The matrix class, also used for vectors and row-vectors. More...
#include <Matrix.h>
Public Types | |
enum | { Options } |
enum | |
enum | |
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typedef Eigen::Map< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Aligned > | AlignedMapType |
typedef PlainObjectBase< Matrix > | Base |
Base class typedef. | |
typedef Base::CoeffReturnType | CoeffReturnType |
typedef VectorwiseOp< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Vertical > | ColwiseReturnType |
typedef const Eigen::Map < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Aligned > | ConstAlignedMapType |
typedef const VectorwiseOp < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Vertical > | ConstColwiseReturnType |
typedef const Diagonal< const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | ConstDiagonalReturnType |
typedef const Eigen::Map < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Unaligned > | ConstMapType |
typedef const Reverse< const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections > | ConstReverseReturnType |
typedef const VectorwiseOp < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Horizontal > | ConstRowwiseReturnType |
typedef const VectorBlock < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | ConstSegmentReturnType |
typedef Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1?SizeMinusOne:1, internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1?1:SizeMinusOne > | ConstStartMinusOne |
typedef const Transpose< const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | ConstTransposeReturnType |
typedef Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > | DenseType |
typedef Diagonal< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | DiagonalReturnType |
typedef internal::add_const_on_value_type < typename internal::eval < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::type >::type | EvalReturnType |
typedef CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar >, const ConstStartMinusOne > | HNormalizedReturnType |
typedef Homogeneous< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , HomogeneousReturnTypeDirection > | HomogeneousReturnType |
typedef internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Index | Index |
The type of indices. | |
typedef Eigen::Map< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Unaligned > | MapType |
typedef internal::packet_traits < Scalar >::type | PacketScalar |
typedef Base::PlainObject | PlainObject |
The plain matrix type corresponding to this expression. | |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Reverse< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections > | ReverseReturnType |
typedef VectorwiseOp< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Horizontal > | RowwiseReturnType |
typedef internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | Scalar |
typedef VectorBlock< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | SegmentReturnType |
typedef internal::stem_function < Scalar >::type | StemFunction |
typedef internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::StorageKind | StorageKind |
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< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | array () |
const ArrayWrapper< const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | array () const |
const DiagonalWrapper< const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | asDiagonal () const |
const PermutationWrapper < const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | asPermutation () const |
Base & | base () |
const Base & | base () const |
const CwiseBinaryOp < CustomBinaryOp, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
RealScalar | blueNorm () const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | bottomLeftCorner (Index cRows, Index cCols) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | bottomLeftCorner (Index cRows, Index cCols) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CRows, CCols > | bottomLeftCorner () |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols > | bottomLeftCorner () const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | bottomRightCorner (Index cRows, Index cCols) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | bottomRightCorner (Index cRows, Index cCols) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CRows, CCols > | bottomRightCorner () |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols > | bottomRightCorner () const |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
NRowsBlockXpr< N >::Type | bottomRows () |
ConstNRowsBlockXpr< N >::Type | bottomRows () const |
internal::cast_return_type < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar, NewType > , const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > >::type | cast () const |
const Scalar & | coeff (Index row, Index col) const |
const Scalar & | coeff (Index index) const |
Scalar & | coeffRef (Index row, Index col) |
Scalar & | coeffRef (Index index) |
const Scalar & | coeffRef (Index row, Index col) const |
const Scalar & | coeffRef (Index index) const |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () const |
Index | cols () const |
ConstColwiseReturnType | colwise () const |
ColwiseReturnType | colwise () |
void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
ConjugateReturnType | conjugate () const |
void | conservativeResize (Index rows, Index cols) |
void | conservativeResize (Index rows, NoChange_t) |
void | conservativeResize (NoChange_t, Index cols) |
void | conservativeResize (Index size) |
void | conservativeResizeLike (const DenseBase< OtherDerived > &other) |
const MatrixFunctionReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cos () const |
const MatrixFunctionReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cosh () const |
Index | count () const |
cross_product_return_type < OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cwiseAbs () const |
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cwiseAbs2 () const |
const CwiseBinaryOp < std::equal_to< Scalar > , const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, const OtherDerived > | cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < std::binder1st < std::equal_to< Scalar > >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cwiseEqual (const Scalar &s) const |
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cwiseInverse () const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType > | cwiseMax (const Scalar &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType > | cwiseMin (const Scalar &other) const |
const CwiseBinaryOp < std::not_equal_to< Scalar > , const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, const OtherDerived > | cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | cwiseSqrt () const |
const Scalar * | data () const |
Scalar * | data () |
Scalar | determinant () const |
DiagonalReturnType | diagonal () |
const ConstDiagonalReturnType | diagonal () const |
DiagonalIndexReturnType< Index > ::Type | diagonal () |
ConstDiagonalIndexReturnType < Index >::Type | diagonal () const |
DiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) |
ConstDiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) const |
Index | diagonalSize () const |
internal::scalar_product_traits < typename internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar, typename internal::traits< OtherDerived > ::Scalar >::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
const | EIGEN_CWISE_PRODUCT_RETURN_TYPE (Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, OtherDerived) cwiseProduct(const Eigen |
EigenvaluesReturnType | eigenvalues () const |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
EvalReturnType | eval () const |
void | evalTo (Dest &) const |
const MatrixExponentialReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | exp () const |
void | fill (const Scalar &value) |
const Flagged< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Added, Removed > | flagged () const |
const ForceAlignedAccess < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | forceAlignedAccess () const |
ForceAlignedAccess< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | forceAlignedAccess () |
internal::add_const_on_value_type < typename internal::conditional< Enable, ForceAlignedAccess< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & >::type >::type | forceAlignedAccessIf () const |
internal::conditional< Enable, ForceAlignedAccess< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & >::type | forceAlignedAccessIf () |
const WithFormat< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | format (const IOFormat &fmt) const |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
const FullPivLU< PlainObject > | fullPivLu () const |
SegmentReturnType | head (Index size) |
DenseBase::ConstSegmentReturnType | head (Index size) const |
FixedSegmentReturnType< Size > ::Type | head () |
ConstFixedSegmentReturnType < Size >::Type | head () const |
const HNormalizedReturnType | hnormalized () const |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
const ImagReturnType | imag () const |
NonConstImagReturnType | imag () |
Index | innerSize () const |
Index | innerStride () const |
const internal::inverse_impl < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | inverse () const |
bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
JacobiSVD< PlainObject > | jacobiSvd (unsigned int computationOptions=0) const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | lazyAssign (const DenseBase< OtherDerived > &other) |
const LazyProductReturnType < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, OtherDerived > ::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
const LDLT< PlainObject > | ldlt () const |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
NColsBlockXpr< N >::Type | leftCols () |
ConstNColsBlockXpr< N >::Type | leftCols () const |
const LLT< PlainObject > | llt () const |
const MatrixLogarithmReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | log () const |
RealScalar | lpNorm () const |
const PartialPivLU< PlainObject > | lu () const |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
Matrix () | |
Default constructor. | |
Matrix (internal::constructor_without_unaligned_array_assert) | |
Matrix (Index dim) | |
Constructs a vector or row-vector with given dimension. 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. | |
Matrix (Index rows, Index cols) | |
Constructs an uninitialized matrix with rows rows and cols columns. | |
Matrix (const Scalar &x, const Scalar &y) | |
Constructs an initialized 2D vector with given coefficients. | |
Matrix (const Scalar &x, const Scalar &y, const Scalar &z) | |
Constructs an initialized 3D vector with given coefficients. | |
Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w) | |
Constructs an initialized 4D vector with given coefficients. | |
Matrix (const Scalar *data) | |
template<typename OtherDerived > | |
Matrix (const MatrixBase< OtherDerived > &other) | |
Constructor copying the value of the expression other. | |
Matrix (const Matrix &other) | |
Copy constructor. | |
template<typename OtherDerived > | |
Matrix (const ReturnByValue< OtherDerived > &other) | |
Copy constructor with in-place evaluation. | |
template<typename OtherDerived > | |
Matrix (const EigenBase< OtherDerived > &other) | |
Copy constructor for generic expressions. | |
MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > & | matrix () |
const MatrixBase< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > & | matrix () const |
template<typename OtherDerived > | |
Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r) | |
Constructs a Dim x Dim rotation matrix from the rotation r. | |
const MatrixFunctionReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | matrixFunction (StemFunction f) const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | maxCoeff () const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | maxCoeff (IndexType *index) const |
Scalar | mean () const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
NColsBlockXpr< N >::Type | middleCols (Index startCol) |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
RowsBlockXpr | middleRows (Index startRow, Index numRows) |
ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | minCoeff () const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
internal::traits< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar | minCoeff (IndexType *index) const |
const NestByValue< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | nestByValue () const |
