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/Eigen3

Eigen::Matrix

template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >

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:

Template Parameters
_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.

Template Parameters
_Options A combination of either RowMajor or ColMajor, and of either AutoAlign or DontAlign. The former controls storage order, and defaults to column-major. The latter controls alignment, which is required for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
_MaxRows Maximum number of rows. Defaults to _Rows (note).
_MaxCols Maximum number of columns. Defaults to _Cols (note).

Eigen provides a number of typedefs covering the usual cases. Here are some examples:

  • Matrix2d is a 2x2 square matrix of doubles (Matrix<double, 2, 2>)
  • Vector4f is a vector of 4 floats (Matrix<float, 4, 1>)
  • RowVector3i is a row-vector of 3 ints (Matrix<int, 1, 3>)
  • MatrixXf is a dynamic-size matrix of floats (Matrix<float, Dynamic, Dynamic>)
  • VectorXf is a dynamic-size vector of floats (Matrix<float, Dynamic, 1>)
  • Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (Matrix<float, 2, Dynamic>)
  • MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (Matrix<double, Dynamic, 3>)

See this page for a complete list of predefined Matrix and Vector typedefs.

You can access elements of vectors and matrices using normal subscripting:

Eigen::VectorXd v(10);
v[0] = 0.1;
v[1] = 0.2;
v(0) = 0.3;
v(1) = 0.4;
 
Eigen::MatrixXi m(10, 10);
m(0, 1) = 1;
m(0, 2) = 2;
m(0, 3) = 3;

This class can be extended with the help of the plugin mechanism described on the page Extending MatrixBase (and other classes) by defining the preprocessor symbol EIGEN_MATRIX_PLUGIN.

Some notes:

Dense versus sparse:

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 versus dynamic-size:

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.

_MaxRows and _MaxCols:
In most cases, one just leaves these parameters to the default values. These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.

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
Matrix<T,Dynamic,Dynamic> 
struct {
  T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
  Eigen::Index rows, cols;
 };
Matrix<T,Dynamic,1>
Matrix<T,1,Dynamic> 
struct {
  T *data;                  // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
  Eigen::Index size;
 };
Matrix<T,Rows,Cols> 
struct {
  T data[Rows*Cols];        // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0
 };
Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> 
struct {
  T data[MaxRows*MaxCols];  // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
  Eigen::Index rows, cols;
 };

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.

