#include <ProductBase.h>
Public Types | |
enum | { HomogeneousReturnTypeDirection } |
enum | { SizeMinusOne } |
enum | { RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor, InnerSizeAtCompileTime, CoeffReadCost, InnerStrideAtCompileTime, OuterStrideAtCompileTime } |
enum | { ThisConstantIsPrivateInPlainObjectBase } |
typedef internal::remove_all < ActualLhsType >::type | _ActualLhsType |
typedef internal::remove_all < ActualRhsType >::type | _ActualRhsType |
typedef internal::remove_all < LhsNested >::type | _LhsNested |
typedef internal::remove_all < RhsNested >::type | _RhsNested |
typedef LhsBlasTraits::DirectLinearAccessType | ActualLhsType |
typedef RhsBlasTraits::DirectLinearAccessType | ActualRhsType |
typedef MatrixBase< Derived > | Base |
typedef Base::CoeffReturnType | CoeffReturnType |
typedef VectorwiseOp< Derived, Vertical > | ColwiseReturnType |
typedef const VectorwiseOp < const Derived, Vertical > | ConstColwiseReturnType |
typedef const Diagonal< const Derived > | ConstDiagonalReturnType |
typedef const Reverse< const Derived, BothDirections > | ConstReverseReturnType |
typedef const VectorwiseOp < const Derived, Horizontal > | ConstRowwiseReturnType |
typedef const VectorBlock < const Derived > | ConstSegmentReturnType |
typedef Block< const Derived, internal::traits< Derived > ::ColsAtCompileTime==1?SizeMinusOne:1, internal::traits< Derived > ::ColsAtCompileTime==1?1:SizeMinusOne > | ConstStartMinusOne |
typedef const Transpose< const Derived > | ConstTransposeReturnType |
typedef Diagonal< Derived > | DiagonalReturnType |
typedef internal::add_const_on_value_type < typename internal::eval < Derived >::type >::type | EvalReturnType |
typedef CoeffBasedProduct < LhsNested, RhsNested, 0 > | FullyLazyCoeffBaseProductType |
typedef CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const ConstStartMinusOne > | HNormalizedReturnType |
typedef Homogeneous< Derived, HomogeneousReturnTypeDirection > | HomogeneousReturnType |
typedef internal::traits < Derived >::Index | Index |
The type of indices. | |
typedef internal::blas_traits < _LhsNested > | LhsBlasTraits |
typedef Lhs::Nested | LhsNested |
typedef internal::traits< Lhs > ::Scalar | LhsScalar |
typedef internal::packet_traits < Scalar >::type | PacketScalar |
typedef Base::PlainObject | PlainObject |
The plain matrix type corresponding to this expression. | |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Reverse< Derived, BothDirections > | ReverseReturnType |
typedef internal::blas_traits < _RhsNested > | RhsBlasTraits |
typedef Rhs::Nested | RhsNested |
typedef internal::traits< Rhs > ::Scalar | RhsScalar |
typedef VectorwiseOp< Derived, Horizontal > | RowwiseReturnType |
typedef internal::traits < Derived >::Scalar | Scalar |
typedef VectorBlock< Derived > | SegmentReturnType |
typedef internal::stem_function < Scalar >::type | StemFunction |
typedef internal::traits < Derived >::StorageKind | StorageKind |
Public Member Functions | |
template<typename Dest > | |
void | addTo (Dest &dst) const |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
bool | all (void) const |
bool | any (void) const |
template<typename EssentialPart > | |
void | applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
template<typename EssentialPart > | |
void | applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
template<typename OtherDerived > | |
void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
template<typename OtherScalar > | |
void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
template<typename OtherDerived > | |
void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
template<typename OtherScalar > | |
void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
ArrayWrapper< Derived > | array () |
const ArrayWrapper< const Derived > | array () const |
const DiagonalWrapper< const Derived > | asDiagonal () const |
const PermutationWrapper < const Derived > | asPermutation () const |
template<typename CustomBinaryOp , typename OtherDerived > | |
const CwiseBinaryOp < CustomBinaryOp, const Derived, const OtherDerived > | binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
Block< Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const Block< const Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
RealScalar | blueNorm () const |
Block< Derived > | bottomLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner () const |
Block< Derived > | bottomRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner () const |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | bottomRows () |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | bottomRows () const |
template<typename NewType > | |
internal::cast_return_type < Derived, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < Derived >::Scalar, NewType > , const Derived > >::type | cast () const |
Base::CoeffReturnType | coeff (Index row, Index col) const |
Base::CoeffReturnType | coeff (Index i) const |
const 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 () |
template<typename ResultType > | |
void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
template<typename ResultType > | |
void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
ConjugateReturnType | conjugate () const |
const MatrixFunctionReturnValue < Derived > | cos () const |
const MatrixFunctionReturnValue < Derived > | cosh () const |
Index | count () const |
template<typename OtherDerived > | |
cross_product_return_type < OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const Derived > | cwiseAbs () const |
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const Derived > | cwiseAbs2 () const |
template<typename OtherDerived > | |
const CwiseBinaryOp < std::equal_to< Scalar > , const Derived, const OtherDerived > | cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < std::binder1st < std::equal_to< Scalar > >, const Derived > | cwiseEqual (const Scalar &s) const |
