Eigen  3.2.90 (mercurial changeset a775856b75c7)
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Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > Class Template Reference

Detailed Description

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@anchormatrix_tparam_scalar Numeric type, e.g. float, double, int or std::complex<float>. User defined sclar types are supported as well (see here).
_RowsNumber of rows, or Dynamic
_ColsNumber of columns, or Dynamic

The remaining template parameters are optional – in most cases you don't have to worry about them.

Template Parameters
_Options@anchormatrix_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.
_MaxRowsMaximum number of rows. Defaults to _Rows (note).
_MaxColsMaximum 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:

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

This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_MATRIX_PLUGIN.

Some notes:

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.
See Also
MatrixBase for the majority of the API methods for matrices, The class hierarchy, Storage orders
+ Inheritance diagram for Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >:

Public Types

enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime,
  MaxRowsAtCompileTime,
  MaxColsAtCompileTime,
  MaxSizeAtCompileTime,
  IsVectorAtCompileTime,
  Flags,
  IsRowMajor ,
  CoeffReadCost
}
 
typedef PlainObjectBase< MatrixBase
 Base class typedef. More...
 

Public Member Functions

bool all () const
 
bool allFinite () const
 
bool any () const
 
EIGEN_DEVICE_FUNC ArrayWrapper
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
array ()
 
EIGEN_DEVICE_FUNC const
ArrayWrapper< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
array () const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp< CustomBinaryOp,
const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
 
EIGEN_DEVICE_FUNC Block< Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
 
EIGEN_DEVICE_FUNC const Block
< const Derived > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 
template<int BlockRows, int BlockCols>
EIGEN_DEVICE_FUNC Block
< Derived, BlockRows,
BlockCols > 
block (Index startRow, Index startCol)
 
template<int BlockRows, int BlockCols>
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC Block< Derived > bottomLeftCorner (Index cRows, Index cCols)
 
EIGEN_DEVICE_FUNC const Block
< const Derived > 
bottomLeftCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC Block
< Derived, CRows, CCols > 
bottomLeftCorner ()
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC Block< Derived > bottomRightCorner (Index cRows, Index cCols)
 
EIGEN_DEVICE_FUNC const Block
< const Derived > 
bottomRightCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC Block
< Derived, CRows, CCols > 
bottomRightCorner ()
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC RowsBlockXpr bottomRows (Index n)
 
EIGEN_DEVICE_FUNC ConstRowsBlockXpr bottomRows (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
NRowsBlockXpr< N >::Type 
bottomRows (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNRowsBlockXpr< N >::Type 
bottomRows (Index n=N) const
 
EIGEN_DEVICE_FUNC
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
 
EIGEN_DEVICE_FUNC ColXpr col (Index i)
 
EIGEN_DEVICE_FUNC ConstColXpr col (Index i) const
 
ConstColwiseReturnType colwise () const
 
ColwiseReturnType colwise ()
 
EIGEN_DEVICE_FUNC
ConjugateReturnType 
conjugate () const
 
EIGEN_DEVICE_FUNC void conservativeResize (Index nbRows, Index nbCols)
 
EIGEN_DEVICE_FUNC void conservativeResize (Index nbRows, NoChange_t)
 
EIGEN_DEVICE_FUNC void conservativeResize (NoChange_t, Index nbCols)
 
EIGEN_DEVICE_FUNC void conservativeResize (Index size)
 
EIGEN_DEVICE_FUNC void conservativeResizeLike (const DenseBase< OtherDerived > &other)
 
Index count () const
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs () const
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs2 () const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp< std::equal_to
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp< std::binder1st
< std::equal_to< Scalar >
>, const Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
cwiseEqual (const Scalar &s) const
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseInverse () const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMax (const Scalar &other) const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMin (const Scalar &other) const
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC const
CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseSqrt () const
 
const Scalar * data () const
 
Scalar * data ()
 
EIGEN_DEVICE_FUNC Index diagonalSize () const
 
EIGEN_DEVICE_FUNC EvalReturnType eval () const
 
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC SegmentReturnType head (Index n)
 
EIGEN_DEVICE_FUNC
ConstSegmentReturnType 
head (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
FixedSegmentReturnType< N >
::Type 
head (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
 
EIGEN_DEVICE_FUNC const
ImagReturnType 
imag () const
 
EIGEN_DEVICE_FUNC
NonConstImagReturnType 
imag ()
 
EIGEN_DEVICE_FUNC Index innerSize () const
 
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec) const
 
EIGEN_DEVICE_FUNC bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
EIGEN_DEVICE_FUNC 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) const
 
EIGEN_DEVICE_FUNC bool isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
EIGEN_DEVICE_FUNC bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
EIGEN_DEVICE_FUNC Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
lazyAssign (const DenseBase< OtherDerived > &other)
 
EIGEN_DEVICE_FUNC ColsBlockXpr leftCols (Index n)
 
EIGEN_DEVICE_FUNC ConstColsBlockXpr leftCols (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
NColsBlockXpr< N >::Type 
leftCols (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNColsBlockXpr< N >::Type 
leftCols (Index n=N) const
 
template<typename OtherDerived >
 Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
 Constructs a Dim x Dim rotation matrix from the rotation r. More...
 
