Expression of one (or a set of) homogeneous vector(s) More...
#include <Homogeneous.h>
Inheritance diagram for Homogeneous< MatrixType, _Direction >:Public Types | |
| typedef internal::traits< Homogeneous< MatrixType, _Direction > >::Index | Index |
| The type of indices. | |
| typedef Matrix< typename internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar, internal::traits< Homogeneous< MatrixType, _Direction > >::RowsAtCompileTime, internal::traits< Homogeneous< MatrixType, _Direction > >::ColsAtCompileTime, AutoAlign|(internal::traits< Homogeneous< MatrixType, _Direction > >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Homogeneous< MatrixType, _Direction > >::MaxRowsAtCompileTime, internal::traits< Homogeneous< MatrixType, _Direction > >::MaxColsAtCompileTime > | PlainObject |
| The plain matrix type corresponding to this expression. | |
Public Member Functions | |
| const AdjointReturnType | adjoint () const |
| void | adjointInPlace () |
| bool | all (void) const |
| bool | any (void) const |
| void | applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
| void | applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
| void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
| void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
| void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
| void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
| ArrayWrapper< Homogeneous< MatrixType, _Direction > > | array () |
| const DiagonalWrapper< const Homogeneous< MatrixType, _Direction > > | asDiagonal () const |
| const CwiseBinaryOp< CustomBinaryOp, const Homogeneous< MatrixType, _Direction >, const OtherDerived > | binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
| Block< Homogeneous< MatrixType, _Direction >, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
| const Block< const Homogeneous< MatrixType, _Direction >, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
| Block< Homogeneous< MatrixType, _Direction > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
| const Block< const Homogeneous< MatrixType, _Direction > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
| RealScalar | blueNorm () const |
| Block< Homogeneous< MatrixType, _Direction >, CRows, CCols > | bottomLeftCorner () |
| const Block< const Homogeneous< MatrixType, _Direction >, CRows, CCols > | bottomLeftCorner () const |
| Block< Homogeneous< MatrixType, _Direction > > | bottomLeftCorner (Index cRows, Index cCols) |
| const Block< const Homogeneous< MatrixType, _Direction > > | bottomLeftCorner (Index cRows, Index cCols) const |
| Block< Homogeneous< MatrixType, _Direction >, CRows, CCols > | bottomRightCorner () |
| const Block< const Homogeneous< MatrixType, _Direction >, CRows, CCols > | bottomRightCorner () const |
| Block< Homogeneous< MatrixType, _Direction > > | bottomRightCorner (Index cRows, Index cCols) |
| const Block< const Homogeneous< MatrixType, _Direction > > | bottomRightCorner (Index cRows, Index cCols) const |
| NRowsBlockXpr< N >::Type | bottomRows () |
| ConstNRowsBlockXpr< N >::Type | bottomRows () const |
| RowsBlockXpr | bottomRows (Index n) |
| ConstRowsBlockXpr | bottomRows (Index n) const |
| internal::cast_return_type< Homogeneous< MatrixType, _Direction >, constCwiseUnaryOp< internal::scalar_cast_op< typenameinternal::traits< Homogeneous< MatrixType, _Direction > >::Scalar, NewType >, constDerived > >::type | cast () const |
| ColXpr | col (Index i) |
| ConstColXpr | col (Index i) const |
| const ColPivHouseholderQR< PlainObject > | colPivHouseholderQr () const |
| ColwiseReturnType | colwise () |
| ConstColwiseReturnType | colwise () const |
| void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
| void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
| ConjugateReturnType | conjugate () const |
| Index | count () const |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template cross_product_return_type< OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template cross_product_return_type< OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
| PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
| const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Homogeneous< MatrixType, _Direction > > | cwiseAbs () const |
| const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const Homogeneous< MatrixType, _Direction > > | cwiseAbs2 () const |
| const CwiseUnaryOp< std::binder1st< std::equal_to< Scalar > >, const Homogeneous< MatrixType, _Direction > > | cwiseEqual (const Scalar &s) const |
