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Eigen
3.2.1
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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@anchor | matrix_tparam_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@anchor | matrix_tparam_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:
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.
Public Types | |
enum | { RowsAtCompileTime, ColsAtCompileTime, SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime, IsVectorAtCompileTime, Flags, IsRowMajor , CoeffReadCost } |
typedef PlainObjectBase< Matrix > | Base |
Base class typedef. More... | |
Public Member Functions | |
bool | all (void) const |
bool | allFinite () const |
bool | any (void) const |
ArrayWrapper< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | array () |
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< Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const Block< const Derived > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
template<int BlockRows, int BlockCols> | |
Block< Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
template<int BlockRows, int BlockCols> | |
const Block< const Derived, BlockRows, BlockCols > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
Block< Derived > | bottomLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomLeftCorner (Index cRows, Index cCols) const |
Block< Derived > | bottomRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | bottomRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | bottomRightCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | bottomRightCorner (Index cRows, Index cCols) const |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | bottomRows (Index n=N) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | bottomRows (Index n=N) 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 |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
ConstColwiseReturnType | colwise () const |
ColwiseReturnType | colwise () |
ConjugateReturnType | conjugate () const |
void | conservativeResize (Index nbRows, Index nbCols) |
void | conservativeResize (Index nbRows, NoChange_t) |
void | conservativeResize (NoChange_t, Index nbCols) |
void | conservativeResize (Index size) |
void | conservativeResizeLike (const DenseBase< OtherDerived > &other) |
Index | count () 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_product_op < typename Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Scalar, typename OtherDerived::Scalar > , const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, const OtherDerived > | cwiseProduct (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 () |
Index | diagonalSize () const |
EvalReturnType | eval () const |
void | fill (const Scalar &value) |
template<unsigned int Added, unsigned int Removed> | |
const Flagged< Derived, Added, Removed > | flagged () const |
const WithFormat< Derived > | format (const IOFormat &fmt) const |
bool | hasNaN () const |
SegmentReturnType | head (Index n) |
ConstSegmentReturnType | head (Index n) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | head (Index n=N) |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | head (Index n=N) const |
const ImagReturnType | imag () const |
NonConstImagReturnType | imag () |
Index | innerSize () const |
template<typename OtherDerived > | |
bool | isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename Derived > | |
bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const |
template<typename OtherDerived > | |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | lazyAssign (const DenseBase< OtherDerived > &other) |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | leftCols (Index n=N) |
template<int N> | |
ConstNColsBlockXpr< N >::Type | leftCols (Index n=N) const |
Matrix () | |
Default constructor. More... | |
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. More... | |
Matrix (Index rows, Index cols) | |
Constructs an uninitialized matrix with rows rows and cols columns. More... | |
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. | |
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. More... | |
template<typename OtherDerived > | |
Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r) | |
Constructs a Dim x Dim rotation matrix from the rotation r. More... | |
internal::traits< Derived >::Scalar | maxCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *index) const |
Scalar | mean () const |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
template<int N> | |
NColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) |
template<int N> | |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) const |
RowsBlockXpr | middleRows (Index startRow, Index n) |
ConstRowsBlockXpr | middleRows (Index startRow, Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) const |
internal::traits< Derived >::Scalar | minCoeff () const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
template<typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *index) const |
const NestByValue< Derived > | nestByValue () const |
Index | nonZeros () const |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
const ScalarMultipleReturnType | operator* (const Scalar &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 CwiseBinaryOp < internal::scalar_sum_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | operator+ (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_difference_op < Scalar >, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived > | operator- (const Eigen::MatrixBase< OtherDerived > &other) const |
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 |
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 |
CommaInitializer< Derived > | operator<< (const Scalar &s) |
template<typename OtherDerived > | |
CommaInitializer< Derived > | operator<< (const DenseBase< OtherDerived > &other) |
Matrix & | operator= (const Matrix &other) |
Assigns matrices to each other. More... | |
template<typename OtherDerived > | |
Matrix< _Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols > & | operator= (const RotationBase< OtherDerived, ColsAtCompileTime > &r) |
Set a Dim x Dim rotation matrix from the rotation r. More... | |
template<typename OtherDerived > | |
Matrix & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. More... | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
Index | outerSize () const |
Scalar | prod () const |
RealReturnType | real () const |
NonConstRealReturnType | real () |
template<typename Func > | |
internal::result_of< Func(typename internal::traits< Derived > ::Scalar)>::type | redux (const Func &func) const |
template<int RowFactor, int ColFactor> | |
const Replicate< Derived, RowFactor, ColFactor > | replicate () const |
const Replicate< Derived, Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
void | resize (Index nbRows, Index nbCols) |
void | resize (Index size) |