NoAlias< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Eigen::MatrixBase > | noalias () |
Index | nonZeros () const |
RealScalar | norm () const |
void | normalize () |
const PlainObject | normalized () const |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
const ScalarMultipleReturnType | operator* (const RealScalar &scalar) const |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator* (const std::complex< Scalar > &scalar) const |
const ProductReturnType < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
const DiagonalProduct< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator*= (const EigenBase< OtherDerived > &other) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator*= (const Scalar &other) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator+= (const MatrixBase< OtherDerived > &other) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator+= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator- () const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator-= (const MatrixBase< OtherDerived > &other) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator-= (const EigenBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator/ (const Scalar &scalar) const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator/= (const Scalar &other) |
CommaInitializer< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator<< (const Scalar &s) |
CommaInitializer< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator<< (const DenseBase< OtherDerived > &other) |
Matrix & | operator= (const Matrix &other) |
Assigns matrices to each other. | |
template<typename OtherDerived > | |
Matrix & | operator= (const MatrixBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Matrix & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
template<typename OtherDerived > | |
Matrix & | operator= (const ReturnByValue< OtherDerived > &func) |
template<typename OtherDerived > | |
Matrix & | operator= (const RotationBase< OtherDerived, ColsAtCompileTime > &r) |
Set a Dim x Dim rotation matrix from the rotation r. | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
RealScalar | operatorNorm () const |
Index | outerSize () const |
Index | outerStride () const |
PacketScalar | packet (Index row, Index col) const |
PacketScalar | packet (Index index) const |
const PartialPivLU< PlainObject > | partialPivLu () const |
Scalar | prod () const |
RealReturnType | real () const |
NonConstRealReturnType | real () |
const Replicate< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , RowFactor, ColFactor > | replicate () const |
const Replicate< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
void | resize (Index rows, Index cols) |
void | resize (Index size) |
void | resize (NoChange_t, Index cols) |
void | resize (Index rows, NoChange_t) |
void | resizeLike (const EigenBase< OtherDerived > &_other) |
ReverseReturnType | reverse () |
ConstReverseReturnType | reverse () const |
void | reverseInPlace () |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
NColsBlockXpr< N >::Type | rightCols () |
ConstNColsBlockXpr< N >::Type | rightCols () const |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
Index | rows () const |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
SegmentReturnType | segment (Index start, Index size) |
DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
FixedSegmentReturnType< Size > ::Type | segment (Index start) |
ConstFixedSegmentReturnType < Size >::Type | segment (Index start) const |
const Select< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
const Select< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
const Select< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
SelfAdjointViewReturnType < UpLo >::Type | selfadjointView () |
ConstSelfAdjointViewReturnType < UpLo >::Type | selfadjointView () const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setConstant (const Scalar &value) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setConstant (Index size, const Scalar &value) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setConstant (Index rows, Index cols, const Scalar &value) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setIdentity () |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setIdentity (Index rows, Index cols) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setLinSpaced (const Scalar &low, const Scalar &high) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setOnes () |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setOnes (Index size) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setOnes (Index rows, Index cols) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setRandom () |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setRandom (Index size) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setRandom (Index rows, Index cols) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setZero () |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setZero (Index size) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | setZero (Index rows, Index cols) |
const MatrixFunctionReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | sin () const |
const MatrixFunctionReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | sinh () const |
const SparseView< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const |
const MatrixSquareRootReturnValue < Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | sqrt () const |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () const |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (MatrixBase< OtherDerived > const &other) |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index size) |
DenseBase::ConstSegmentReturnType | tail (Index size) const |
FixedSegmentReturnType< Size > ::Type | tail () |
ConstFixedSegmentReturnType < Size >::Type | tail () const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | topLeftCorner (Index cRows, Index cCols) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | topLeftCorner (Index cRows, Index cCols) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CRows, CCols > | topLeftCorner () |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols > | topLeftCorner () const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | topRightCorner (Index cRows, Index cCols) |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | topRightCorner (Index cRows, Index cCols) const |
Block< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, CRows, CCols > | topRightCorner () |
const Block< const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols > | topRightCorner () const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
NRowsBlockXpr< N >::Type | topRows () |
ConstNRowsBlockXpr< N >::Type | topRows () const |
Scalar | trace () const |
Eigen::Transpose< Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
TriangularViewReturnType< Mode > ::Type | triangularView () |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
const CwiseUnaryOp < CustomUnaryOp, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. | |
const CwiseUnaryView < CustomViewOp, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
PlainObject | unitOrthogonal (void) const |
CoeffReturnType | value () const |
void | visit (Visitor &func) const |
void | writePacket (Index row, Index col, const PacketScalar &x) |
void | writePacket (Index index, const PacketScalar &x) |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
static const CwiseNullaryOp < CustomNullaryOp, Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
static const CwiseNullaryOp < CustomNullaryOp, Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | NullaryExpr (Index size, const CustomNullaryOp &func) |
static const CwiseNullaryOp < CustomNullaryOp, Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | NullaryExpr (const CustomNullaryOp &func) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | Random () |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
static const ConstantReturnType | Zero () |
Map | |
static ConstMapType | Map (const Scalar *data) |
static MapType | Map (Scalar *data) |
static ConstMapType | Map (const Scalar *data, Index size) |
static MapType | Map (Scalar *data, Index size) |
static ConstMapType | Map (const Scalar *data, Index rows, Index cols) |
static MapType | Map (Scalar *data, Index rows, Index cols) |
static StridedConstMapType < Stride< Outer, Inner > >::type | Map (const Scalar *data, const Stride< Outer, Inner > &stride) |
static StridedMapType< Stride < Outer, Inner > >::type | Map (Scalar *data, const Stride< Outer, Inner > &stride) |
static StridedConstMapType < Stride< Outer, Inner > >::type | Map (const Scalar *data, Index size, const Stride< Outer, Inner > &stride) |
static StridedMapType< Stride < Outer, Inner > >::type | Map (Scalar *data, Index size, const Stride< Outer, Inner > &stride) |
static StridedConstMapType < Stride< Outer, Inner > >::type | Map (const Scalar *data, Index rows, Index cols, const Stride< Outer, Inner > &stride) |
static StridedMapType< Stride < Outer, Inner > >::type | Map (Scalar *data, Index rows, Index cols, const Stride< Outer, Inner > &stride) |
static ConstAlignedMapType | MapAligned (const Scalar *data) |
static AlignedMapType | MapAligned (Scalar *data) |
static ConstAlignedMapType | MapAligned (const Scalar *data, Index size) |
static AlignedMapType | MapAligned (Scalar *data, Index size) |
static ConstAlignedMapType | MapAligned (const Scalar *data, Index rows, Index cols) |
static AlignedMapType | MapAligned (Scalar *data, Index rows, Index cols) |
static StridedConstAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (const Scalar *data, const Stride< Outer, Inner > &stride) |
static StridedAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (Scalar *data, const Stride< Outer, Inner > &stride) |
static StridedConstAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (const Scalar *data, Index size, const Stride< Outer, Inner > &stride) |
static StridedAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (Scalar *data, Index size, const Stride< Outer, Inner > &stride) |
static StridedConstAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (const Scalar *data, Index rows, Index cols, const Stride< Outer, Inner > &stride) |
static StridedAlignedMapType < Stride< Outer, Inner > >::type | MapAligned (Scalar *data, Index rows, Index cols, const Stride< Outer, Inner > &stride) |
Protected Member Functions | |
void | _init2 (Index rows, Index cols, typename internal::enable_if< Base::SizeAtCompileTime!=2, T0 >::type *=0) |
void | _init2 (const Scalar &x, const Scalar &y, typename internal::enable_if< Base::SizeAtCompileTime==2, T0 >::type *=0) |
void | _resize_to_match (const EigenBase< OtherDerived > &other) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | _set (const DenseBase< OtherDerived > &other) |
Copies the value of the expression other into *this with automatic resizing. | |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | _set_noalias (const DenseBase< OtherDerived > &other) |
void | _set_selector (const OtherDerived &other, const internal::true_type &) |
void | _set_selector (const OtherDerived &other, const internal::false_type &) |
void | _swap (DenseBase< OtherDerived > const &other) |
void | checkTransposeAliasing (const OtherDerived &other) const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator+= (const ArrayBase< OtherDerived > &) |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | operator-= (const ArrayBase< OtherDerived > &) |
Protected Attributes | |
DenseStorage< Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options > | m_storage |
Friends | |
const ScalarMultipleReturnType | operator* (const Scalar &scalar, const StorageBaseType &matrix) |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | operator* (const std::complex< Scalar > &scalar, const StorageBaseType &matrix) |
The matrix class, also used for vectors and row-vectors.
The Matrix class is the work-horse for all dense (note) matrices and vectors within Eigen. Vectors are matrices with one column, and row-vectors are matrices with one row.
The Matrix class encompasses both fixed-size and dynamic-size objects (note).
The first three template parameters are required:
_Scalar | Numeric type, e.g. float, double, int or std::complex<float>. User defined sclar types are supported as well (see here). |
_Rows | Number of rows, or Dynamic |
_Cols | Number of columns, or Dynamic |
The remaining template parameters are optional -- in most cases you don't have to worry about them.