| const CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const Homogeneous< MatrixType, _Direction > > | cwiseInverse () const |
| const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const Homogeneous< MatrixType, _Direction > > | cwiseSqrt () const |
| Scalar | determinant () const |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template DiagonalIndexReturnType< Index >::Type | diagonal () |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template DiagonalIndexReturnType< Index >::Type | diagonal () |
| DiagonalReturnType | diagonal () |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template ConstDiagonalIndexReturnType< Index >::Type | diagonal () const |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template ConstDiagonalIndexReturnType< Index >::Type | diagonal () const |
| const ConstDiagonalReturnType | diagonal () const |
| DiagonalIndexReturnType< Dynamic >::Type | diagonal (Index index) |
| ConstDiagonalIndexReturnType< Dynamic >::Type | diagonal (Index index) const |
| Index | diagonalSize () const |
| internal::scalar_product_traits< typenameinternal::traits< Homogeneous< MatrixType, _Direction > >::Scalar, typenameinternal::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) |
| const Flagged< Homogeneous< MatrixType, _Direction >, Added, Removed > | flagged () const |
| ForceAlignedAccess< Homogeneous< MatrixType, _Direction > > | forceAlignedAccess () |
| const ForceAlignedAccess< Homogeneous< MatrixType, _Direction > > | forceAlignedAccess () const |
| internal::conditional< Enable, ForceAlignedAccess< Homogeneous< MatrixType, _Direction > >, Homogeneous< MatrixType, _Direction > & >::type | forceAlignedAccessIf () |
| internal::add_const_on_value_type< typenameinternal::conditional< Enable, ForceAlignedAccess< Homogeneous< MatrixType, _Direction > >, Homogeneous< MatrixType, _Direction > & >::type >::type | forceAlignedAccessIf () const |
| const WithFormat< Homogeneous< MatrixType, _Direction > > | format (const IOFormat &fmt) const |
| const FullPivHouseholderQR< PlainObject > | fullPivHouseholderQr () const |
| const FullPivLU< PlainObject > | fullPivLu () const |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template FixedSegmentReturnType< Size >::Type | head () |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template ConstFixedSegmentReturnType< Size >::Type | head () const |
| SegmentReturnType | head (Index size) |
| DenseBase::ConstSegmentReturnType | head (Index size) const |
| 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< Homogeneous< MatrixType, _Direction > > | inverse () const |
| bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const |
| bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| JacobiSVD< PlainObject > | jacobiSvd (unsigned int computationOptions=0) const |
| const LazyProductReturnType< Homogeneous< MatrixType, _Direction >, OtherDerived >::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
| const LDLT< PlainObject > | ldlt () const |
| NColsBlockXpr< N >::Type | leftCols () |
| ConstNColsBlockXpr< N >::Type | leftCols () const |
| ColsBlockXpr | leftCols (Index n) |
| ConstColsBlockXpr | leftCols (Index n) const |
| const LLT< PlainObject > | llt () const |
| NumTraits< typenameinternal::traits< Homogeneous< MatrixType, _Direction > >::Scalar >::Real | lpNorm () const |
| NumTraits< typenameinternal::traits< Homogeneous< MatrixType, _Direction > >::Scalar >::Real | lpNorm () const |
| const PartialPivLU< PlainObject > | lu () const |
| void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
| void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | maxCoeff () const |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | maxCoeff (IndexType *index) const |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
| Scalar | mean () const |
| NColsBlockXpr< N >::Type | middleCols (Index startCol) |
| ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
| ColsBlockXpr | middleCols (Index startCol, Index numCols) |
| ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
| NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
| ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
| RowsBlockXpr | middleRows (Index startRow, Index numRows) |
| ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | minCoeff () const |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | minCoeff (IndexType *index) const |
| internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
