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Eigen
3.4.90 (git rev 5a9f66fb35d03a4da9ef8976e67a61b30aa16dcf)
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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_ | Numeric type, e.g. float, double, int or std::complex<float>. User defined scalar types are supported as well (see here). |
Rows_ | Number of rows, or Dynamic |
Cols_ | Number of columns, or Dynamic |
The remaining template parameters are optional – in most cases you don't have to worry about them.
Options_ | A combination of either RowMajor or ColMajor, and of either AutoAlign or DontAlign. The former controls storage order, and defaults to column-major. The latter controls alignment, which is required for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size. |
MaxRows_ | Maximum number of rows. Defaults to Rows_ (note). |
MaxCols_ | Maximum number of columns. Defaults to Cols_ (note). |
Eigen provides a number of typedefs covering the usual cases. Here are some examples:
Matrix2d
is a 2x2 square matrix of doubles (Matrix<double, 2, 2>
) Vector4f
is a vector of 4 floats (Matrix<float, 4, 1>
) RowVector3i
is a row-vector of 3 ints (Matrix<int, 1, 3>
)MatrixXf
is a dynamic-size matrix of floats (Matrix<float, Dynamic, Dynamic>
) VectorXf
is a dynamic-size vector of floats (Matrix<float, Dynamic, 1>
)Matrix2Xf
is a partially fixed-size (dynamic-size) matrix of floats (Matrix<float, 2, Dynamic>
) MatrixX3d
is a partially dynamic-size (fixed-size) matrix of double (Matrix<double, Dynamic, 3>
)See this page for a complete list of predefined Matrix and Vector typedefs.
You can access elements of vectors and matrices using normal subscripting:
This class can be extended with the help of the plugin mechanism described on the page Extending MatrixBase (and other classes) 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 at 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.
ABI and storage layout
The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
Matrix type | Equivalent C structure |
---|---|
struct {
T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
Eigen::Index rows, cols;
};
const Scalar * data() const Definition PlainObjectBase.h:273 EIGEN_DEFAULT_DENSE_INDEX_TYPE Index The Index type as used for the API. Definition Meta.h:83 | |
struct {
T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
};
EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT Definition EigenBase.h:64 | |
struct {
T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
Eigen::Index rows, cols;
};
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Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
Public Types | |
typedef PlainObjectBase< Matrix > | Base |
Base class typedef. | |
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enum | { RowsAtCompileTime , ColsAtCompileTime , SizeAtCompileTime , MaxRowsAtCompileTime , MaxColsAtCompileTime , MaxSizeAtCompileTime , IsVectorAtCompileTime , NumDimensions , Flags , IsRowMajor , InnerSizeAtCompileTime , InnerStrideAtCompileTime , OuterStrideAtCompileTime } |
typedef random_access_iterator_type | const_iterator |
typedef random_access_iterator_type | iterator |
typedef Array< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime > | PlainArray |
typedef Matrix< typename internal::traits< Derived >::Scalar, internal::traits< Derived >::RowsAtCompileTime, internal::traits< Derived >::ColsAtCompileTime, AutoAlign|(internal::traits< Derived >::Flags &RowMajorBit ? RowMajor :ColMajor), internal::traits< Derived >::MaxRowsAtCompileTime, internal::traits< Derived >::MaxColsAtCompileTime > | PlainMatrix |
typedef std::conditional_t< internal::is_same< typename internal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray > | PlainObject |
The plain matrix or array type corresponding to this expression. | |
typedef internal::traits< Derived >::Scalar | Scalar |
typedef internal::traits< Derived >::StorageIndex | StorageIndex |
The type used to store indices. | |
typedef Scalar | value_type |
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typedef Eigen::Index | Index |
The interface type of indices. | |
Public Member Functions | |
constexpr Scalar & | coeffRef (Index index) |
constexpr const Scalar & | coeffRef (Index index) const |
constexpr Scalar & | coeffRef (Index rowId, Index colId) |
constexpr const Scalar & | coeffRef (Index rowId, Index colId) const |
constexpr | Matrix () |
Default constructor. | |
template<typename OtherDerived > | |
Matrix (const EigenBase< OtherDerived > &other) | |
Copy constructor for generic expressions. | |
Matrix (const Matrix &other) | |
Copy constructor. | |
template<typename OtherDerived > | |
Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r) | |
Constructs a Dim x Dim rotation matrix from the rotation r. | |
template<typename... ArgTypes> | |
Matrix (const Scalar &a0, const Scalar &a1, const Scalar &a2, const Scalar &a3, const ArgTypes &... args) | |
Matrix (const Scalar &x) | |
Constructs an initialized 1x1 matrix with the given coefficient. | |
Matrix (const Scalar &x, const Scalar &y) | |
Constructs an initialized 2D vector with given coefficients. | |
Matrix (const Scalar &x, const Scalar &y, const Scalar &z) | |
Constructs an initialized 3D vector with given coefficients. | |
Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w) | |
Constructs an initialized 4D vector with given coefficients. | |
Matrix (const Scalar *data) | |
Constructs a fixed-sized matrix initialized with coefficients starting at data. | |
constexpr | Matrix (const std::initializer_list< std::initializer_list< Scalar > > &list) |
Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. [c++11] | |
Matrix (Index dim) | |
Constructs a vector or row-vector with given dimension. This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column. | |
Matrix (Index rows, Index cols) | |
Constructs an uninitialized matrix with rows rows and cols columns. | |
template<typename OtherDerived > | |
Matrix & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
constexpr Matrix & | operator= (const Matrix &other) |
Assigns matrices to each other. | |
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. | |
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constexpr const Scalar & | coeff (Index index) const |
constexpr const Scalar & | coeff (Index rowId, Index colId) const |
constexpr Scalar & | coeffRef (Index index) |
constexpr const Scalar & | coeffRef (Index index) const |
constexpr Scalar & | coeffRef (Index rowId, Index colId) |
constexpr const Scalar & | coeffRef (Index rowId, Index colId) const |
void | conservativeResize (Index rows, Index cols) |
void | conservativeResize (Index rows, NoChange_t) |
void | conservativeResize (Index size) |
void | conservativeResize (NoChange_t, Index cols) |
void | conservativeResizeLike (const DenseBase< OtherDerived > &other) |
Scalar * | data () |
const Scalar * | data () const |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | lazyAssign (const DenseBase< OtherDerived > &other) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
constexpr Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | operator= (const PlainObjectBase &other) |
constexpr void | resize (Index rows, Index cols) |
constexpr void | resize (Index rows, NoChange_t) |
constexpr void | resize (Index size) |
constexpr void | resize (NoChange_t, Index cols) |
void | resizeLike (const EigenBase< OtherDerived > &_other) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setConstant (Index rows, Index cols, const Scalar &val) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setConstant (Index rows, NoChange_t, const Scalar &val) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setConstant (Index size, const Scalar &val) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setConstant (NoChange_t, Index cols, const Scalar &val) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setOnes (Index rows, Index cols) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setOnes (Index rows, NoChange_t) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setOnes (Index size) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setOnes (NoChange_t, Index cols) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setRandom (Index rows, Index cols) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setRandom (Index rows, NoChange_t) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setRandom (Index size) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setRandom (NoChange_t, Index cols) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setZero (Index rows, Index cols) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setZero (Index rows, NoChange_t) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setZero (Index size) |
Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | setZero (NoChange_t, Index cols) |
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const MatrixFunctionReturnValue< Derived > | acosh () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh . | |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
template<typename EssentialPart > | |
void | applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
template<typename EssentialPart > | |
void | applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
template<typename OtherDerived > | |
void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
template<typename OtherScalar > | |
void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
template<typename OtherDerived > | |
void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
template<typename OtherScalar > | |
void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
ArrayWrapper< Derived > | array () |
const ArrayWrapper< const Derived > | array () const |
const DiagonalWrapper< const Derived > | asDiagonal () const |
const MatrixFunctionReturnValue< Derived > | asinh () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic sine use ArrayBase::asinh . | |
const SkewSymmetricWrapper< const Derived > | asSkewSymmetric () const |
const MatrixFunctionReturnValue< Derived > | atanh () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh . | |
template<int Options> | |
BDCSVD< typename MatrixBase< Derived >::PlainObject, Options > | bdcSvd () const |
template<int Options> | |
BDCSVD< typename MatrixBase< Derived >::PlainObject, Options > | bdcSvd (unsigned int computationOptions) const |
RealScalar | blueNorm () const |
Matrix< Scalar, 3, 1 > | canonicalEulerAngles (Index a0, Index a1, Index a2) const |
template<typename PermutationIndexType > | |