EIGEN_DEVICE_FUNC Matrix ()
 Default constructor. More...
 
EIGEN_DEVICE_FUNC 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...
 
EIGEN_DEVICE_FUNC 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.
 
EIGEN_DEVICE_FUNC Matrix (const Scalar &x, const Scalar &y, const Scalar &z)
 Constructs an initialized 3D vector with given coefficients.
 
EIGEN_DEVICE_FUNC Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w)
 Constructs an initialized 4D vector with given coefficients.
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Matrix (const MatrixBase< OtherDerived > &other)
 Constructor copying the value of the expression other.
 
EIGEN_DEVICE_FUNC Matrix (const Matrix &other)
 Copy constructor.
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Matrix (const ReturnByValue< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Matrix (const EigenBase< OtherDerived > &other)
 Copy constructor for generic expressions. More...
 
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *rowPtr, IndexType *colPtr) const
 
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
 
EIGEN_DEVICE_FUNC
internal::traits< Derived >
::Scalar 
maxCoeff () const
 
EIGEN_DEVICE_FUNC Scalar mean () const
 
EIGEN_DEVICE_FUNC ColsBlockXpr middleCols (Index startCol, Index numCols)
 
EIGEN_DEVICE_FUNC ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
 
template<int N>
EIGEN_DEVICE_FUNC
NColsBlockXpr< N >::Type 
middleCols (Index startCol, Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNColsBlockXpr< N >::Type 
middleCols (Index startCol, Index n=N) const
 
EIGEN_DEVICE_FUNC RowsBlockXpr middleRows (Index startRow, Index n)
 
EIGEN_DEVICE_FUNC ConstRowsBlockXpr middleRows (Index startRow, Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
NRowsBlockXpr< N >::Type 
middleRows (Index startRow, Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNRowsBlockXpr< N >::Type 
middleRows (Index startRow, Index n=N) const
 
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *rowId, IndexType *colId) const
 
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
 
EIGEN_DEVICE_FUNC
internal::traits< Derived >
::Scalar 
minCoeff () const
 
EIGEN_DEVICE_FUNC const
NestByValue< Derived > 
nestByValue () const
 
EIGEN_DEVICE_FUNC Index nonZeros () const
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index size, const CustomNullaryOp &func)
 
template<typename CustomNullaryOp >
const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (const CustomNullaryOp &func)
 
bool operator!= (const MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC const
ScalarMultipleReturnType 
operator* (const Scalar &scalar) const
 
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC 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
 
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
 
EIGEN_DEVICE_FUNC
CommaInitializer< Derived > 
operator<< (const Scalar &s)
 
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...
 
EIGEN_DEVICE_FUNC Matrixoperator= (const Matrix &other)
 Assigns matrices to each other. More...
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC Matrixoperator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this. More...
 
bool operator== (const MatrixBase< OtherDerived > &other) const
 
EIGEN_DEVICE_FUNC Index outerSize () const
 
EIGEN_DEVICE_FUNC Scalar prod () const
 
EIGEN_DEVICE_FUNC RealReturnType real () const
 
EIGEN_DEVICE_FUNC
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
 
EIGEN_DEVICE_FUNC void resize (Index nbRows, Index nbCols)
 
EIGEN_DEVICE_FUNC void resize (Index size)
 
EIGEN_DEVICE_FUNC void resize (NoChange_t, Index nbCols)
 
EIGEN_DEVICE_FUNC void resize (Index nbRows, NoChange_t)
 
EIGEN_DEVICE_FUNC void resizeLike (const EigenBase< OtherDerived > &_other)
 
ReverseReturnType reverse ()
 
ConstReverseReturnType reverse () const
 
void reverseInPlace ()
 
EIGEN_DEVICE_FUNC ColsBlockXpr rightCols (Index n)
 
EIGEN_DEVICE_FUNC ConstColsBlockXpr rightCols (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
NColsBlockXpr< N >::Type 
rightCols (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNColsBlockXpr< N >::Type 
rightCols (Index n=N) const
 
EIGEN_DEVICE_FUNC RowXpr row (Index i)
 
EIGEN_DEVICE_FUNC ConstRowXpr row (Index i) const
 
ConstRowwiseReturnType rowwise () const
 
RowwiseReturnType rowwise ()
 
EIGEN_DEVICE_FUNC SegmentReturnType segment (Index start, Index n)
 
EIGEN_DEVICE_FUNC
ConstSegmentReturnType 
segment (Index start, Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
FixedSegmentReturnType< N >
::Type 
segment (Index start, Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
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
 