See also
MatrixBase for the majority of the API methods for matrices, The class hierarchy, Storage orders
typedef PlainObjectBase< Matrix > Base
Base class typedef. More...
- Public Types inherited from Eigen::DenseBase< Derived >
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 internal::conditional< internal::is_same< typename internal::traits< Derived >::XprKind, MatrixXpr >::value, PlainMatrix, PlainArray >::type PlainObject
The plain matrix or array type corresponding to this expression. More...
typedef internal::traits< Derived >::Scalar Scalar
typedef internal::traits< Derived >::StorageIndex StorageIndex
The type used to store indices. More...
typedef Scalar value_type
- Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
The interface type of indices. More...
Matrix ()
Default constructor. More...
template<typename OtherDerived >
Matrix (const EigenBase< OtherDerived > &other)
Copy constructor for generic expressions. More...
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. More...
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. More...
Matrix (const Scalar &x, const Scalar &y)
Constructs an initialized 2D vector with given coefficients. More...
Matrix (const Scalar &x, const Scalar &y, const Scalar &z)
Constructs an initialized 3D vector with given coefficients. More...
Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w)
Constructs an initialized 4D vector with given coefficients. More...
Matrix (const Scalar *data)
Constructs a fixed-sized matrix initialized with coefficients starting at data.
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] 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...
template<typename OtherDerived >
Matrix & operator= (const EigenBase< OtherDerived > &other)
Copies the generic expression other into *this. More...
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...
- Public Member Functions inherited from Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >
const Scalar & coeff (Index index) const
const Scalar & coeff (Index rowId, Index colId) const
Scalar & coeffRef (Index index)
const Scalar & coeffRef (Index index) const
Scalar & coeffRef (Index rowId, Index colId)
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. More...
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator= (const PlainObjectBase &other)
void resize (Index rows, Index cols)
void resize (Index rows, NoChange_t)
void resize (Index size)
void resize (NoChange_t, Index cols)
void resizeLike (const EigenBase< OtherDerived > &_other)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant (Index size, const Scalar &val)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant (Index rows, Index cols, 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 > & setConstant (Index rows, NoChange_t, const Scalar &val)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero (Index size)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero (NoChange_t, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero (Index rows, NoChange_t)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes (Index size)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes (NoChange_t, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes (Index rows, NoChange_t)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom (Index size)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom (NoChange_t, Index cols)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom (Index rows, NoChange_t)
- Public Member Functions inherited from Eigen::MatrixBase< Derived >
const MatrixFunctionReturnValue< Derived > acosh () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh . More...
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 unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh . More...
const MatrixFunctionReturnValue< Derived > atanh () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh . More...
BDCSVD< PlainObject > bdcSvd (unsigned int computationOptions=0) const
RealScalar blueNorm () const
const ColPivHouseholderQR< PlainObject > colPivHouseholderQr () const
const CompleteOrthogonalDecomposition< PlainObject > 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 unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos . More...
const MatrixFunctionReturnValue< Derived > cosh () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh . More...
template<typename OtherDerived >
PlainObject cross (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
Scalar determinant () const
DiagonalReturnType diagonal ()
ConstDiagonalReturnType diagonal () const
DiagonalDynamicIndexReturnType diagonal (Index index)
ConstDiagonalDynamicIndexReturnType diagonal (Index index) const
Index diagonalSize () const
template<typename OtherDerived >
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot (const MatrixBase< OtherDerived > &other) const
EigenvaluesReturnType eigenvalues () const
Computes the eigenvalues of a matrix. More...
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
const MatrixExponentialReturnValue< Derived > exp () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp . More...
Derived & forceAlignedAccess ()
const Derived & forceAlignedAccess () const
template<bool Enable>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf ()
template<bool Enable>
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf () const
const FullPivHouseholderQR< PlainObject > fullPivHouseholderQr () const
const FullPivLU< PlainObject > fullPivLu () const
const HNormalizedReturnType hnormalized () const
homogeneous normalization More...
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 isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObject > jacobiSvd (unsigned int computationOptions=0) 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 unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log . More...
template<int p>
RealScalar lpNorm () const
const PartialPivLU< PlainObject > lu () const
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
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 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. More...
const PartialPivLU< PlainObject > partialPivLu () const
const MatrixPowerReturnValue< Derived > pow (const RealScalar &p) const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow . More...
const MatrixComplexPowerReturnValue< Derived > pow (const std::complex< RealScalar > &p) const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow . More...
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. More...
