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Eigen
3.2.5
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Base class for all dense matrices, vectors, and expressions. More...
Public Types | |
enum | { RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor , CoeffReadCost } |
typedef internal::traits < Derived >::Index | Index |
The type of indices. | |
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. | |
Public Member Functions | |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
bool | all (void) const |
bool | allFinite () 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 OtherScalar > | |
void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
template<typename OtherDerived > | |
void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
template<typename OtherScalar > | |
void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
template<typename OtherDerived > | |
void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
ArrayWrapper< Derived > | array () |
const DiagonalWrapper< const Derived > | asDiagonal () const |
template<typename CustomBinaryOp , typename OtherDerived > | |
const CwiseBinaryOp < CustomBinaryOp, const Derived, const OtherDerived > | binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
const Block< const Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
Block< Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
RealScalar | blueNorm () const |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner () |
const Block< const Derived > | bottomLeftCorner (Index cRows, Index cCols) const |
Block< Derived > | bottomLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner () |
const Block< const Derived > | bottomRightCorner (Index cRows, Index cCols) const |
Block< Derived > | bottomRightCorner (Index cRows, Index cCols) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | bottomRows (Index n=N) const |
template<int N> | |
NRowsBlockXpr< N >::Type | bottomRows (Index n=N) |
ConstRowsBlockXpr | bottomRows (Index n) const |
RowsBlockXpr | bottomRows (Index n) |
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 |
ConstColXpr | col (Index i) const |
ColXpr | col (Index i) |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () const |
ColwiseReturnType | colwise () |
ConstColwiseReturnType | colwise () const |
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 |
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 |
const CwiseScalarEqualReturnType | cwiseEqual (const Scalar &s) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < std::equal_to< Scalar > , const Derived, const OtherDerived > | cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const Derived > | cwiseInverse () const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const ConstantReturnType > | cwiseMax (const Scalar &other) 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_min_op < Scalar >, const Derived, const ConstantReturnType > | cwiseMin (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 |
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_product_op < typename Derived::Scalar, typename OtherDerived::Scalar > , const Derived, const OtherDerived > | cwiseProduct (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 |
ConstDiagonalDynamicIndexReturnType | diagonal (Index index) const |
DiagonalDynamicIndexReturnType | diagonal (Index index) |
ConstDiagonalReturnType | diagonal () const |
DiagonalReturnType | diagonal () |
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 |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. | |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
EvalReturnType | eval () const |
void | fill (const Scalar &value) |
template<unsigned int Added, unsigned int Removed> | |
const Flagged< Derived, Added, Removed > | flagged () const |
ForceAlignedAccess< Derived > | forceAlignedAccess () |
const ForceAlignedAccess< Derived > | forceAlignedAccess () const |
template<bool Enable> | |
internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type | forceAlignedAccessIf () |
template<bool Enable> | |
internal::add_const_on_value_type < typename internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type >::type | forceAlignedAccessIf () const |
const WithFormat< Derived > | format (const IOFormat &fmt) const |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
const FullPivLU< PlainObject > | fullPivLu () const |
bool | hasNaN () const |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | head (Index n=N) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | head (Index n=N) |
ConstSegmentReturnType | head (Index n) const |
SegmentReturnType | head (Index n) |
const HNormalizedReturnType | hnormalized () const |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
NonConstImagReturnType | imag () |
const ImagReturnType | imag () const |
Index | innerSize () const |
const internal::inverse_impl < Derived > | inverse () const |
template<typename OtherDerived > | |
bool | isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename Derived > | |
bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const |
template<typename OtherDerived > | |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (const 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 |
template<int N> | |
ConstNColsBlockXpr< N >::Type | leftCols (Index n=N) const |
template<int N> | |
NColsBlockXpr< N >::Type | leftCols (Index n=N) |
ConstColsBlockXpr | leftCols (Index n) const |
ColsBlockXpr | leftCols (Index n) |
const LLT< PlainObject > | llt () 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) |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *index) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
internal::traits< Derived >::Scalar | maxCoeff () const |
Scalar | mean () const |
template<int N> | |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) const |
template<int N> | |
NColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) const |
template<int N> | |
NRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) |
ConstRowsBlockXpr | middleRows (Index startRow, Index n) const |
RowsBlockXpr | middleRows (Index startRow, Index n) |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *index) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
internal::traits< Derived >::Scalar | minCoeff () 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 |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
template<typename DiagonalDerived > | |
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
template<typename OtherDerived > | |
const ProductReturnType < Derived, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Derived > | operator* (const std::complex< Scalar > &scalar) const |
const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
template<typename OtherDerived > | |
Derived & | operator*= (const EigenBase< OtherDerived > &other) |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_sum_op < Scalar >, const Derived, const OtherDerived > | operator+ (const Eigen::MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
Derived & | operator+= (const MatrixBase< OtherDerived > &other) |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_difference_op < Scalar >, const Derived, const OtherDerived > | operator- (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator- () const |
template<typename OtherDerived > | |
Derived & | operator-= (const MatrixBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator/ (const Scalar &scalar) const |
template<typename OtherDerived > | |
CommaInitializer< Derived > | operator<< (const DenseBase< OtherDerived > &other) |
CommaInitializer< Derived > | operator<< (const Scalar &s) |
template<typename OtherDerived > | |
Derived & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
Derived & | operator= (const MatrixBase &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 |
NonConstRealReturnType | real () |
RealReturnType | real () const |
const ReplicateReturnType | replicate (Index rowFacor, Index colFactor) const |
template<int RowFactor, int ColFactor> | |
const Replicate< Derived, RowFactor, ColFactor > | replicate () const |
void | resize (Index nbRows, Index nbCols) |
void | resize (Index newSize) |
ConstReverseReturnType | reverse () const |
ReverseReturnType | reverse () |
void | reverseInPlace () |
template<int N> | |
ConstNColsBlockXpr< N >::Type | rightCols (Index n=N) const |
template<int N> | |
NColsBlockXpr< N >::Type | rightCols (Index n=N) |
ConstColsBlockXpr | rightCols (Index n) const |
ColsBlockXpr | rightCols (Index n) |
ConstRowXpr | row (Index i) const |
RowXpr | row (Index i) |
RowwiseReturnType | rowwise () |
ConstRowwiseReturnType | rowwise () const |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | segment (Index start, Index n=N) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | segment (Index start, Index n=N) |
ConstSegmentReturnType | segment (Index start, Index n) const |
SegmentReturnType | segment (Index start, Index n) |
template<typename ElseDerived > | |
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > | select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
template<typename ThenDerived > | |
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const |
template<typename ThenDerived , typename ElseDerived > | |
const Select< Derived, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
Derived & | setConstant (const Scalar &value) |
Derived & | setIdentity (Index rows, Index cols) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
Derived & | setIdentity () |
Derived & | setLinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
Derived & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
Derived & | setOnes () |
Derived & | setRandom () |
Derived & | setZero () |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () const |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | tail (Index n=N) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | tail (Index n=N) |
ConstSegmentReturnType | tail (Index n) const |
SegmentReturnType | tail (Index n) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner () |
const Block< const Derived > | topLeftCorner (Index cRows, Index cCols) const |
Block< Derived > | topLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner () |
const Block< const Derived > | topRightCorner (Index cRows, Index cCols) const |
Block< Derived > | topRightCorner (Index cRows, Index cCols) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | topRows (Index n=N) const |
template<int N> | |
NRowsBlockXpr< N >::Type | topRows (Index n=N) |
ConstRowsBlockXpr | topRows (Index n) const |
RowsBlockXpr | topRows (Index n) |
Scalar | trace () const |
ConstTransposeReturnType | transpose () const |
Eigen::Transpose< Derived > | transpose () |
void | transposeInPlace () |
template<unsigned int Mode> | |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
template<unsigned int Mode> | |
TriangularViewReturnType< Mode > ::Type | triangularView () |
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 (const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const IdentityReturnType | Identity () |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. | |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (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 (Index rows, Index cols, const CustomNullaryOp &func) |
static const ConstantReturnType | Ones () |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index rows, Index cols) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const ConstantReturnType | Zero () |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero (Index rows, Index cols) |
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.