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const Derived > | cwiseInverse () const |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const OtherDerived > | cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const ConstantReturnType > | cwiseMax (const Scalar &other) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Derived, const OtherDerived > | cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Derived, const ConstantReturnType > | cwiseMin (const Scalar &other) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < std::not_equal_to< Scalar > , const Derived, const OtherDerived > | cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const Derived, const OtherDerived > | cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const Derived > | cwiseSqrt () const |
Scalar | determinant () const |
const Diagonal< const FullyLazyCoeffBaseProductType, 0 > | diagonal () const |
template<int Index> | |
const Diagonal < FullyLazyCoeffBaseProductType, Index > | diagonal () const |
const Diagonal < FullyLazyCoeffBaseProductType, Dynamic > | diagonal (Index index) const |
DiagonalReturnType | diagonal () |
DiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) |
Index | diagonalSize () const |
template<typename OtherDerived > | |
internal::scalar_product_traits < typename internal::traits < Derived >::Scalar, typename internal::traits< OtherDerived > ::Scalar >::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
const | EIGEN_CWISE_PRODUCT_RETURN_TYPE (Derived, OtherDerived) cwiseProduct(const Eigen |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. | |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
EvalReturnType | eval () const |
template<typename Dest > | |
void | evalTo (Dest &dst) const |
const MatrixExponentialReturnValue < Derived > | exp () const |
void | fill (const Scalar &value) |
template<unsigned int Added, unsigned int Removed> | |
const Flagged< Derived, Added, Removed > | flagged () const |
const ForceAlignedAccess< Derived > | forceAlignedAccess () const |
ForceAlignedAccess< Derived > | forceAlignedAccess () |
template<bool Enable> | |
internal::add_const_on_value_type < typename internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type >::type | forceAlignedAccessIf () const |
template<bool Enable> | |
internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type | forceAlignedAccessIf () |
const WithFormat< Derived > | format (const IOFormat &fmt) const |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
const FullPivLU< PlainObject > | fullPivLu () const |
SegmentReturnType | head (Index size) |
DenseBase::ConstSegmentReturnType | head (Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | head () |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | head () const |
const HNormalizedReturnType | hnormalized () const |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
const ImagReturnType | imag () const |
NonConstImagReturnType | imag () |
Index | innerSize () const |
const internal::inverse_impl < Derived > | inverse () const |
template<typename OtherDerived > | |
bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename Derived > | |
bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const |
bool | isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
JacobiSVD< PlainObject > | jacobiSvd (unsigned int computationOptions=0) const |
template<typename OtherDerived > | |
const LazyProductReturnType < Derived, OtherDerived > ::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
const LDLT< PlainObject > | ldlt () const |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | leftCols () |
template<int N> | |
ConstNColsBlockXpr< N >::Type | leftCols () const |
const _LhsNested & | lhs () const |
const LLT< PlainObject > | llt () const |
const MatrixLogarithmReturnValue < Derived > | log () const |
template<int p> | |
RealScalar | lpNorm () const |
const PartialPivLU< PlainObject > | lu () const |
template<typename EssentialPart > | |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
MatrixBase< Derived > & | matrix () |
const MatrixBase< Derived > & | matrix () const |
const MatrixFunctionReturnValue < Derived > | matrixFunction (StemFunction f) const |
internal::traits< Derived >::Scalar | maxCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *index) const |
Scalar | mean () const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
template<int N> | |
NColsBlockXpr< N >::Type | middleCols (Index startCol) |
template<int N> | |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
RowsBlockXpr | middleRows (Index startRow, Index numRows) |
ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
template<int N> | |
NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
internal::traits< Derived >::Scalar | minCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *index) const |
const NestByValue< Derived > | nestByValue () const |
NoAlias< Derived, Eigen::MatrixBase > | noalias () |
Index | nonZeros () const |
RealScalar | norm () const |
void | normalize () |
const PlainObject | normalized () const |
operator const PlainObject & () const | |
template<typename OtherDerived > | |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
const ScalarMultipleReturnType | operator* (const RealScalar &scalar) const |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Derived > | operator* (const std::complex< Scalar > &scalar) const |
template<typename OtherDerived > | |
const ProductReturnType < Derived, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
template<typename DiagonalDerived > | |
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
template<typename OtherDerived > | |
Derived & | operator*= (const EigenBase< OtherDerived > &other) |
Derived & | operator*= (const Scalar &other) |
template<typename OtherDerived > | |
Derived & | operator+= (const MatrixBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator+= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator- () const |
template<typename OtherDerived > | |