EIGEN_DEVICE_FUNC Derived & setConstant (const Scalar &value)
 
EIGEN_DEVICE_FUNC Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
EIGEN_DEVICE_FUNC Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
EIGEN_DEVICE_FUNC Derived & setOnes ()
 
EIGEN_DEVICE_FUNC Derived & setRandom ()
 
EIGEN_DEVICE_FUNC Derived & setZero ()
 
EIGEN_DEVICE_FUNC Scalar sum () const
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
 
template<typename OtherDerived >
EIGEN_DEVICE_FUNC void swap (PlainObjectBase< OtherDerived > &other)
 
EIGEN_DEVICE_FUNC SegmentReturnType tail (Index n)
 
EIGEN_DEVICE_FUNC
ConstSegmentReturnType 
tail (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
FixedSegmentReturnType< N >
::Type 
tail (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
 
EIGEN_DEVICE_FUNC Block< Derived > topLeftCorner (Index cRows, Index cCols)
 
EIGEN_DEVICE_FUNC const Block
< const Derived > 
topLeftCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC Block
< Derived, CRows, CCols > 
topLeftCorner ()
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC Block< Derived > topRightCorner (Index cRows, Index cCols)
 
EIGEN_DEVICE_FUNC const Block
< const Derived > 
topRightCorner (Index cRows, Index cCols) const
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC Block
< Derived, CRows, CCols > 
topRightCorner ()
 
template<int CRows, int CCols>
EIGEN_DEVICE_FUNC 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
 
EIGEN_DEVICE_FUNC RowsBlockXpr topRows (Index n)
 
EIGEN_DEVICE_FUNC ConstRowsBlockXpr topRows (Index n) const
 
template<int N>
EIGEN_DEVICE_FUNC
NRowsBlockXpr< N >::Type 
topRows (Index n=N)
 
template<int N>
EIGEN_DEVICE_FUNC
ConstNRowsBlockXpr< N >::Type 
topRows (Index n=N) const
 
EIGEN_DEVICE_FUNC
Eigen::Transpose< Derived > 
transpose ()
 
EIGEN_DEVICE_FUNC
ConstTransposeReturnType 
transpose () const
 
EIGEN_DEVICE_FUNC void transposeInPlace ()
 
EIGEN_DEVICE_FUNC const
CwiseUnaryOp< CustomUnaryOp,
const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise. More...
 
EIGEN_DEVICE_FUNC const
CwiseUnaryView< CustomViewOp,
const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
 
EIGEN_DEVICE_FUNC CoeffReturnType value () const
 
template<typename Visitor >
void visit (Visitor &visitor) const
 

Static Public Member Functions

static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Constant (Index rows, Index cols, const Scalar &value)
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Constant (Index size, const Scalar &value)
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Constant (const Scalar &value)
 
static EIGEN_DEVICE_FUNC const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static EIGEN_DEVICE_FUNC const
RandomAccessLinSpacedReturnType 
LinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static EIGEN_DEVICE_FUNC const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static EIGEN_DEVICE_FUNC const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector. More...
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Ones (Index rows, Index cols)
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Ones (Index size)
 
static EIGEN_DEVICE_FUNC 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 EIGEN_DEVICE_FUNC const
ConstantReturnType 
Zero (Index rows, Index cols)
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Zero (Index size)
 
static EIGEN_DEVICE_FUNC const
ConstantReturnType 
Zero ()
 
Map

These are convenience functions returning Map objects. The Map() static functions return unaligned Map objects, while the AlignedMap() functions return aligned Map objects and thus should be called only with 16-byte-aligned data pointers.

See Also
class 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

EIGEN_DEVICE_FUNC 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)
 

Member Typedef Documentation

typedef PlainObjectBase<Matrix> Base

Base class typedef.

See Also
PlainObjectBase

Member Enumeration Documentation

anonymous enum
inherited
Enumerator
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.

See Also
MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime
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.

See Also
MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime
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.

See Also
RowsAtCompileTime, ColsAtCompileTime
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.

See Also
RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
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.

See Also
ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
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.

See Also
SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
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.

Constructor & Destructor Documentation

EIGEN_DEVICE_FUNC 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)
EIGEN_DEVICE_FUNC 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.

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.

EIGEN_DEVICE_FUNC 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.

EIGEN_DEVICE_FUNC Matrix ( const EigenBase< OtherDerived > &  other)
inline

Copy constructor for generic expressions.

See Also
MatrixBase::operator=(const EigenBase<OtherDerived>&)
Matrix ( const RotationBase< OtherDerived, ColsAtCompileTime > &  r)

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

This is defined in the Geometry module.

#include <Eigen/Geometry>

Member Function Documentation

EIGEN_DEVICE_FUNC Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set ( const DenseBase< OtherDerived > &  other)
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.