template<typename Derived> void printFirstRow(const Eigen::MatrixBase<Derived>& x) { cout << x.row(0) << endl; }
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
.
The type of indices.
To change this, #define
the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE
.
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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.
anonymous enum [inherited] |
RowsAtCompileTime |
The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
|
ColsAtCompileTime |
The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
|
SizeAtCompileTime |
This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.
|
MaxRowsAtCompileTime |
This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxColsAtCompileTime |
This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxSizeAtCompileTime |
This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
IsVectorAtCompileTime |
This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row). |
Flags |
This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags. |
IsRowMajor |
True if this expression has row-major storage order. |
CoeffReadCost |
This is a rough measure of how expensive it is to read one coefficient from this expression. |
const MatrixBase< Derived >::AdjointReturnType adjoint | ( | ) | const [inline] |
Example:
Matrix2cf m = Matrix2cf::Random(); cout << "Here is the 2x2 complex matrix m:" << endl << m << endl; cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
Output:
Here is the 2x2 complex matrix m: (-0.211,0.68) (-0.605,0.823) (0.597,0.566) (0.536,-0.33) Here is the adjoint of m: (-0.211,-0.68) (0.597,-0.566) (-0.605,-0.823) (0.536,0.33)
m = m.adjoint(); // bug!!! caused by aliasing effect
m.adjointInPlace();
m = m.adjoint().eval();
References DenseBase< Derived >::transpose().
Referenced by MatrixBase< Derived >::adjointInPlace().
void adjointInPlace | ( | ) | [inline] |
This is the "in place" version of adjoint(): it replaces *this
by its own transpose. Thus, doing
m.adjointInPlace();
has the same effect on m as doing
m = m.adjoint().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
*this
must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.References MatrixBase< Derived >::adjoint().
bool all | ( | void | ) | const [inline, inherited] |
Example:
Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones()); Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs(); // let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax: cout << "Is (" << p0.transpose() << ") inside the box: " << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl; cout << "Is (" << p1.transpose() << ") inside the box: " << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;
Output:
Is ( 0.68 -0.211 0.566) inside the box: 0 Is (0.597 0.823 0.605) inside the box: 1
References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.
Referenced by DenseBase< Derived >::hasNaN().
bool allFinite | ( | ) | const [inline, inherited] |
*this
contains only finite numbers, i.e., no NaN and no +/-INF values.References DenseBase< Derived >::hasNaN().
bool any | ( | void | ) | const [inline, inherited] |
References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.
void applyHouseholderOnTheLeft | ( | const EssentialPart & | essential, | |
const Scalar & | tau, | |||
Scalar * | workspace | |||
) | [inline] |
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 DenseBase< Derived >::row().
void applyHouseholderOnTheRight | ( | const EssentialPart & | essential, | |
const Scalar & | tau, | |||
Scalar * | workspace | |||
) | [inline] |
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 DenseBase< Derived >::col().
void applyOnTheLeft | ( | Index | p, | |
Index | q, | |||
const JacobiRotation< OtherScalar > & | j | |||
) | [inline] |
This is defined in the Jacobi module.
#include <Eigen/Jacobi>
Applies the rotation in the plane j to the rows p and q of *this
, i.e., it computes B = J * B, with .
References DenseBase< Derived >::row().
void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by other * *this
.
Example:
Matrix3f A = Matrix3f::Random(3,3), B; B << 0,1,0, 0,0,1, 1,0,0; cout << "At start, A = " << endl << A << endl; A.applyOnTheLeft(B); cout << "After applyOnTheLeft, A = " << endl << A << endl;
Output:
At start, A = 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 After applyOnTheLeft, A = -0.211 0.823 0.536 0.566 -0.605 -0.444 0.68 0.597 -0.33
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=().
Example:
Matrix3f A = Matrix3f::Random(3,3), B; B << 0,1,0, 0,0,1, 1,0,0; cout << "At start, A = " << endl << A << endl; A *= B; cout << "After A *= B, A = " << endl << A << endl; A.applyOnTheRight(B); // equivalent to A *= B cout << "After applyOnTheRight, A = " << endl << A << endl;
Output:
At start, A = 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 After A *= B, A = -0.33 0.68 0.597 0.536 -0.211 0.823 -0.444 0.566 -0.605 After applyOnTheRight, A = 0.597 -0.33 0.68 0.823 0.536 -0.211 -0.605 -0.444 0.566
ArrayWrapper<Derived> array | ( | ) | [inline] |
const DiagonalWrapper< const Derived > asDiagonal | ( | ) | const [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.
Example:
cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;
Output:
2 0 0 0 5 0 0 0 6
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::fromPositionOrientationScale(), Transform< _Scalar, _Dim, _Mode, _Options >::prescale(), and Transform< _Scalar, _Dim, _Mode, _Options >::scale().
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> binaryExpr | ( | const Eigen::MatrixBase< OtherDerived > & | other, | |
const CustomBinaryOp & | func = CustomBinaryOp() | |||
) | const [inline] |
The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template binary functor template<typename Scalar> struct MakeComplexOp { EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp) typedef complex<Scalar> result_type; complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); } }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random(); cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl; return 0; }
Output:
(0.68,0.271) (0.823,-0.967) (-0.444,-0.687) (-0.27,0.998) (-0.211,0.435) (-0.605,-0.514) (0.108,-0.198) (0.0268,-0.563) (0.566,-0.717) (-0.33,-0.726) (-0.0452,-0.74) (0.904,0.0259) (0.597,0.214) (0.536,0.608) (0.258,-0.782) (0.832,0.678)
const Block<const Derived, BlockRows, BlockCols> block | ( | Index | startRow, | |
Index | startCol, | |||
Index | blockRows, | |||
Index | blockCols | |||
) | const [inline, inherited] |
This is the const version of block<>(Index, Index, Index, Index).