Derived & | operator-= (const MatrixBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator-= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator/ (const Scalar &scalar) const |
Derived & | operator/= (const Scalar &other) |
CommaInitializer< Derived > | operator<< (const Scalar &s) |
template<typename OtherDerived > | |
CommaInitializer< Derived > | operator<< (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
RealScalar | operatorNorm () const |
Computes the L2 operator norm. | |
Index | outerSize () const |
const PartialPivLU< PlainObject > | partialPivLu () const |
Scalar | prod () const |
ProductBase (const Lhs &lhs, const Rhs &rhs) | |
RealReturnType | real () const |
NonConstRealReturnType | real () |
template<int RowFactor, int ColFactor> | |
const Replicate< Derived, RowFactor, ColFactor > | replicate () const |
const Replicate< Derived, Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
void | resize (Index size) |
void | resize (Index rows, Index cols) |
ReverseReturnType | reverse () |
ConstReverseReturnType | reverse () const |
void | reverseInPlace () |
const _RhsNested & | rhs () const |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | rightCols () |
template<int N> | |
ConstNColsBlockXpr< N >::Type | rightCols () const |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
Index | rows () const |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
template<typename Dest > | |
void | scaleAndAddTo (Dest &dst, Scalar alpha) const |
SegmentReturnType | segment (Index start, Index size) |
DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | segment (Index start) |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | segment (Index start) const |
template<typename ThenDerived , typename ElseDerived > | |
const Select< Derived, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
template<typename ThenDerived > | |
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
template<typename ElseDerived > | |
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
template<unsigned int UpLo> | |
SelfAdjointViewReturnType < UpLo >::Type | selfadjointView () |
template<unsigned int UpLo> | |
ConstSelfAdjointViewReturnType < UpLo >::Type | selfadjointView () const |
Derived & | setConstant (const Scalar &value) |
Derived & | setIdentity () |
Derived & | setIdentity (Index rows, Index cols) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
Derived & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
Derived & | setLinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
Derived & | setOnes () |
Derived & | setRandom () |
Derived & | setZero () |
const MatrixFunctionReturnValue < Derived > | sin () const |
const MatrixFunctionReturnValue < Derived > | sinh () const |
const SparseView< Derived > | sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const |
const MatrixSquareRootReturnValue < Derived > | sqrt () const |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () const |
template<typename Dest > | |
void | subTo (Dest &dst) const |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index size) |
DenseBase::ConstSegmentReturnType | tail (Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | tail () |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | tail () const |
Block< Derived > | topLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | topLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner () const |
Block< Derived > | topRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | topRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner () const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | topRows () |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | topRows () const |
Scalar | trace () const |
Eigen::Transpose< Derived > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
template<unsigned int Mode> | |
TriangularViewReturnType< Mode > ::Type | triangularView () |
template<unsigned int Mode> | |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
template<typename CustomUnaryOp > | |
const CwiseUnaryOp < CustomUnaryOp, const Derived > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. | |
template<typename CustomViewOp > | |
const CwiseUnaryView < CustomViewOp, const Derived > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
PlainObject | unitOrthogonal (void) const |
CoeffReturnType | value () const |
template<typename Visitor > | |
void | visit (Visitor &func) const |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index size, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (const CustomNullaryOp &func) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random () |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero () |
Protected Member Functions | |
template<typename OtherDerived > | |
void | checkTransposeAliasing (const OtherDerived &other) const |
template<typename OtherDerived > | |
Derived & | operator+= (const ArrayBase< OtherDerived > &) |
template<typename OtherDerived > | |
Derived & | operator-= (const ArrayBase< OtherDerived > &) |
Protected Attributes | |
LhsNested | m_lhs |
PlainObject | m_result |
RhsNested | m_rhs |
Friends | |
const ScalarMultipleReturnType | operator* (const Scalar &scalar, const StorageBaseType &matrix) |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Derived > | operator* (const std::complex< Scalar > &scalar, const StorageBaseType &matrix) |
Related Functions | |
(Note that these are not member functions.) | |
template<typename Derived > | |
std::ostream & | operator<< (std::ostream &s, const DenseBase< Derived > &m) |
typedef internal::remove_all<ActualLhsType>::type _ActualLhsType |
typedef internal::remove_all<ActualRhsType>::type _ActualRhsType |
typedef internal::remove_all<LhsNested>::type _LhsNested |
typedef internal::remove_all<RhsNested>::type _RhsNested |
typedef LhsBlasTraits::DirectLinearAccessType ActualLhsType |
typedef RhsBlasTraits::DirectLinearAccessType ActualRhsType |
typedef MatrixBase<Derived> Base |
Reimplemented from DenseBase< Derived >.