void | resize (NoChange_t, Index nbCols) |
void | resize (Index nbRows, NoChange_t) |
void | resizeLike (const EigenBase< OtherDerived > &_other) |
ReverseReturnType | reverse () |
ConstReverseReturnType | reverse () const |
void | reverseInPlace () |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
template<int N> | |
NColsBlockXpr< N >::Type | rightCols (Index n=N) |
template<int N> | |
ConstNColsBlockXpr< N >::Type | rightCols (Index n=N) const |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
ConstRowwiseReturnType | rowwise () const |
RowwiseReturnType | rowwise () |
SegmentReturnType | segment (Index start, Index n) |
ConstSegmentReturnType | segment (Index start, Index n) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | segment (Index start, Index n=N) |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | segment (Index start, Index n=N) const |
template<typename ThenDerived , typename ElseDerived > | |
const Select< Derived, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
template<typename ThenDerived > | |
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const |
template<typename ElseDerived > | |
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > | select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
Derived & | setConstant (const Scalar &value) |
Derived & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
Derived & | setLinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
Derived & | setOnes () |
Derived & | setRandom () |
Derived & | setZero () |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
SegmentReturnType | tail (Index n) |
ConstSegmentReturnType | tail (Index n) const |
template<int N> | |
FixedSegmentReturnType< N >::Type | tail (Index n=N) |
template<int N> | |
ConstFixedSegmentReturnType< N > ::Type | tail (Index n=N) const |
Block< Derived > | topLeftCorner (Index cRows, Index cCols) |
const Block< const Derived > | topLeftCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topLeftCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topLeftCorner (Index cRows, Index cCols) const |
Block< Derived > | topRightCorner (Index cRows, Index cCols) |
const Block< const Derived > | topRightCorner (Index cRows, Index cCols) const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner () |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner () const |
template<int CRows, int CCols> | |
Block< Derived, CRows, CCols > | topRightCorner (Index cRows, Index cCols) |
template<int CRows, int CCols> | |
const Block< const Derived, CRows, CCols > | topRightCorner (Index cRows, Index cCols) const |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
template<int N> | |
NRowsBlockXpr< N >::Type | topRows (Index n=N) |
template<int N> | |
ConstNRowsBlockXpr< N >::Type | topRows (Index n=N) const |
Eigen::Transpose< Derived > | transpose () |
ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
const CwiseUnaryOp < CustomUnaryOp, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. More... | |
const CwiseUnaryView < CustomViewOp, const Matrix < _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
CoeffReturnType | value () const |
template<typename Visitor > | |
void | visit (Visitor &func) const |
Static Public Member Functions | |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const ConstantReturnType | Constant (const Scalar &value) |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly space vector. More... | |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (Index size, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp < CustomNullaryOp, Derived > | NullaryExpr (const CustomNullaryOp &func) |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const ConstantReturnType | Ones () |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index rows, Index cols) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random (Index size) |
static const CwiseNullaryOp < internal::scalar_random_op < Scalar >, Derived > | Random () |
static const 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 | |
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & | _set (const DenseBase< OtherDerived > &other) |
Copies the value of the expression other into *this with automatic resizing. More... | |
Related Functions | |
(Note that these are not member functions.) | |
template<typename Derived > | |
std::ostream & | operator<< (std::ostream &s, const DenseBase< Derived > &m) |
typedef PlainObjectBase<Matrix> Base |
Base class typedef.
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inherited |
Enumerator | |
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RowsAtCompileTime |
The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
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ColsAtCompileTime |
The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.
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SizeAtCompileTime |
This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.
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MaxRowsAtCompileTime |
This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxColsAtCompileTime |
This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
MaxSizeAtCompileTime |
This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic. This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation. |
IsVectorAtCompileTime |
This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row). |
Flags |
This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags. |
IsRowMajor |
True if this expression has row-major storage order. |
CoeffReadCost |
This is a rough measure of how expensive it is to read one coefficient from this expression. |
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inline |
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.
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.
Copy constructor for generic expressions.
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explicit |
Constructs a Dim x Dim rotation matrix from the rotation r.
This is defined in the Geometry module.
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inlineprotectedinherited |
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.
References Eigen::EvalBeforeAssigningBit.
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inherited |
Example:
Output:
Here is the 2x2 complex matrix m: (-0.649,0.0277) (-0.657,0.895) (0.0691,-0.383) (-0.547,0.404) Here is the adjoint of m: (-0.649,-0.0277) (0.0691,0.383) (-0.657,-0.895) (-0.547,-0.404)
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inherited |
This is the "in place" version of adjoint(): it replaces *this
by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
*this
must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.
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inlineinherited |
Example:
Output:
Is (0.0277 -0.649 -0.383) inside the box: 0 Is (0.0691 0.895 0.657) inside the box: 1
References Eigen::Dynamic.