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndexType > | colPivHouseholderQr () const |
template<typename PermutationIndex > | |
const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject, PermutationIndex > | completeOrthogonalDecomposition () const |
template<typename ResultType > | |
void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
template<typename ResultType > | |
void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
const MatrixFunctionReturnValue< Derived > | cos () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise cosine use ArrayBase::cos . | |
const MatrixFunctionReturnValue< Derived > | cosh () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic cosine use ArrayBase::cosh . | |
template<typename OtherDerived > | |
std::conditional_t< SizeAtCompileTime==2, Scalar, PlainObject > | cross (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
MatrixBase< Derived >::PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
Scalar | determinant () const |
template<int Index_> | |
Diagonal< Derived, Index_ > | diagonal () |
DiagonalReturnType | diagonal () |
template<int Index_> | |
const Diagonal< const Derived, Index_ > | diagonal () const |
const ConstDiagonalReturnType | diagonal () const |
Diagonal< Derived, DynamicIndex > | diagonal (Index index) |
const Diagonal< const Derived, DynamicIndex > | diagonal (Index index) const |
Index | diagonalSize () const |
template<typename OtherDerived > | |
ScalarBinaryOpTraits< typenameinternal::traits< Derived >::Scalar, typenameinternal::traits< OtherDerived >::Scalar >::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. | |
EIGEN_DEPRECATED Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
const MatrixExponentialReturnValue< Derived > | exp () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise exponential use ArrayBase::exp . | |
Derived & | forceAlignedAccess () |
const Derived & | forceAlignedAccess () const |
template<bool Enable> | |
std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > | forceAlignedAccessIf () |
template<bool Enable> | |
add_const_on_value_type_t< std::conditional_t< Enable, ForceAlignedAccess< Derived >, Derived & > > | forceAlignedAccessIf () const |
template<typename PermutationIndex > | |
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject, PermutationIndex > | fullPivHouseholderQr () const |
template<typename PermutationIndex > | |
const FullPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex > | fullPivLu () const |
const HNormalizedReturnType | hnormalized () const |
homogeneous normalization | |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
const Inverse< Derived > | inverse () const |
bool | isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isSkewSymmetric (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<int Options> | |
JacobiSVD< typename MatrixBase< Derived >::PlainObject, Options > | jacobiSvd () const |
template<typename OtherDerived > | |
const Product< Derived, OtherDerived, LazyProduct > | lazyProduct (const MatrixBase< OtherDerived > &other) const |
const LDLT< PlainObject > | ldlt () const |
const LLT< PlainObject > | llt () const |
const MatrixLogarithmReturnValue< Derived > | log () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise logarithm use ArrayBase::log . | |
template<int p> | |
MatrixBase< Derived >::RealScalar | lpNorm () const |
template<typename PermutationIndex > | |
const PartialPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex > | lu () const |
template<typename EssentialPart > | |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
const MatrixFunctionReturnValue< Derived > | matrixFunction (StemFunction f) const |
Helper function for the unsupported MatrixFunctions module. | |
NoAlias< Derived, Eigen::MatrixBase > | noalias () |
RealScalar | norm () const |
void | normalize () |
const PlainObject | normalized () const |
template<typename OtherDerived > | |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
template<typename DiagonalDerived > | |
const Product< Derived, DiagonalDerived, LazyProduct > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
template<typename OtherDerived > | |
const Product< Derived, OtherDerived > | operator* (const MatrixBase< OtherDerived > &other) const |
template<typename SkewDerived > | |
const Product< Derived, SkewDerived, LazyProduct > | operator* (const SkewSymmetricBase< SkewDerived > &skew) const |
template<typename OtherDerived > | |
Derived & | operator*= (const EigenBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator+= (const MatrixBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator-= (const MatrixBase< OtherDerived > &other) |
Derived & | operator= (const MatrixBase &other) |
template<typename OtherDerived > | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
RealScalar | operatorNorm () const |
Computes the L2 operator norm. | |
template<typename PermutationIndex > | |
const PartialPivLU< typename MatrixBase< Derived >::PlainObject, PermutationIndex > | partialPivLu () const |
const MatrixPowerReturnValue< Derived > | pow (const RealScalar &p) const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow . | |
const MatrixComplexPowerReturnValue< Derived > | pow (const std::complex< RealScalar > &p) const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise power to p use ArrayBase::pow . | |