Derived & setUnit (Index i)
Set the coefficients of *this to the i-th unit (basis) vector. More...
Derived & setUnit (Index newSize, Index i)
Resizes to the given newSize, and writes the i-th unit (basis) vector into *this. More...
const MatrixFunctionReturnValue< Derived > sin () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin . More...
const MatrixFunctionReturnValue< Derived > sinh () const
This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh . More...
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 unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt . More...
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
- Public Member Functions inherited from Eigen::DenseBase< Derived >
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
bool hasNaN () 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
EIGEN_CONSTEXPR Index nonZeros () 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. More...
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 >
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 (const Scalar &low, const Scalar &high)
Sets a linearly spaced vector. More...
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
Sets a linearly spaced vector. More...
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 ()
ConstTransposeReturnType transpose () const
void transposeInPlace ()
CoeffReturnType value () const
template<typename Visitor >
void visit (Visitor &func) const
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >
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
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, WriteAccessors >
Scalar & coeffRef (Index index)
Scalar & coeffRef (Index row, Index col)
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
Derived & derived ()
const Derived & derived () const
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
Scalar & w ()
Scalar & x ()
Scalar & y ()
Scalar & z ()
- Public Member Functions inherited from Eigen::DenseCoeffsBase< Derived, ReadOnlyAccessors >
CoeffReturnType coeff (Index index) const
CoeffReturnType coeff (Index row, Index col) const
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
Derived & derived ()
const Derived & derived () const
CoeffReturnType operator() (Index index) const
CoeffReturnType operator() (Index row, Index col) const
CoeffReturnType operator[] (Index index) const
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index size () const EIGEN_NOEXCEPT
CoeffReturnType w () const
CoeffReturnType x () const
CoeffReturnType y () const
CoeffReturnType z () const
- Public Member Functions inherited from Eigen::EigenBase< Derived >
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
- Static Public Member Functions inherited from Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >
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)
- Static Public Member Functions inherited from Eigen::MatrixBase< Derived >
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 ()
- Static Public Member Functions inherited from Eigen::DenseBase< Derived >
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. More...
static const RandomAccessLinSpacedReturnType LinSpaced (Index size, const Scalar &low, const Scalar &high)
Sets a linearly spaced vector. More...
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)
- Protected Member Functions inherited from Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >
PlainObjectBase (const DenseBase< OtherDerived > &other)
PlainObjectBase (const EigenBase< OtherDerived > &other)
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. [c++11] More...
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 [c++11]
void _resize_to_match (const EigenBase< OtherDerived > &other)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set (const DenseBase< OtherDerived > &other)
Copies the value of the expression other into *this with automatic resizing. More...
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set_noalias (const DenseBase< OtherDerived > &other)
void _init2 (Index rows, Index cols, typename internal::enable_if< Base::SizeAtCompileTime!=2, T0 >::type *=0)
void _init2 (const T0 &val0, const T1 &val1, typename internal::enable_if< Base::SizeAtCompileTime==2, T0 >::type *=0)
void _init2 (const Index &val0, const Index &val1, typename internal::enable_if<(!internal::is_same< Index, Scalar >::value) &&(internal::is_same< T0, Index >::value) &&(internal::is_same< T1, Index >::value) &&Base::SizeAtCompileTime==2, T1 >::type *=0)
void _init1 (Index size, typename internal::enable_if<(Base::SizeAtCompileTime!=1||!internal::is_convertible< T, Scalar >::value) &&((!internal::is_same< typename internal::traits< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::XprKind, ArrayXpr >::value||Base::SizeAtCompileTime==Dynamic)), T >::type *=0)
void _init1 (const Scalar &val0, typename internal::enable_if< Base::SizeAtCompileTime==1 &&internal::is_convertible< T, Scalar >::value, T >::type *=0)
void _init1 (const Index &val0, typename internal::enable_if<(!internal::is_same< Index, Scalar >::value) &&(internal::is_same< Index, T >::value) &&Base::SizeAtCompileTime==1 &&internal::is_convertible< T, Scalar >::value, T * >::type *=0)
void _init1 (const Scalar *data)
void _init1 (const DenseBase< OtherDerived > &other)
void _init1 (const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &other)
void _init1 (const EigenBase< OtherDerived > &other)
void _init1 (const ReturnByValue< OtherDerived > &other)
void _init1 (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
void _init1 (const Scalar &val0, typename internal::enable_if< Base::SizeAtCompileTime!=Dynamic &&Base::SizeAtCompileTime!=1 &&internal::is_convertible< T, Scalar >::value &&internal::is_same< typename internal::traits< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::XprKind, ArrayXpr >::value, T >::type *=0)
void _init1 (const Index &val0, typename internal::enable_if<(!internal::is_same< Index, Scalar >::value) &&(internal::is_same< Index, T >::value) &&Base::SizeAtCompileTime!=Dynamic &&Base::SizeAtCompileTime!=1 &&internal::is_convertible< T, Scalar >::value &&internal::is_same< typename internal::traits< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::XprKind, ArrayXpr >::value, T * >::type *=0)
- Protected Member Functions inherited from Eigen::DenseBase< Derived >
DenseBase ()
- Related Functions inherited from Eigen::DenseBase< Derived >
template<typename Derived >
std::ostream & operator<< (std::ostream &s, const DenseBase< Derived > &m)