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inlineinherited |
*this
contains only finite numbers, i.e., no NaN and no +/-INF values.
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inlineinherited |
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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 |
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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 |
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inherited |
replaces *this
by other * *this
.
Example:
Output:
At start, A = 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 After applyOnTheLeft, A = -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 0.0277 0.0691 0.404
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inherited |
This is defined in the Jacobi module.
Applies the rotation in the plane j to the rows p and q of *this
, i.e., it computes B = J * B, with .
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inherited |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=().
Example:
Output:
At start, A = 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 After A *= B, A = 0.404 0.0277 0.0691 -0.547 -0.649 0.895 -0.0105 -0.383 -0.657 After applyOnTheRight, A = 0.0691 0.404 0.0277 0.895 -0.547 -0.649 -0.657 -0.0105 -0.383
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inherited |
Applies the rotation in the plane j to the columns p and q of *this
, i.e., it computes B = B * J with .
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inlineinherited |
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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:
Output:
2 0 0 0 5 0 0 0 6
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inlineinherited |
The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
Output:
(0.0277,0.531) (0.895,0.646) (-0.0105,-0.306) (-0.446,0.214) (-0.649,0.293) (-0.657,-0.696) (-0.751,0.834) (-0.264,0.571) (-0.383,0.534) (0.404,0.251) (-0.832,0.0395) (0.967,0.863) (0.0691,0.56) (-0.547,-0.371) (-0.221,-0.198) (0.0708,0.74)
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inlineinherited |
startRow | the first row in the block |
startCol | the first column in the block |
blockRows | the number of rows in the block |
blockCols | the number of columns in the block |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.block(1, 1, 2, 2): -7 -8 4 -9 Now the matrix m is: 0 9 0 -5 -7 0 0 -3 -4 0 0 10 1 -6 -2 1
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inlineinherited |
This is the const version of block(Index,Index,Index,Index).
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
startRow | the first row in the block |
startCol | the first column in the block |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.block<2,2>(1,1): -7 -8 4 -9 Now the matrix m is: 0 9 0 -5 -7 0 0 -3 -4 0 0 10 1 -6 -2 1
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inlineinherited |
This is the const version of block<>(Index, Index).
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inlineinherited |
BlockRows | number of rows in block as specified at compile-time |
BlockCols | number of columns in block as specified at compile-time |
startRow | the first row in the block |
startCol | the first column in the block |
blockRows | number of rows in block as specified at run-time |
blockCols | number of columns in block as specified at run-time |
This function is mainly useful for blocks where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, blockRows should equal BlockRows unless BlockRows is Dynamic, and the same for the number of columns.
Example:
Output:
Matrix4i m = Matrix4i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl; m.block<2, Dynamic>(1, 1, 2, 3).setZero(); cout << "Now the matrix m is:" << endl << m << endl;
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inlineinherited |
This is the const version of block<>(Index, Index, Index, Index).
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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.
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomLeftCorner(2, 2): -4 4 1 -6 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 0 0 -9 10 0 0 -2 1
This is the const version of bottomLeftCorner(Index, Index).
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomLeftCorner<2,2>(): -4 4 1 -6 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 0 0 -9 10 0 0 -2 1
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inlineinherited |
This is the const version of bottomLeftCorner<int, int>().
CRows | number of rows in corner as specified at compile-time |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomLeftCorner<2,Dynamic>(2,2): -4 4 1 -6 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 0 0 -9 10 0 0 -2 1
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inlineinherited |
This is the const version of bottomLeftCorner<int, int>(Index, Index).
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomRightCorner(2, 2): -9 10 -2 1 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 -4 4 0 0 1 -6 0 0
This is the const version of bottomRightCorner(Index, Index).
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomRightCorner<2,2>(): -9 10 -2 1 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 -4 4 0 0 1 -6 0 0
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inlineinherited |
This is the const version of bottomRightCorner<int, int>().
CRows | number of rows in corner as specified at compile-time |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.bottomRightCorner<2,Dynamic>(2,2): -9 10 -2 1 Now the matrix m is: 0 9 0 -5 -7 -7 -8 -3 -4 4 0 0 1 -6 0 0
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inlineinherited |
This is the const version of bottomRightCorner<int, int>(Index, Index).
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inlineinherited |
n | the number of rows in the block |
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.bottomRows(2): -4 4 -9 10 1 -6 -2 1 Now the array a is: 0 9 0 -5 -7 -7 -8 -3 0 0 0 0 0 0 0 0
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inlineinherited |
This is the const version of bottomRows(Index).
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inlineinherited |
N | the number of rows in the block as specified at compile-time |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.bottomRows<2>(): -4 4 -9 10 1 -6 -2 1 Now the array a is: 0 9 0 -5 -7 -7 -8 -3 0 0 0 0 0 0 0 0
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inlineinherited |
This is the const version of bottomRows<int>().