See Also
operator=(const MatrixBase<OtherDerived>&), _set_noalias()

References Eigen::EvalBeforeAssigningBit.

bool all ( ) const
inlineinherited
Returns
true if all coefficients are true

Example:

Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());
Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();
// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:
cout << "Is (" << p0.transpose() << ") inside the box: "
<< ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;
cout << "Is (" << p1.transpose() << ") inside the box: "
<< ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;

Output:

Is (  0.68 -0.211  0.566) inside the box: 0
Is (0.597 0.823 0.605) inside the box: 1
See Also
any(), Cwise::operator<()

References Eigen::Dynamic.

bool allFinite ( ) const
inlineinherited
Returns
true if *this contains only finite numbers, i.e., no NaN and no +/-INF values.
See Also
hasNaN()
bool any ( ) const
inlineinherited
Returns
true if at least one coefficient is true
See Also
all()

References Eigen::Dynamic.

EIGEN_DEVICE_FUNC ArrayWrapper<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array ( )
inlineinherited
Returns
an Array expression of this matrix
See Also
ArrayBase::matrix()
EIGEN_DEVICE_FUNC const ArrayWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array ( ) const
inlineinherited
Returns
a const Array expression of this matrix
See Also
ArrayBase::matrix()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<CustomBinaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const
inlineinherited
Returns
an expression of a custom coefficient-wise operator func of *this and other

The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)

Here is an example illustrating the use of custom functors:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template binary functor
template<typename Scalar> struct MakeComplexOp {
EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)
typedef complex<Scalar> result_type;
complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }
};
int main(int, char**)
{
Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;
return 0;
}

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)
See Also
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
EIGEN_DEVICE_FUNC Block<Derived> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inlineinherited
Returns
a dynamic-size expression of a block in *this.
Parameters
startRowthe first row in the block
startColthe first column in the block
blockRowsthe number of rows in the block
blockColsthe number of columns in the block

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
m.block(1, 1, 2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See Also
class Block, block(Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

This is the const version of block(Index,Index,Index,Index).

EIGEN_DEVICE_FUNC Block<Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
)
inlineinherited
Returns
a fixed-size expression of a block in *this.

The template parameters BlockRows and BlockCols are the number of rows and columns in the block.

Parameters
startRowthe first row in the block
startColthe first column in the block

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
m.block<2,2>(1,1).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note
since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:
m.template block<3,3>(1,1);
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const
inlineinherited

This is the const version of block<>(Index, Index).

Block<Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
)
inlineinherited
Returns
an expression of a block in *this.
Template Parameters
BlockRowsnumber of rows in block as specified at compile-time
BlockColsnumber of columns in block as specified at compile-time
Parameters
startRowthe first row in the block
startColthe first column in the block
blockRowsnumber of rows in block as specified at run-time
blockColsnumber 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:

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;

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;
See Also
class Block, block(Index,Index,Index,Index)
const Block<const Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const
inlineinherited

This is the const version of block<>(Index, Index, Index, Index).

EIGEN_DEVICE_FUNC Block<Derived> bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a bottom-left corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
cout << m.bottomLeftCorner(2, 2) << endl;
m.bottomLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomLeftCorner(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived, CRows, CCols> bottomLeftCorner ( )
inlineinherited
Returns
an expression of a fixed-size bottom-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
cout << m.bottomLeftCorner<2,2>() << endl;
m.bottomLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived, CRows, CCols> bottomLeftCorner ( ) const
inlineinherited

This is the const version of bottomLeftCorner<int, int>().

Block<Derived, CRows, CCols> bottomLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a bottom-left corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber 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:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,Dynamic>(2,2):" << endl;
cout << m.bottomLeftCorner<2,Dynamic>(2,2) << endl;
m.bottomLeftCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,Dynamic>(2,2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See Also
class Block
const Block<const Derived, CRows, CCols> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomLeftCorner<int, int>(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived> bottomRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a bottom-right corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner(2, 2):" << endl;
cout << m.bottomRightCorner(2, 2) << endl;
m.bottomRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived> bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomRightCorner(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived, CRows, CCols> bottomRightCorner ( )
inlineinherited
Returns
an expression of a fixed-size bottom-right corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,2>():" << endl;
cout << m.bottomRightCorner<2,2>() << endl;
m.bottomRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived, CRows, CCols> bottomRightCorner ( ) const
inlineinherited

This is the const version of bottomRightCorner<int, int>().

Block<Derived, CRows, CCols> bottomRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a bottom-right corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber 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:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,Dynamic>(2,2):" << endl;
cout << m.bottomRightCorner<2,Dynamic>(2,2) << endl;
m.bottomRightCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,Dynamic>(2,2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See Also
class Block
const Block<const Derived, CRows, CCols> bottomRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of bottomRightCorner<int, int>(Index, Index).