Block<Derived, BlockRows, BlockCols> block | ( | Index | startRow, | |
Index | startCol, | |||
Index | blockRows, | |||
Index | blockCols | |||
) | [inline, inherited] |
BlockRows | number of rows in block as specified at compile-time | |
BlockCols | number of columns in block as specified at compile-time |
startRow | the first row in the block | |
startCol | the first column in the block | |
blockRows | number of rows in block as specified at run-time | |
blockCols | number of columns in block as specified at run-time |
This function is mainly useful for blocks where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, blockRows should equal BlockRows unless BlockRows is Dynamic, and the same for the number of columns.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl; m.block<2, Dynamic>(1, 1, 2, 3).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl; m.block<2, Dynamic>(1, 1, 2, 3).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
const Block<const Derived, BlockRows, BlockCols> block | ( | Index | startRow, | |
Index | startCol | |||
) | const [inline, inherited] |
This is the const version of block<>(Index, Index).
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
startRow | the first row in the block | |
startCol | the first column in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl; m.block<2,2>(1,1).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
m.template block<3,3>(1,1);
const Block<const Derived> block | ( | Index | startRow, | |
Index | startCol, | |||
Index | blockRows, | |||
Index | blockCols | |||
) | const [inline, inherited] |
This is the const version of block(Index,Index,Index,Index).
Block<Derived> block | ( | Index | startRow, | |
Index | startCol, | |||
Index | blockRows, | |||
Index | blockCols | |||
) | [inline, inherited] |
startRow | the first row in the block | |
startCol | the first column in the block | |
blockRows | the number of rows in the block | |
blockCols | the number of columns in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl; m.block(1, 1, 2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm | ( | ) | const [inline] |
*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.
const Block<const Derived, CRows, CCols> bottomLeftCorner | ( | Index | cRows, | |
Index | cCols | |||
) | const [inline, inherited] |
This is the const version of bottomLeftCorner<int, int>(Index, Index).
CRows | number of rows in corner as specified at compile-time | |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time | |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner<2,Dynamic>(2,2):" << endl; cout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl; m.bottomLeftCorner<2,Dynamic>(2,2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,Dynamic>(2,2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const Derived, CRows, CCols> bottomLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomLeftCorner<int, int>().
Block<Derived, CRows, CCols> bottomLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner<2,2>():" << endl; cout << m.bottomLeftCorner<2,2>() << endl; m.bottomLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
This is the const version of bottomLeftCorner(Index, Index).
cRows | the number of rows in the corner | |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner(2, 2):" << endl; cout << m.bottomLeftCorner(2, 2) << endl; m.bottomLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const Derived, CRows, CCols> bottomRightCorner | ( | Index | cRows, | |
Index | cCols | |||
) | const [inline, inherited] |
This is the const version of bottomRightCorner<int, int>(Index, Index).
CRows | number of rows in corner as specified at compile-time | |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time | |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner<2,Dynamic>(2,2):" << endl; cout << m.bottomRightCorner<2,Dynamic>(2,2) << endl; m.bottomRightCorner<2,Dynamic>(2,2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,Dynamic>(2,2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
const Block<const Derived, CRows, CCols> bottomRightCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomRightCorner<int, int>().
Block<Derived, CRows, CCols> bottomRightCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner<2,2>():" << endl; cout << m.bottomRightCorner<2,2>() << endl; m.bottomRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
This is the const version of bottomRightCorner(Index, Index).
cRows | the number of rows in the corner | |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner(2, 2):" << endl; cout << m.bottomRightCorner(2, 2) << endl; m.bottomRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
ConstNRowsBlockXpr<N>::Type bottomRows | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of bottomRows<int>().
NRowsBlockXpr<N>::Type bottomRows | ( | Index | n = N |
) | [inline, inherited] |
N | the number of rows in the block as specified at compile-time |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.bottomRows<2>():" << endl; cout << a.bottomRows<2>() << endl; a.bottomRows<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows<2>(): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
ConstRowsBlockXpr bottomRows | ( | Index | n | ) | const [inline, inherited] |
This is the const version of bottomRows(Index).
RowsBlockXpr bottomRows | ( | Index | n | ) | [inline, inherited] |
n | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.bottomRows(2):" << endl; cout << a.bottomRows(2) << endl; a.bottomRows(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows(2): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type cast | ( | ) | const [inline] |
The template parameter NewScalar is the type we are casting the scalars to.
ColXpr col | ( | Index | i | ) | [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Identity(); m.col(1) = Vector3d(4,5,6); cout << m << endl;
Output:
1 4 0 0 5 0 0 6 1
Referenced by MatrixBase< Derived >::applyHouseholderOnTheRight(), and MatrixBase< Derived >::applyOnTheRight().
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > colPivHouseholderQr | ( | ) | const [inline] |
*this
.References DenseBase< Derived >::eval().
DenseBase< Derived >::ColwiseReturnType colwise | ( | ) | [inline, inherited] |
const DenseBase< Derived >::ConstColwiseReturnType colwise | ( | ) | const [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl; cout << "Here is the maximum absolute value of each column:" << endl << m.cwiseAbs().colwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
Referenced by Eigen::umeyama().
void computeInverseAndDetWithCheck | ( | ResultType & | inverse, | |
typename ResultType::Scalar & | determinant, | |||
bool & | invertible, | |||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. | |
determinant | Reference to the variable in which to store the determinant. | |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. | |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; double determinant; m.computeInverseAndDetWithCheck(inverse,determinant,invertible); cout << "Its determinant is " << determinant << endl; if(invertible) { cout << "It is invertible, and its inverse is:" << endl << inverse << endl; } else { cout << "It is not invertible." << endl; }
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its determinant is 0.209 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
References DenseBase< Derived >::RowsAtCompileTime.
Referenced by MatrixBase< Derived >::computeInverseWithCheck().
void computeInverseWithCheck | ( | ResultType & | inverse, | |
bool & | invertible, | |||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. | |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. | |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; m.computeInverseWithCheck(inverse,invertible); if(invertible) { cout << "It is invertible, and its inverse is:" << endl << inverse << endl; } else { cout << "It is not invertible." << endl; }
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
References MatrixBase< Derived >::computeInverseAndDetWithCheck().
ConjugateReturnType conjugate | ( | ) | const [inline] |
*this
.const DenseBase< Derived >::ConstantReturnType Constant | ( | const Scalar & | value | ) | [inline, static, inherited] |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.
const DenseBase< Derived >::ConstantReturnType Constant | ( | Index | size, | |
const Scalar & | value | |||
) | [inline, static, inherited] |
The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::NullaryExpr().
const DenseBase< Derived >::ConstantReturnType Constant | ( | Index | nbRows, | |
Index | nbCols, | |||
const Scalar & | value | |||
) | [inline, static, inherited] |
The parameters nbRows and nbCols 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 nbRows and nbCols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::NullaryExpr().
Referenced by DenseBase< Derived >::Ones(), DenseBase< Derived >::select(), DenseBase< Derived >::setConstant(), and DenseBase< Derived >::Zero().
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other Here is a very good explanation of cross-product: http://xkcd.com/199/
MatrixBase< Derived >::PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other using only the x, y, and z coefficientsThe size of *this
and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> cwiseAbs | ( | ) | const [inline] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs() << endl;
Output:
2 4 6 5 1 0
Referenced by MatrixBase< Derived >::hypotNorm(), and SelfAdjointView< MatrixType, UpLo >::operatorNorm().