_Options | A combination of either RowMajor or ColMajor, and of either AutoAlign or DontAlign. The former controls storage order, and defaults to column-major. The latter controls alignment, which is required for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size. |
_MaxRows | Maximum number of rows. Defaults to _Rows (note). |
_MaxCols | Maximum number of columns. Defaults to _Cols (note). |
Eigen provides a number of typedefs covering the usual cases. Here are some examples:
Matrix2d
is a 2x2 square matrix of doubles (Matrix<double, 2, 2>
) Vector4f
is a vector of 4 floats (Matrix<float, 4, 1>
) RowVector3i
is a row-vector of 3 ints (Matrix<int, 1, 3>
)MatrixXf
is a dynamic-size matrix of floats (Matrix<float, Dynamic, Dynamic>
) VectorXf
is a dynamic-size vector of floats (Matrix<float, Dynamic, 1>
)Matrix2Xf
is a partially fixed-size (dynamic-size) matrix of floats (Matrix<float, 2, Dynamic>
) MatrixX3d
is a partially dynamic-size (fixed-size) matrix of double (Matrix<double, Dynamic, 3>
)See this page for a complete list of predefined Matrix and Vector typedefs.
You can access elements of vectors and matrices using normal subscripting:
Eigen::VectorXd v(10); v[0] = 0.1; v[1] = 0.2; v(0) = 0.3; v(1) = 0.4; Eigen::MatrixXi m(10, 10); m(0, 1) = 1; m(0, 2) = 2; m(0, 3) = 3;
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_MATRIX_PLUGIN
.
Some notes:
This Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array. This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.
Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime variables, and the array of coefficients is allocated dynamically on the heap.
Note that dense matrices, be they Fixed-size or Dynamic-size, do not expand dynamically in the sense of a std::map. If you want this behavior, see the Sparse module.
typedef Eigen::Map<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Aligned> AlignedMapType [inherited] |
typedef PlainObjectBase<Matrix> Base |
Base class typedef.
Reimplemented from PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef Base::CoeffReturnType CoeffReturnType [inherited] |
typedef VectorwiseOp<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Vertical> ColwiseReturnType [inherited] |
typedef const Eigen::Map<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Aligned> ConstAlignedMapType [inherited] |
typedef const VectorwiseOp<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Vertical> ConstColwiseReturnType [inherited] |
typedef const Diagonal<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstDiagonalReturnType [inherited] |
typedef const Eigen::Map<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Unaligned> ConstMapType [inherited] |
typedef const Reverse<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections> ConstReverseReturnType [inherited] |
typedef const VectorwiseOp<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Horizontal> ConstRowwiseReturnType [inherited] |
typedef const VectorBlock<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstSegmentReturnType [inherited] |
typedef Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne [inherited] |
typedef const Transpose<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstTransposeReturnType [inherited] |
typedef Diagonal<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > DiagonalReturnType [inherited] |
typedef internal::add_const_on_value_type<typename internal::eval<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::type>::type EvalReturnType [inherited] |
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const ConstStartMinusOne > HNormalizedReturnType [inherited] |
typedef Homogeneous<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , HomogeneousReturnTypeDirection> HomogeneousReturnType [inherited] |
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Index Index [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef Eigen::Map<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Unaligned> MapType [inherited] |
typedef internal::packet_traits<Scalar>::type PacketScalar [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef Base::PlainObject PlainObject |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
Reimplemented from MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef NumTraits<Scalar>::Real RealScalar [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef Reverse<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections> ReverseReturnType [inherited] |
typedef VectorwiseOp<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Horizontal> RowwiseReturnType [inherited] |
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar Scalar [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
typedef VectorBlock<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > SegmentReturnType [inherited] |
typedef internal::stem_function<Scalar>::type StemFunction [inherited] |
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::StorageKind StorageKind [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
anonymous enum [inherited] |
Matrix | ( | ) | [inline, explicit] |
Default constructor.
For fixed-size matrices, does nothing.
For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix is called a null matrix. This constructor is the unique way to create null matrices: resizing a matrix to 0 is not supported.
Matrix | ( | internal::constructor_without_unaligned_array_assert | ) | [inline] |
Constructs a vector or row-vector with given dimension. 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.
Note that this is only useful for dynamic-size vectors. For fixed-size vectors, it is redundant to pass the dimension here, so it makes more sense to use the default constructor Matrix() instead.
Constructs an uninitialized matrix with rows rows and cols columns.
This is useful for dynamic-size matrices. For fixed-size matrices, it is redundant to pass these parameters, so one should use the default constructor Matrix() instead.
Constructs an initialized 2D vector with given coefficients.
Constructs an initialized 3D vector with given coefficients.
Constructs an initialized 4D vector with given coefficients.
Matrix | ( | const MatrixBase< OtherDerived > & | other | ) | [inline] |
Constructor copying the value of the expression other.
Copy constructor.
Matrix | ( | const ReturnByValue< OtherDerived > & | other | ) | [inline] |
Copy constructor with in-place evaluation.
Copy constructor for generic expressions.
Matrix | ( | const RotationBase< OtherDerived, ColsAtCompileTime > & | r | ) | [explicit] |
Constructs a Dim x Dim rotation matrix from the rotation r.
This is defined in the Geometry module.
#include <Eigen/Geometry>
References EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE, and RotationBase< Derived, _Dim >::toRotationMatrix().
void _init2 | ( | Index | rows, |
Index | cols, | ||
typename internal::enable_if< Base::SizeAtCompileTime!=2, T0 >::type * | = 0 |
||
) | [inline, protected, inherited] |
void _init2 | ( | const Scalar & | x, |
const Scalar & | y, | ||
typename internal::enable_if< Base::SizeAtCompileTime==2, T0 >::type * | = 0 |
||
) | [inline, protected, inherited] |
void _resize_to_match | ( | const EigenBase< OtherDerived > & | other | ) | [inline, protected, inherited] |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set | ( | const DenseBase< OtherDerived > & | other | ) | [inline, protected, inherited] |
Copies the value of the expression other into *this
with automatic resizing.
*this might be resized to match the dimensions of other. If *this was a null matrix (not already initialized), it will be initialized.
Note that copying a row-vector into a vector (and conversely) is allowed. The resizing, if any, is then done in the appropriate way so that row-vectors remain row-vectors and vectors remain vectors.
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set_noalias | ( | const DenseBase< OtherDerived > & | other | ) | [inline, protected, inherited] |
void _set_selector | ( | const OtherDerived & | other, |
const internal::true_type & | |||
) | [inline, protected, inherited] |
void _set_selector | ( | const OtherDerived & | other, |
const internal::false_type & | |||
) | [inline, protected, inherited] |
const AdjointReturnType adjoint | ( | ) | const [inherited] |
Example:
Matrix2cf m = Matrix2cf::Random(); cout << "Here is the 2x2 complex matrix m:" << endl << m << endl; cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;
Output:
Here is the 2x2 complex matrix m: (-0.211,0.68) (-0.605,0.823) (0.597,0.566) (0.536,-0.33) Here is the adjoint of m: (-0.211,-0.68) (0.597,-0.566) (-0.605,-0.823) (0.536,0.33)
m = m.adjoint(); // bug!!! caused by aliasing effect
m.adjointInPlace();
m = m.adjoint().eval();
void adjointInPlace | ( | ) | [inherited] |
This is the "in place" version of adjoint(): it replaces *this
by its own transpose. Thus, doing
m.adjointInPlace();
has the same effect on m as doing
m = m.adjoint().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
*this
must be a resizable matrix.Example:
Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones()); Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs(); // let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax: cout << "Is (" << p0.transpose() << ") inside the box: " << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl; cout << "Is (" << p1.transpose() << ") inside the box: " << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;
Output:
Is ( 0.68 -0.211 0.566) inside the box: 0 Is (0.597 0.823 0.605) inside the box: 1
void applyHouseholderOnTheLeft | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) | [inherited] |
Apply the elementary reflector H given by with
from the left to a vector or matrix.
On input:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
workspace | a pointer to working space with at least this->cols() * essential.size() entries |
void applyHouseholderOnTheRight | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) | [inherited] |
Apply the elementary reflector H given by with
from the right to a vector or matrix.
On input:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
workspace | a pointer to working space with at least this->cols() * essential.size() entries |
void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other.
Referenced by Eigen::internal::real_2x2_jacobi_svd().
void applyOnTheLeft | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) | [inherited] |
This is defined in the Jacobi module.
#include <Eigen/Jacobi>
Applies the rotation in the plane j to the rows p and q of *this
, i.e., it computes B = J * B, with .
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=()
void applyOnTheRight | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) | [inherited] |
Applies the rotation in the plane j to the columns p and q of *this
, i.e., it computes B = B * J with .