EIGEN_DEVICE_FUNC RowsBlockXpr bottomRows ( Index  n)
inlineinherited
Returns
a block consisting of the bottom rows of *this.
Parameters
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows(2):" << endl;
cout << a.bottomRows(2) << endl;
a.bottomRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstRowsBlockXpr bottomRows ( Index  n) const
inlineinherited

This is the const version of bottomRows(Index).

EIGEN_DEVICE_FUNC NRowsBlockXpr<N>::Type bottomRows ( Index  n = N)
inlineinherited
Returns
a block consisting of the bottom rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
nthe 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:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.bottomRows<2>():" << endl;
cout << a.bottomRows<2>() << endl;
a.bottomRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr<N>::Type bottomRows ( Index  n = N) const
inlineinherited

This is the const version of bottomRows<int>().

EIGEN_DEVICE_FUNC 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
inlineinherited
Returns
an expression of *this with the Scalar type casted to NewScalar.

The template parameter NewScalar is the type we are casting the scalars to.

See Also
class CwiseUnaryOp
EIGEN_DEVICE_FUNC ColXpr col ( Index  i)
inlineinherited
Returns
an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

m.col(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 4 0
0 5 0
0 6 1
See Also
row(), class Block

Referenced by VectorwiseOp< ExpressionType, Direction >::cross().

EIGEN_DEVICE_FUNC ConstColXpr col ( Index  i) const
inlineinherited

This is the const version of col().

const DenseBase< Derived >::ConstColwiseReturnType colwise ( ) const
inlineinherited
Returns
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl;
cout << "Here is the maximum absolute value of each column:"
<< endl << m.cwiseAbs().colwise().maxCoeff() << endl;

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Here is the sum of each column:
  1.04  0.815 -0.238
Here is the maximum absolute value of each column:
 0.68 0.823 0.536
See Also
rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Referenced by Eigen::umeyama().

DenseBase< Derived >::ColwiseReturnType colwise ( )
inlineinherited
Returns
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See Also
rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting
EIGEN_DEVICE_FUNC ConjugateReturnType conjugate ( ) const
inlineinherited
Returns
an expression of the complex conjugate of *this.
See Also
adjoint()
EIGEN_DEVICE_FUNC void conservativeResize ( Index  nbRows,
Index  nbCols 
)
inlineinherited

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.

EIGEN_DEVICE_FUNC void conservativeResize ( Index  nbRows,
NoChange_t   
)
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().

EIGEN_DEVICE_FUNC void conservativeResize ( NoChange_t  ,
Index  nbCols 
)
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().

EIGEN_DEVICE_FUNC void conservativeResize ( Index  size)
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.

EIGEN_DEVICE_FUNC void conservativeResizeLike ( const DenseBase< OtherDerived > &  other)
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.

const DenseBase< Derived >::ConstantReturnType Constant ( Index  nbRows,
Index  nbCols,
const Scalar &  value 
)
inlinestaticinherited
Returns
an expression of a constant matrix of value value

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.

See Also
class CwiseNullaryOp
const DenseBase< Derived >::ConstantReturnType Constant ( Index  size,
const Scalar &  value 
)
inlinestaticinherited
Returns
an expression of a constant matrix of value value

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.

See Also
class CwiseNullaryOp
const DenseBase< Derived >::ConstantReturnType Constant ( const Scalar &  value)
inlinestaticinherited
Returns
an expression of a constant matrix of value value

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.

See Also
class CwiseNullaryOp
DenseBase< Derived >::Index count ( ) const
inlineinherited
Returns
the number of coefficients which evaluate to true
See Also
all(), any()
EIGEN_DEVICE_FUNC const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs ( ) const
inlineinherited
Returns
an expression of the coefficient-wise absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,
-5, 1, 0;
cout << m.cwiseAbs() << endl;

Output:

2 4 6
5 1 0
See Also
cwiseAbs2()
EIGEN_DEVICE_FUNC const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs2 ( ) const
inlineinherited
Returns
an expression of the coefficient-wise squared absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,
-5, 1, 0;
cout << m.cwiseAbs2() << endl;

Output:

 4 16 36
25  1  0
See Also
cwiseAbs()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<std::equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseEqual ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise == operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

MatrixXi m(2,2);
m << 1, 0,
1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are equal: " << count << endl;

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3
See Also
cwiseNotEqual(), isApprox(), isMuchSmallerThan()
EIGEN_DEVICE_FUNC const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseEqual ( const Scalar &  s) const
inlineinherited
Returns
an expression of the coefficient-wise == operator of *this and a scalar s
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().
See Also
cwiseEqual(const MatrixBase<OtherDerived> &) const
EIGEN_DEVICE_FUNC const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseInverse ( ) const
inlineinherited
Returns
an expression of the coefficient-wise inverse of *this.