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inlineinherited |
The template parameter NewScalar is the type we are casting the scalars to.
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inlineinherited |
Example:
Output:
1 4 0 0 5 0 0 6 1
Referenced by VectorwiseOp< ExpressionType, Direction >::cross().
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inherited |
*this
.
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inlineinherited |
Example:
Output:
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 Here is the sum of each column: -1 0.308 -0.153 Here is the maximum absolute value of each column: 0.649 0.895 0.547
Referenced by Eigen::umeyama().
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inlineinherited |
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inherited |
This is defined in the LU module.
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
determinant | Reference to the variable in which to store the determinant. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Output:
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 Its determinant is 0.315 It is invertible, and its inverse is: -1.17 -0.842 -1.27 0.644 0.491 -0.786 2.44 -0.0261 0.221
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inherited |
This is defined in the LU module.
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
inverse | Reference to the matrix in which to store the inverse. |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
Output:
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 It is invertible, and its inverse is: -1.17 -0.842 -1.27 0.644 0.491 -0.786 2.44 -0.0261 0.221
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inlineinherited |
*this
.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.
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inlineinherited |
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.
References PlainObjectBase< Derived >::conservativeResize().
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inlineinherited |
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.
References PlainObjectBase< Derived >::conservativeResize().
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inlineinherited |
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.
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inlineinherited |
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
.
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inlinestaticinherited |
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass nbRows and nbCols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::NullaryExpr().
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inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::NullaryExpr().
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inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
References DenseBase< Derived >::NullaryExpr().
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inlineinherited |
*this
Example:
Output:
2 4 6 5 1 0
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inlineinherited |
*this
Example:
Output:
4 16 36 25 1 0
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inlineinherited |
Example:
Output:
Comparing m with identity matrix: 1 1 0 1 Number of coefficients that are equal: 3
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inlineinherited |
*this
and a scalar s
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inlineinherited |
Example:
Output:
0.5 2 1 0.333 4 1
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inlineinherited |
Example:
Output:
4 3 4
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inlineinherited |
|
inlineinherited |
Example:
Output:
2 2 3
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inlineinherited |
|
inlineinherited |
Example:
Output:
Comparing m with identity matrix: 0 0 1 0 Number of coefficients that are not equal: 1
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inlineinherited |
Example:
Output:
a: 0 1 4 -7 9 -6 -4 -7 0 b: -8 -5 1 -9 -3 6 -2 10 3 c: 0 -5 4 63 -27 -36 8 -70 0
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inlineinherited |
Example:
Output:
0.5 1.5 1.33
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inlineinherited |
Example:
Output:
1 1.41 2
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inlineinherited |
|
inlineinherited |
|
inherited |
This is defined in the LU module.
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inherited |
*this
*this
is not required to be square.
Example:
Output:
Here is the matrix m: 0 1 4 -7 9 -6 -4 -7 0 Here are the coefficients on the main diagonal of m: 0 9 0
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 -8 10 -4 -6
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inherited |
This is the const version of diagonal().
This is the const version of diagonal<int>().
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inherited |
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m: 9 -8 10 -4 -6
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inherited |
This is the const version of diagonal(Index).
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inlineinherited |
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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.
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inherited |
Computes the eigenvalues of a matrix.
This is defined in the Eigenvalues module.
This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
Output:
The eigenvalues of the 3x3 matrix of ones are: (-5.31e-17,0) (3,0) (0,0)
This is defined in the Geometry module.
*this
using the convention defined by the triplet (a0,a1,a2)Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:
"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:
This corresponds to the right-multiply conventions (with right hand side frames).
The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
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inlineinherited |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
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inlineinherited |
Alias for setConstant(): sets all coefficients in this expression to val.
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inlineinherited |
This is mostly for internal use.
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inlineinherited |
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inlineinherited |
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inlineinherited |
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inlineinherited |
|
inlineinherited |
See class IOFormat for some examples.
|
inherited |
*this
.
|
inherited |
This is defined in the LU module.
*this
.
|
inlineinherited |
*this
contains at least one Not A Number (NaN).
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inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
n | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.head(2): 0 -7 Now the vector v is: 0 0 -4 1
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inlineinherited |
This is the const version of head(Index).
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
N | the number of coefficients in the segment as specified at compile-time |
n | the number of coefficients in the segment as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.head(2): 0 -7 Now the vector v is: 0 0 -4 1
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inlineinherited |
This is the const version of head<int>().
|
inherited |
This is defined in the Geometry module.
*this
Example:
Output:
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inherited |
This is defined in the Geometry module.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
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inherited |
*this
.
|
inherited |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
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staticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
Output:
1 0 0 0 0 1 0 0 0 0 1 0
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.