ArrayWrapper<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array | ( | ) | [inline, inherited] |
const ArrayWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array | ( | ) | const [inline, inherited] |
const DiagonalWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > asDiagonal | ( | ) | const [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;
Output:
2 0 0 0 5 0 0 0 6
const PermutationWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > asPermutation | ( | ) | const [inherited] |
const CwiseBinaryOp<CustomBinaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> binaryExpr | ( | const Eigen::MatrixBase< OtherDerived > & | other, |
const CustomBinaryOp & | func = CustomBinaryOp() |
||
) | const [inline, inherited] |
*this
and other *this
and other The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template binary functor template<typename Scalar> struct MakeComplexOp { EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp) typedef complex<Scalar> result_type; complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); } }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random(); cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl; return 0; }
Output:
(0.68,0.271) (0.823,-0.967) (-0.444,-0.687) (-0.27,0.998) (-0.211,0.435) (-0.605,-0.514) (0.108,-0.198) (0.0268,-0.563) (0.566,-0.717) (-0.33,-0.726) (-0.0452,-0.74) (0.904,0.0259) (0.597,0.214) (0.536,0.608) (0.258,-0.782) (0.832,0.678)
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > block | ( | Index | startRow, |
Index | startCol, | ||
Index | blockRows, | ||
Index | blockCols | ||
) | [inline, inherited] |
startRow | the first row in the block |
startCol | the first column in the block |
blockRows | the number of rows in the block |
blockCols | the number of columns in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl; m.block(1, 1, 2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > block | ( | Index | startRow, |
Index | startCol, | ||
Index | blockRows, | ||
Index | blockCols | ||
) | const [inline, inherited] |
This is the const version of block(Index,Index,Index,Index).
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block | ( | Index | startRow, |
Index | startCol | ||
) | [inline, inherited] |
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
startRow | the first row in the block |
startCol | the first column in the block |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl; m.block<2,2>(1,1).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
m.template block<3,3>(1,1);
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block | ( | Index | startRow, |
Index | startCol | ||
) | const [inline, inherited] |
This is the const version of block<>(Index, Index).
RealScalar blueNorm | ( | ) | const [inherited] |
*this
using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.For architecture/scalar types without vectorization, this version is much faster than stableNorm(). Otherwise the stableNorm() is faster.
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner(2, 2):" << endl; cout << m.bottomLeftCorner(2, 2) << endl; m.bottomLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomLeftCorner(Index, Index).
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomLeftCorner<2,2>():" << endl; cout << m.bottomLeftCorner<2,2>() << endl; m.bottomLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomLeftCorner<int, int>().
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner(2, 2):" << endl; cout << m.bottomRightCorner(2, 2) << endl; m.bottomRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of bottomRightCorner(Index, Index).
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.bottomRightCorner<2,2>():" << endl; cout << m.bottomRightCorner<2,2>() << endl; m.bottomRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner | ( | ) | const [inline, inherited] |
This is the const version of bottomRightCorner<int, int>().
RowsBlockXpr bottomRows | ( | Index | n | ) | [inline, inherited] |
n | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.bottomRows(2):" << endl; cout << a.bottomRows(2) << endl; a.bottomRows(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows(2): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
ConstRowsBlockXpr bottomRows | ( | Index | n | ) | const [inline, inherited] |
This is the const version of bottomRows(Index).
NRowsBlockXpr<N>::Type bottomRows | ( | ) | [inline, inherited] |
N | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.bottomRows<2>():" << endl; cout << a.bottomRows<2>() << endl; a.bottomRows<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows<2>(): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
ConstNRowsBlockXpr<N>::Type bottomRows | ( | ) | const [inline, inherited] |
This is the const version of bottomRows<int>().
internal::cast_return_type<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar, NewType>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > >::type cast | ( | ) | const [inline, inherited] |
The template parameter NewScalar is the type we are casting the scalars to.
void checkTransposeAliasing | ( | const OtherDerived & | other | ) | const [protected, inherited] |
Referenced by Eigen::internal::compute_inverse_size3_helper().
Example:
Output:
1 4 0 0 5 0 0 6 1
Referenced by IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::_solve_sparse().
const ColPivHouseholderQR<PlainObject> colPivHouseholderQr | ( | ) | const [inherited] |
*this
.ConstColwiseReturnType colwise | ( | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl; cout << "Here is the maximum absolute value of each column:" << endl << m.cwiseAbs().colwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
ColwiseReturnType colwise | ( | ) | [inherited] |
void computeInverseAndDetWithCheck | ( | ResultType & | inverse, |
typename ResultType::Scalar & | determinant, | ||
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
determinant | Reference to the variable in which to store the inverse. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; double determinant; m.computeInverseAndDetWithCheck(inverse,determinant,invertible); cout << "Its determinant is " << determinant << endl; if(invertible) { cout << "It is invertible, and its inverse is:" << endl << inverse << endl; } else { cout << "It is not invertible." << endl; }
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its determinant is 0.209 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
void computeInverseWithCheck | ( | ResultType & | inverse, |
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; Matrix3d inverse; bool invertible; m.computeInverseWithCheck(inverse,invertible); if(invertible) { cout << "It is invertible, and its inverse is:" << endl << inverse << endl; } else { cout << "It is not invertible." << endl; }
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 It is invertible, and its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
ConjugateReturnType conjugate | ( | ) | const [inline, inherited] |
*this
.void conservativeResize | ( | Index | rows, |
Index | cols | ||
) | [inline, inherited] |
Resizes the matrix to rows x cols while leaving old values untouched.
The method is intended for matrices of dynamic size. If you only want to change the number of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or conservativeResize(Index, NoChange_t).
Matrices are resized relative to the top-left element. In case values need to be appended to the matrix they will be uninitialized.
void conservativeResize | ( | Index | rows, |
NoChange_t | |||
) | [inline, inherited] |
Resizes the matrix to rows x cols while leaving old values untouched.
As opposed to conservativeResize(Index rows, Index cols), this version leaves the number of columns unchanged.
In case the matrix is growing, new rows will be uninitialized.
void conservativeResize | ( | NoChange_t | , |
Index | cols | ||
) | [inline, inherited] |
Resizes the matrix to rows x cols while leaving old values untouched.
As opposed to conservativeResize(Index rows, Index cols), this version leaves the number of rows unchanged.
In case the matrix is growing, new columns will be uninitialized.
void conservativeResize | ( | Index | size | ) | [inline, inherited] |
Resizes the vector to size while retaining old values.
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 method does not work for partially dynamic matrices when the static dimension is anything other than 1. For example it will not work with Matrix<double, 2, Dynamic>.
When values are appended, they will be uninitialized.
void conservativeResizeLike | ( | const DenseBase< OtherDerived > & | other | ) | [inline, inherited] |
Resizes the matrix to rows x cols of other
, while leaving old values untouched.
The method is intended for matrices of dynamic size. If you only want to change the number of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or conservativeResize(Index, NoChange_t).
Matrices are resized relative to the top-left element. In case values need to be appended to the matrix they will copied from other
.
static const ConstantReturnType Constant | ( | Index | rows, |
Index | cols, | ||
const Scalar & | value | ||
) | [static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cos | ( | ) | const [inherited] |
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cosh | ( | ) | const [inherited] |
cross_product_return_type<OtherDerived>::type cross | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other Here is a very good explanation of cross-product: http://xkcd.com/199/
PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other using only the x, y, and z coefficientsThe size of *this
and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs | ( | ) | const [inline, inherited] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs() << endl;
Output:
2 4 6 5 1 0
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs2 | ( | ) | const [inline, inherited] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs2() << endl;
Output:
4 16 36 25 1 0
const CwiseBinaryOp<std::equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
MatrixXi m(2,2); m << 1, 0, 1, 1; cout << "Comparing m with identity matrix:" << endl; cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl; int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count(); cout << "Number of coefficients that are equal: " << count << endl;
Output:
Comparing m with identity matrix: 1 1 0 1 Number of coefficients that are equal: 3
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseEqual | ( | const Scalar & | s | ) | const [inline, inherited] |
*this
and a scalar s const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseInverse | ( | ) | const [inline, inherited] |
Example:
MatrixXd m(2,3); m << 2, 0.5, 1, 3, 0.25, 1; cout << m.cwiseInverse() << endl;
Output:
0.5 2 1 0.333 4 1
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMax | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMax(w) << endl;
Output:
4 3 4
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMax | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMin | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMin(w) << endl;
Output:
2 2 3
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMin | ( | const Scalar & | other | ) | const [inline, inherited] |
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseNotEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
MatrixXi m(2,2); m << 1, 0, 1, 1; cout << "Comparing m with identity matrix:" << endl; cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl; int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count(); cout << "Number of coefficients that are not equal: " << count << endl;
Output:
Comparing m with identity matrix: 0 0 1 0 Number of coefficients that are not equal: 1
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseQuotient | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseQuotient(w) << endl;
Output:
0.5 1.5 1.33
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseSqrt | ( | ) | const [inline, inherited] |
Example:
Vector3d v(1,2,4); cout << v.cwiseSqrt() << endl;
Output:
1 1.41 2
Referenced by PardisoImpl< Derived >::_solve().
