCols(Index,Index).
NColsBlockXpr<N>::Type middleCols | ( | Index | startCol | ) | [inline, inherited] |
N | the number of columns in the block |
startCol | the 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
ConstNColsBlockXpr<N>::Type middleCols | ( | Index | startCol | ) | const [inline, inherited] |
This is the const version of middleCols<int>().
RowsBlockXpr middleRows | ( | Index | startRow, |
Index | numRows | ||
) | [inline, inherited] |
startRow | the index of the first row in the block |
numRows | the 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
ConstRowsBlockXpr middleRows | ( | Index | startRow, |
Index | numRows | ||
) | const [inline, inherited] |
This is the const version of middleRows(Index,Index).
NRowsBlockXpr<N>::Type middleRows | ( | Index | startRow | ) | [inline, inherited] |
N | the number of rows in the block |
startRow | the 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
ConstNRowsBlockXpr<N>::Type middleRows | ( | Index | startRow | ) | const [inline, inherited] |
This is the const version of middleRows<int>().
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar minCoeff | ( | ) | const [inherited] |
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar minCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const [inherited] |
internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar minCoeff | ( | IndexType * | index | ) | const [inherited] |
const NestByValue<GeneralProduct< Lhs, Rhs, GemvProduct > > nestByValue | ( | ) | const [inline, inherited] |
NoAlias<GeneralProduct< Lhs, Rhs, GemvProduct > ,Eigen::MatrixBase > noalias | ( | ) | [inherited] |
*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;
RealScalar norm | ( | ) | const [inherited] |
*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.void normalize | ( | void | ) | [inherited] |
Normalizes the vector, i.e. divides it by its own norm.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
const PlainObject normalized | ( | ) | const [inherited] |
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.
static const CwiseNullaryOp<CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > NullaryExpr | ( | Index | rows, |
Index | cols, | ||
const CustomNullaryOp & | func | ||
) | [static, inherited] |
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.
static const CwiseNullaryOp<CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > NullaryExpr | ( | Index | size, |
const CustomNullaryOp & | func | ||
) | [static, inherited] |
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.
static const CwiseNullaryOp<CustomNullaryOp, GeneralProduct< Lhs, Rhs, GemvProduct > > NullaryExpr | ( | const CustomNullaryOp & | func | ) | [static, inherited] |
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.
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
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
static const ConstantReturnType Ones | ( | ) | [static, inherited] |
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
operator const PlainObject & | ( | ) | const [inline, inherited] |
bool operator!= | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other are not exactly equal to each other. const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar | ) | const [inline, inherited] |
*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 GeneralProduct< Lhs, Rhs, GemvProduct > > operator* | ( | const std::complex< Scalar > & | scalar | ) | const [inline, inherited] |
Overloaded for efficient real matrix times complex scalar value
const ProductReturnType<GeneralProduct< Lhs, Rhs, GemvProduct > ,OtherDerived>::Type operator* | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
*this
and other.const DiagonalProduct<GeneralProduct< Lhs, Rhs, GemvProduct > , DiagonalDerived, OnTheRight> operator* | ( | const DiagonalBase< DiagonalDerived > & | diagonal | ) | const [inherited] |
*this
by the diagonal matrix diagonal. ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const [inherited] |
Concatenates a linear transformation matrix and a uniform scaling
GeneralProduct< Lhs, Rhs, GemvProduct > & operator*= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other.
*this
GeneralProduct< Lhs, Rhs, GemvProduct > & operator*= | ( | const Scalar & | other | ) | [inline, inherited] |
GeneralProduct< Lhs, Rhs, GemvProduct > & operator+= | ( | const MatrixBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
+ other.
*this
GeneralProduct< Lhs, Rhs, GemvProduct > & operator+= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
GeneralProduct< Lhs, Rhs, GemvProduct > & operator+= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > operator- | ( | ) | const [inline, inherited] |
*this
GeneralProduct< Lhs, Rhs, GemvProduct > & operator-= | ( | const MatrixBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
- other.