Reimplemented in ScaledProduct< NestedProduct >.
typedef Base::CoeffReturnType CoeffReturnType [inherited] |
typedef VectorwiseOp<Derived, Vertical> ColwiseReturnType [inherited] |
typedef const VectorwiseOp<const Derived, Vertical> ConstColwiseReturnType [inherited] |
typedef const Diagonal<const Derived> ConstDiagonalReturnType [inherited] |
typedef const Reverse<const Derived, BothDirections> ConstReverseReturnType [inherited] |
typedef const VectorwiseOp<const Derived, Horizontal> ConstRowwiseReturnType [inherited] |
typedef const VectorBlock<const Derived> ConstSegmentReturnType [inherited] |
typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne [inherited] |
typedef const Transpose<const Derived> ConstTransposeReturnType [inherited] |
typedef Diagonal<Derived> DiagonalReturnType [inherited] |
typedef internal::add_const_on_value_type<typename internal::eval<Derived>::type>::type EvalReturnType [inherited] |
typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType |
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const ConstStartMinusOne > HNormalizedReturnType [inherited] |
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType [inherited] |
The type of indices.
To change this, #define
the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE
.
Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef internal::blas_traits<_LhsNested> LhsBlasTraits |
typedef Lhs::Nested LhsNested |
Reimplemented in GeneralProduct< Lhs, Rhs, GemmProduct >, and GeneralProduct< Lhs, Rhs, GemvProduct >.
typedef internal::packet_traits<Scalar>::type PacketScalar [inherited] |
typedef Base::PlainObject PlainObject |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
Reimplemented from MatrixBase< Derived >.
Reimplemented in ScaledProduct< NestedProduct >.
typedef NumTraits<Scalar>::Real RealScalar [inherited] |
typedef Reverse<Derived, BothDirections> ReverseReturnType [inherited] |
typedef internal::blas_traits<_RhsNested> RhsBlasTraits |
typedef Rhs::Nested RhsNested |
Reimplemented in GeneralProduct< Lhs, Rhs, GemmProduct >, and GeneralProduct< Lhs, Rhs, GemvProduct >.
typedef VectorwiseOp<Derived, Horizontal> RowwiseReturnType [inherited] |
typedef VectorBlock<Derived> SegmentReturnType [inherited] |
typedef internal::stem_function<Scalar>::type StemFunction [inherited] |
typedef internal::traits<Derived>::StorageKind StorageKind [inherited] |
anonymous enum [inherited] |
RowsAtCompileTime |
The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
|
ColsAtCompileTime |
The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
|
SizeAtCompileTime |
This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.
|
MaxRowsAtCompileTime |
This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxColsAtCompileTime |
This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxSizeAtCompileTime |
This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
IsVectorAtCompileTime |
This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row). |
Flags |
This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags. |
IsRowMajor |
True if this expression has row-major storage order. |
InnerSizeAtCompileTime | |
CoeffReadCost |
This is a rough measure of how expensive it is to read one coefficient from this expression. |
InnerStrideAtCompileTime | |
OuterStrideAtCompileTime |
ProductBase | ( | const Lhs & | lhs, |
const Rhs & | rhs | ||
) | [inline] |
void addTo | ( | Dest & | dst | ) | const [inline] |
Reimplemented in ScaledProduct< NestedProduct >.
const MatrixBase< Derived >::AdjointReturnType adjoint | ( | ) | const [inline, 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 | ( | ) | [inline, 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.References DenseBase< Derived >::eval().
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
References Eigen::Dynamic.
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 |
References row().
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 |
References col().
void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other | ) | [inline, inherited] |
replaces *this
by *this
* other.
References EigenBase< Derived >::derived().
void applyOnTheLeft | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) | [inline, 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 .
References Eigen::internal::apply_rotation_in_the_plane(), row(), and Eigen::internal::y.
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other | ) | [inline, inherited] |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=()
References EigenBase< Derived >::derived().