Example:
Output:
1 0 0 0 1 0 0 0 1 0 0 0
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inlineinherited |
*this
.
|
inlineinherited |
*this
.
|
inlineinherited |
|
inherited |
This is defined in the LU module.
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 Its inverse is: -1.17 -0.842 -1.27 0.644 0.491 -0.786 2.44 -0.0261 0.221
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inherited |
true
if *this
is approximately equal to other, within the precision determined by prec.
*this
is approximately equal to the zero matrix or vector. Indeed, isApprox(zero)
returns false unless *this
itself is exactly the zero matrix or vector. If you want to test whether *this
is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.Referenced by Transform< Scalar, Dim, Mode, _Options >::isApprox().
|
inherited |
|
inherited |
This is just an alias for isApproxToConstant().
|
inherited |
Example:
Output:
Here's the matrix m: 1e+04 0 1 0 1e+04 0 0 0 1e+04 m.isDiagonal() returns: 0 m.isDiagonal(1e-3) returns: 1
|
inherited |
Example:
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isIdentity() returns: 0 m.isIdentity(1e-3) returns: 1
|
inherited |
|
inherited |
true
if the norm of *this
is much smaller than other, within the precision determined by prec.
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
|
inherited |
true
if the norm of *this
is much smaller than the norm of other, within the precision determined by prec.
|
inherited |
Example:
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
|
inherited |
Example:
Output:
Here's the vector v: 1 0 0 Here's the vector w: 0.0001 0 1 v.isOrthogonal(w) returns: 0 v.isOrthogonal(w,1e-3) returns: 1
|
inherited |
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.Example:
Output:
Here's the matrix m: 1 0 0.0001 0 1 0 0 0 1 m.isUnitary() returns: 0 m.isUnitary(1e-3) returns: 1
|
inherited |
|
inherited |
Example:
Output:
Here's the matrix m: 0 0 0.0001 0 0 0 0 0 0 m.isZero() returns: 0 m.isZero(1e-3) returns: 1
|
inherited |
This is defined in the SVD module.
*this
computed by two-sided Jacobi transformations.
|
inlineinherited |
|
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.
|
inherited |
This is defined in the Cholesky module.
*this
|
inlineinherited |
n | the number of columns in the block |
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.leftCols(2): 0 9 -7 -7 -4 4 1 -6 Now the array a is: 0 0 0 -5 0 0 -8 -3 0 0 -9 10 0 0 -2 1
|
inlineinherited |
This is the const version of leftCols(Index).
|
inlineinherited |
N | the number of columns in the block as specified at compile-time |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.leftCols<2>(): 0 9 -7 -7 -4 4 1 -6 Now the array a is: 0 0 0 -5 0 0 -8 -3 0 0 -9 10 0 0 -2 1
|
inlineinherited |
This is the const version of leftCols<int>().
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
References DenseBase< Derived >::NullaryExpr().
|
inherited |
This is defined in the Cholesky module.
*this
|
inherited |
This is defined in the LU module.
Synonym of partialPivLu().
*this
.
|
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 |
|
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 |
|
inlineinherited |
*this
. *this
contains NaN.
|
inherited |
*this
contains NaN.
|
inherited |
*this
contains NaN.
|
inlineinherited |
startCol | the index of the first column in the block |
numCols | the number of columns in the block |
Example:
Output:
A = 0 -7 -9 1 7 -7 4 -2 6 -7 -4 -6 -5 3 3 1 0 -3 6 -4 9 -8 10 6 -3 A(1..3,:) = -7 -9 1 4 -2 6 -6 -5 3 0 -3 6 -8 10 6
This is the const version of middleCols(Index,Index).
N | the number of columns in the block as specified at compile-time |
startCol | the index of the first column in the block |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
A = 0 -7 -9 1 7 -7 4 -2 6 -7 -4 -6 -5 3 3 1 0 -3 6 -4 9 -8 10 6 -3 A(:,1..3) = -7 -9 1 4 -2 6 -6 -5 3 0 -3 6 -8 10 6
This is the const version of middleCols<int>().
startRow | the index of the first row in the block |
n | the number of rows in the block |
Example:
Output:
A = 0 -7 -9 1 7 -7 4 -2 6 -7 -4 -6 -5 3 3 1 0 -3 6 -4 9 -8 10 6 -3 A(2..3,:) = -4 -6 -5 3 3 1 0 -3 6 -4
This is the const version of middleRows(Index,Index).