*this
GeneralProduct< Lhs, Rhs, GemvProduct > & operator-= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
GeneralProduct< Lhs, Rhs, GemvProduct > & operator-= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<GeneralProduct< Lhs, Rhs, GemvProduct > >::Scalar>, const GeneralProduct< Lhs, Rhs, GemvProduct > > operator/ | ( | const Scalar & | scalar | ) | const [inline, inherited] |
*this
divided by the scalar value scalar GeneralProduct< Lhs, Rhs, GemvProduct > & operator/= | ( | const Scalar & | other | ) | [inline, inherited] |
CommaInitializer<GeneralProduct< Lhs, Rhs, GemvProduct > > operator<< | ( | const Scalar & | s | ) | [inherited] |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Matrix3i m1; m1 << 1, 2, 3, 4, 5, 6, 7, 8, 9; cout << m1 << endl << endl; Matrix3i m2 = Matrix3i::Identity(); m2.block(0,0, 2,2) << 10, 11, 12, 13; cout << m2 << endl << endl; Vector2i v1; 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
CommaInitializer<GeneralProduct< Lhs, Rhs, GemvProduct > > operator<< | ( | const DenseBase< OtherDerived > & | other | ) | [inherited] |
bool operator== | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other are all exactly equal. RealScalar operatorNorm | ( | ) | const [inherited] |
Computes the L2 operator norm.
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 is defined to be
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 .
The current implementation uses the eigenvalues of , 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
rows()==1 || cols()==1
const PartialPivLU<PlainObject> partialPivLu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,GeneralProduct< Lhs, Rhs, GemvProduct > > Random | ( | Index | rows, |
Index | cols | ||
) | [static, inherited] |
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.
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,GeneralProduct< Lhs, Rhs, GemvProduct > > Random | ( | Index | size | ) | [static, inherited] |
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.
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,GeneralProduct< Lhs, Rhs, GemvProduct > > Random | ( | ) | [static, inherited] |
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.
RealReturnType real | ( | ) | const [inline, inherited] |
*this
.NonConstRealReturnType real | ( | ) | [inline, inherited] |
*this
.const Replicate<GeneralProduct< Lhs, Rhs, GemvProduct > ,RowFactor,ColFactor> replicate | ( | ) | const [inherited] |
*this
Example:
MatrixXi m = MatrixXi::Random(2,3); cout << "Here is the matrix m:" << endl << m << endl; cout << "m.replicate<3,2>() = ..." << endl; cout << m.replicate<3,2>() << endl;
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
const Replicate<GeneralProduct< Lhs, Rhs, GemvProduct > ,Dynamic,Dynamic> replicate | ( | Index | rowFacor, |
Index | colFactor | ||
) | const [inherited] |
*this
Example:
Vector3i v = Vector3i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "v.replicate(2,5) = ..." << endl; cout << v.replicate(2,5) << endl;
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
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.
Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
ReverseReturnType reverse | ( | ) | [inherited] |
Example:
MatrixXi m = MatrixXi::Random(3,4); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the reverse of m:" << endl << m.reverse() << endl; cout << "Here is the coefficient (1,0) in the reverse of m:" << endl << m.reverse()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 4." << endl; m.reverse()(1,0) = 4; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
ConstReverseReturnType reverse | ( | ) | const [inherited] |
This is the const version of reverse().
void reverseInPlace | ( | ) | [inherited] |
This is the "in place" version of reverse: it reverses *this
.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
m = m.reverse().eval();
const _RhsNested& rhs | ( | ) | const [inline, inherited] |
n | the 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
This is the const version of rightCols(Index).
NColsBlockXpr<N>::Type rightCols | ( | ) | [inline, inherited] |
N | the 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
ConstNColsBlockXpr<N>::Type rightCols | ( | ) | const [inline, inherited] |
This is the const version of rightCols<int>().
ConstRowwiseReturnType rowwise | ( | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; cout << "Here is the maximum absolute value of each row:" << endl << m.cwiseAbs().rowwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
RowwiseReturnType rowwise | ( | ) | [inherited] |
void scaleAndAddTo | ( | Dest & | dst, |
Scalar | alpha | ||
) | const [inline] |
Reimplemented from ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >.
References Eigen::ColMajor, Eigen::RowMajor, and Eigen::RowMajorBit.
SegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | [inherited] |
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.
start | the first coefficient in the segment |
size | the number of coefficients in the segment |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl; v.segment(1, 2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
DenseBase::ConstSegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | const [inherited] |
This is the const version of segment(Index,Index).