ArrayWrapper<Derived> array | ( | ) | [inline, inherited] |
const ArrayWrapper<const Derived> array | ( | ) | const [inline, inherited] |
const DiagonalWrapper< const Derived > asDiagonal | ( | ) | const [inline, 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
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::fromPositionOrientationScale(), Transform< _Scalar, _Dim, _Mode, _Options >::prescale(), and Transform< _Scalar, _Dim, _Mode, _Options >::scale().
const PermutationWrapper< const Derived > asPermutation | ( | ) | const [inherited] |
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> binaryExpr | ( | const Eigen::MatrixBase< OtherDerived > & | other, |
const CustomBinaryOp & | func = CustomBinaryOp() |
||
) | const [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<Derived> 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
Referenced by main().
const Block<const Derived> block | ( | Index | startRow, |
Index | startCol, | ||
Index | blockRows, | ||
Index | blockCols | ||
) | const [inline, inherited] |
This is the const version of block(Index,Index,Index,Index).
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 Derived, BlockRows, BlockCols> block | ( | Index | startRow, |
Index | startCol | ||
) | const [inline, inherited] |
This is the const version of block<>(Index, Index).
NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm | ( | ) | const [inline, 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<Derived> 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 Derived> bottomLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomLeftCorner(Index, Index).
Block<Derived, 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 Derived, CRows, CCols> bottomLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomLeftCorner<int, int>().
Block<Derived> 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 Derived> bottomRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomRightCorner(Index, Index).
Block<Derived, 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 Derived, 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<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::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] |
Base::CoeffReturnType coeff | ( | Index | row, |
Index | col | ||
) | const [inline] |
Base::CoeffReturnType coeff | ( | Index | i | ) | const [inline] |
Example:
Matrix3d m = Matrix3d::Identity(); m.col(1) = Vector3d(4,5,6); cout << m << endl;
Output:
1 4 0 0 5 0 0 6 1
Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), and main().
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > colPivHouseholderQr | ( | ) | const [inherited] |
*this
.const DenseBase< Derived >::ConstColwiseReturnType colwise | ( | ) | const [inline, 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
Referenced by main(), and Eigen::umeyama().
DenseBase< Derived >::ColwiseReturnType colwise | ( | ) | [inline, inherited] |
void computeInverseAndDetWithCheck | ( | ResultType & | inverse, |
typename ResultType::Scalar & | determinant, | ||
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const [inline, 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 [inline, 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
.const DenseBase< Derived >::ConstantReturnType Constant | ( | Index | rows, |
Index | cols, | ||
const Scalar & | value | ||
) | [inline, 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.
const DenseBase< Derived >::ConstantReturnType Constant | ( | Index | size, |
const Scalar & | value | ||
) | [inline, static, inherited] |
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.
const DenseBase< Derived >::ConstantReturnType Constant | ( | const Scalar & | value | ) | [inline, 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.
References EIGEN_STATIC_ASSERT_FIXED_SIZE.
const MatrixFunctionReturnValue<Derived> cos | ( | ) | const [inherited] |
Referenced by main().
const MatrixFunctionReturnValue<Derived> cosh | ( | ) | const [inherited] |
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, 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/
References conj(), and EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE.
MatrixBase< Derived >::PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, 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.
References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, and Eigen::Architecture::Target.
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> 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 Derived> 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 Derived, 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 Derived> cwiseEqual | ( | const Scalar & | s | ) | const [inline, inherited] |
*this
and a scalar s Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator==().
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> 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 Derived, 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 Derived, const ConstantReturnType> cwiseMax | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, 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 Derived, const ConstantReturnType> cwiseMin | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, 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
Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator!=().
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> cwiseQuotient | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [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 Derived> cwiseSqrt | ( | ) | const [inline, inherited] |
Example:
Vector3d v(1,2,4); cout << v.cwiseSqrt() << endl;
Output:
1 1.41 2
internal::traits< Derived >::Scalar determinant | ( | ) | const [inline, inherited] |
const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal | ( | ) | const [inline] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
Reimplemented from MatrixBase< Derived >.
const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal | ( | ) | const [inline] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
Reimplemented from MatrixBase< Derived >.
const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal | ( | Index | index | ) | const [inline] |
This is the const version of diagonal(Index).
Reimplemented from MatrixBase< Derived >.
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal | ( | ) | [inline, 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
Referenced by main(), AngleAxis< _Scalar >::toRotationMatrix(), and MatrixBase< Derived >::trace().
MatrixBase< Derived >::template DiagonalIndexReturnType< Dynamic >::Type diagonal | ( | Index | index | ) | [inline, inherited] |
*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< Derived >::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.
References EIGEN_CHECK_BINARY_COMPATIBILIY, EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const EIGEN_CWISE_PRODUCT_RETURN_TYPE | ( | Derived | , |
OtherDerived | |||
) | const [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
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues | ( | ) | const [inline, 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)
References Eigen::internal::IsComplex.
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.