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> cwiseAbs2 | ( | ) | const [inline] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs2() << endl;
Output:
4 16 36 25 1 0
const CwiseScalarEqualReturnType cwiseEqual | ( | const Scalar & | s | ) | const [inline] |
*this
and a scalar s const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> cwiseEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
MatrixXi m(2,2); m << 1, 0, 1, 1; cout << "Comparing m with identity matrix:" << endl; cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl; int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count(); cout << "Number of coefficients that are equal: " << count << endl;
Output:
Comparing m with identity matrix: 1 1 0 1 Number of coefficients that are equal: 3
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> cwiseInverse | ( | ) | const [inline] |
Example:
MatrixXd m(2,3); m << 2, 0.5, 1, 3, 0.25, 1; cout << m.cwiseInverse() << endl;
Output:
0.5 2 1 0.333 4 1
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType> cwiseMax | ( | const Scalar & | other | ) | const [inline] |
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> cwiseMax | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMax(w) << endl;
Output:
4 3 4
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType> cwiseMin | ( | const Scalar & | other | ) | const [inline] |
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> cwiseMin | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMin(w) << endl;
Output:
2 2 3
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> cwiseNotEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
MatrixXi m(2,2); m << 1, 0, 1, 1; cout << "Comparing m with identity matrix:" << endl; cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl; int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count(); cout << "Number of coefficients that are not equal: " << count << endl;
Output:
Comparing m with identity matrix: 0 0 1 0 Number of coefficients that are not equal: 1
const CwiseBinaryOp<internal::scalar_product_op<typename Derived ::Scalar, typename OtherDerived ::Scalar >, const Derived , const OtherDerived > cwiseProduct | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random(); Matrix3i c = a.cwiseProduct(b); cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;
Output:
a: 7 6 -3 -2 9 6 6 -6 -5 b: 1 -3 9 0 0 3 3 9 5 c: 7 -18 -27 0 0 18 18 -54 -25
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> cwiseQuotient | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseQuotient(w) << endl;
Output:
0.5 1.5 1.33
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> cwiseSqrt | ( | ) | const [inline] |
Example:
Vector3d v(1,2,4); cout << v.cwiseSqrt() << endl;
Output:
1 1.41 2
internal::traits< Derived >::Scalar determinant | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType diagonal | ( | Index | index | ) | const [inline] |
This is the const version of diagonal(Index).
MatrixBase< Derived >::DiagonalDynamicIndexReturnType diagonal | ( | Index | index | ) | [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:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal(1).transpose() << endl << m.diagonal(-2).transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type diagonal | ( | ) | const [inline] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal | ( | ) | [inline] |
*this
*this
is not required to be square.
Example:
Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the main diagonal of m:" << endl << m.diagonal() << endl;
Output:
Here is the matrix m: 7 6 -3 -2 9 6 6 -6 -5 Here are the coefficients on the main diagonal of m: 7 9 -5
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal<1>().transpose() << endl << m.diagonal<-2>().transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::conjugate(), and AngleAxis< _Scalar >::toRotationMatrix().
Index diagonalSize | ( | ) | const [inline] |
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other | ) | const [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.
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues | ( | ) | const [inline] |
Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
MatrixXd ones = MatrixXd::Ones(3,3); VectorXcd eivals = ones.eigenvalues(); cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
Output:
The eigenvalues of the 3x3 matrix of ones are: (-2.98e-17,0) (3,0) (1.81e-32,0)
Referenced by MatrixBase< Derived >::operatorNorm().
EvalReturnType eval | ( | ) | const [inline, inherited] |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
Referenced by MatrixBase< Derived >::colPivHouseholderQr(), MatrixBase< Derived >::fullPivHouseholderQr(), MatrixBase< Derived >::fullPivLu(), MatrixBase< Derived >::householderQr(), MatrixBase< Derived >::lu(), MatrixBase< Derived >::operatorNorm(), and MatrixBase< Derived >::partialPivLu().
void fill | ( | const Scalar & | val | ) | [inline, inherited] |
Alias for setConstant(): sets all coefficients in this expression to val.
References DenseBase< Derived >::setConstant().
const Flagged< Derived, Added, Removed > flagged | ( | ) | const [inline, inherited] |
This is mostly for internal use.
ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | [inline] |
Reimplemented from DenseBase< Derived >.
const ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf | ( | ) | [inline] |
Reimplemented from DenseBase< Derived >.
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
const WithFormat< Derived > format | ( | const IOFormat & | fmt | ) | const [inline, inherited] |
See class IOFormat for some examples.
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr | ( | ) | const [inline] |
*this
.References DenseBase< Derived >::eval().
const FullPivLU< typename MatrixBase< Derived >::PlainObject > fullPivLu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.References DenseBase< Derived >::eval().
bool hasNaN | ( | ) | const [inline, inherited] |
*this
contains at least one Not A Number (NaN).References DenseBase< Derived >::all().
Referenced by DenseBase< Derived >::allFinite().
ConstFixedSegmentReturnType<N>::Type head | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of head<int>().
FixedSegmentReturnType<N>::Type head | ( | Index | n = N |
) | [inline, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
N | the number of coefficients in the segment as specified at compile-time |
n | the number of coefficients in the segment as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head<2>() << endl; v.head<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
ConstSegmentReturnType head | ( | Index | n | ) | const [inline, inherited] |
This is the const version of head(Index).
SegmentReturnType head | ( | Index | n | ) | [inline, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
n | the number of coefficients in the segment |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head(2) << endl; v.head(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
Referenced by MatrixBase< Derived >::stableNorm().
const MatrixBase< Derived >::HNormalizedReturnType hnormalized | ( | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
Example:
Output:
References DenseBase< Derived >::ColsAtCompileTime.
MatrixBase< Derived >::HomogeneousReturnType homogeneous | ( | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > householderQr | ( | ) | const [inline] |
*this
.References DenseBase< Derived >::eval().
NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm | ( | ) | const [inline] |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.References MatrixBase< Derived >::cwiseAbs().
const MatrixBase< Derived >::IdentityReturnType Identity | ( | Index | nbRows, | |
Index | nbCols | |||
) | [inline, static] |
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.
Example:
cout << MatrixXd::Identity(4, 3) << endl;
Output:
1 0 0 0 1 0 0 0 1 0 0 0
References DenseBase< Derived >::NullaryExpr().
const MatrixBase< Derived >::IdentityReturnType Identity | ( | ) | [inline, static] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
cout << Matrix<double, 3, 4>::Identity() << endl;
Output:
1 0 0 0 0 1 0 0 0 0 1 0
References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.
NonConstImagReturnType imag | ( | ) | [inline] |
*this
.const ImagReturnType imag | ( | ) | const [inline] |
*this
.Index innerSize | ( | ) | const [inline, inherited] |
const internal::inverse_impl< Derived > inverse | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Its inverse is:" << endl << m.inverse() << endl;
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
Referenced by Hyperplane< _Scalar, _AmbientDim, _Options >::transform().
bool isApprox | ( | const DenseBase< OtherDerived > & | other, | |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline, inherited] |
true
if *this
is approximately equal to other, within the precision determined by prec.