template<unsigned int UpLo> | |
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type | selfadjointView () |
template<unsigned int UpLo> | |
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type | selfadjointView () const |
Derived & | setIdentity () |
Derived & | setIdentity (Index rows, Index cols) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
Derived & | setUnit (Index i) |
Set the coefficients of *this to the i-th unit (basis) vector. | |
Derived & | setUnit (Index newSize, Index i) |
Resizes to the given newSize, and writes the i-th unit (basis) vector into *this. | |
const MatrixFunctionReturnValue< Derived > | sin () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise sine use ArrayBase::sin . | |
const MatrixFunctionReturnValue< Derived > | sinh () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise hyperbolic sine use ArrayBase::sinh . | |
const SparseView< Derived > | sparseView (const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const |
const MatrixSquareRootReturnValue< Derived > | sqrt () const |
This function requires the <a * href="unsupported/group__MatrixFunctions__Module.html"> unsupported MatrixFunctions module. To compute the * coefficient-wise square root use ArrayBase::sqrt . | |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () const |
void | stableNormalize () |
const PlainObject | stableNormalized () const |
Scalar | trace () const |
template<unsigned int Mode> | |
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type | triangularView () |
template<unsigned int Mode> | |
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type | triangularView () const |
PlainObject | unitOrthogonal (void) const |
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bool | all () const |
bool | allFinite () const |
bool | any () const |
iterator | begin () |
const_iterator | begin () const |
const_iterator | cbegin () const |
const_iterator | cend () const |
ColwiseReturnType | colwise () |
ConstColwiseReturnType | colwise () const |
Index | count () const |
iterator | end () |
const_iterator | end () const |
EvalReturnType | eval () const |
void | fill (const Scalar &value) |
template<unsigned int Added, unsigned int Removed> | |
EIGEN_DEPRECATED const Derived & | flagged () const |
const WithFormat< Derived > | format (const IOFormat &fmt) const |
EIGEN_CONSTEXPR 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 OtherDerived > | |
bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename Derived > | |
bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const |
bool | isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
EIGEN_DEPRECATED Derived & | lazyAssign (const DenseBase< OtherDerived > &other) |
template<int NaNPropagation> | |
internal::traits< Derived >::Scalar | maxCoeff () const |
template<int NaNPropagation, typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *index) const |
template<int NaNPropagation, typename IndexType > | |
internal::traits< Derived >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
Scalar | mean () const |
template<int NaNPropagation> | |
internal::traits< Derived >::Scalar | minCoeff () const |
template<int NaNPropagation, typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *index) const |
template<int NaNPropagation, typename IndexType > | |
internal::traits< Derived >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
const NestByValue< Derived > | nestByValue () const |
template<typename OtherDerived > | |
CommaInitializer< Derived > | operator<< (const DenseBase< OtherDerived > &other) |
CommaInitializer< Derived > | operator<< (const Scalar &s) |
Derived & | operator= (const DenseBase &other) |
template<typename OtherDerived > | |
Derived & | operator= (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
Derived & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
EIGEN_CONSTEXPR Index | outerSize () const |
Scalar | prod () const |
template<typename Func > | |
internal::traits< Derived >::Scalar | redux (const Func &func) const |
template<int RowFactor, int ColFactor> | |
const Replicate< Derived, RowFactor, ColFactor > | replicate () const |
const Replicate< Derived, Dynamic, Dynamic > | replicate (Index rowFactor, Index colFactor) const |
void | resize (Index newSize) |
void | resize (Index rows, Index cols) |
ReverseReturnType | reverse () |
ConstReverseReturnType | reverse () const |
void | reverseInPlace () |
RowwiseReturnType | rowwise () |
ConstRowwiseReturnType | rowwise () const |
template<typename ThenDerived , typename ElseDerived > | |
CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, typename DenseBase< Derived >::Scalar >, ThenDerived, ElseDerived, Derived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
template<typename ThenDerived > | |
CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ThenDerived >::Scalar, typename DenseBase< ThenDerived >::Scalar, typename DenseBase< Derived >::Scalar >, ThenDerived, typename DenseBase< ThenDerived >::ConstantReturnType, Derived > | select (const DenseBase< ThenDerived > &thenMatrix, const typename DenseBase< ThenDerived >::Scalar &elseScalar) const |
template<typename ElseDerived > | |