Scalar determinant | ( | ) | const [inherited] |
DiagonalReturnType diagonal | ( | ) | [inherited] |
*this
*this
is not required to be square.
Example:
Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the main diagonal of m:" << endl << m.diagonal() << endl;
Output:
Here is the matrix m: 7 6 -3 -2 9 6 6 -6 -5 Here are the coefficients on the main diagonal of m: 7 9 -5
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal<1>().transpose() << endl << m.diagonal<-2>().transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
const ConstDiagonalReturnType diagonal | ( | ) | const [inherited] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl << m.diagonal(1).transpose() << endl << m.diagonal(-2).transpose() << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 1 9 6 6
This is the const version of diagonal(Index).
Index diagonalSize | ( | ) | const [inline, inherited] |
internal::scalar_product_traits<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
const EIGEN_CWISE_PRODUCT_RETURN_TYPE | ( | Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > | , |
OtherDerived | |||
) | const [inline, inherited] |
Example:
Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random(); Matrix3i c = a.cwiseProduct(b); cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;
Output:
a: 7 6 -3 -2 9 6 6 -6 -5 b: 1 -3 9 0 0 3 3 9 5 c: 7 -18 -27 0 0 18 18 -54 -25
EigenvaluesReturnType eigenvalues | ( | ) | const [inherited] |
Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
MatrixXd ones = MatrixXd::Ones(3,3); VectorXcd eivals = ones.eigenvalues(); cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;
Output:
The eigenvalues of the 3x3 matrix of ones are: (-2.98e-17,0) (3,0) (1.81e-32,0)
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
using the convention defined by the triplet (a0,a1,a2)Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:
Vector3f ea = mat.eulerAngles(2, 0, 2);
"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:
mat == AngleAxisf(ea[0], Vector3f::UnitZ()) * AngleAxisf(ea[1], Vector3f::UnitX()) * AngleAxisf(ea[2], Vector3f::UnitZ());
This corresponds to the right-multiply conventions (with right hand side frames).
EvalReturnType eval | ( | ) | const [inline, inherited] |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
void evalTo | ( | Dest & | ) | const [inline, inherited] |
const MatrixExponentialReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > exp | ( | ) | const [inherited] |
Alias for setConstant(): sets all coefficients in this expression to value.
const Flagged<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Added, Removed> flagged | ( | ) | const [inherited] |
This is mostly for internal use.
const ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > forceAlignedAccess | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > forceAlignedAccess | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &>::type>::type forceAlignedAccessIf | ( | ) | const [inline, inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
internal::conditional<Enable,ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &>::type forceAlignedAccessIf | ( | ) | [inline, inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
const WithFormat<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > format | ( | const IOFormat & | fmt | ) | const [inline, inherited] |
See class IOFormat for some examples.
const FullPivHouseholderQR<PlainObject> fullPivHouseholderQr | ( | ) | const [inherited] |
*this
.const FullPivLU<PlainObject> fullPivLu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.SegmentReturnType head | ( | Index | size | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
size | the number of coefficients in the block |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head(2) << endl; v.head(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
DenseBase::ConstSegmentReturnType head | ( | Index | size | ) | const [inherited] |
This is the const version of head(Index).
FixedSegmentReturnType<Size>::Type head | ( | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.head(2):" << endl << v.head<2>() << endl; v.head<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
ConstFixedSegmentReturnType<Size>::Type head | ( | ) | const [inherited] |
This is the const version of head<int>().
const HNormalizedReturnType hnormalized | ( | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
Example:
Output:
HomogeneousReturnType homogeneous | ( | ) | const [inherited] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
const HouseholderQR<PlainObject> householderQr | ( | ) | const [inherited] |
*this
.RealScalar hypotNorm | ( | ) | const [inherited] |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.static const IdentityReturnType Identity | ( | ) | [static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
cout << Matrix<double, 3, 4>::Identity() << endl;
Output:
1 0 0 0 0 1 0 0 0 0 1 0
Referenced by main().
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.
Example:
cout << MatrixXd::Identity(4, 3) << endl;
Output:
1 0 0 0 1 0 0 0 1 0 0 0
const ImagReturnType imag | ( | ) | const [inline, inherited] |
*this
.NonConstImagReturnType imag | ( | ) | [inline, inherited] |
*this
.Index innerStride | ( | ) | const [inline] |
const internal::inverse_impl<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > inverse | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Its inverse is:" << endl << m.inverse() << endl;
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Its inverse is: -0.199 2.23 2.84 1.01 -0.555 -1.42 -1.62 3.59 3.29
bool isApprox | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
true
if *this
is approximately equal to other, within the precision determined by prec.
*this
is approximately equal to the zero matrix or vector. Indeed, isApprox(zero)
returns false unless *this
itself is exactly the zero matrix or vector. If you want to test whether *this
is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.bool isApproxToConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
bool isConstant | ( | const Scalar & | value, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
This is just an alias for isApproxToConstant().
bool isDiagonal | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = 10000 * Matrix3d::Identity(); m(0,2) = 1; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl; cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;
Output:
Here's the matrix m: 1e+04 0 1 0 1e+04 0 0 0 1e+04 m.isDiagonal() returns: 0 m.isDiagonal(1e-3) returns: 1
bool isIdentity | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isIdentity() returns: " << m.isIdentity() << endl; cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isIdentity() returns: 0 m.isIdentity(1e-3) returns: 1
bool isLowerTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
bool isMuchSmallerThan | ( | const RealScalar & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
bool isMuchSmallerThan | ( | const DenseBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
bool isOnes | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Ones(); m(0,2) += 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isOnes() returns: " << m.isOnes() << endl; cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
bool isOrthogonal | ( | const MatrixBase< OtherDerived > & | other, |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
Example:
Vector3d v(1,0,0); Vector3d w(1e-4,0,1); cout << "Here's the vector v:" << endl << v << endl; cout << "Here's the vector w:" << endl << w << endl; cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl; cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;
Output:
Here's the vector v: 1 0 0 Here's the vector w: 0.0001 0 1 v.isOrthogonal(w) returns: 0 v.isOrthogonal(w,1e-3) returns: 1
bool isUnitary | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
Matrix3d m = Matrix3d::Identity(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isUnitary() returns: " << m.isUnitary() << endl; cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isUnitary() returns: 0 m.isUnitary(1e-3) returns: 1
bool isUpperTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
bool isZero | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Zero(); m(0,2) = 1e-4; cout << "Here's the matrix m:" << endl << m << endl; cout << "m.isZero() returns: " << m.isZero() << endl; cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;
Output:
Here's the matrix m: 0 0 0.0001 0 0 0 0 0 0 m.isZero() returns: 0 m.isZero(1e-3) returns: 1
JacobiSVD<PlainObject> jacobiSvd | ( | unsigned int | computationOptions = 0 | ) | const [inherited] |
This is defined in the SVD module.
#include <Eigen/SVD>
*this
computed by two-sided Jacobi transformations.Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & lazyAssign | ( | const DenseBase< OtherDerived > & | other | ) | [inline, inherited] |
const LazyProductReturnType<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,OtherDerived>::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
*this
and other without implicit evaluation.The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.
const LDLT<PlainObject> ldlt | ( | ) | const [inherited] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
n | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.leftCols(2):" << endl; cout << a.leftCols(2) << endl; a.leftCols(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols(2): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
Referenced by PardisoImpl< PardisoLU< MatrixType > >::_solve_sparse(), and PastixBase< PastixLU< _MatrixType > >::_solve_sparse().
This is the const version of leftCols(Index).
NColsBlockXpr<N>::Type leftCols | ( | ) | [inline, inherited] |
N | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.leftCols<2>():" << endl; cout << a.leftCols<2>() << endl; a.leftCols<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols<2>(): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
ConstNColsBlockXpr<N>::Type leftCols | ( | ) | const [inline, inherited] |
This is the const version of leftCols<int>().
static const SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
Index | size, | ||
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
static const RandomAccessLinSpacedReturnType LinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
cout << VectorXi::LinSpaced(4,7,10).transpose() << endl; cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;
Output:
7 8 9 10 0 0.25 0.5 0.75 1
static const SequentialLinSpacedReturnType LinSpaced | ( | Sequential_t | , |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [static, inherited] |
static const RandomAccessLinSpacedReturnType LinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [static, inherited] |
const LLT<PlainObject> llt | ( | ) | const [inherited] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
const MatrixLogarithmReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > log | ( | ) | const [inherited] |
RealScalar lpNorm | ( | ) | const [inherited] |
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
const PartialPivLU<PlainObject> lu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
Synonym of partialPivLu().
*this
.void makeHouseholder | ( | EssentialPart & | essential, |
Scalar & | tau, | ||
RealScalar & | beta | ||
) | const [inherited] |
Computes the elementary reflector H such that: where the transformation H is:
and the vector v is:
On output:
essential | the essential part of the vector v |
tau | the scaling factor of the Householder transformation |
beta | the result of H * *this |
void makeHouseholderInPlace | ( | Scalar & | tau, |
RealScalar & | beta | ||
) | [inherited] |
Computes the elementary reflector H such that: where the transformation H is:
and the vector v is:
The essential part of the vector v
is stored in *this.