*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
start | the index of the first element of the sub-vector |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl; v.segment<2>(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
This is the const version of segment<int>(Index).
const Select<GeneralProduct< Lhs, Rhs, GemvProduct > ,ThenDerived,ElseDerived> select | ( | const DenseBase< ThenDerived > & | thenMatrix, |
const DenseBase< ElseDerived > & | elseMatrix | ||
) | const [inherited] |
const Select<GeneralProduct< Lhs, Rhs, GemvProduct > ,ThenDerived, typename ThenDerived::ConstantReturnType> select | ( | const DenseBase< ThenDerived > & | thenMatrix, |
typename ThenDerived::Scalar | elseScalar | ||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
const Select<GeneralProduct< Lhs, Rhs, GemvProduct > , typename ElseDerived::ConstantReturnType, ElseDerived > select | ( | typename ElseDerived::Scalar | thenScalar, |
const DenseBase< ElseDerived > & | elseMatrix | ||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
SelfAdjointViewReturnType<UpLo>::Type selfadjointView | ( | ) | [inherited] |
ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView | ( | ) | const [inherited] |
GeneralProduct< Lhs, Rhs, GemvProduct > & setConstant | ( | const Scalar & | value | ) | [inherited] |
Sets all coefficients in this expression to value.
GeneralProduct< Lhs, Rhs, GemvProduct > & setIdentity | ( | ) | [inherited] |
Writes the identity expression (not necessarily square) into *this.
Example:
Matrix4i m = Matrix4i::Zero(); m.block<3,3>(1,0).setIdentity(); cout << m << endl;
Output:
0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
GeneralProduct< Lhs, Rhs, GemvProduct > & setIdentity | ( | Index | rows, |
Index | cols | ||
) | [inherited] |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
rows | the new number of rows |
cols | the new number of columns |
Example:
MatrixXf m; m.setIdentity(3, 3); cout << m << endl;
Output:
1 0 0 0 1 0 0 0 1
GeneralProduct< Lhs, Rhs, GemvProduct > & setLinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
VectorXf v; v.setLinSpaced(5,0.5f,1.5f).transpose(); cout << v << endl;
Output:
0.5 0.75 1 1.25 1.5
GeneralProduct< Lhs, Rhs, GemvProduct > & setLinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [inherited] |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
GeneralProduct< Lhs, Rhs, GemvProduct > & setOnes | ( | ) | [inherited] |
Sets all coefficients in this expression to one.
Example:
Matrix4i m = Matrix4i::Random(); m.row(1).setOnes(); cout << m << endl;
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
GeneralProduct< Lhs, Rhs, GemvProduct > & setRandom | ( | ) | [inherited] |
Sets all coefficients in this expression to random values.
Example:
Matrix4i m = Matrix4i::Zero(); m.col(1).setRandom(); cout << m << endl;
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
GeneralProduct< Lhs, Rhs, GemvProduct > & setZero | ( | ) | [inherited] |
Sets all coefficients in this expression to zero.
Example:
Matrix4i m = Matrix4i::Random(); m.row(1).setZero(); cout << m << endl;
Output:
7 9 -5 -3 0 0 0 0 6 -3 0 9 6 6 3 9
const MatrixFunctionReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > sin | ( | ) | const [inherited] |
const MatrixFunctionReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > sinh | ( | ) | const [inherited] |
const SparseView<GeneralProduct< Lhs, Rhs, GemvProduct > > sparseView | ( | const Scalar & | m_reference = Scalar(0) , |
typename NumTraits< Scalar >::Real | m_epsilon = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
const MatrixSquareRootReturnValue<GeneralProduct< Lhs, Rhs, GemvProduct > > sqrt | ( | ) | const [inherited] |
RealScalar squaredNorm | ( | ) | const [inherited] |
*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.RealScalar stableNorm | ( | ) | const [inherited] |
*this
avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s
2 - compute For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.
void subTo | ( | Dest & | dst | ) | const [inline, inherited] |
void swap | ( | const DenseBase< OtherDerived > & | other, |
int | = OtherDerived::ThisConstantIsPrivateInPlainObjectBase |
||
) | [inline, inherited] |
swaps *this with the expression other.
void swap | ( | PlainObjectBase< OtherDerived > & | other | ) | [inline, inherited] |
swaps *this with the matrix or array other.
SegmentReturnType tail | ( | Index | size | ) | [inherited] |
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.
size | the number of coefficients in the block |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail(2) << endl; v.tail(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
DenseBase::ConstSegmentReturnType tail | ( | Index | size | ) | const [inherited] |
This is the const version of tail(Index).
FixedSegmentReturnType<Size>::Type tail | ( | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl; v.tail<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
ConstFixedSegmentReturnType<Size>::Type tail | ( | ) | const [inherited] |
This is the const version of tail<int>.
Block<GeneralProduct< Lhs, Rhs, GemvProduct > > topLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner(2, 2):" << endl; cout << m.topLeftCorner(2, 2) << endl; m.topLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > > topLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topLeftCorner(Index, Index).