*this
is approximately equal to the zero matrix or vector. Indeed, isApprox(zero)
returns false unless *this
itself is exactly the zero matrix or vector. If you want to test whether *this
is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::isApprox().
bool isApproxToConstant | ( | const Scalar & | val, | |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline, inherited] |
bool isConstant | ( | const Scalar & | val, | |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline, inherited] |
This is just an alias for isApproxToConstant().
bool isDiagonal | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline] |
Example:
Matrix3d m = 10000 * Matrix3d::Identity(); m(0,2) = 1; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl; cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;
Output:
Here's the matrix m: 1e+04 0 1 0 1e+04 0 0 0 1e+04 m.isDiagonal() returns: 0 m.isDiagonal(1e-3) returns: 1
bool isIdentity | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline] |
Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isIdentity() returns: " << m.isIdentity() << endl; cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isIdentity() returns: 0 m.isIdentity(1e-3) returns: 1
bool isLowerTriangular | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline] |
bool isMuchSmallerThan | ( | const typename NumTraits< Scalar >::Real & | other, | |
const RealScalar & | prec | |||
) | const [inline, inherited] |
true
if the norm of *this
is much smaller than other, within the precision determined by prec.
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
bool isMuchSmallerThan | ( | const DenseBase< OtherDerived > & | other, | |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline, inherited] |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
bool isOnes | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Ones(); m(0,2) += 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isOnes() returns: " << m.isOnes() << endl; cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
bool isOrthogonal | ( | const MatrixBase< OtherDerived > & | other, | |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const [inline] |
Example:
Vector3d v(1,0,0); Vector3d w(1e-4,0,1); cout << "Here's the vector v:" << endl << v << endl; cout << "Here's the vector w:" << endl << w << endl; cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl; cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;
Output:
Here's the vector v: 1 0 0 Here's the vector w: 0.0001 0 1 v.isOrthogonal(w) returns: 0 v.isOrthogonal(w,1e-3) returns: 1
bool isUnitary | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline] |
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isUnitary() returns: " << m.isUnitary() << endl; cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isUnitary() returns: 0 m.isUnitary(1e-3) returns: 1
bool isUpperTriangular | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline] |
bool isZero | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
) | const [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Zero(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isZero() returns: " << m.isZero() << endl; cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;
Output:
Here's the matrix m: 0 0 0.0001 0 0 0 0 0 0 m.isZero() returns: 0 m.isZero(1e-3) returns: 1
JacobiSVD< typename MatrixBase< Derived >::PlainObject > jacobiSvd | ( | unsigned int | computationOptions = 0 |
) | const [inline] |
This is defined in the SVD module.
#include <Eigen/SVD>
*this
computed by two-sided Jacobi transformations.const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other without implicit evaluation.The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.
const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt | ( | ) | const [inline] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
ConstNColsBlockXpr<N>::Type leftCols | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of leftCols<int>().
NColsBlockXpr<N>::Type leftCols | ( | Index | n = N |
) | [inline, inherited] |
N | the number of columns in the block as specified at compile-time |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.leftCols<2>():" << endl; cout << a.leftCols<2>() << endl; a.leftCols<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols<2>(): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
ConstColsBlockXpr leftCols | ( | Index | n | ) | const [inline, inherited] |
This is the const version of leftCols(Index).
ColsBlockXpr leftCols | ( | Index | n | ) | [inline, inherited] |
n | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.leftCols(2):" << endl; cout << a.leftCols(2) << endl; a.leftCols(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols(2): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced | ( | const Scalar & | low, | |
const Scalar & | high | |||
) | [inline, static, inherited] |
Sets a linearly space vector. The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
cout << VectorXi::LinSpaced(4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , | |
const Scalar & | low, | |||
const Scalar & | high | |||
) | [inline, static, inherited] |
Sets a linearly space vector. The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.When size is set to 1, a vector of length 1 containing 'high' is returned.This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.Example:
cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced | ( | Index | size, | |
const Scalar & | low, | |||
const Scalar & | high | |||
) | [inline, static, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << VectorXi::LinSpaced(4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , | |
Index | size, | |||
const Scalar & | low, | |||
const Scalar & | high | |||
) | [inline, static, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
const LLT< typename MatrixBase< Derived >::PlainObject > llt | ( | ) | const [inline] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
Synonym of partialPivLu().
*this
.References DenseBase< Derived >::eval().
void makeHouseholder | ( | EssentialPart & | essential, | |
Scalar & | tau, | |||
RealScalar & | beta | |||
) | const [inline] |
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 MatrixBase< Derived >::real(), and DenseBase< Derived >::tail().
Referenced by MatrixBase< Derived >::makeHouseholderInPlace().
void makeHouseholderInPlace | ( | Scalar & | tau, | |
RealScalar & | beta | |||
) | [inline] |
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 |
References MatrixBase< Derived >::makeHouseholder().
internal::traits< Derived >::Scalar maxCoeff | ( | IndexType * | index | ) | const [inline, inherited] |
*this
contains NaN.References DenseBase< Derived >::RowsAtCompileTime, and DenseBase< Derived >::visit().
internal::traits< Derived >::Scalar maxCoeff | ( | IndexType * | rowPtr, | |
IndexType * | colPtr | |||
) | const [inline, inherited] |
*this
contains NaN.References DenseBase< Derived >::visit().
internal::traits< Derived >::Scalar maxCoeff | ( | ) | const [inline, inherited] |
*this
. *this
contains NaN. internal::traits< Derived >::Scalar mean | ( | ) | const [inline, inherited] |
This is the const version of middleCols<int>().
N | the number of columns in the block as specified at compile-time |
startCol | the index of the first column in the block | |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(:,1..3) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
This is the const version of middleCols(Index,Index).
startCol | the index of the first column in the block | |
numCols | the number of columns in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
This is the const version of middleRows<int>().
N | the number of rows in the block as specified at compile-time |
startRow | the index of the first row in the block | |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6
This is the const version of middleRows(Index,Index).
startRow | the index of the first row in the block | |
n | the number of rows in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(2..3,:) = 6 6 -3 5 -8 6 -5 0 -8 6
internal::traits< Derived >::Scalar minCoeff | ( | IndexType * | index | ) | const [inline, inherited] |
*this
contains NaN.References DenseBase< Derived >::RowsAtCompileTime, and DenseBase< Derived >::visit().
internal::traits< Derived >::Scalar minCoeff | ( | IndexType * | rowId, | |
IndexType * | colId | |||
) | const [inline, inherited] |
*this
contains NaN.References DenseBase< Derived >::visit().
internal::traits< Derived >::Scalar minCoeff | ( | ) | const [inline, inherited] |
*this
. *this
contains NaN. const NestByValue< Derived > nestByValue | ( | ) | const [inline, inherited] |
NoAlias< Derived, MatrixBase > noalias | ( | ) | [inline] |
*this
with an operator= assuming no aliasing between *this
and the source expression.More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.