| const NestByValue< Homogeneous< MatrixType, _Direction > > | nestByValue () const |
| NoAlias< Homogeneous< MatrixType, _Direction >, Eigen::MatrixBase > | noalias () |
| Index | nonZeros () const |
| RealScalar | norm () const |
| void | normalize () |
| const PlainObject | normalized () const |
| bool | operator!= (const MatrixBase< OtherDerived > &other) const |
| const DiagonalProduct< Homogeneous< MatrixType, _Direction >, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
| const ProductReturnType< Homogeneous< MatrixType, _Direction >, OtherDerived >::Type | operator* (const MatrixBase< OtherDerived > &other) const |
| const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
| const CwiseUnaryOp< internal::scalar_multiple2_op< Scalar, std::complex< Scalar > >, const Homogeneous< MatrixType, _Direction > > | operator* (const std::complex< Scalar > &scalar) const |
| ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
| Homogeneous< MatrixType, _Direction > & | operator*= (const EigenBase< OtherDerived > &other) |
| Homogeneous< MatrixType, _Direction > & | operator+= (const MatrixBase< OtherDerived > &other) |
| const CwiseUnaryOp< internal::scalar_opposite_op< typename internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar >, const Homogeneous< MatrixType, _Direction > > | operator- () const |
| Homogeneous< MatrixType, _Direction > & | operator-= (const MatrixBase< OtherDerived > &other) |
| const CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< Homogeneous< MatrixType, _Direction > >::Scalar >, const Homogeneous< MatrixType, _Direction > > | operator/ (const Scalar &scalar) const |
| CommaInitializer< Homogeneous< MatrixType, _Direction > > | operator<< (const DenseBase< OtherDerived > &other) |
| CommaInitializer< Homogeneous< MatrixType, _Direction > > | operator<< (const Scalar &s) |
| 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 |
| internal::result_of< Func(typenameinternal::traits< Homogeneous< MatrixType, _Direction > >::Scalar)>::type | redux (const Func &func) const |
| const Replicate< Homogeneous< MatrixType, _Direction >, RowFactor, ColFactor > | replicate () const |
| const Replicate< Homogeneous< MatrixType, _Direction >, Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
| void | resize (Index rows, Index cols) |
| void | resize (Index size) |
| ReverseReturnType | reverse () |
| ConstReverseReturnType | reverse () const |
| void | reverseInPlace () |
| NColsBlockXpr< N >::Type | rightCols () |
| ConstNColsBlockXpr< N >::Type | rightCols () const |
| ColsBlockXpr | rightCols (Index n) |
| ConstColsBlockXpr | rightCols (Index n) const |
| RowXpr | row (Index i) |
| ConstRowXpr | row (Index i) const |
| RowwiseReturnType | rowwise () |
| ConstRowwiseReturnType | rowwise () const |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template FixedSegmentReturnType< Size >::Type | segment (Index start) |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template ConstFixedSegmentReturnType< Size >::Type | segment (Index start) const |
| SegmentReturnType | segment (Index start, Index size) |
| DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
| const Select< Homogeneous< MatrixType, _Direction >, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
| const Select< Homogeneous< MatrixType, _Direction >, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
| const Select< Homogeneous< MatrixType, _Direction >, typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
| Homogeneous< MatrixType, _Direction > & | setConstant (const Scalar &value) |
| Homogeneous< MatrixType, _Direction > & | setIdentity () |
| Homogeneous< MatrixType, _Direction > & | setIdentity (Index rows, Index cols) |
| Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
| Homogeneous< MatrixType, _Direction > & | setLinSpaced (const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| Homogeneous< MatrixType, _Direction > & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| Homogeneous< MatrixType, _Direction > & | setOnes () |
| Homogeneous< MatrixType, _Direction > & | setRandom () |
| Homogeneous< MatrixType, _Direction > & | setZero () |
| RealScalar | squaredNorm () const |
| RealScalar | stableNorm () const |
| Scalar | sum () const |
| void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
| void | swap (PlainObjectBase< OtherDerived > &other) |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template FixedSegmentReturnType< Size >::Type | tail () |