Base

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
typedef PlainObjectBase<Matrix> Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Base

Base class typedef.

See also
PlainObjectBase

Matrix() [1/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( )
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.

See also
resize(Index,Index)

Matrix() [2/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
template<typename... ArgTypes>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const Scalar & a0,
const Scalar & a1,
const Scalar & a2,
const Scalar & a3,
const ArgTypes &... args
)
inline

Example:

Matrix<int, 1, 6> a(1, 2, 3, 4, 5, 6);
Matrix<int, 3, 1> b {1, 2, 3};
cout << a << "\n\n" << b << endl;

Output:

1 2 3 4 5 6

1
2
3
See also
Matrix(const std::initializer_list<std::initializer_list<Scalar>>&)

Matrix() [3/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const std::initializer_list< std::initializer_list< Scalar >> & list )
inlineexplicit

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:

MatrixXd m {
  {1, 2, 3},
  {4, 5, 6}
};
cout << m << endl;

Output:

1 2 3
4 5 6

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:

VectorXi v {{1, 2}};
cout << v << endl;

Output:

1
2

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.

See also
Matrix(const Scalar& a0, const Scalar& a1, const Scalar& a2, const Scalar& a3, const ArgTypes&... args)

Matrix() [4/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( Index dim )
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.

Warning
This constructor is disabled for fixed-size 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).

Matrix() [5/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const Scalar & x )

Constructs an initialized 1x1 matrix with the given coefficient.

See also
Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)

Matrix() [6/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
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.

Warning
This constructor is disabled for fixed-size 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).

Matrix() [7/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const Scalar & x,
const Scalar & y
)

Constructs an initialized 2D vector with given coefficients.

See also
Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)

Matrix() [8/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const Scalar & x,
const Scalar & y,
const Scalar & z
)
inline

Constructs an initialized 3D vector with given coefficients.

See also
Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)

Matrix() [9/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const Scalar & x,
const Scalar & y,
const Scalar & z,
const Scalar & w
)
inline

Constructs an initialized 4D vector with given coefficients.

See also
Matrix(const Scalar&, const Scalar&, const Scalar&, const Scalar&, const ArgTypes&...)

Matrix() [10/11]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
template<typename OtherDerived >
Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::Matrix ( const EigenBase< OtherDerived > & other )
inline

Copy constructor for generic expressions.

See also
MatrixBase::operator=(const EigenBase<OtherDerived>&)

Matrix() [11/11]

template<typename _Scalar , int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
template<typename OtherDerived >
Eigen::Matrix< _Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols >::Matrix ( const RotationBase< OtherDerived, ColsAtCompileTime > & r )
explicit

Constructs a Dim x Dim rotation matrix from the rotation r.

This is defined in the Geometry module.

#include <Eigen/Geometry> 

operator=() [1/3]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
template<typename OtherDerived >
Matrix& Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::operator= ( const EigenBase< OtherDerived > & other )
inline

Copies the generic expression other into *this.

The expression must provide a (templated) evalTo(Derived& dst) const function which does the actual job. In practice, this allows any user to write its own special matrix without having to modify MatrixBase

Returns
a reference to *this.

operator=() [2/3]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
Matrix& Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::operator= ( const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & other )
inline

Assigns matrices to each other.

Note
This is a special case of the templated operator=. Its purpose is to prevent a default operator= from hiding the templated operator=.

operator=() [3/3]

template<typename _Scalar , int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
template<typename OtherDerived >
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.

#include <Eigen/Geometry> 

The documentation for this class was generated from the following files:

© Eigen.
Licensed under the MPL2 License.
https://eigen.tuxfamily.org/dox/classEigen_1_1Matrix.html