Here are some examples where noalias is usefull:
D.noalias() = A * B; D.noalias() += A.transpose() * B; D.noalias() -= 2 * A * B.adjoint();
On the other hand the following example will lead to a wrong result:
A.noalias() = A * B;
because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:
A = A * B;
Index nonZeros | ( | ) | const [inline, inherited] |
NumTraits< typename internal::traits< Derived >::Scalar >::Real norm | ( | ) | const [inline] |
*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 MatrixBase< Derived >::squaredNorm().
Referenced by MatrixBase< Derived >::normalize().
void normalize | ( | ) | [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.
References MatrixBase< Derived >::norm().
const MatrixBase< Derived >::PlainObject normalized | ( | ) | const [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().
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | const CustomNullaryOp & | func | ) | [inline, static, inherited] |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::ColsAtCompileTime, and DenseBase< Derived >::RowsAtCompileTime.
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | Index | size, | |
const CustomNullaryOp & | func | |||
) | [inline, static, inherited] |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::RowsAtCompileTime.
const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr | ( | Index | rows, | |
Index | cols, | |||
const CustomNullaryOp & | func | |||
) | [inline, static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
Referenced by DenseBase< Derived >::Constant(), MatrixBase< Derived >::Identity(), DenseBase< Derived >::LinSpaced(), DenseBase< Derived >::Random(), and DenseBase< Derived >::setLinSpaced().
const DenseBase< Derived >::ConstantReturnType Ones | ( | ) | [inline, static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << Matrix2d::Ones() << endl; cout << 6 * RowVector4i::Ones() << endl;
Output:
1 1 1 1 6 6 6 6
References DenseBase< Derived >::Constant().
The parameter newSize is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
cout << 6 * RowVectorXi::Ones(4) << endl; cout << VectorXf::Ones(2) << endl;
Output:
6 6 6 6 1 1
References DenseBase< Derived >::Constant().
const DenseBase< Derived >::ConstantReturnType Ones | ( | Index | nbRows, | |
Index | nbCols | |||
) | [inline, static, inherited] |
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
cout << MatrixXi::Ones(2,3) << endl;
Output:
1 1 1 1 1 1
References DenseBase< Derived >::Constant().
bool operator!= | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other are not exactly equal to each other. MatrixBase< Derived >::ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const [inline] |
Concatenates a linear transformation matrix and a uniform scaling
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* | ( | const DiagonalBase< DiagonalDerived > & | a_diagonal | ) | const [inline] |
*this
by the diagonal matrix diagonal. const ProductReturnType< Derived, OtherDerived >::Type operator* | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other.const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> operator* | ( | const std::complex< Scalar > & | scalar | ) | const [inline] |
Overloaded for efficient real matrix times complex scalar value
const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar | ) | const [inline] |
*this
scaled by the scalar factor scalar Derived & operator*= | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
* other.
*this
Example:
Matrix3f A = Matrix3f::Random(3,3), B; B << 0,1,0, 0,0,1, 1,0,0; cout << "At start, A = " << endl << A << endl; A *= B; cout << "After A *= B, A = " << endl << A << endl; A.applyOnTheRight(B); // equivalent to A *= B cout << "After applyOnTheRight, A = " << endl << A << endl;
Output:
At start, A = 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 After A *= B, A = -0.33 0.68 0.597 0.536 -0.211 0.823 -0.444 0.566 -0.605 After applyOnTheRight, A = 0.597 -0.33 0.68 0.823 0.536 -0.211 -0.605 -0.444 0.566
const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Derived, const OtherDerived> operator+ | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other Derived & operator+= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
+ other.
*this
const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const Derived, const OtherDerived> operator- | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> operator- | ( | ) | const [inline] |
*this
Derived & operator-= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
- other.
*this
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> operator/ | ( | const Scalar & | scalar | ) | const [inline] |
*this
divided by the scalar value scalar CommaInitializer< Derived > operator<< | ( | const DenseBase< OtherDerived > & | other | ) | [inline, inherited] |
CommaInitializer< Derived > operator<< | ( | const Scalar & | s | ) | [inline, inherited] |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Matrix3i m1; m1 << 1, 2, 3, 4, 5, 6, 7, 8, 9; cout << m1 << endl << endl; Matrix3i m2 = Matrix3i::Identity(); m2.block(0,0, 2,2) << 10, 11, 12, 13; cout << m2 << endl << endl; Vector2i v1; v1 << 14, 15; m2 << v1.transpose(), 16, v1, m1.block(1,1,2,2); cout << m2 << endl;
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
Derived & operator= | ( | const EigenBase< OtherDerived > & | other | ) | [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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
References EigenBase< Derived >::derived().
Derived & operator= | ( | const MatrixBase< Derived > & | other | ) | [inline] |
Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)
Reimplemented from DenseBase< Derived >.
bool operator== | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other are all exactly equal. MatrixBase< Derived >::RealScalar operatorNorm | ( | ) | const [inline] |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix is defined to be
where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix .
The current implementation uses the eigenvalues of , as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
MatrixXd ones = MatrixXd::Ones(3,3); cout << "The operator norm of the 3x3 matrix of ones is " << ones.operatorNorm() << endl;
Output:
The operator norm of the 3x3 matrix of ones is 3
References MatrixBase< Derived >::eigenvalues(), and DenseBase< Derived >::eval().
Index outerSize | ( | ) | const [inline, inherited] |
rows()==1 || cols()==1
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > partialPivLu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.References DenseBase< Derived >::eval().
internal::traits< Derived >::Scalar prod | ( | ) | const [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
References DenseBase< Derived >::SizeAtCompileTime.
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | ) | [inline, static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << 100 * Matrix2i::Random() << endl;
Output:
700 600 -200 600
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.
Referenced by DenseBase< Derived >::setRandom().
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | Index | size | ) | [inline, static, inherited] |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
cout << VectorXi::Random(2) << endl;
Output:
7 -2
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
References DenseBase< Derived >::NullaryExpr().
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random | ( | Index | rows, | |
Index | cols | |||
) | [inline, static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
cout << MatrixXi::Random(2,3) << endl;
Output:
7 6 9 -2 6 -6
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
References DenseBase< Derived >::NullaryExpr().
NonConstRealReturnType real | ( | ) | [inline] |
*this
.RealReturnType real | ( | ) | const [inline] |
*this
.Referenced by MatrixBase< Derived >::makeHouseholder(), and MatrixBase< Derived >::squaredNorm().
const DenseBase< Derived >::ReplicateReturnType replicate | ( | Index | rowFactor, | |
Index | colFactor | |||
) | const [inline, inherited] |
*this
Example:
Vector3i v = Vector3i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "v.replicate(2,5) = ..." << endl; cout << v.replicate(2,5) << endl;
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
const Replicate< Derived, RowFactor, ColFactor > replicate | ( | ) | const [inline, inherited] |
*this
Example:
MatrixXi m = MatrixXi::Random(2,3); cout << "Here is the matrix m:" << endl << m << endl; cout << "m.replicate<3,2>() = ..." << endl; cout << m.replicate<3,2>() << endl;
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
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 ArrayWrapper< ExpressionType >, MatrixWrapper< ExpressionType >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
void resize | ( | Index | newSize | ) | [inline, inherited] |
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 ArrayWrapper< ExpressionType >, MatrixWrapper< ExpressionType >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
const DenseBase< Derived >::ConstReverseReturnType reverse | ( | ) | const [inline, inherited] |
This is the const version of reverse().