| DenseBase< Homogeneous< MatrixType, _Direction > >::template ConstFixedSegmentReturnType< Size >::Type | tail () const |
| SegmentReturnType | tail (Index size) |
| DenseBase::ConstSegmentReturnType | tail (Index size) const |
| Block< Homogeneous< MatrixType, _Direction >, CRows, CCols > | topLeftCorner () |
| const Block< const Homogeneous< MatrixType, _Direction >, CRows, CCols > | topLeftCorner () const |
| Block< Homogeneous< MatrixType, _Direction > > | topLeftCorner (Index cRows, Index cCols) |
| const Block< const Homogeneous< MatrixType, _Direction > > | topLeftCorner (Index cRows, Index cCols) const |
| Block< Homogeneous< MatrixType, _Direction >, CRows, CCols > | topRightCorner () |
| const Block< const Homogeneous< MatrixType, _Direction >, CRows, CCols > | topRightCorner () const |
| Block< Homogeneous< MatrixType, _Direction > > | topRightCorner (Index cRows, Index cCols) |
| const Block< const Homogeneous< MatrixType, _Direction > > | topRightCorner (Index cRows, Index cCols) const |
| NRowsBlockXpr< N >::Type | topRows () |
| ConstNRowsBlockXpr< N >::Type | topRows () const |
| RowsBlockXpr | topRows (Index n) |
| ConstRowsBlockXpr | topRows (Index n) const |
| Scalar | trace () const |
| Eigen::Transpose< Homogeneous< MatrixType, _Direction > > | transpose () |
| ConstTransposeReturnType | transpose () const |
| void | transposeInPlace () |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template TriangularViewReturnType< Mode >::Type | triangularView () |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template TriangularViewReturnType< Mode >::Type | triangularView () |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template ConstTriangularViewReturnType< Mode >::Type | triangularView () const |
| MatrixBase< Homogeneous< MatrixType, _Direction > >::template ConstTriangularViewReturnType< Mode >::Type | triangularView () const |
| const CwiseUnaryOp< CustomUnaryOp, const Homogeneous< MatrixType, _Direction > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
| Apply a unary operator coefficient-wise. | |
| const CwiseUnaryView< CustomViewOp, const Homogeneous< MatrixType, _Direction > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
| PlainObject | unitOrthogonal (void) const |
| CoeffReturnType | value () const |
| void | visit (Visitor &func) const |
Static Public Member Functions | |
| static const ConstantReturnType | Constant (const Scalar &value) |
| static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
| static const ConstantReturnType | Constant (Index size, const Scalar &value) |
| static const IdentityReturnType | Identity () |
| static const IdentityReturnType | Identity (Index rows, Index cols) |
| static const RandomAccessLinSpacedReturnType | LinSpaced (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, const Scalar &low, const Scalar &high) |
| static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| static const CwiseNullaryOp< CustomNullaryOp, Homogeneous< MatrixType, _Direction > > | NullaryExpr (const CustomNullaryOp &func) |
| static const CwiseNullaryOp< CustomNullaryOp, Homogeneous< MatrixType, _Direction > > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
| static const CwiseNullaryOp< CustomNullaryOp, Homogeneous< MatrixType, _Direction > > | NullaryExpr (Index size, const CustomNullaryOp &func) |
| static const ConstantReturnType | Ones () |
| static const ConstantReturnType | Ones (Index rows, Index cols) |
| static const ConstantReturnType | Ones (Index size) |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Homogeneous< MatrixType, _Direction > > | Random () |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Homogeneous< MatrixType, _Direction > > | Random (Index rows, Index cols) |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Homogeneous< MatrixType, _Direction > > | Random (Index size) |
| 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 rows, Index cols) |
| static const ConstantReturnType | Zero (Index size) |
Related Symbols | |
(Note that these are not member symbols.) | |
| std::ostream & | operator<< (std::ostream &s, const DenseBase< Homogeneous< MatrixType, _Direction > > &m) |
Expression of one (or a set of) homogeneous vector(s)
This is defined in the Geometry module.
| MatrixType | the type of the object in which we are making homogeneous |
This class represents an expression of one (or a set of) homogeneous vector(s). It is the return type of MatrixBase::homogeneous() and most of the time this is the only way it is used.