N | the number of rows in the block as specified at compile-time |
startRow | the index of the first row in the block |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
A = 0 -7 -9 1 7 -7 4 -2 6 -7 -4 -6 -5 3 3 1 0 -3 6 -4 9 -8 10 6 -3 A(1..3,:) = -7 4 -2 6 -7 -4 -6 -5 3 3 1 0 -3 6 -4
This is the const version of middleRows<int>().
|
inlineinherited |
*this
. *this
contains NaN.
|
inherited |
*this
contains NaN.
|
inherited |
*this
contains NaN.
|
inlineinherited |
|
inherited |
*this
with an operator= assuming no aliasing between *this
and the source expression.More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.
Here are some examples where noalias is usefull:
On the other hand the following example will lead to a wrong result:
because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:
|
inlineinherited |
|
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.
|
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.
|
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.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
Referenced by DenseBase< Derived >::Constant(), MatrixBase< Derived >::Identity(), and DenseBase< Derived >::LinSpaced().
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
Output:
1 1 1 1 1 1
The parameter newSize is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
Output:
6 6 6 6 1 1
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
1 1 1 1 6 6 6 6
|
inlineinherited |
*this
and other are not exactly equal to each other.
|
inlineinherited |
*this
scaled by the scalar factor scalar
|
inlineinherited |
Overloaded for efficient real matrix times complex scalar value
|
inherited |
*this
and other.
|
inherited |
*this
by the diagonal matrix diagonal.
|
inherited |
Concatenates a linear transformation matrix and a uniform scaling
|
inherited |
replaces *this
by *this
* other.
*this
Example:
Output:
At start, A = 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 After A *= B, A = 0.404 0.0277 0.0691 -0.547 -0.649 0.895 -0.0105 -0.383 -0.657 After applyOnTheRight, A = 0.0691 0.404 0.0277 0.895 -0.547 -0.649 -0.657 -0.0105 -0.383
|
inherited |
*this
and other
|
inherited |
replaces *this
by *this
+ other.
*this
|
inherited |
*this
and other
|
inlineinherited |
*this
|
inherited |
replaces *this
by *this
- other.
*this
|
inlineinherited |
*this
divided by the scalar value scalar
|
inlineinherited |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
|
inlineinherited |
|
inline |
Assigns matrices to each other.
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.
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
|
inlineinherited |
*this
and other are all exactly equal.
|
inherited |
Computes the L2 operator norm.
This is defined in the Eigenvalues module.
This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix is defined to be
where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix .
The current implementation uses the eigenvalues of , as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
Output:
The operator norm of the 3x3 matrix of ones is 3
|
inlineinherited |
References DenseBase< Derived >::IsRowMajor, and DenseBase< Derived >::IsVectorAtCompileTime.
|
inherited |
This is defined in the LU module.
*this
.
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 Here is the product of all the coefficients: -6.48e-07
References Eigen::Dynamic.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
Output:
0 -4 9 -7 1 -7
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
Output:
0 -7
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.
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 -400 -700 100
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.
|
inlineinherited |
*this
.
|
inlineinherited |
*this
.
|
inlineinherited |
The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current STL and TR1 functor styles are handled.
|
inlineinherited |
*this
Example:
Output:
Here is the matrix m: 0 -4 9 -7 1 -7 m.replicate<3,2>() = ... 0 -4 9 0 -4 9 -7 1 -7 -7 1 -7 0 -4 9 0 -4 9 -7 1 -7 -7 1 -7 0 -4 9 0 -4 9 -7 1 -7 -7 1 -7
|
inlineinherited |
*this
Example:
Output:
Here is the vector v: 0 -7 -4 v.replicate(2,5) = ... 0 0 0 0 0 -7 -7 -7 -7 -7 -4 -4 -4 -4 -4 0 0 0 0 0 -7 -7 -7 -7 -7 -4 -4 -4 -4 -4
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:
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
References Eigen::Dynamic.
|
inlineinherited |
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:
Output:
v: 3 rows, 1 cols w: 1 rows, 3 cols
References Eigen::Dynamic.
|
inlineinherited |
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:
Output:
m: 3 rows, 5 cols
References PlainObjectBase< Derived >::resize().
|
inlineinherited |
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:
Output:
m: 5 rows, 4 cols
References PlainObjectBase< Derived >::resize().
|
inlineinherited |
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.
References EigenBase< Derived >::derived(), and PlainObjectBase< Derived >::resize().