DenseBase< Derived >::ReverseReturnType reverse | ( | ) | [inline, inherited] |
Example:
MatrixXi m = MatrixXi::Random(3,4); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the reverse of m:" << endl << m.reverse() << endl; cout << "Here is the coefficient (1,0) in the reverse of m:" << endl << m.reverse()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 4." << endl; m.reverse()(1,0) = 4; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
void reverseInPlace | ( | ) | [inline, inherited] |
This is the "in place" version of reverse: it reverses *this
.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
m = m.reverse().eval();
ConstNColsBlockXpr<N>::Type rightCols | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of rightCols<int>().
NColsBlockXpr<N>::Type rightCols | ( | Index | n = N |
) | [inline, inherited] |
N | the number of columns in the block as specified at compile-time |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.rightCols<2>():" << endl; cout << a.rightCols<2>() << endl; a.rightCols<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols<2>(): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
ConstColsBlockXpr rightCols | ( | Index | n | ) | const [inline, inherited] |
This is the const version of rightCols(Index).
ColsBlockXpr rightCols | ( | Index | n | ) | [inline, inherited] |
n | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.rightCols(2):" << endl; cout << a.rightCols(2) << endl; a.rightCols(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols(2): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
RowXpr row | ( | Index | i | ) | [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Identity(); m.row(1) = Vector3d(4,5,6); cout << m << endl;
Output:
1 0 0 4 5 6 0 0 1
Referenced by MatrixBase< Derived >::applyHouseholderOnTheLeft(), MatrixBase< Derived >::applyOnTheLeft(), and Transform< _Scalar, _Dim, _Mode, _Options >::pretranslate().
DenseBase< Derived >::RowwiseReturnType rowwise | ( | ) | [inline, inherited] |
const DenseBase< Derived >::ConstRowwiseReturnType rowwise | ( | ) | const [inline, inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; cout << "Here is the maximum absolute value of each row:" << endl << m.cwiseAbs().rowwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
Referenced by Eigen::umeyama().
This is the const version of segment<int>(Index).
*this
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
N | the number of coefficients in the segment as specified at compile-time |
start | the index of the first element in the segment | |
n | the number of coefficients in the segment as specified at compile-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl; v.segment<2>(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
This is the const version of segment(Index,Index).
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 | |
n | the number of coefficients in the segment |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl; v.segment(1, 2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
Referenced by MatrixBase< Derived >::stableNorm().
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > select | ( | const typename ElseDerived::Scalar & | thenScalar, | |
const DenseBase< ElseDerived > & | elseMatrix | |||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
References DenseBase< Derived >::Constant().
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > select | ( | const DenseBase< ThenDerived > & | thenMatrix, | |
const typename ThenDerived::Scalar & | elseScalar | |||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
References DenseBase< Derived >::Constant().
Derived & setConstant | ( | const Scalar & | val | ) | [inline, inherited] |
Sets all coefficients in this expression to value.
References DenseBase< Derived >::Constant().
Referenced by DenseBase< Derived >::fill(), DenseBase< Derived >::setOnes(), and DenseBase< Derived >::setZero().
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
nbRows | the new number of rows | |
nbCols | the new number of columns |
Example:
MatrixXf m; m.setIdentity(3, 3); cout << m << endl;
Output:
1 0 0 0 1 0 0 0 1
References MatrixBase< Derived >::setIdentity().
Derived & setIdentity | ( | ) | [inline] |
Writes the identity expression (not necessarily square) into *this.
Example:
Matrix4i m = Matrix4i::Zero(); m.block<3,3>(1,0).setIdentity(); cout << m << endl;
Output:
0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity(), and MatrixBase< Derived >::setIdentity().
Derived & setLinSpaced | ( | const Scalar & | low, | |
const Scalar & | high | |||
) | [inline, inherited] |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
References DenseBase< Derived >::setLinSpaced().
Derived & setLinSpaced | ( | Index | newSize, | |
const Scalar & | low, | |||
const Scalar & | high | |||
) | [inline, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
VectorXf v; v.setLinSpaced(5,0.5f,1.5f); cout << v << endl;
Output:
0.5 0.75 1 1.25 1.5
References DenseBase< Derived >::NullaryExpr().
Referenced by DenseBase< Derived >::setLinSpaced().
Derived & setOnes | ( | ) | [inline, inherited] |
Sets all coefficients in this expression to one.
Example:
Matrix4i m = Matrix4i::Random(); m.row(1).setOnes(); cout << m << endl;
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
References DenseBase< Derived >::setConstant().
Derived & setRandom | ( | ) | [inline, inherited] |
Sets all coefficients in this expression to random values.
Example:
Matrix4i m = Matrix4i::Zero(); m.col(1).setRandom(); cout << m << endl;
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
References DenseBase< Derived >::Random().
Derived & setZero | ( | ) | [inline, inherited] |
Sets all coefficients in this expression to zero.
Example:
Matrix4i m = Matrix4i::Random(); m.row(1).setZero(); cout << m << endl;
Output:
7 9 -5 -3 0 0 0 0 6 -3 0 9 6 6 3 9
References DenseBase< Derived >::setConstant().
NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm | ( | ) | const [inline] |
*this
, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this
with itself.References MatrixBase< Derived >::real().
Referenced by MatrixBase< Derived >::norm().
NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm | ( | ) | const [inline] |
*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, DenseBase< Derived >::Flags, DenseBase< Derived >::head(), and DenseBase< Derived >::segment().
internal::traits< Derived >::Scalar sum | ( | ) | const [inline, inherited] |
References DenseBase< Derived >::SizeAtCompileTime.
void swap | ( | PlainObjectBase< OtherDerived > & | other | ) | [inline, inherited] |
swaps *this with the matrix or array other.
void swap | ( | const DenseBase< OtherDerived > & | other, | |
int | = OtherDerived::ThisConstantIsPrivateInPlainObjectBase | |||
) | [inline, inherited] |
swaps *this with the expression other.
ConstFixedSegmentReturnType<N>::Type tail | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of tail<int>.
FixedSegmentReturnType<N>::Type tail | ( | Index | n = N |
) | [inline, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
N | the number of coefficients in the segment as specified at compile-time |
n | the number of coefficients in the segment as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl; v.tail<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
ConstSegmentReturnType tail | ( | Index | n | ) | const [inline, inherited] |
This is the const version of tail(Index).
SegmentReturnType tail | ( | Index | n | ) | [inline, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
n | the number of coefficients in the segment |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail(2) << endl; v.tail(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
Referenced by MatrixBase< Derived >::makeHouseholder().
const Block<const Derived, CRows, CCols> topLeftCorner | ( | Index | cRows, | |
Index | cCols | |||
) | const [inline, inherited] |
This is the const version of topLeftCorner<int, int>(Index, Index).