Referenced by MatrixBase< Derived >::adjointInPlace().
void evalTo | ( | Dest & | dst | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
Reimplemented in ScaledProduct< NestedProduct >.
const MatrixExponentialReturnValue<Derived> exp | ( | ) | const [inherited] |
Alias for setConstant(): sets all coefficients in this expression to value.
const Flagged< Derived, Added, Removed > flagged | ( | ) | const [inline, inherited] |
This is mostly for internal use.
const ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< Derived >.
ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< Derived >.
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< Derived >.
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< Derived >.
const WithFormat< Derived > format | ( | const IOFormat & | fmt | ) | const [inline, inherited] |
See class IOFormat for some examples.
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr | ( | ) | const [inherited] |
*this
.const FullPivLU< typename MatrixBase< Derived >::PlainObject > fullPivLu | ( | ) | const [inline, inherited] |
DenseBase< Derived >::SegmentReturnType head | ( | Index | size | ) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::ConstSegmentReturnType head | ( | Index | size | ) | const [inline, inherited] |
This is the const version of head(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type head | ( | ) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type head | ( | ) | const [inline, inherited] |
This is the const version of head<int>().
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const MatrixBase< Derived >::HNormalizedReturnType hnormalized | ( | ) | const [inline, inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
Example:
Output:
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
MatrixBase< Derived >::HomogeneousReturnType homogeneous | ( | ) | const [inline, 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:
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > householderQr | ( | ) | const [inherited] |
*this
.NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm | ( | ) | const [inline, inherited] |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.References cwiseAbs().
const MatrixBase< Derived >::IdentityReturnType Identity | ( | ) | [inline, 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
References EIGEN_STATIC_ASSERT_FIXED_SIZE.
const MatrixBase< Derived >::IdentityReturnType Identity | ( | Index | rows, |
Index | cols | ||
) | [inline, 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 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< Derived > inverse | ( | ) | const [inline, 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
References EIGEN_STATIC_ASSERT.
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse(), and Hyperplane< _Scalar, _AmbientDim, _Options >::transform().
bool isApprox | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
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.Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::isApprox().
bool isApproxToConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
References Eigen::internal::isApprox().
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
References abs(), and Eigen::internal::isMuchSmallerThan().
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
References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().
bool isLowerTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
References abs().
bool isMuchSmallerThan | ( | const typename NumTraits< Scalar >::Real & | other, |
RealScalar | prec | ||
) | const [inherited] |
true
if the norm of *this
is much smaller than other, within the precision determined by prec.
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
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
References abs2().
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
References Eigen::internal::isApprox(), and Eigen::internal::isMuchSmallerThan().
bool isUpperTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
References abs().
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
References Eigen::internal::isMuchSmallerThan().
JacobiSVD< typename MatrixBase< Derived >::PlainObject > jacobiSvd | ( | unsigned int | computationOptions = 0 | ) | const [inherited] |
const LazyProductReturnType< Derived, 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.
References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.
const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt | ( | ) | const [inline, 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] |
Referenced by TriangularView< _MatrixType, _Mode >::assignProduct().
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
Index | size, | ||
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_FIXED_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_FIXED_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const LLT< typename MatrixBase< Derived >::PlainObject > llt | ( | ) | const [inline, inherited] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
const MatrixLogarithmReturnValue<Derived> log | ( | ) | const [inherited] |
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< Derived >.
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu | ( | ) | const [inline, 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 |
References abs2(), conj(), EIGEN_STATIC_ASSERT_VECTOR_ONLY, imag(), real(), and sqrt().
void makeHouseholderInPlace | ( | Scalar & | tau, |
RealScalar & | beta | ||
) | [inherited] |
Computes the elementary reflector H such that: 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<Derived>& matrix | ( | ) | [inline, inherited] |
const MatrixBase<Derived>& matrix | ( | ) | const [inline, inherited] |
const MatrixFunctionReturnValue<Derived> matrixFunction | ( | StemFunction | f | ) | const [inherited] |
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
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>().
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const NestByValue< Derived > nestByValue | ( | ) | const [inline, inherited] |
NoAlias< Derived, 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;
*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.References sqrt().
void normalize | ( | ) | [inline, 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 MatrixBase< Derived >::PlainObject normalized | ( | ) | const [inline, 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.
Referenced by QuaternionBase< Derived >::setFromTwoVectors().
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | Index | rows, |
Index | cols, | ||
const CustomNullaryOp & | func | ||
) | [inline, 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.
