Base class for all dense matrices, vectors, and expressions. More...
#include <MatrixBase.h>
Classes | |
struct | ConstDiagonalIndexReturnType |
struct | ConstSelfAdjointViewReturnType |
struct | ConstTriangularViewReturnType |
struct | DiagonalIndexReturnType |
struct | SelfAdjointViewReturnType |
struct | TriangularViewReturnType |
Public Types | |
enum | { HomogeneousReturnTypeDirection } |
enum | { SizeMinusOne } |
enum | { RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor, InnerSizeAtCompileTime, CoeffReadCost, InnerStrideAtCompileTime, OuterStrideAtCompileTime } |
enum | { ThisConstantIsPrivateInPlainObjectBase } |
typedef DenseCoeffsBase< 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 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::packet_traits < Scalar >::type | PacketScalar |
typedef Matrix< typename internal::traits< Derived > ::Scalar, internal::traits < Derived >::RowsAtCompileTime, internal::traits< Derived > ::ColsAtCompileTime, AutoAlign|(internal::traits < Derived >::Flags &RowMajorBit?RowMajor:ColMajor), internal::traits< Derived > ::MaxRowsAtCompileTime, internal::traits< Derived > ::MaxColsAtCompileTime > | PlainObject |
The plain matrix type corresponding to this expression. | |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Reverse< Derived, BothDirections > | ReverseReturnType |
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 | |
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 |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () 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 |
DiagonalReturnType | diagonal () |
const ConstDiagonalReturnType | diagonal () const |
template<int Index> | |
DiagonalIndexReturnType< Index > ::Type | diagonal () |
template<int Index> | |
ConstDiagonalIndexReturnType < Index >::Type | diagonal () const |
DiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) |
ConstDiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) const |
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 &) 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 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 |
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) |
Derived & | operator= (const MatrixBase &other) |
template<typename OtherDerived > | |
Derived & | operator= (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
template<typename OtherDerived > | |
Derived & | operator= (const ReturnByValue< 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 |
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 () |
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 |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
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 |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index size) |
DenseBase::ConstSegmentReturnType | tail (Index size) const |
template<int Size> | |
FixedSegmentReturnType< Size > ::Type | tail () |
template<int Size> | |
ConstFixedSegmentReturnType < Size >::Type | tail () const |
Block< Derived > | topLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | topLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner () const |
Block< Derived > | topRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | topRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner () const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | topRows () |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | topRows () const |
Scalar | trace () const |
Eigen::Transpose< Derived > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
template<unsigned int Mode> | |
TriangularViewReturnType< Mode > ::Type | triangularView () |
template<unsigned int Mode> | |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
template<typename CustomUnaryOp > | |
const CwiseUnaryOp < CustomUnaryOp, const Derived > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. | |
template<typename CustomViewOp > | |
const CwiseUnaryView < CustomViewOp, const Derived > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
PlainObject | unitOrthogonal (void) const |
CoeffReturnType | value () const |
template<typename Visitor > | |
void | visit (Visitor &func) const |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index size, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (const CustomNullaryOp &func) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random () |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero () |
Protected Member Functions | |
template<typename OtherDerived > | |
void | checkTransposeAliasing (const OtherDerived &other) const |
MatrixBase () | |
template<typename OtherDerived > | |
Derived & | operator+= (const ArrayBase< OtherDerived > &) |
template<typename OtherDerived > | |
Derived & | operator-= (const ArrayBase< OtherDerived > &) |
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) |
Base class for all dense matrices, vectors, and expressions.
This class is the base that is inherited by all matrix, vector, and related expression types. Most of the Eigen API is contained in this class, and its base classes. Other important classes for the Eigen API are Matrix, and VectorwiseOp.
Note that some methods are defined in other modules such as the LU module LU module for all functions related to matrix inversions.
Derived | is the derived type, e.g. a matrix type, or an expression, etc. |
When writing a function taking Eigen objects as argument, if you want your function to take as argument any matrix, vector, or expression, just let it take a MatrixBase argument. As an example, here is a function printFirstRow which, given a matrix, vector, or expression x, prints the first row of x.
This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN
.
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Reimplemented in ScaledProduct< NestedProduct >, MatrixWrapper< ExpressionType >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, Homogeneous< MatrixType, _Direction >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >, DiagonalProduct< MatrixType, DiagonalType, ProductOrder >, Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, and ArrayWrapper< ExpressionType >.