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inherited |
The type of indices.
To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.
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inherited |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
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inlineinherited |
Example:
Output:
Here is the 2x2 complex matrix m: (0.68,-0.211) (0.823,-0.605) (0.566,0.597) (-0.33,0.536) Here is the adjoint of m: (0.68,0.211) (0.566,-0.597) (0.823,0.605) (-0.33,-0.536)
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inlineinherited |
This is the "in place" version of adjoint(): it replaces *this by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
*this must be a resizable matrix.
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inlineinherited |
Example:
Output:
Is ( 0.68 -0.211 0.566) inside the box: 0 Is (0.597 0.823 0.605) inside the box: 1
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inlineinherited |
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inherited |
Apply the elementary reflector H given by 
![$ v^T = [1 essential^T] $](form_124_dark.png)
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 |
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inherited |
Apply the elementary reflector H given by
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 |
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inlineinherited |
replaces *this by *this * other.
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inlineinherited |
This is defined in the Jacobi module.
Applies the rotation in the plane j to the rows p and q of *this, i.e., it computes B = J * B, with 
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inlineinherited |
replaces *this by *this * other. It is equivalent to MatrixBase::operator*=()
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inlineinherited |
Applies the rotation in the plane j to the columns p and q of *this, i.e., it computes B = B * J with 
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inlineinherited |
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inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
2 0 0 0 5 0 0 0 6
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inlineinherited |
*this and other *this and other The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
Output:
(0.68,0.271) (0.823,-0.967) (-0.444,-0.687) (-0.27,0.998) (-0.211,0.435) (-0.605,-0.514) (0.108,-0.198) (0.0268,-0.563) (0.566,-0.717) (-0.33,-0.726) (-0.0452,-0.74) (0.904,0.0259) (0.597,0.214) (0.536,0.608) (0.258,-0.782) (0.832,0.678)
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inlineinherited |
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
| startRow | the first row in the block |
| startCol | the first column in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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inlineinherited |
This is the const version of block<>(Index, Index).
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inlineinherited |
| startRow | the first row in the block |
| startCol | the first column in the block |
| blockRows | the number of rows in the block |
| blockCols | the number of columns in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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inlineinherited |
This is the const version of block(Index,Index,Index,Index).
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inlineinherited |
*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.
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of bottomLeftCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of bottomLeftCorner(Index, Index).
|
inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
|
inlineinherited |
This is the const version of bottomRightCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
|
inlineinherited |
This is the const version of bottomRightCorner(Index, Index).
|
inlineinherited |
| N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.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
|
inlineinherited |
This is the const version of bottomRows<int>().
|
inlineinherited |
| n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.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
|
inlineinherited |
This is the const version of bottomRows(Index).
|
inlineinherited |
The template parameter NewScalar is the type we are casting the scalars to.
|
inlineinherited |
Example:
Output:
1 4 0 0 5 0 0 6 1
|
inherited |
*this.
|
inlineinherited |
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
|
inlineinherited |
This is defined in the LU module.
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
| inverse | Reference to the matrix in which to store the inverse. |
| determinant | Reference to the variable in which to store the inverse. |
| invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
| absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its determinant is 0.209 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
|
inlineinherited |
This is defined in the LU module.
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
| inverse | Reference to the matrix in which to store the inverse. |
| invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
| absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
|
inlineinherited |
*this.
|
inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
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.
|
inlineinherited |
|
inlineinherited |
This is defined in the Geometry module.