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0 1 4 -8 -7 9 -6 -9 -4 -7 0 -2 Here is the reverse of m: -2 0 -7 -4 -9 -6 9 -7 -8 4 1 0 Here is the coefficient (1,0) in the reverse of m: -9 Let us overwrite this coefficient with the value 4. Now the matrix m is: 0 1 4 -8 -7 9 -6 4 -4 -7 0 -2
|
inlineinherited |
This is the const version of reverse().
|
inlineinherited |
This is the "in place" version of reverse: it reverses *this
.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
|
inlineinherited |
n | the number of columns in the block |
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.rightCols(2): 0 -5 -8 -3 -9 10 -2 1 Now the array a is: 0 9 0 0 -7 -7 0 0 -4 4 0 0 1 -6 0 0
|
inlineinherited |
This is the const version of rightCols(Index).
|
inlineinherited |
N | the number of columns in the block as specified at compile-time |
n | the number of columns in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.rightCols<2>(): 0 -5 -8 -3 -9 10 -2 1 Now the array a is: 0 9 0 0 -7 -7 0 0 -4 4 0 0 1 -6 0 0
|
inlineinherited |
This is the const version of rightCols<int>().
|
inlineinherited |
Example:
Output:
1 0 0 4 5 6 0 0 1
Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), and Transform< Scalar, Dim, Mode, _Options >::pretranslate().
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105 Here is the sum of each row: 0.501 -0.3 -1.05 Here is the maximum absolute value of each row: 0.404 0.895 0.657
Referenced by Eigen::umeyama().
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
start | the first coefficient in the segment |
n | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.segment(1, 2): -7 -4 Now the vector v is: 0 0 0 1
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.
N | the number of coefficients in the segment as specified at compile-time |
start | the index of the first element in the segment |
n | the number of coefficients in the segment as specified at compile-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.segment<2>(1): -7 -4 Now the vector v is: 0 -7 0 0
This is the const version of segment<int>(Index).
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
|
inlineinherited |
Sets all coefficients in this expression to value.
|
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:
Output:
5 5 5
|
inherited |
Resizes to the given size, and sets all coefficients in this expression to the given value.
nbRows | the new number of rows |
nbCols | the new number of columns |
val | the value to which all coefficients are set |
Example:
Output:
5 5 5 5 5 5 5 5 5
|
inherited |
Writes the identity expression (not necessarily square) into *this.
Example:
Output:
0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
|
inherited |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
nbRows | the new number of rows |
nbCols | the new number of columns |
Example:
Output:
1 0 0 0 1 0 0 0 1
|
inlineinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
0.5 0.75 1 1.25 1.5
|
inlineinherited |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
Sets all coefficients in this expression to one.
Example:
Output:
0 9 0 -5 1 1 1 1 -4 4 -9 10 1 -6 -2 1
Resizes to the given newSize, 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:
Output:
1 1 1
|
inherited |
Resizes to the given size, and sets all coefficients in this expression to one.
nbRows | the new number of rows |
nbCols | the new number of columns |
Example:
Output:
1 1 1 1 1 1 1 1 1
|
inlineinherited |
Sets all coefficients in this expression to random values.
Example:
Output:
0 0 0 0 0 -7 0 0 0 -4 0 0 0 1 0 0
Resizes to the given newSize, 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:
Output:
0.0277 -0.649 -0.383
|
inherited |
Resizes to the given size, and sets all coefficients in this expression to random values.
nbRows | the new number of rows |
nbCols | the new number of columns |
Example:
Output:
0.0277 0.0691 0.404 -0.649 0.895 -0.547 -0.383 -0.657 -0.0105
|
inlineinherited |
Sets all coefficients in this expression to zero.
Example:
Output:
0 9 0 -5 0 0 0 0 -4 4 -9 10 1 -6 -2 1
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:
Output:
0 0 0
|
inherited |
Resizes to the given size, and sets all coefficients in this expression to zero.
nbRows | the new number of rows |
nbCols | the new number of columns |
Example:
Output:
0 0 0 0 0 0 0 0 0
|
inherited |
|
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.
|
inlineinherited |
References Eigen::Dynamic.
|
inlineinherited |
swaps *this with the expression other.
|
inlineinherited |
swaps *this with the matrix or array other.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
n | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.tail(2): -4 1 Now the vector v is: 0 -7 0 0
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inlineinherited |
This is the const version of tail(Index).
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
N | the number of coefficients in the segment as specified at compile-time |
n | the number of coefficients in the segment as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the vector v: 0 -7 -4 1 Here is v.tail(2): -4 1 Now the vector v is: 0 -7 0 0
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inlineinherited |
This is the const version of tail<int>.
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topLeftCorner(2, 2): 0 9 -7 -7 Now the matrix m is: 0 0 0 -5 0 0 -8 -3 -4 4 -9 10 1 -6 -2 1
This is the const version of topLeftCorner(Index, Index).
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topLeftCorner<2,2>(): 0 9 -7 -7 Now the matrix m is: 0 0 0 -5 0 0 -8 -3 -4 4 -9 10 1 -6 -2 1
|
inlineinherited |
This is the const version of topLeftCorner<int, int>().