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typedef const Diagonal<const Derived> ConstDiagonalReturnType |
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typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne |
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typedef Diagonal<Derived> DiagonalReturnType |
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typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const ConstStartMinusOne > HNormalizedReturnType |
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> HomogeneousReturnType |
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 > >.
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typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime, AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor), internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime > 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 in ScaledProduct< NestedProduct >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.
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typedef internal::stem_function<Scalar>::type StemFunction |
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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.
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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.
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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.
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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 |
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Example:
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)
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This is the "in place" version of adjoint(): it replaces *this
by its own transpose. Thus, doing
has the same effect on m as doing
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().
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Example:
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, and EIGEN_UNROLLING_LIMIT.
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References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.
void applyHouseholderOnTheLeft | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) |
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 | ||
) |
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().
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replaces *this
by *this
* other.
References EigenBase< Derived >::derived().
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This is defined in the Jacobi module.
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.
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replaces this
by *this
* other. It is equivalent to MatrixBase::operator</em>=()
References EigenBase< Derived >::derived().
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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:
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 |
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*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:
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)
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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:
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().
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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:
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
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This is the const version of block<>(Index, Index).
*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.
References abs(), abs2(), eigen_assert, pow(), and sqrt().
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
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
This is the const version of bottomLeftCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
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
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This is the const version of bottomLeftCorner<int, int>().
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
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
This is the const version of bottomRightCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
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
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This is the const version of bottomRightCorner<int, int>().
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n | the number of rows in the block |
Example:
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
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This is the const version of bottomRows(Index).
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N | the number of rows in the block |
Example:
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
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This is the const version of bottomRows<int>().
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The template parameter NewScalar is the type we are casting the scalars to.
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Example:
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 |
*this
.
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Example:
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().
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This is defined in the LU module.
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:
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
References eigen_assert.
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This is defined in the LU module.
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:
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
References eigen_assert.
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*this
.
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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.
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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.
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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 |
Referenced by main().
const MatrixFunctionReturnValue<Derived> cosh | ( | ) | const |
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This is defined in the Geometry module.
*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.
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This is defined in the Geometry module.
*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.
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*this
Example:
Output:
2 4 6 5 1 0
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*this
Example:
Output:
4 16 36 25 1 0
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Example:
Output:
Comparing m with identity matrix: 1 1 0 1 Number of coefficients that are equal: 3
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*this
and a scalar s Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator==().
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Example:
Output:
0.5 2 1 0.333 4 1
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Example:
Output:
4 3 4
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Example:
Output:
2 2 3
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Example:
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!=().
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Example:
Output:
0.5 1.5 1.33
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Example:
Output:
1 1.41 2
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*this
*this
is not required to be square.
Example:
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:
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().
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This is the const version of diagonal().
This is the const version of diagonal<int>().
Reimplemented in CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.
DiagonalIndexReturnType<Index>::Type diagonal | ( | ) |
ConstDiagonalIndexReturnType<Index>::Type diagonal | ( | ) | const |
Reimplemented in CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.
|
inline |
*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:
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
|
inline |
This is the const version of diagonal(Index).
Reimplemented in CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.
|
inline |
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other | ) | const |
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_assert, EIGEN_CHECK_BINARY_COMPATIBILIY, EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE, and EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inline |
Example:
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
|
inline |
Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
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:
Output:
The eigenvalues of the 3x3 matrix of ones are: (-2.98e-17,0) (3,0) (1.81e-32,0)
References Eigen::internal::IsComplex.
|
inlineinherited |
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().
|
inlineinherited |
Reimplemented in ScaledProduct< NestedProduct >, ArrayWrapper< ExpressionType >, ProductBase< Derived, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.
const MatrixExponentialReturnValue<Derived> exp | ( | ) | const |
|
inlineinherited |
Alias for setConstant(): sets all coefficients in this expression to value.
|
inlineinherited |
This is mostly for internal use.
|
inline |
Reimplemented from DenseBase< Derived >.
|
inline |
Reimplemented from DenseBase< Derived >.
|
inline |
Reimplemented from DenseBase< Derived >.
|
inline |
Reimplemented from DenseBase< Derived >.
|
inlineinherited |
See class IOFormat for some examples.