Example:

MatrixXd m(2,3);
m << 2, 0.5, 1,
3, 0.25, 1;
cout << m.cwiseInverse() << endl;

Output:

  0.5     2     1
0.333     4     1
See Also
cwiseProduct()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise max of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMax(w) << endl;

Output:

4
3
4
See Also
class CwiseBinaryOp, min()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMax ( const Scalar &  other) const
inlineinherited
Returns
an expression of the coefficient-wise max of *this and scalar other
See Also
class CwiseBinaryOp, min()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise min of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMin(w) << endl;

Output:

2
2
3
See Also
class CwiseBinaryOp, max()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMin ( const Scalar &  other) const
inlineinherited
Returns
an expression of the coefficient-wise min of *this and scalar other
See Also
class CwiseBinaryOp, min()
EIGEN_DEVICE_FUNC const CwiseBinaryOp<std::not_equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseNotEqual ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise != operator of *this and other
Warning
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

MatrixXi m(2,2);
m << 1, 0,
1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are not equal: " << count << endl;

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1
See Also
cwiseEqual(), isApprox(), isMuchSmallerThan()
EIGEN_DEVICE_FUNC 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
inlineinherited
Returns
an expression of the Schur product (coefficient wise product) of *this and other

Example:

Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random();
Matrix3i c = a.cwiseProduct(b);
cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25
See Also
class CwiseBinaryOp, cwiseAbs2
EIGEN_DEVICE_FUNC const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
an expression of the coefficient-wise quotient of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseQuotient(w) << endl;

Output:

 0.5
 1.5
1.33
See Also
class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
EIGEN_DEVICE_FUNC const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseSqrt ( ) const
inlineinherited
Returns
an expression of the coefficient-wise square root of *this.

Example:

Vector3d v(1,2,4);
cout << v.cwiseSqrt() << endl;

Output:

   1
1.41
   2
See Also
cwisePow(), cwiseSquare()
const Scalar* data ( ) const
inlineinherited
Returns
a const pointer to the data array of this matrix
Scalar* data ( )
inlineinherited
Returns
a pointer to the data array of this matrix
EIGEN_DEVICE_FUNC Index diagonalSize ( ) const
inlineinherited
Returns
the size of the main diagonal, which is min(rows(),cols()).
See Also
rows(), cols(), SizeAtCompileTime.
EIGEN_DEVICE_FUNC EvalReturnType eval ( ) const
inlineinherited
Returns
the matrix or vector obtained by evaluating this expression.

Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.

void fill ( const Scalar &  val)
inlineinherited

Alias for setConstant(): sets all coefficients in this expression to val.

See Also
setConstant(), Constant(), class CwiseNullaryOp
const Flagged< Derived, Added, Removed > flagged ( ) const
inlineinherited
Returns
an expression of *this with added and removed flags

This is mostly for internal use.

See Also
class Flagged
const WithFormat< Derived > format ( const IOFormat fmt) const
inlineinherited
Returns
a WithFormat proxy object allowing to print a matrix the with given format fmt.

See class IOFormat for some examples.

See Also
class IOFormat, class WithFormat
bool hasNaN ( ) const
inlineinherited
Returns
true is *this contains at least one Not A Number (NaN).
See Also
allFinite()
EIGEN_DEVICE_FUNC SegmentReturnType head ( Index  n)
inlineinherited
Returns
a dynamic-size expression of the first coefficients of *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.

Parameters
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head(2) << endl;
v.head(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See Also
class Block, block(Index,Index)
EIGEN_DEVICE_FUNC ConstSegmentReturnType head ( Index  n) const
inlineinherited

This is the const version of head(Index).

EIGEN_DEVICE_FUNC FixedSegmentReturnType<N>::Type head ( Index  n = N)
inlineinherited
Returns
a fixed-size expression of the first coefficients of *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.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
nthe 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:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
v.head<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
See Also
class Block
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType<N>::Type head ( Index  n = N) const
inlineinherited

This is the const version of head<int>().

EIGEN_DEVICE_FUNC const ImagReturnType imag ( ) const
inlineinherited
Returns
an read-only expression of the imaginary part of *this.
See Also
real()
EIGEN_DEVICE_FUNC NonConstImagReturnType imag ( )
inlineinherited
Returns
a non const expression of the imaginary part of *this.
See Also
real()
EIGEN_DEVICE_FUNC Index innerSize ( ) const
inlineinherited
Returns
the inner size.
Note
For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension with respect to the storage order, i.e., the number of rows for a column-major matrix, and the number of columns for a row-major matrix.

References DenseBase< Derived >::IsRowMajor, and DenseBase< Derived >::IsVectorAtCompileTime.

bool isApprox ( const DenseBase< OtherDerived > &  other,
const RealScalar &  prec 
) const
inherited
Returns
true if *this is approximately equal to other, within the precision determined by prec.
Note
The fuzzy compares are done multiplicatively. Two vectors $ v $ and $ w $ are considered to be approximately equal within precision $ p $ if

\[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \]

For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm L2 norm).
Because of the multiplicativeness of this comparison, one can't use this function to check whether *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.
See Also
internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
bool isApproxToConstant ( const Scalar &  val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited
Returns
true if all coefficients in this matrix are approximately equal to val, to within precision prec
bool isConstant ( const Scalar &  val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
inherited

This is just an alias for isApproxToConstant().