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | Index | size, |
const CustomNullaryOp & | func | ||
) | [inline, 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.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | const CustomNullaryOp & | func | ) | [inline, 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.
const DenseBase< Derived >::ConstantReturnType Ones | ( | Index | rows, |
Index | cols | ||
) | [inline, 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 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
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] |
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 Derived> operator* | ( | const std::complex< Scalar > & | scalar | ) | const [inline, inherited] |
Overloaded for efficient real matrix times complex scalar value
const ProductReturnType< Derived, OtherDerived >::Type operator* | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other.References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* | ( | const DiagonalBase< DiagonalDerived > & | diagonal | ) | const [inline, inherited] |
*this
by the diagonal matrix diagonal. MatrixBase< Derived >::ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const [inherited] |
Concatenates a linear transformation matrix and a uniform scaling
References UniformScaling< _Scalar >::factor().
Derived & operator*= | ( | const EigenBase< OtherDerived > & | other | ) | [inline, inherited] |
replaces *this
by *this
* other.
*this
References EigenBase< Derived >::derived().
Derived & operator*= | ( | const Scalar & | other | ) | [inline, inherited] |
Derived & operator+= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline, inherited] |
replaces *this
by *this
+ other.
*this
Derived & operator+= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
References EigenBase< Derived >::derived().
Derived& operator+= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> operator- | ( | ) | const [inline, inherited] |
*this
Derived & operator-= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline, inherited] |
replaces *this
by *this
- other.
*this
Derived & operator-= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
References EigenBase< Derived >::derived().
Derived& operator-= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> operator/ | ( | const Scalar & | scalar | ) | const [inline, inherited] |
*this
divided by the scalar value scalar Derived & operator/= | ( | const Scalar & | other | ) | [inline, inherited] |
CommaInitializer< Derived > operator<< | ( | const Scalar & | s | ) | [inline, 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< Derived > operator<< | ( | const DenseBase< OtherDerived > & | other | ) | [inline, inherited] |
bool operator== | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other are all exactly equal. MatrixBase< Derived >::RealScalar operatorNorm | ( | ) | const [inline, 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
References sqrt().
rows()==1 || cols()==1
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > partialPivLu | ( | ) | const [inline, 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
References Eigen::Dynamic.
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | Index | rows, |
Index | cols | ||
) | [inline, 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.
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | Index | size | ) | [inline, 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.
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | ) | [inline, 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
.*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< Derived, Dynamic, Dynamic > replicate | ( | Index | rowFactor, |
Index | colFactor | ||
) | const [inline, 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.
Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Referenced by TriangularBase< Derived >::evalToLazy(), LDLT< _MatrixType, _UpLo >::rankUpdate(), and MatrixBase< Derived >::setIdentity().
Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
DenseBase< Derived >::ReverseReturnType reverse | ( | ) | [inline, 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
Referenced by DenseBase< Derived >::reverseInPlace().
const DenseBase< Derived >::ConstReverseReturnType reverse | ( | ) | const [inline, inherited] |
This is the const version of reverse().
void reverseInPlace | ( | ) | [inline, 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();
References DenseBase< Derived >::reverse().
const _RhsNested& rhs | ( | ) | const [inline] |
Referenced by TriangularView< _MatrixType, _Mode >::assignProduct().
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>().
Example:
Matrix3d m = Matrix3d::Identity(); m.row(1) = Vector3d(4,5,6); cout << m << endl;
Output:
1 0 0 4 5 6 0 0 1
Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), main(), Translation< _Scalar, _Dim >::operator*(), and Transform< _Scalar, _Dim, _Mode, _Options >::pretranslate().
const DenseBase< Derived >::ConstRowwiseReturnType rowwise | ( | ) | const [inline, 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
Referenced by main(), and Eigen::umeyama().
DenseBase< Derived >::RowwiseReturnType rowwise | ( | ) | [inline, inherited] |
void scaleAndAddTo | ( | Dest & | dst, |
Scalar | alpha | ||
) | const [inline] |
Reimplemented in GeneralProduct< Lhs, Rhs, GemmProduct >, SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, GeneralProduct< Lhs, Rhs, GemvProduct >, DenseTimeSparseProduct< Lhs, Rhs >, DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, GeneralProduct< Lhs, Rhs, OuterProduct >, SparseTimeDenseProduct< Lhs, Rhs >, SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, TriangularProduct< Mode, false, Lhs, true, Rhs, false >, SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, and TriangularProduct< Mode, true, Lhs, false, Rhs, true >.
DenseBase< Derived >::SegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::ConstSegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | const [inline, inherited] |
This is the const version of segment(Index,Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type segment | ( | Index | start | ) | [inline, inherited] |
*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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type segment | ( | Index | start | ) | const [inline, inherited] |
This is the const version of segment<int>(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const Select< Derived, 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< Derived, 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.
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView | ( | ) | [inherited] |
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView | ( | ) | const [inherited] |
Derived & setConstant | ( | const Scalar & | value | ) | [inline, inherited] |
Sets all coefficients in this expression to value.