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr | ( | ) | const |
*this
.
|
inline |
|
inlineinherited |
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:
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.
|
inlineinherited |
This is the const version of head(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inlineinherited |
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:
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.
|
inlineinherited |
This is the const version of head<int>().
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inline |
This is defined in the Geometry module.
*this
Example:
Output:
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inline |
This is defined in the Geometry module.
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 |
*this
.*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.References cwiseAbs().
|
inlinestatic |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
Output:
1 0 0 0 0 1 0 0 0 0 1 0
References EIGEN_STATIC_ASSERT_FIXED_SIZE.
|
inlinestatic |
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:
Output:
1 0 0 0 1 0 0 0 1 0 0 0
|
inline |
*this
.
|
inline |
*this
.
|
inlineinherited |
|
inline |
This is defined in the LU module.
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
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_assert, and EIGEN_STATIC_ASSERT.
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse(), and Hyperplane< _Scalar, _AmbientDim, _Options >::transform().
|
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().
|
inherited |
References Eigen::internal::isApprox().
|
inherited |
This is just an alias for isApproxToConstant().
bool isDiagonal | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const |
Example:
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 |
Example:
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 |
References abs().
|
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.
|
inherited |
|
inherited |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
|
inherited |
Example:
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 |
Example:
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 |
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
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 |
References abs().
|
inherited |
Example:
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 |
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other | ) | const |
*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.
|
inline |
This is defined in the Cholesky module.
*this
|
inlineinherited |
n | the number of columns in the block |
Example:
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
|
inlineinherited |
This is the const version of leftCols(Index).
|
inlineinherited |
N | the number of columns in the block |
Example:
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
|
inlineinherited |
This is the const version of leftCols<int>().
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.When size is set to 1, a vector of length 1 containing 'high' is returned.This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
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.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
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.
|
inline |
This is defined in the Cholesky module.
*this
const MatrixLogarithmReturnValue<Derived> log | ( | ) | const |
Reimplemented from DenseBase< Derived >.
|
inline |
This is defined in the LU module.
Synonym of partialPivLu().
*this
.void makeHouseholder | ( | EssentialPart & | essential, |
Scalar & | tau, | ||
RealScalar & | beta | ||
) | const |
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 | ||
) |
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 |
|
inline |
|
inline |
const MatrixFunctionReturnValue<Derived> matrixFunction | ( | StemFunction | f | ) | const |
|
inlineinherited |
|
inherited |
|
inherited |
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inlineinherited |
startCol | the index of the first column in the block |
numCols | the number of columns in the block |
Example:
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
This is the const version of middleCols(Index,Index).
|
inlineinherited |
N | the number of columns in the block |
startCol | the index of the first column in the block |
Example:
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
|
inlineinherited |
This is the const version of middleCols<int>().
startRow | the index of the first row in the block |
numRows | the number of rows in the block |
Example:
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
This is the const version of middleRows(Index,Index).
|
inlineinherited |
N | the number of rows in the block |
startRow | the index of the first row in the block |
Example:
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
|
inlineinherited |
This is the const version of middleRows<int>().
|
inlineinherited |
|
inherited |
|
inherited |
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
|
inlineinherited |
NoAlias< Derived, MatrixBase > noalias | ( | ) |
*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:
On the other hand the following example will lead to a wrong result:
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:
|
inlineinherited |
*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().
|
inline |
Normalizes the vector, i.e. divides it by its own norm.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inline |
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().
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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:
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:
Output:
6 6 6 6 1 1
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
1 1 1 1 6 6 6 6
|
inline |
*this
and other are not exactly equal to each other.
|
inline |
*this
scaled by the scalar factor scalar const ScalarMultipleReturnType operator* | ( | const RealScalar & | scalar | ) | const |
|
inline |
Overloaded for efficient real matrix times complex scalar value
|
inline |
*this
and other.References Eigen::Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.
|
inline |
*this
by the diagonal matrix diagonal. MatrixBase< Derived >::ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const |
Concatenates a linear transformation matrix and a uniform scaling
References UniformScaling< _Scalar >::factor().
|
inline |
replaces *this
by *this
* other.
*this
References EigenBase< Derived >::derived().
|
inlineinherited |
|
inline |
replaces *this
by *this
+ other.
*this
|
inherited |
References EigenBase< Derived >::derived().
|
inlineprotected |
|
inline |
*this
|
inline |
replaces *this
by *this
- other.