Returns
true if all coefficients in this matrix are approximately equal to value, to within precision prec
bool isMuchSmallerThan ( const typename NumTraits< Scalar >::Real &  other,
const RealScalar &  prec 
) const
inherited
Returns
true if the norm of *this is much smaller than other, within the precision determined by prec.
Note
The fuzzy compares are done multiplicatively. A vector $ v $ is considered to be much smaller than $ x $ within precision $ p $ if

\[ \Vert v \Vert \leqslant p\,\vert x\vert. \]

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.

See Also
isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
bool isMuchSmallerThan ( const DenseBase< OtherDerived > &  other,
const RealScalar &  prec 
) const
inherited
Returns
true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.
Note
The fuzzy compares are done multiplicatively. A vector $ v $ is considered to be much smaller than a vector $ w $ within precision $ p $ if

\[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \]

For matrices, the comparison is done using the Hilbert-Schmidt norm.
See Also
isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
bool isOnes ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns
true if *this is approximately equal to the matrix where all coefficients are equal to 1, within the precision given by prec.

Example:

m(0,2) += 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isOnes() returns: " << m.isOnes() << endl;
cout << "m.isOnes(1e-3) returns: " << m.isOnes(1e-3) << endl;

Output:

Here's the matrix m:
1 1 1
1 1 1
1 1 1
m.isOnes() returns: 0
m.isOnes(1e-3) returns: 1
See Also
class CwiseNullaryOp, Ones()
bool isZero ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
inherited
Returns
true if *this is approximately equal to the zero matrix, within the precision given by prec.

Example:

m(0,2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isZero() returns: " << m.isZero() << endl;
cout << "m.isZero(1e-3) returns: " << m.isZero(1e-3) << endl;

Output:

Here's the matrix m:
     0      0 0.0001
     0      0      0
     0      0      0
m.isZero() returns: 0
m.isZero(1e-3) returns: 1
See Also
class CwiseNullaryOp, Zero()
EIGEN_DEVICE_FUNC Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & lazyAssign ( const DenseBase< OtherDerived > &  other)
inlineinherited
See Also
MatrixBase::lazyAssign()
EIGEN_DEVICE_FUNC ColsBlockXpr leftCols ( Index  n)
inlineinherited
Returns
a block consisting of the left columns of *this.
Parameters
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols(2):" << endl;
cout << a.leftCols(2) << endl;
a.leftCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstColsBlockXpr leftCols ( Index  n) const
inlineinherited

This is the const version of leftCols(Index).

EIGEN_DEVICE_FUNC NColsBlockXpr<N>::Type leftCols ( Index  n = N)
inlineinherited
Returns
a block consisting of the left columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
nthe 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:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.leftCols<2>():" << endl;
cout << a.leftCols<2>() << endl;
a.leftCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNColsBlockXpr<N>::Type leftCols ( Index  n = N) const
inlineinherited

This is the const version of leftCols<int>().

const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
Index  size,
const Scalar &  low,
const Scalar &  high 
)
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:

cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See Also
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( Index  size,
const Scalar &  low,
const Scalar &  high 
)
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:

cout << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See Also
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp
const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
const Scalar &  low,
const Scalar &  high 
)
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:

cout << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See Also
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Index,Scalar,Scalar), CwiseNullaryOp Special version for fixed size types which does not require the size parameter.
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( const Scalar &  low,
const Scalar &  high 
)
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:

cout << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1
See Also
setLinSpaced(Index,const Scalar&,const Scalar&), LinSpaced(Sequential_t,Index,const Scalar&,const Scalar&,Index), CwiseNullaryOp Special version for fixed size types which does not require the size parameter.
internal::traits<Derived>::Scalar maxCoeff ( IndexType *  rowPtr,
IndexType *  colPtr 
) const
inherited
Returns
the maximum of all coefficients of *this and puts in *row and *col its location.
Warning
the result is undefined if *this contains NaN.
See Also
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
internal::traits<Derived>::Scalar maxCoeff ( IndexType *  index) const
inherited
Returns
the maximum of all coefficients of *this and puts in *index its location.
Warning
the result is undefined if *this contains NaN.
See Also
DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
internal::traits< Derived >::Scalar maxCoeff ( ) const
inlineinherited
Returns
the maximum of all coefficients of *this.
Warning
the result is undefined if *this contains NaN.
internal::traits< Derived >::Scalar mean ( ) const
inlineinherited
Returns
the mean of all coefficients of *this
See Also
trace(), prod(), sum()
EIGEN_DEVICE_FUNC ColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
)
inlineinherited
Returns
a block consisting of a range of columns of *this.
Parameters
startColthe index of the first column in the block
numColsthe number of columns in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) const
inlineinherited

This is the const version of middleCols(Index,Index).