On output:
tau | the scaling factor of the Householder transformation |
beta | the result of H * *this |
static ConstMapType Map | ( | const Scalar * | data | ) | [inline, static, inherited] |
Referenced by SparseVector< _Scalar, _Options, _Index >::sum().
static ConstMapType Map | ( | const Scalar * | data, |
Index | size | ||
) | [inline, static, inherited] |
static ConstMapType Map | ( | const Scalar * | data, |
Index | rows, | ||
Index | cols | ||
) | [inline, static, inherited] |
static StridedConstMapType<Stride<Outer, Inner> >::type Map | ( | const Scalar * | data, |
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedMapType<Stride<Outer, Inner> >::type Map | ( | Scalar * | data, |
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedConstMapType<Stride<Outer, Inner> >::type Map | ( | const Scalar * | data, |
Index | size, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedMapType<Stride<Outer, Inner> >::type Map | ( | Scalar * | data, |
Index | size, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedConstMapType<Stride<Outer, Inner> >::type Map | ( | const Scalar * | data, |
Index | rows, | ||
Index | cols, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedMapType<Stride<Outer, Inner> >::type Map | ( | Scalar * | data, |
Index | rows, | ||
Index | cols, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static ConstAlignedMapType MapAligned | ( | const Scalar * | data | ) | [inline, static, inherited] |
static AlignedMapType MapAligned | ( | Scalar * | data | ) | [inline, static, inherited] |
static ConstAlignedMapType MapAligned | ( | const Scalar * | data, |
Index | size | ||
) | [inline, static, inherited] |
static AlignedMapType MapAligned | ( | Scalar * | data, |
Index | size | ||
) | [inline, static, inherited] |
static ConstAlignedMapType MapAligned | ( | const Scalar * | data, |
Index | rows, | ||
Index | cols | ||
) | [inline, static, inherited] |
static AlignedMapType MapAligned | ( | Scalar * | data, |
Index | rows, | ||
Index | cols | ||
) | [inline, static, inherited] |
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | const Scalar * | data, |
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | Scalar * | data, |
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | const Scalar * | data, |
Index | size, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | Scalar * | data, |
Index | size, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | const Scalar * | data, |
Index | rows, | ||
Index | cols, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned | ( | Scalar * | data, |
Index | rows, | ||
Index | cols, | ||
const Stride< Outer, Inner > & | stride | ||
) | [inline, static, inherited] |
MatrixBase<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >& matrix | ( | ) | [inline, inherited] |
const MatrixBase<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >& matrix | ( | ) | const [inline, inherited] |
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > matrixFunction | ( | StemFunction | f | ) | const [inherited] |
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff | ( | ) | const [inherited] |
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const [inherited] |
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff | ( | IndexType * | index | ) | const [inherited] |
ColsBlockXpr middleCols | ( | Index | startCol, |
Index | numCols | ||
) | [inline, inherited] |
startCol | the index of the first column in the block |
numCols | the number of columns in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
ConstColsBlockXpr middleCols | ( | Index | startCol, |
Index | numCols | ||
) | const [inline, inherited] |
This is the const version of middleCols(Index,Index).
NColsBlockXpr<N>::Type middleCols | ( | Index | startCol | ) | [inline, inherited] |
N | the number of columns in the block |
startCol | the index of the first column in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(:,1..3) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
ConstNColsBlockXpr<N>::Type middleCols | ( | Index | startCol | ) | const [inline, inherited] |
This is the const version of middleCols<int>().
RowsBlockXpr middleRows | ( | Index | startRow, |
Index | numRows | ||
) | [inline, inherited] |
startRow | the index of the first row in the block |
numRows | the number of rows in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(2..3,:) = 6 6 -3 5 -8 6 -5 0 -8 6
ConstRowsBlockXpr middleRows | ( | Index | startRow, |
Index | numRows | ||
) | const [inline, inherited] |
This is the const version of middleRows(Index,Index).
NRowsBlockXpr<N>::Type middleRows | ( | Index | startRow | ) | [inline, inherited] |
N | the number of rows in the block |
startRow | the index of the first row in the block |
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; int main(void) { int const N = 5; MatrixXi A(N,N); A.setRandom(); cout << "A =\n" << A << '\n' << endl; cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl; return 0; }
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6
ConstNRowsBlockXpr<N>::Type middleRows | ( | Index | startRow | ) | const [inline, inherited] |
This is the const version of middleRows<int>().
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff | ( | ) | const [inherited] |
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff | ( | IndexType * | row, |
IndexType * | col | ||
) | const [inherited] |
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff | ( | IndexType * | index | ) | const [inherited] |
const NestByValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > nestByValue | ( | ) | const [inline, inherited] |
NoAlias<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,Eigen::MatrixBase > noalias | ( | ) | [inherited] |
*this
with an operator= assuming no aliasing between *this
and the source expression.More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.
Here are some examples where noalias is usefull:
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;
Referenced by Eigen::internal::apply_block_householder_on_the_left().
RealScalar norm | ( | ) | const [inherited] |
*this
, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this
with itself.void normalize | ( | void | ) | [inherited] |
Normalizes the vector, i.e. divides it by its own norm.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
const PlainObject normalized | ( | ) | const [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr | ( | Index | rows, |
Index | cols, | ||
const CustomNullaryOp & | func | ||
) | [static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr | ( | Index | size, |
const CustomNullaryOp & | func | ||
) | [static, inherited] |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr | ( | const CustomNullaryOp & | func | ) | [static, inherited] |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
cout << MatrixXi::Ones(2,3) << endl;
Output:
1 1 1 1 1 1
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
cout << 6 * RowVectorXi::Ones(4) << endl; cout << VectorXf::Ones(2) << endl;
Output:
6 6 6 6 1 1
static const ConstantReturnType Ones | ( | ) | [static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << Matrix2d::Ones() << endl; cout << 6 * RowVector4i::Ones() << endl;
Output:
1 1 1 1 6 6 6 6
bool operator!= | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other are not exactly equal to each other. const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar | ) | const [inline, inherited] |
*this
scaled by the scalar factor scalar const ScalarMultipleReturnType operator* | ( | const RealScalar & | scalar | ) | const [inherited] |
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator* | ( | const std::complex< Scalar > & | scalar | ) | const [inline, inherited] |
Overloaded for efficient real matrix times complex scalar value
const ProductReturnType<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,OtherDerived>::Type operator* | ( | const MatrixBase< OtherDerived > & | other | ) | const [inherited] |
*this
and other.const DiagonalProduct<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , DiagonalDerived, OnTheRight> operator* | ( | const DiagonalBase< DiagonalDerived > & | diagonal | ) | const [inherited] |
*this
by the diagonal matrix diagonal. ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const [inherited] |
Concatenates a linear transformation matrix and a uniform scaling
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator*= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
* other.
*this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator*= | ( | const Scalar & | other | ) | [inline, inherited] |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= | ( | const MatrixBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
+ other.
*this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator- | ( | ) | const [inline, inherited] |
*this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= | ( | const MatrixBase< OtherDerived > & | other | ) | [inherited] |
replaces *this
by *this
- other.
*this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= | ( | const EigenBase< OtherDerived > & | other | ) | [inherited] |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= | ( | const ArrayBase< OtherDerived > & | ) | [inline, protected, inherited] |
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator/ | ( | const Scalar & | scalar | ) | const [inline, inherited] |
*this
divided by the scalar value scalar Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator/= | ( | const Scalar & | other | ) | [inline, inherited] |
CommaInitializer<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator<< | ( | const Scalar & | s | ) | [inherited] |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Matrix3i m1; m1 << 1, 2, 3, 4, 5, 6, 7, 8, 9; cout << m1 << endl << endl; Matrix3i m2 = Matrix3i::Identity(); m2.block(0,0, 2,2) << 10, 11, 12, 13; cout << m2 << endl << endl; Vector2i v1; v1 << 14, 15; m2 << v1.transpose(), 16, v1, m1.block(1,1,2,2); cout << m2 << endl;
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
CommaInitializer<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator<< | ( | const DenseBase< OtherDerived > & | other | ) | [inherited] |
Matrix& operator= | ( | const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | other | ) | [inline] |
Assigns matrices to each other.
Matrix& operator= | ( | const MatrixBase< 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 PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Matrix& operator= | ( | const ReturnByValue< OtherDerived > & | func | ) | [inline] |
Reimplemented from PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Matrix< _Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols > & operator= | ( | const RotationBase< OtherDerived, ColsAtCompileTime > & | r | ) |
Set a Dim x Dim rotation matrix from the rotation r.
This is defined in the Geometry module.