CRows | number of rows in corner as specified at compile-time |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topLeftCorner<2,Dynamic>(2,2): 0 9 -7 -7 Now the matrix m is: 0 0 0 -5 0 0 -8 -3 -4 4 -9 10 1 -6 -2 1
References DenseBase< Derived >::IsRowMajor, and DenseBase< Derived >::IsVectorAtCompileTime.
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inlineinherited |
This is the const version of topLeftCorner<int, int>(Index, Index).
cRows | the number of rows in the corner |
cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topRightCorner(2, 2): 0 -5 -8 -3 Now the matrix m is: 0 9 0 0 -7 -7 0 0 -4 4 -9 10 1 -6 -2 1
This is the const version of topRightCorner(Index, Index).
|
inlineinherited |
CRows | the number of rows in the corner |
CCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topRightCorner<2,2>(): 0 -5 -8 -3 Now the matrix m is: 0 9 0 0 -7 -7 0 0 -4 4 -9 10 1 -6 -2 1
|
inlineinherited |
This is the const version of topRightCorner<int, int>().
CRows | number of rows in corner as specified at compile-time |
CCols | number of columns in corner as specified at compile-time |
cRows | number of rows in corner as specified at run-time |
cCols | number of columns in corner as specified at run-time |
This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.
Example:
Output:
Here is the matrix m: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is m.topRightCorner<2,Dynamic>(2,2): 0 -5 -8 -3 Now the matrix m is: 0 9 0 0 -7 -7 0 0 -4 4 -9 10 1 -6 -2 1
|
inlineinherited |
This is the const version of topRightCorner<int, int>(Index, Index).
|
inlineinherited |
n | the number of rows in the block |
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.topRows(2): 0 9 0 -5 -7 -7 -8 -3 Now the array a is: 0 0 0 0 0 0 0 0 -4 4 -9 10 1 -6 -2 1
|
inlineinherited |
This is the const version of topRows(Index).
|
inlineinherited |
N | the number of rows in the block as specified at compile-time |
n | the number of rows in the block as specified at run-time |
The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.
Example:
Output:
Here is the array a: 0 9 0 -5 -7 -7 -8 -3 -4 4 -9 10 1 -6 -2 1 Here is a.topRows<2>(): 0 9 0 -5 -7 -7 -8 -3 Now the array a is: 0 0 0 0 0 0 0 0 -4 4 -9 10 1 -6 -2 1
|
inlineinherited |
This is the const version of topRows<int>().
|
inherited |
*this
, i.e. the sum of the coefficients on the main diagonal.*this
can be any matrix, not necessarily square.
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0 -4 -7 1 Here is the transpose of m: 0 -7 -4 1 Here is the coefficient (1,0) in the transpose of m: -4 Let us overwrite this coefficient with the value 0. Now the matrix m is: 0 0 -7 1
|
inlineinherited |
This is the const version of transpose().
Make sure you read the warning for transpose() !
|
inlineinherited |
This is the "in place" version of transpose(): it replaces *this
by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this
must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.References Eigen::Dynamic.
|
inlineinherited |
Apply a unary operator coefficient-wise.
[in] | func | Functor implementing the unary operator |
CustomUnaryOp | Type of func |
The function ptr_fun()
from the C++ standard library can be used to make functors out of normal functions.
Example:
Output:
0.0277 0.895 -0.0105 -0.446 -0.649 -0.657 -0.751 -0.264 -0.383 0.404 -0.832 0.967 0.0691 -0.547 -0.221 0.0708 becomes: 0.0277 0.895 0 0 0 0 0 0 0 0.404 0 0.967 0.0691 0 0 0.0708
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
Output:
0.0277 0.895 -0.0105 -0.446 -0.649 -0.657 -0.751 -0.264 -0.383 0.404 -0.832 0.967 0.0691 -0.547 -0.221 0.0708 becomes: 0.0277 0.5 -0.0105 -0.446 -0.5 -0.5 -0.5 -0.264 -0.383 0.404 -0.5 0.5 0.0691 -0.5 -0.221 0.0708
|
inlineinherited |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
Output:
0.0277 0.895 -0.0105 -0.446 -0.649 -0.657 -0.751 -0.264 -0.383 0.404 -0.832 0.967 0.0691 -0.547 -0.221 0.0708 becomes: 0.0277 0.5 -0.0105 -0.446 -0.5 -0.5 -0.5 -0.264 -0.383 0.404 -0.5 0.5 0.0691 -0.5 -0.221 0.0708
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.
|
staticinherited |
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.
|
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().
|
staticinherited |
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.
|
staticinherited |
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.
|
staticinherited |
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.
|
staticinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
|
inherited |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
References Eigen::Dynamic.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 0 0 0 0 0 0 0
|
related |
Outputs the matrix, to the given stream.
If you wish to print the matrix with a format different than the default, use DenseBase::format().
It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.