*this and other Here is a very good explanation of cross-product: http://xkcd.com/199/
|
inlineinherited |
This is defined in the Geometry module.
*this and other Here is a very good explanation of cross-product: http://xkcd.com/199/
|
inlineinherited |
This is defined in the Geometry module.
*this and other using only the x, y, and z coefficientsThe size of *this and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
|
inlineinherited |
*this Example:
Output:
2 4 6 5 1 0
|
inlineinherited |
*this Example:
Output:
4 16 36 25 1 0
|
inlineinherited |
*this and a scalar s
|
inlineinherited |
Example:
Output:
0.5 2 1 0.333 4 1
|
inlineinherited |
Example:
Output:
1 1.41 2
|
inlineinherited |
This is defined in the LU module.
|
inlineinherited |
*this *this is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
|
inlineinherited |
*this *this is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
|
inlineinherited |
*this *this is not required to be square.
Example:
Output:
Here is the matrix m: 7 6 -3 -2 9 6 6 -6 -5 Here are the coefficients on the main diagonal of m: 7 9 -5
|
inlineinherited |
This is the const version of diagonal<int>().
|
inlineinherited |
This is the const version of diagonal<int>().
|
inlineinherited |
This is the const version of diagonal().
|
inlineinherited |
*this *this is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
|
inlineinherited |
This is the const version of diagonal(Index).
|
inlineinherited |
|
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.
|
inlineinherited |
Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
Output:
The eigenvalues of the 3x3 matrix of ones are: (-5.31e-17,0) (3,0) (0,0)
|
inlineinherited |
This is defined in the Geometry module.
*this using the convention defined by the triplet (a0,a1,a2)Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:
"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:
This corresponds to the right-multiply conventions (with right hand side frames).
|
inlineinherited |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
|
inlineinherited |
Alias for setConstant(): sets all coefficients in this expression to value.
|
inlineinherited |
This is mostly for internal use.
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
See class IOFormat for some examples.
|
inherited |
*this.
|
inlineinherited |
This is defined in the LU module.
*this.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
|
inlineinherited |
This is the const version of head<int>().
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
|
inlineinherited |
This is the const version of head(Index).
|
inlineinherited |
This is defined in the Geometry module.
*this Example:
Output:
|
inlineinherited |
This is defined in the Geometry module.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
|
inherited |
*this.
|
inlineinherited |
*this avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
Output:
1 0 0 0 0 1 0 0 0 0 1 0
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.
Example:
Output:
1 0 0 0 1 0 0 0 1 0 0 0
|
inlineinherited |
*this.
|
inlineinherited |
*this.
|
inlineinherited |
|
inlineinherited |
This is defined in the LU module.
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
|
inherited |
true if *this is approximately equal to other, within the precision determined by prec.
![\[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \]](form_15_dark.png)
*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.
|
inherited |
|
inherited |
This is just an alias for isApproxToConstant().
|
inherited |
Example:
Output:
Here's the matrix m:
1e+04 0 1
0 1e+04 0
0 0 1e+04
m.isDiagonal() returns: 0
m.isDiagonal(1e-3) returns: 1
|
inherited |
Example:
Output:
Here's the matrix m:
1 0 0.0001
0 1 0
0 0 1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1
|
inherited |
|
inherited |
true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.
![\[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \]](form_18_dark.png)
|
inherited |
true if the norm of *this is much smaller than other, within the precision determined by prec.