Block<GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> topLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner<2,2>():" << endl; cout << m.topLeftCorner<2,2>() << endl; m.topLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> topLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of topLeftCorner<int, int>().
Block<GeneralProduct< Lhs, Rhs, GemvProduct > > topRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner(2, 2):" << endl; cout << m.topRightCorner(2, 2) << endl; m.topRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > > topRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topRightCorner(Index, Index).
Block<GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> topRightCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner<2,2>():" << endl; cout << m.topRightCorner<2,2>() << endl; m.topRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
const Block<const GeneralProduct< Lhs, Rhs, GemvProduct > , CRows, CCols> topRightCorner | ( | ) | const [inline, inherited] |
This is the const version of topRightCorner<int, int>().
n | the 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
This is the const version of topRows(Index).
NRowsBlockXpr<N>::Type topRows | ( | ) | [inline, inherited] |
N | the 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
ConstNRowsBlockXpr<N>::Type topRows | ( | ) | const [inline, inherited] |
This is the const version of topRows<int>().
*this
, i.e. the sum of the coefficients on the main diagonal.*this
can be any matrix, not necessarily square.
Reimplemented from DenseBase< GeneralProduct< Lhs, Rhs, GemvProduct > >.
Eigen::Transpose<GeneralProduct< Lhs, Rhs, GemvProduct > > transpose | ( | ) | [inherited] |
Example:
Matrix2i m = Matrix2i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the transpose of m:" << endl << m.transpose() << endl; cout << "Here is the coefficient (1,0) in the transpose of m:" << endl << m.transpose()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 0." << endl; m.transpose()(1,0) = 0; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
m = m.transpose(); // bug!!! caused by aliasing effect
m.transposeInPlace();
m = m.transpose().eval();
ConstTransposeReturnType transpose | ( | ) | const [inherited] |
This is the const version of transpose().
Make sure you read the warning for transpose() !
void transposeInPlace | ( | ) | [inherited] |
This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
m.transposeInPlace();
has the same effect on m as doing
m = m.transpose().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this
must be a resizable matrix.TriangularViewReturnType<Mode>::Type triangularView | ( | ) | [inherited] |
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:
ConstTriangularViewReturnType<Mode>::Type triangularView | ( | ) | const [inherited] |
This is the const version of MatrixBase::triangularView()
const CwiseUnaryOp<CustomUnaryOp, const GeneralProduct< Lhs, Rhs, GemvProduct > > unaryExpr | ( | const CustomUnaryOp & | func = CustomUnaryOp() | ) | const [inline, inherited] |
Apply a unary operator coefficient-wise.
[in] | func | Functor implementing the unary operator |
CustomUnaryOp | Type of func |
The function ptr_fun()
from the C++ standard library can be used to make functors out of normal functions.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define function to be applied coefficient-wise double ramp(double x) { if (x > 0) return x; else return 0; } int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.68 0.823 0 0 0 0 0.108 0.0268 0.566 0 0 0.904 0.597 0.536 0.258 0.832
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
const CwiseUnaryView<CustomViewOp, const GeneralProduct< Lhs, Rhs, GemvProduct > > unaryViewExpr | ( | const CustomViewOp & | func = CustomViewOp() | ) | const [inline, inherited] |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
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 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.
PlainObject unitOrthogonal | ( | void | ) | const [inherited] |
*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().
static const BasisReturnType UnitW | ( | ) | [static, inherited] |
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.
static const BasisReturnType UnitX | ( | ) | [static, inherited] |
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.
static const BasisReturnType UnitY | ( | ) | [static, inherited] |
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.
static const BasisReturnType UnitZ | ( | ) | [static, inherited] |
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.
CoeffReturnType value | ( | ) | const [inline, inherited] |
void visit | ( | Visitor & | func | ) | const [inherited] |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
struct MyVisitor { // called for the first coefficient void init(const Scalar& value, Index i, Index j); // called for all other coefficients void operator() (const Scalar& value, Index i, Index j); };
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
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
static const ConstantReturnType Zero | ( | ) | [static, inherited] |
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
const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar, |
const StorageBaseType & | matrix | ||
) | [friend, inherited] |
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const GeneralProduct< Lhs, Rhs, GemvProduct > > operator* | ( | const std::complex< Scalar > & | scalar, |
const StorageBaseType & | matrix | ||
) | [friend, inherited] |
PlainObject m_result [mutable, protected, inherited] |