CwiseTernaryOp< internal::scalar_boolean_select_op< typename DenseBase< ElseDerived >::Scalar, typename DenseBase< ElseDerived >::Scalar, typename DenseBase< Derived >::Scalar >, typename DenseBase< ElseDerived >::ConstantReturnType, ElseDerived, Derived > | select (const typename DenseBase< ElseDerived >::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
Derived & | setConstant (const Scalar &value) |
Derived & | setLinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly spaced vector. | |
Derived & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly spaced vector. | |
Derived & | setOnes () |
Derived & | setRandom () |
Derived & | setZero () |
Scalar | sum () const |
template<typename OtherDerived > | |
void | swap (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
void | swap (PlainObjectBase< OtherDerived > &other) |
TransposeReturnType | transpose () |
const ConstTransposeReturnType | transpose () const |
void | transposeInPlace () |
CoeffReturnType | value () const |
template<typename Visitor > | |
void | visit (Visitor &func) const |
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EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | colStride () const EIGEN_NOEXCEPT |
Derived & | derived () |
const Derived & | derived () const |
EIGEN_CONSTEXPR Index | innerStride () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | outerStride () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | rowStride () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
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EIGEN_CONSTEXPR CoeffReturnType | coeff (Index index) const |
EIGEN_CONSTEXPR CoeffReturnType | coeff (Index row, Index col) const |
Scalar & | coeffRef (Index index) |
Scalar & | coeffRef (Index row, Index col) |
EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
Derived & | derived () |
const Derived & | derived () const |
EIGEN_CONSTEXPR Scalar & | operator() (Index index) |
Scalar & | operator() (Index row, Index col) |
Scalar & | operator[] (Index index) |
EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Scalar & | w () |
EIGEN_CONSTEXPR CoeffReturnType | w () const |
EIGEN_CONSTEXPR Scalar & | x () |
EIGEN_CONSTEXPR CoeffReturnType | x () const |
EIGEN_CONSTEXPR Scalar & | y () |
EIGEN_CONSTEXPR CoeffReturnType | y () const |
EIGEN_CONSTEXPR Scalar & | z () |
EIGEN_CONSTEXPR CoeffReturnType | z () const |
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EIGEN_CONSTEXPR CoeffReturnType | coeff (Index index) const |
EIGEN_CONSTEXPR CoeffReturnType | coeff (Index row, Index col) const |
EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
Derived & | derived () |
const Derived & | derived () const |
EIGEN_CONSTEXPR CoeffReturnType | operator() (Index index) const |
EIGEN_CONSTEXPR CoeffReturnType | operator() (Index row, Index col) const |
EIGEN_CONSTEXPR CoeffReturnType | operator[] (Index index) const |
EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR CoeffReturnType | w () const |
EIGEN_CONSTEXPR CoeffReturnType | x () const |
EIGEN_CONSTEXPR CoeffReturnType | y () const |
EIGEN_CONSTEXPR CoeffReturnType | z () const |
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EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
Derived & | derived () |
const Derived & | derived () const |
EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
Additional Inherited Members | |
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static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
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static const ConstantReturnType | Constant (const Scalar &value) |
static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
static const ConstantReturnType | Constant (Index size, const Scalar &value) |
static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
Sets a linearly spaced vector. | |
static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
Sets a linearly spaced vector. | |
static EIGEN_DEPRECATED const RandomAccessLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
static EIGEN_DEPRECATED const RandomAccessLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp< CustomNullaryOp, PlainObject > | NullaryExpr (const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp< CustomNullaryOp, PlainObject > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
template<typename CustomNullaryOp > | |
static const CwiseNullaryOp< CustomNullaryOp, PlainObject > | NullaryExpr (Index size, const CustomNullaryOp &func) |
static const ConstantReturnType | Ones () |
static const ConstantReturnType | Ones (Index rows, Index cols) |
static const ConstantReturnType | Ones (Index size) |
static const RandomReturnType | Random () |
static const RandomReturnType | Random (Index rows, Index cols) |
static const RandomReturnType | Random (Index size) |
static const ConstantReturnType | Zero () |
static const ConstantReturnType | Zero (Index rows, Index cols) |
static const ConstantReturnType | Zero (Index size) |
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constexpr Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ > & | _set (const DenseBase< OtherDerived > &other) |
Copies the value of the expression other into *this with automatic resizing. | |
PlainObjectBase (const DenseBase< OtherDerived > &other) | |
PlainObjectBase (const EigenBase< OtherDerived > &other) | |