![\[ \Vert v \Vert \leqslant p\,\vert x\vert. \]](form_17_dark.png)
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
|
inherited |
Example:
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
|
inherited |
Example:
Output:
Here's the vector v: 1 0 0 Here's the vector w: 0.0001 0 1 v.isOrthogonal(w) returns: 0 v.isOrthogonal(w,1e-3) returns: 1
|
inherited |
m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
Output:
Here's the matrix m:
1 0 0.0001
0 1 0
0 0 1
m.isUnitary() returns: 0
m.isUnitary(1e-3) returns: 1
|
inherited |
|
inherited |
Example:
Output:
Here's the matrix m:
0 0 0.0001
0 0 0
0 0 0
m.isZero() returns: 0
m.isZero(1e-3) returns: 1
|
inherited |
This is defined in the SVD module.
*this computed by two-sided Jacobi transformations.
|
inherited |
*this and other without implicit evaluation.The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.
|
inlineinherited |
This is defined in the Cholesky module.
*this
|
inlineinherited |
| N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols<2>(): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of leftCols<int>().
|
inlineinherited |
| n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols(2): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of leftCols(Index).
|
inlinestaticinherited |
Special version for fixed size types which does not require the size parameter.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
|
inlinestaticinherited |
Special version for fixed size types which does not require the size parameter.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
|
inlineinherited |
This is defined in the Cholesky module.
*this
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
This is defined in the LU module.
Synonym of partialPivLu().
*this.
|
inherited |
Computes the elementary reflector H such that: ![$ H *this = [ beta 0 ... 0]^T $](form_122_dark.png)
On output:
| essential | the essential part of the vector v |
| tau | the scaling factor of the Householder transformation |
| beta | the result of H * *this |
|
inherited |
Computes the elementary reflector H such that:
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 |
|
inlineinherited |
|
inherited |
|
inherited |
|
inlineinherited |
|
inlineinherited |
| N | the number of columns in the block |
| startCol | the index of the first column in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(:,1..3) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
|
inlineinherited |
This is the const version of middleCols<int>().
| startCol | the index of the first column in the block |
| numCols | the number of columns in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
This is the const version of middleCols(Index,Index).
|
inlineinherited |
| N | the number of rows in the block |
| startRow | the index of the first row in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6
|
inlineinherited |
This is the const version of middleRows<int>().
| startRow | the index of the first row in the block |
| numRows | the number of rows in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(2..3,:) = 6 6 -3 5 -8 6 -5 0 -8 6
This is the const version of middleRows(Index,Index).
|
inlineinherited |
|
inherited |
|
inherited |
|
inlineinherited |
|
inherited |
*this with an operator= assuming no aliasing between *this and the source expression.More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.
Here are some examples where noalias is usefull:
On the other hand the following example will lead to a wrong result:
because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:
|
inlineinherited |
|
inlineinherited |
*this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.
|
inlineinherited |
Normalizes the vector, i.e. divides it by its own norm.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
1 1 1 1 6 6 6 6
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
Output:
1 1 1 1 1 1
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
Output:
6 6 6 6 1 1
|
inlineinherited |
*this and other are not exactly equal to each other.
|
inlineinherited |
*this by the diagonal matrix diagonal.
|
inlineinherited |
*this and other.
|
inlineinherited |
*this scaled by the scalar factor scalar
|
inlineinherited |
Overloaded for efficient real matrix times complex scalar value
|
inherited |
Concatenates a linear transformation matrix and a uniform scaling
|
inlineinherited |
replaces *this by *this * other.
*this
|
inlineinherited |
replaces *this by *this + other.
*this
|
inlineinherited |
*this
|
inlineinherited |
replaces *this by *this - other.
*this
|
inlineinherited |
*this divided by the scalar value scalar
|
inlineinherited |
|
inlineinherited |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
|
inlineinherited |
*this and other are all exactly equal.
|
inlineinherited |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix 
![\[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \]](form_82_dark.png)
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
Example:
Output:
The operator norm of the 3x3 matrix of ones is 3
|
inlineinherited |
|
inlineinherited |
This is defined in the LU module.
*this.