Derived & setIdentity | ( | ) | [inline, 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
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity().
Derived & setIdentity | ( | Index | rows, |
Index | cols | ||
) | [inline, 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
References DenseBase< Derived >::resize().
Derived & setLinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
Derived & setLinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [inline, 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.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
Derived & setOnes | ( | ) | [inline, 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
Derived & setRandom | ( | ) | [inline, 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
Derived & setZero | ( | ) | [inline, 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
Referenced by SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::evalTo().
const MatrixFunctionReturnValue<Derived> sin | ( | ) | const [inherited] |
const MatrixFunctionReturnValue<Derived> sinh | ( | ) | const [inherited] |
const SparseView< Derived > sparseView | ( | const Scalar & | m_reference = Scalar(0) , |
typename NumTraits< Scalar >::Real | m_epsilon = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
const MatrixSquareRootReturnValue<Derived> sqrt | ( | ) | const [inherited] |
NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm | ( | ) | const [inline, inherited] |
NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm | ( | ) | const [inline, 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.
References Eigen::AlignedBit, Eigen::DirectAccessBit, sqrt(), and Eigen::internal::stable_norm_kernel().
void subTo | ( | Dest & | dst | ) | const [inline] |
Reimplemented in ScaledProduct< NestedProduct >.
void swap | ( | const DenseBase< OtherDerived > & | other, |
int | = OtherDerived::ThisConstantIsPrivateInPlainObjectBase |
||
) | [inline, inherited] |
swaps *this with the expression other.
Referenced by TriangularBase< Derived >::evalTo().
void swap | ( | PlainObjectBase< OtherDerived > & | other | ) | [inline, inherited] |
swaps *this with the matrix or array other.
DenseBase< Derived >::SegmentReturnType tail | ( | Index | size | ) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::ConstSegmentReturnType tail | ( | Index | size | ) | const [inline, inherited] |
This is the const version of tail(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template FixedSegmentReturnType< Size >::Type tail | ( | ) | [inline, 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
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
DenseBase< Derived >::template ConstFixedSegmentReturnType< Size >::Type tail | ( | ) | const [inline, inherited] |
This is the const version of tail<int>.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
Block<Derived> 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 Derived> topLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topLeftCorner(Index, Index).
Block<Derived, 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 Derived, CRows, CCols> topLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of topLeftCorner<int, int>().
Block<Derived> 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 Derived> topRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topRightCorner(Index, Index).
Block<Derived, 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 Derived, 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< Derived >.
References MatrixBase< Derived >::diagonal().
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();
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse().
const DenseBase< Derived >::ConstTransposeReturnType transpose | ( | ) | const [inline, inherited] |
This is the const version of transpose().
Make sure you read the warning for transpose() !
void transposeInPlace | ( | ) | [inline, 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.MatrixBase< Derived >::template 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:
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView | ( | ) | const [inherited] |
This is the const version of MatrixBase::triangularView()
const CwiseUnaryOp<CustomUnaryOp, const Derived> unaryExpr | ( | const CustomUnaryOp & | func = CustomUnaryOp() | ) | const [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 Derived> 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
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | size, |
Index | i | ||
) | [inline, 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.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | i | ) | [inline, 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.
This variant is for fixed-size vector only.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
MatrixBase< Derived >::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().
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
const MatrixBase< Derived >::BasisReturnType UnitW | ( | ) | [inline, 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.
const MatrixBase< Derived >::BasisReturnType UnitX | ( | ) | [inline, 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.
const MatrixBase< Derived >::BasisReturnType UnitY | ( | ) | [inline, 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.
const MatrixBase< Derived >::BasisReturnType UnitZ | ( | ) | [inline, 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] |
Referenced by SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::evalTo().
void visit | ( | Visitor & | visitor | ) | const [inherited] |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
struct MyVisitor { // called for the first coefficient void init(const Scalar& value, Index i, Index j); // called for all other coefficients void operator() (const Scalar& value, Index i, Index j); };
References Eigen::Dynamic.
const DenseBase< Derived >::ConstantReturnType Zero | ( | Index | rows, |
Index | cols | ||
) | [inline, 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.
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
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 Derived> operator* | ( | const std::complex< Scalar > & | scalar, |
const StorageBaseType & | matrix | ||
) | [friend, inherited] |
std::ostream & operator<< | ( | std::ostream & | s, |
const DenseBase< Derived > & | m | ||
) | [related] |
Outputs the matrix, to the given stream.
If you wish to print the matrix with a format different than the default, use DenseBase::format().
It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.
References Eigen::internal::print_matrix().
PlainObject m_result [mutable, protected] |