#include <Eigen/Geometry>
References EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE, and RotationBase< Derived, _Dim >::toRotationMatrix().
bool operator== | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline, inherited] |
*this
and other are all exactly equal. RealScalar operatorNorm | ( | ) | const [inherited] |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
#include <Eigen/Eigenvalues>
This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix is defined to be
where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix .
The current implementation uses the eigenvalues of , as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
<< ones.operatorNorm() << endl;
Output:
The operator norm of the 3x3 matrix of ones is 3
rows()==1 || cols()==1
Index outerStride | ( | ) | const [inline] |
PacketScalar packet | ( | Index | row, |
Index | col | ||
) | const [inline, inherited] |
PacketScalar packet | ( | Index | index | ) | const [inline, inherited] |
const PartialPivLU<PlainObject> partialPivLu | ( | ) | const [inherited] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random | ( | Index | rows, |
Index | cols | ||
) | [static, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
cout << MatrixXi::Random(2,3) << endl;
Output:
7 6 9 -2 6 -6
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random | ( | Index | size | ) | [static, inherited] |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
cout << VectorXi::Random(2) << endl;
Output:
7 -2
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random | ( | ) | [static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << 100 * Matrix2i::Random() << endl;
Output:
700 600 -200 600
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
Referenced by main().
RealReturnType real | ( | ) | const [inline, inherited] |
*this
.NonConstRealReturnType real | ( | ) | [inline, inherited] |
*this
.const Replicate<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,RowFactor,ColFactor> replicate | ( | ) | const [inherited] |
*this
Example:
MatrixXi m = MatrixXi::Random(2,3); cout << "Here is the matrix m:" << endl << m << endl; cout << "m.replicate<3,2>() = ..." << endl; cout << m.replicate<3,2>() << endl;
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
const Replicate<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,Dynamic,Dynamic> replicate | ( | Index | rowFacor, |
Index | colFactor | ||
) | const [inherited] |
*this
Example:
Vector3i v = Vector3i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "v.replicate(2,5) = ..." << endl; cout << v.replicate(2,5) << endl;
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
Resizes *this
to a rows x cols matrix.
This method is intended for dynamic-size matrices, although it is legal to call it on any matrix as long as fixed dimensions are left unchanged. If you only want to change the number of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).
If the current number of coefficients of *this
exactly matches the product rows * cols, then no memory allocation is performed and the current values are left unchanged. In all other cases, including shrinking, the data is reallocated and all previous values are lost.
Example:
MatrixXd m(2,3); m << 1,2,3,4,5,6; cout << "here's the 2x3 matrix m:" << endl << m << endl; cout << "let's resize m to 3x2. This is a conservative resizing because 2*3==3*2." << endl; m.resize(3,2); cout << "here's the 3x2 matrix m:" << endl << m << endl; cout << "now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:" << endl; m.resize(2,2); cout << m << endl;
Output:
here's the 2x3 matrix m: 1 2 3 4 5 6 let's resize m to 3x2. This is a conservative resizing because 2*3==3*2. here's the 3x2 matrix m: 1 5 4 3 2 6 now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized: 1 2 4 5
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Resizes *this
to a vector of length size
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 method does not work for partially dynamic matrices when the static dimension is anything other than 1. For example it will not work with Matrix<double, 2, Dynamic>.
Example:
VectorXd v(10); v.resize(3); RowVector3d w; w.resize(3); // this is legal, but has no effect cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl; cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl;
Output:
v: 3 rows, 1 cols w: 1 rows, 3 cols
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
void resize | ( | NoChange_t | , |
Index | cols | ||
) | [inline, inherited] |
Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value NoChange
as in the example below.
Example:
MatrixXd m(3,4); m.resize(NoChange, 5); cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;
Output:
m: 3 rows, 5 cols
void resize | ( | Index | rows, |
NoChange_t | |||
) | [inline, inherited] |
Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value NoChange
as in the example below.
Example:
MatrixXd m(3,4); m.resize(5, NoChange); cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;
Output:
m: 5 rows, 4 cols
void resizeLike | ( | const EigenBase< OtherDerived > & | _other | ) | [inline, inherited] |
Resizes *this
to have the same dimensions as other. Takes care of doing all the checking that's needed.
Note that copying a row-vector into a vector (and conversely) is allowed. The resizing, if any, is then done in the appropriate way so that row-vectors remain row-vectors and vectors remain vectors.
ReverseReturnType reverse | ( | ) | [inherited] |
Example:
MatrixXi m = MatrixXi::Random(3,4); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the reverse of m:" << endl << m.reverse() << endl; cout << "Here is the coefficient (1,0) in the reverse of m:" << endl << m.reverse()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 4." << endl; m.reverse()(1,0) = 4; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
ConstReverseReturnType reverse | ( | ) | const [inherited] |
This is the const version of reverse().
void reverseInPlace | ( | ) | [inherited] |
This is the "in place" version of reverse: it reverses *this
.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
m = m.reverse().eval();
n | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.rightCols(2):" << endl; cout << a.rightCols(2) << endl; a.rightCols(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols(2): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
This is the const version of rightCols(Index).
NColsBlockXpr<N>::Type rightCols | ( | ) | [inline, inherited] |
N | the number of columns in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.rightCols<2>():" << endl; cout << a.rightCols<2>() << endl; a.rightCols<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols<2>(): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
ConstNColsBlockXpr<N>::Type rightCols | ( | ) | const [inline, inherited] |
This is the const version of rightCols<int>().
ConstRowwiseReturnType rowwise | ( | ) | const [inherited] |
Example:
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl; cout << "Here is the maximum absolute value of each row:" << endl << m.cwiseAbs().rowwise().maxCoeff() << endl;
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
RowwiseReturnType rowwise | ( | ) | [inherited] |
SegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
start | the first coefficient in the segment |
size | the number of coefficients in the segment |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl; v.segment(1, 2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
DenseBase::ConstSegmentReturnType segment | ( | Index | start, |
Index | size | ||
) | const [inherited] |
This is the const version of segment(Index,Index).
*this
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
start | the index of the first element of the sub-vector |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl; v.segment<2>(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
This is the const version of segment<int>(Index).
const Select<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,ThenDerived, typename ThenDerived::ConstantReturnType> select | ( | const DenseBase< ThenDerived > & | thenMatrix, |
typename ThenDerived::Scalar | elseScalar | ||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
const Select<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , typename ElseDerived::ConstantReturnType, ElseDerived > select | ( | typename ElseDerived::Scalar | thenScalar, |
const DenseBase< ElseDerived > & | elseMatrix | ||
) | const [inline, inherited] |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
SelfAdjointViewReturnType<UpLo>::Type selfadjointView | ( | ) | [inherited] |
ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView | ( | ) | const [inherited] |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant | ( | const Scalar & | value | ) | [inherited] |
Sets all coefficients in this expression to value.
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant | ( | Index | size, |
const Scalar & | value | ||
) | [inherited] |
Resizes to the given size, and sets all coefficients in this expression to the given value.
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.setConstant(3, 5); cout << v << endl;
Output:
5 5 5
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant | ( | Index | rows, |
Index | cols, | ||
const Scalar & | value | ||
) | [inherited] |
Resizes to the given size, and sets all coefficients in this expression to the given value.
rows | the new number of rows |
cols | the new number of columns |
value | the value to which all coefficients are set |
Example:
MatrixXf m; m.setConstant(3, 3, 5); cout << m << endl;
Output:
5 5 5 5 5 5 5 5 5
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setIdentity | ( | ) | [inherited] |
Writes the identity expression (not necessarily square) into *this.
Example:
Matrix4i m = Matrix4i::Zero(); m.block<3,3>(1,0).setIdentity(); cout << m << endl;
Output:
0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setIdentity | ( | Index | rows, |
Index | cols | ||
) | [inherited] |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
rows | the new number of rows |
cols | the new number of columns |
Example:
MatrixXf m; m.setIdentity(3, 3); cout << m << endl;
Output:
1 0 0 0 1 0 0 0 1
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setLinSpaced | ( | Index | size, |
const Scalar & | low, | ||
const Scalar & | high | ||
) | [inherited] |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
VectorXf v; v.setLinSpaced(5,0.5f,1.5f).transpose(); cout << v << endl;
Output:
0.5 0.75 1 1.25 1.5
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setLinSpaced | ( | const Scalar & | low, |
const Scalar & | high | ||
) | [inherited] |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
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
Resizes to the given size, and sets all coefficients in this expression to one.
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.setOnes(3); cout << v << endl;
Output:
1 1 1
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes | ( | Index | rows, |
Index | cols | ||
) | [inherited] |
Resizes to the given size, and sets all coefficients in this expression to one.
rows | the new number of rows |
cols | the new number of columns |
Example:
MatrixXf m; m.setOnes(3, 3); cout << m << endl;
Output:
1 1 1 1 1 1 1 1 1
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
Resizes to the given size, and sets all coefficients in this expression to random values.