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
700 600 -200 600
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
Output:
7 6 9 -2 6 -6
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
Output:
7 -2
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlineinherited |
*this.
|
inlineinherited |
*this.
|
inlineinherited |
The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current STL and TR1 functor styles are handled.
|
inlineinherited |
*this Example:
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
|
inlineinherited |
*this Example:
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
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.
|
inlineinherited |
Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.
|
inlineinherited |
Example:
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
|
inlineinherited |
This is the const version of reverse().
|
inlineinherited |
This is the "in place" version of reverse: it reverses *this.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
|
inlineinherited |
| N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.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
|
inlineinherited |
This is the const version of rightCols<int>().
|
inlineinherited |
| n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.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
|
inlineinherited |
This is the const version of rightCols(Index).
|
inlineinherited |
Example:
Output:
1 0 0 4 5 6 0 0 1
|
inlineinherited |
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
|
inlineinherited |
*this This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
| start | the index of the first element of the sub-vector |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of segment<int>(Index).
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| start | the first coefficient in the segment |
| size | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
|
inlineinherited |
This is the const version of segment(Index,Index).
|
inlineinherited |
*this(i,j), and elseMatrix(i,j) otherwise.Example:
Output:
1 2 3 4 -5 -6 -7 -8 -9
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
|
inlineinherited |
Sets all coefficients in this expression to value.
|
inlineinherited |
Writes the identity expression (not necessarily square) into *this.
Example:
Output:
0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
|
inlineinherited |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
| rows | the new number of rows |
| cols | the new number of columns |
Example:
Output:
1 0 0 0 1 0 0 0 1
|
inlineinherited |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
0.5 0.75 1 1.25 1.5
|
inlineinherited |
Sets all coefficients in this expression to one.
Example:
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
|
inlineinherited |
Sets all coefficients in this expression to random values.
Example:
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
|
inlineinherited |
Sets all coefficients in this expression to zero.
Example:
Output:
7 9 -5 -3 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
|
inlineinherited |
*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.
|
inlineinherited |
|
inlineinherited |
swaps *this with the expression other.
|
inlineinherited |
swaps *this with the matrix or array other.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of tail<int>.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of tail(Index).
|
inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topLeftCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topLeftCorner(Index, Index).
|
inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRightCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRightCorner(Index, Index).
|
inlineinherited |
| N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows<2>(): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRows<int>().
|
inlineinherited |
| n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows(2): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRows(Index).
|
inlineinherited |
*this, i.e. the sum of the coefficients on the main diagonal.*this can be any matrix, not necessarily square.
|
inlineinherited |
Example:
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
|
inlineinherited |
This is the const version of transpose().
Make sure you read the warning for transpose() !
|
inlineinherited |
This is the "in place" version of transpose(): it replaces *this by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this must be a resizable matrix.
|
inherited |
The parameter Mode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.
Example:
Output:
|
inherited |
The parameter Mode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.
Example:
Output:
|
inherited |
This is the const version of MatrixBase::triangularView()
|
inherited |
This is the const version of MatrixBase::triangularView()
|
inlineinherited |
Apply a unary operator coefficient-wise.
| [in] | func | Functor implementing the unary operator |
| CustomUnaryOp | Type of func |
The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.68 0.823 0 0
0 0 0.108 0.0268
0.566 0 0 0.904
0.597 0.536 0.258 0.832
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.5 0.5 -0.444 -0.27
-0.211 -0.5 0.108 0.0268
0.5 -0.33 -0.0452 0.5
0.5 0.5 0.258 0.5
|
inlineinherited |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.5 0.5 -0.444 -0.27
-0.211 -0.5 0.108 0.0268
0.5 -0.33 -0.0452 0.5
0.5 0.5 0.258 0.5
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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.
|
inherited |
*this The size of *this must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this, i.e., (-y,x).normalized().
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
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.
|
inlinestaticinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
|
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:
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 0 0 0 0 0 0 0
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
|
Outputs the matrix, to the given stream.
If you wish to print the matrix with a format different than the default, use DenseBase::format().
It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.