constexpr | PlainObjectBase (const PlainObjectBase &other) |
PlainObjectBase (const ReturnByValue< OtherDerived > &other) | |
Copy constructor with in-place evaluation. | |
PlainObjectBase (const Scalar &a0, const Scalar &a1, const Scalar &a2, const Scalar &a3, const ArgTypes &... args) | |
Construct a row of column vector with fixed size from an arbitrary number of coefficients. | |
constexpr | PlainObjectBase (const std::initializer_list< std::initializer_list< Scalar > > &list) |
Constructs a Matrix or Array and initializes it by elements given by an initializer list of initializer lists. | |
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constexpr | DenseBase ()=default |
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template<typename Derived > | |
std::ostream & | operator<< (std::ostream &s, const DenseBase< Derived > &m) |
typedef PlainObjectBase<Matrix> Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::Base |
Base class typedef.
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inlineconstexpr |
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.
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inline |
Example:
Output:
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inlineexplicitconstexpr |
Constructs a Matrix and initializes it from the coefficients given as initializer-lists grouped by row. [c++11]
In the general case, the constructor takes a list of rows, each row being represented as a list of coefficients:
Example:
Output:
Each of the inner initializer lists must contain the exact same number of elements, otherwise an assertion is triggered.
In the case of a compile-time column vector, implicit transposition from a single row is allowed. Therefore VectorXd{{1,2,3,4,5}}
is legal and the more verbose syntax RowVectorXd{{1},{2},{3},{4},{5}}
can be avoided:
Example:
Output:
In the case of fixed-sized matrices, the initializer list sizes must exactly match the matrix sizes, and implicit transposition is allowed for compile-time vectors only.
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inlineexplicit |
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.
This is useful for dynamic-size vectors. For fixed-size vectors, it is redundant to pass these parameters, so one should use the default constructor Matrix() instead.
1x1
matrices. For instance, calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&). For fixed-size 1x1
matrices it is therefore recommended to use the default constructor Matrix() instead, especially when using one of the non standard EIGEN_INITIALIZE_MATRICES_BY_{ZERO
,NAN}
macros (see Preprocessor directives). Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::Matrix | ( | const Scalar & | x | ) |
Constructs an initialized 1x1 matrix with the given coefficient.
Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::Matrix | ( | Index | rows, |
Index | cols ) |
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.
1x2
and 2x1
vectors. For instance, calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y). For fixed-size 1x2
or 2x1
vectors it is therefore recommended to use the default constructor Matrix() instead, especially when using one of the non standard EIGEN_INITIALIZE_MATRICES_BY_{ZERO
,NAN}
macros (see Preprocessor directives). Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::Matrix | ( | const Scalar & | x, |
const Scalar & | y ) |
Constructs an initialized 2D vector with given coefficients.
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inline |
Constructs an initialized 3D vector with given coefficients.
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inline |
Constructs an initialized 4D vector with given coefficients.
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inline |
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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inlineconstexpr |
This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index) const for details.
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inlineconstexpr |
This is the const version of coeffRef(Index) which is thus synonym of coeff(Index). It is provided for convenience.
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inlineconstexpr |
This is an overloaded version of DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const provided to by-pass the creation of an evaluator of the expression, thus saving compilation efforts.
See DenseCoeffsBase<Derived,WriteAccessors>::coeffRef(Index,Index) const for details.
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inlineconstexpr |
This is the const version of coeffRef(Index,Index) which is thus synonym of coeff(Index,Index). It is provided for convenience.
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inline |
Copies the generic expression other into *this.
The expression must provide a (templated) evalTo(Derived& dst) const function which does the actual job. In practice, this allows any user to write its own special matrix without having to modify MatrixBase
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inlineconstexpr |
Assigns matrices to each other.
Matrix< Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_ > & Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, 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.