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.setRandom(3); cout << v << endl;
Output:
0.68 -0.211 0.566
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom | ( | Index | rows, |
Index | cols | ||
) | [inherited] |
Resizes to the given size, and sets all coefficients in this expression to random values.
rows | the new number of rows |
cols | the new number of columns |
Example:
MatrixXf m; m.setRandom(3, 3); cout << m << endl;
Output:
0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444
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
Resizes to the given size, and sets all coefficients in this expression to zero.
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.setZero(3); cout << v << endl;
Output:
0 0 0
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero | ( | Index | rows, |
Index | cols | ||
) | [inherited] |
Resizes to the given size, and sets all coefficients in this expression to zero.
rows | the new number of rows |
cols | the new number of columns |
Example:
MatrixXf m; m.setZero(3, 3); cout << m << endl;
Output:
0 0 0 0 0 0 0 0 0
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sin | ( | ) | const [inherited] |
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sinh | ( | ) | const [inherited] |
const SparseView<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sparseView | ( | const Scalar & | m_reference = Scalar(0) , |
typename NumTraits< Scalar >::Real | m_epsilon = NumTraits<Scalar>::dummy_precision() |
||
) | const [inherited] |
const MatrixSquareRootReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sqrt | ( | ) | const [inherited] |
RealScalar squaredNorm | ( | ) | const [inherited] |
*this
, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this
with itself.RealScalar stableNorm | ( | ) | const [inherited] |
*this
avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s
2 - compute For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.
void swap | ( | MatrixBase< OtherDerived > const & | other | ) | [inline] |
void swap | ( | const DenseBase< OtherDerived > & | other, |
int | = OtherDerived::ThisConstantIsPrivateInPlainObjectBase |
||
) | [inline, inherited] |
swaps *this with the expression other.
void swap | ( | PlainObjectBase< OtherDerived > & | other | ) | [inline, inherited] |
swaps *this with the matrix or array other.
SegmentReturnType tail | ( | Index | size | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
size | the number of coefficients in the block |
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail(2) << endl; v.tail(2).setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
DenseBase::ConstSegmentReturnType tail | ( | Index | size | ) | const [inherited] |
This is the const version of tail(Index).
FixedSegmentReturnType<Size>::Type tail | ( | ) | [inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
RowVector4i v = RowVector4i::Random(); cout << "Here is the vector v:" << endl << v << endl; cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl; v.tail<2>().setZero(); cout << "Now the vector v is:" << endl << v << endl;
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
ConstFixedSegmentReturnType<Size>::Type tail | ( | ) | const [inherited] |
This is the const version of tail<int>.
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner(2, 2):" << endl; cout << m.topLeftCorner(2, 2) << endl; m.topLeftCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topLeftCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topLeftCorner(Index, Index).
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topLeftCorner<2,2>():" << endl; cout << m.topLeftCorner<2,2>() << endl; m.topLeftCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner | ( | ) | const [inline, inherited] |
This is the const version of topLeftCorner<int, int>().
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | [inline, inherited] |
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner(2, 2):" << endl; cout << m.topRightCorner(2, 2) << endl; m.topRightCorner(2, 2).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topRightCorner | ( | Index | cRows, |
Index | cCols | ||
) | const [inline, inherited] |
This is the const version of topRightCorner(Index, Index).
Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner | ( | ) | [inline, inherited] |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is m.topRightCorner<2,2>():" << endl; cout << m.topRightCorner<2,2>() << endl; m.topRightCorner<2,2>().setZero(); cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner | ( | ) | const [inline, inherited] |
This is the const version of topRightCorner<int, int>().
n | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.topRows(2):" << endl; cout << a.topRows(2) << endl; a.topRows(2).setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows(2): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
This is the const version of topRows(Index).
NRowsBlockXpr<N>::Type topRows | ( | ) | [inline, inherited] |
N | the number of rows in the block |
Example:
Array44i a = Array44i::Random(); cout << "Here is the array a:" << endl << a << endl; cout << "Here is a.topRows<2>():" << endl; cout << a.topRows<2>() << endl; a.topRows<2>().setZero(); cout << "Now the array a is:" << endl << a << endl;
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows<2>(): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
ConstNRowsBlockXpr<N>::Type topRows | ( | ) | const [inline, inherited] |
This is the const version of topRows<int>().
*this
, i.e. the sum of the coefficients on the main diagonal.*this
can be any matrix, not necessarily square.
Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.
Eigen::Transpose<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > transpose | ( | ) | [inherited] |
Example:
Matrix2i m = Matrix2i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the transpose of m:" << endl << m.transpose() << endl; cout << "Here is the coefficient (1,0) in the transpose of m:" << endl << m.transpose()(1,0) << endl; cout << "Let us overwrite this coefficient with the value 0." << endl; m.transpose()(1,0) = 0; cout << "Now the matrix m is:" << endl << m << endl;
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
m = m.transpose(); // bug!!! caused by aliasing effect
m.transposeInPlace();
m = m.transpose().eval();
ConstTransposeReturnType transpose | ( | ) | const [inherited] |
This is the const version of transpose().
Make sure you read the warning for transpose() !
void transposeInPlace | ( | ) | [inherited] |
This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
m.transposeInPlace();
has the same effect on m as doing
m = m.transpose().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this
must be a resizable matrix.TriangularViewReturnType<Mode>::Type triangularView | ( | ) | [inherited] |
The parameter Mode can have the following values: #Upper
, #StrictlyUpper
, #UnitUpper
, #Lower
, #StrictlyLower
, #UnitLower
.
Example:
#ifndef _MSC_VER #warning deprecated #endif /* deprecated Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the upper-triangular matrix extracted from m:" << endl << m.part<Eigen::UpperTriangular>() << endl; cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl << m.part<Eigen::StrictlyUpperTriangular>() << endl; cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl << m.part<Eigen::UnitLowerTriangular>() << endl; */
Output:
ConstTriangularViewReturnType<Mode>::Type triangularView | ( | ) | const [inherited] |
This is the const version of MatrixBase::triangularView()
const CwiseUnaryOp<CustomUnaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryExpr | ( | const CustomUnaryOp & | func = CustomUnaryOp() | ) | const [inline, inherited] |
Apply a unary operator coefficient-wise.
[in] | func | Functor implementing the unary operator |
CustomUnaryOp | Type of func |
The function ptr_fun()
from the C++ standard library can be used to make functors out of normal functions.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define function to be applied coefficient-wise double ramp(double x) { if (x > 0) return x; else return 0; } int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.68 0.823 0 0 0 0 0.108 0.0268 0.566 0 0 0.904 0.597 0.536 0.258 0.832
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
const CwiseUnaryView<CustomViewOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryViewExpr | ( | const CustomViewOp & | func = CustomViewOp() | ) | const [inline, inherited] |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
#include <Eigen/Core> #include <iostream> using namespace Eigen; using namespace std; // define a custom template unary functor template<typename Scalar> struct CwiseClampOp { CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {} const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); } Scalar m_inf, m_sup; }; int main(int, char**) { Matrix4d m1 = Matrix4d::Random(); cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl; return 0; }
Output:
0.68 0.823 -0.444 -0.27 -0.211 -0.605 0.108 0.0268 0.566 -0.33 -0.0452 0.904 0.597 0.536 0.258 0.832 becomes: 0.5 0.5 -0.444 -0.27 -0.211 -0.5 0.108 0.0268 0.5 -0.33 -0.0452 0.5 0.5 0.5 0.258 0.5
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is for fixed-size vector only.
PlainObject unitOrthogonal | ( | void | ) | const [inherited] |
*this
The size of *this
must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this
, i.e., (-y,x).normalized().
static const BasisReturnType UnitW | ( | ) | [static, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
static const BasisReturnType UnitX | ( | ) | [static, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
static const BasisReturnType UnitY | ( | ) | [static, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
static const BasisReturnType UnitZ | ( | ) | [static, inherited] |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
CoeffReturnType value | ( | ) | const [inline, inherited] |
void visit | ( | Visitor & | func | ) | const [inherited] |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
struct MyVisitor { // called for the first coefficient void init(const Scalar& value, Index i, Index j); // called for all other coefficients void operator() (const Scalar& value, Index i, Index j); };
void writePacket | ( | Index | row, |
Index | col, | ||
const PacketScalar & | x | ||
) | [inline, inherited] |
void writePacket | ( | Index | index, |
const PacketScalar & | x | ||
) | [inline, inherited] |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
cout << MatrixXi::Zero(2,3) << endl;
Output:
0 0 0 0 0 0
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
cout << RowVectorXi::Zero(4) << endl; cout << VectorXf::Zero(2) << endl;
Output:
0 0 0 0 0 0
static const ConstantReturnType Zero | ( | ) | [static, inherited] |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
cout << Matrix2d::Zero() << endl; cout << RowVector4i::Zero() << endl;
Output:
0 0 0 0 0 0 0 0
const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar, |
const StorageBaseType & | matrix | ||
) | [friend, inherited] |
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator* | ( | const std::complex< Scalar > & | scalar, |
const StorageBaseType & | matrix | ||
) | [friend, inherited] |
DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage [protected, inherited] |