CRows | number of rows in corner as specified at compile-time | |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time | |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner<2,Dynamic>(2,2):" << endl; cout << m.topLeftCorner<2,Dynamic>(2,2) << endl; m.topLeftCorner<2,Dynamic>(2,2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,Dynamic>(2,2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const Derived, CRows, CCols> topLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of topLeftCorner<int, int>().
Block<Derived, CRows, CCols> topLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner<2,2>():" << endl; cout << m.topLeftCorner<2,2>() << endl; m.topLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
This is the const version of topLeftCorner(Index, Index).
cRows | the number of rows in the corner | |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner(2, 2):" << endl; cout << m.topLeftCorner(2, 2) << endl; m.topLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const Derived, CRows, CCols> topRightCorner | ( | Index | cRows, | |
Index | cCols | |||
) | const [inline, inherited] |
This is the const version of topRightCorner<int, int>(Index, Index).
CRows | number of rows in corner as specified at compile-time | |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time | |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner<2,Dynamic>(2,2):" << endl; cout << m.topRightCorner<2,Dynamic>(2,2) << endl; m.topRightCorner<2,Dynamic>(2,2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,Dynamic>(2,2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
const Block<const Derived, CRows, CCols> topRightCorner | ( | ) | const [inline, inherited] |
This is the const version of topRightCorner<int, int>().
Block<Derived, CRows, CCols> topRightCorner | ( | ) | [inline, inherited] |
CRows | the number of rows in the corner | |
CCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner<2,2>():" << endl; cout << m.topRightCorner<2,2>() << endl; m.topRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
This is the const version of topRightCorner(Index, Index).
cRows | the number of rows in the corner | |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner(2, 2):" << endl; cout << m.topRightCorner(2, 2) << endl; m.topRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
ConstNRowsBlockXpr<N>::Type topRows | ( | Index | n = N |
) | const [inline, inherited] |
This is the const version of topRows<int>().
NRowsBlockXpr<N>::Type topRows | ( | Index | n = N |
) | [inline, inherited] |
N | the number of rows in the block as specified at compile-time |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.topRows<2>():" << endl; cout << a.topRows<2>() << endl; a.topRows<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows<2>(): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
ConstRowsBlockXpr topRows | ( | Index | n | ) | const [inline, inherited] |
This is the const version of topRows(Index).
RowsBlockXpr topRows | ( | Index | n | ) | [inline, inherited] |
n | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.topRows(2):" << endl; cout << a.topRows(2) << endl; a.topRows(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows(2): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
internal::traits< Derived >::Scalar trace | ( | ) | const [inline] |
*this
, i.e. the sum of the coefficients on the main diagonal.*this
can be any matrix, not necessarily square.
Reimplemented from DenseBase< Derived >.
DenseBase< Derived >::ConstTransposeReturnType transpose | ( | ) | const [inline, inherited] |
This is the const version of transpose().
Make sure you read the warning for transpose() !
Transpose< Derived > transpose | ( | ) | [inline, inherited] |
Example:
Matrix2i m = Matrix2i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the transpose of m:" << endl << m.transpose() << endl; cout << "Here is the coefficient (1,0) in the transpose of m:" << endl << m.transpose()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 0." << endl; m.transpose()(1,0) = 0; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
m = m.transpose(); // bug!!! caused by aliasing effect
m.transposeInPlace();
m = m.transpose().eval();
Referenced by MatrixBase< Derived >::adjoint().
void transposeInPlace | ( | ) | [inline, inherited] |
This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
m.transposeInPlace();
has the same effect on m as doing
m = m.transpose().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this
must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.References DenseBase< Derived >::ColsAtCompileTime, and DenseBase< Derived >::RowsAtCompileTime.
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView | ( | ) | const [inline] |
This is the const version of MatrixBase::triangularView()
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView | ( | ) | [inline] |
The parameter Mode can have the following values: Upper
, StrictlyUpper
, UnitUpper
, Lower
, StrictlyLower
, UnitLower
.
Example:
#ifndef _MSC_VER #warning deprecated #endif /* deprecated Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the upper-triangular matrix extracted from m:" << endl << m.part<Eigen::UpperTriangular>() << endl; cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl << m.part<Eigen::StrictlyUpperTriangular>() << endl; cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl << m.part<Eigen::UnitLowerTriangular>() << endl; */
Output:
const CwiseUnaryOp<CustomUnaryOp, const Derived> unaryExpr | ( | const CustomUnaryOp & | func = CustomUnaryOp() |
) | const [inline] |
Apply a unary operator coefficient-wise.
[in] | func | Functor implementing the unary operator |
CustomUnaryOp | Type of func |
The function ptr_fun()
from the C++ standard library can be used to make functors out of normal functions.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define function to be applied coefficient-wise double ramp(double x) { if (x > 0) return x; else return 0; } int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.68 0.823 0 0 0 0 0.108 0.0268 0.566 0 0 0.904 0.597 0.536 0.258 0.832
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
const CwiseUnaryView<CustomViewOp, const Derived> unaryViewExpr | ( | const CustomViewOp & | func = CustomViewOp() |
) | const [inline] |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | i | ) | [inline, static] |
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.
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | newSize, | |
Index | i | |||
) | [inline, static] |
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 MatrixBase< Derived >::UnitW(), MatrixBase< Derived >::UnitX(), MatrixBase< Derived >::UnitY(), and MatrixBase< Derived >::UnitZ().
MatrixBase< Derived >::PlainObject unitOrthogonal | ( | void | ) | const [inline] |
*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().
const MatrixBase< Derived >::BasisReturnType UnitW | ( | ) | [inline, static] |
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 MatrixBase< Derived >::Unit().
const MatrixBase< Derived >::BasisReturnType UnitX | ( | ) | [inline, static] |
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 MatrixBase< Derived >::Unit().
const MatrixBase< Derived >::BasisReturnType UnitY | ( | ) | [inline, static] |
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 MatrixBase< Derived >::Unit().
const MatrixBase< Derived >::BasisReturnType UnitZ | ( | ) | [inline, static] |
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 MatrixBase< Derived >::Unit().
CoeffReturnType value | ( | ) | const [inline, inherited] |
void visit | ( | Visitor & | visitor | ) | const [inline, inherited] |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
struct MyVisitor { // called for the first coefficient void init(const Scalar& value, Index i, Index j); // called for all other coefficients void operator() (const Scalar& value, Index i, Index j); };
References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.
Referenced by DenseBase< Derived >::maxCoeff(), and DenseBase< Derived >::minCoeff().
const DenseBase< Derived >::ConstantReturnType Zero | ( | ) | [inline, static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << Matrix2d::Zero() << endl; cout << RowVector4i::Zero() << endl;
Output:
0 0 0 0 0 0 0 0
References DenseBase< Derived >::Constant().
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
cout << RowVectorXi::Zero(4) << endl; cout << VectorXf::Zero(2) << endl;
Output:
0 0 0 0 0 0
References DenseBase< Derived >::Constant().
const DenseBase< Derived >::ConstantReturnType Zero | ( | Index | nbRows, | |
Index | nbCols | |||
) | [inline, static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
cout << MatrixXi::Zero(2,3) << endl;
Output:
0 0 0 0 0 0
References DenseBase< Derived >::Constant().