*this
|
inherited |
References EigenBase< Derived >::derived().
|
inlineprotected |
|
inline |
*this
divided by the scalar value scalar
|
inlineinherited |
|
inlineinherited |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
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
|
inlineinherited |
|
inline |
Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)
|
inline |
|
inline |
Copies the generic expression other into *this.
The expression must provide a (templated) evalTo(Derived& dst) const function which does the actual job. In practice, this allows any user to write its own special matrix without having to modify MatrixBase
Reimplemented from DenseBase< Derived >.
Reimplemented in PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.
References EigenBase< Derived >::derived().
|
inline |
Reimplemented from DenseBase< Derived >.
Reimplemented in PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.
References ReturnByValue< Derived >::evalTo().
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*this
and other are all exactly equal.
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inline |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
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:
Output:
The operator norm of the 3x3 matrix of ones is 3
References sqrt().
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This is defined in the LU module.
*this
.
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Example:
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.
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inlinestaticinherited |
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:
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.
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inlinestaticinherited |
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:
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.
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inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
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.
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*this
.
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inline |
*this
.
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inlineinherited |
*this
Example:
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
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*this
Example:
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
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inlineinherited |
Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
Reimplemented in PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Referenced by TriangularBase< Derived >::evalToLazy(), and MatrixBase< Derived >::setIdentity().
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 > >.
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Example:
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().
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This is the const version of reverse().
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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:
References DenseBase< Derived >::reverse().
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n | the number of columns in the block |
Example:
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
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This is the const version of rightCols(Index).
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N | the number of columns in the block |
Example:
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
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This is the const version of rightCols<int>().
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Example:
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().
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Example:
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().
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inlineinherited |
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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:
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.
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This is the const version of segment(Index,Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
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*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:
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.
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This is the const version of segment<int>(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
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Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
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Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type selfadjointView | ( | ) |
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type selfadjointView | ( | ) | const |
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Sets all coefficients in this expression to value.
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Writes the identity expression (not necessarily square) into *this.
Example:
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().
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:
Output:
1 0 0 0 1 0 0 0 1
References DenseBase< Derived >::resize().
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:
Output:
0.5 0.75 1 1.25 1.5
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
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.
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Sets all coefficients in this expression to one.
Example:
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
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Sets all coefficients in this expression to random values.
Example:
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
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Sets all coefficients in this expression to zero.
Example:
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 |
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 |
*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().
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swaps *this with the expression other.
Referenced by TriangularBase< Derived >::evalTo().
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inlineinherited |
swaps *this with the matrix or array other.
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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:
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.
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This is the const version of tail(Index).
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
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inlineinherited |
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:
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.
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inlineinherited |
This is the const version of tail<int>.
References EIGEN_STATIC_ASSERT_VECTOR_ONLY.
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
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
This is the const version of topLeftCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
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
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This is the const version of topLeftCorner<int, int>().
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
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
This is the const version of topRightCorner(Index, Index).
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The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
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
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inlineinherited |
This is the const version of topRightCorner<int, int>().
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n | the number of rows in the block |
Example:
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
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inlineinherited |
This is the const version of topRows(Index).
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inlineinherited |
N | the number of rows in the block |
Example:
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
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This is the const version of topRows<int>().
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*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().
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inlineinherited |
Example:
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
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::inverse().
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inlineinherited |
This is the const version of transpose().
Make sure you read the warning for transpose() !
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inlineinherited |
This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
has the same effect on m as doing
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 | ( | ) |
The parameter Mode can have the following values: Upper
, StrictlyUpper
, UnitUpper
, Lower
, StrictlyLower
, UnitLower
.
Example:
Output:
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView | ( | ) | const |
This is the const version of MatrixBase::triangularView()
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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:
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:
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
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inline |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
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
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inlinestatic |
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.
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inlinestatic |
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 |
*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.
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inlinestatic |
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.
|
inlinestatic |
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.
|
inlinestatic |
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.
|
inlinestatic |
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.
|
inlineinherited |
Referenced by SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::evalTo().
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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:
References Eigen::Dynamic, and EIGEN_UNROLLING_LIMIT.
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inlinestaticinherited |
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:
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:
Output:
0 0 0 0 0 0
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inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 0 0 0 0 0 0 0
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friend |
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friend |
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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_DEFAULT_IO_FORMAT, and Eigen::internal::print_matrix().