EIGEN_DEVICE_FUNC NColsBlockXpr<N>::Type middleCols ( Index  startCol,
Index  n = N 
)
inlineinherited
Returns
a block consisting of a range of columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
startColthe index of the first column in the block
nthe 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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(:,1..3) =\n" << A.middleCols<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol,
Index  n = N 
) const
inlineinherited

This is the const version of middleCols<int>().

EIGEN_DEVICE_FUNC RowsBlockXpr middleRows ( Index  startRow,
Index  n 
)
inlineinherited
Returns
a block consisting of a range of rows of *this.
Parameters
startRowthe index of the first row in the block
nthe number of rows in the block

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstRowsBlockXpr middleRows ( Index  startRow,
Index  n 
) const
inlineinherited

This is the const version of middleRows(Index,Index).

EIGEN_DEVICE_FUNC NRowsBlockXpr<N>::Type middleRows ( Index  startRow,
Index  n = N 
)
inlineinherited
Returns
a block consisting of a range of rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
startRowthe index of the first row in the block
nthe 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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
int main(void)
{
int const N = 5;
MatrixXi A(N,N);
A.setRandom();
cout << "A =\n" << A << '\n' << endl;
cout << "A(1..3,:) =\n" << A.middleRows<3>(1) << endl;
return 0;
}

Output:

A =
  7  -6   0   9 -10
 -2  -3   3   3  -5
  6   6  -3   5  -8
  6  -5   0  -8   6
  9   1   9   2  -7

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr<N>::Type middleRows ( Index  startRow,
Index  n = N 
) const
inlineinherited

This is the const version of middleRows<int>().

internal::traits<Derived>::Scalar minCoeff ( IndexType *  rowId,
IndexType *  colId 
) const
inherited
Returns
the minimum of all coefficients of *this and puts in *row and *col its location.
Warning
the result is undefined if *this contains NaN.
See Also
DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
internal::traits<Derived>::Scalar minCoeff ( IndexType *  index) const
inherited
Returns
the minimum of all coefficients of *this and puts in *index its location.
Warning
the result is undefined if *this contains NaN.
See Also
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
internal::traits< Derived >::Scalar minCoeff ( ) const
inlineinherited
Returns
the minimum of all coefficients of *this.
Warning
the result is undefined if *this contains NaN.
const NestByValue< Derived > nestByValue ( ) const
inlineinherited
Returns
an expression of the temporary version of *this.
EIGEN_DEVICE_FUNC Index nonZeros ( ) const
inlineinherited
Returns
the number of nonzero coefficients which is in practice the number of stored coefficients.
const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
)
inlineinherited
Returns
an expression of a matrix defined by a custom functor func

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.

See Also
class CwiseNullaryOp
const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
)
inlineinherited
Returns
an expression of a matrix defined by a custom functor func

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.

Here is an example with C++11 random generators:

#include <Eigen/Core>
#include <iostream>
#include <random>
using namespace Eigen;
int main() {
std::default_random_engine generator;
std::poisson_distribution<int> distribution(4.1);
auto poisson = [&] (int) {return distribution(generator);};
RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson );
std::cout << v << "\n";
}

Output:

2 3 1 4 3 4 4 3 2 3
See Also
class CwiseNullaryOp
const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr ( const CustomNullaryOp &  func)
inlineinherited
Returns
an expression of a matrix defined by a custom functor func

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.

See Also
class CwiseNullaryOp
const DenseBase< Derived >::ConstantReturnType Ones ( Index  nbRows,
Index  nbCols 
)
inlinestaticinherited
Returns
an expression of a matrix where all coefficients equal one.

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:

cout << MatrixXi::Ones(2,3) << endl;

Output:

1 1 1
1 1 1
See Also
Ones(), Ones(Index), isOnes(), class Ones
const DenseBase< Derived >::ConstantReturnType Ones ( Index  newSize)
inlinestaticinherited
Returns
an expression of a vector where all coefficients equal one.

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:

cout << 6 * RowVectorXi::Ones(4) << endl;
cout << VectorXf::Ones(2) << endl;

Output:

6 6 6 6
1
1
See Also
Ones(), Ones(Index,Index), isOnes(), class Ones
const DenseBase< Derived >::ConstantReturnType Ones ( )
inlinestaticinherited
Returns
an expression of a fixed-size matrix or vector where all coefficients equal one.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << Matrix2d::Ones() << endl;
cout << 6 * RowVector4i::Ones() << endl;

Output:

1 1
1 1
6 6 6 6
See Also
Ones(Index), Ones(Index,Index), isOnes(), class Ones
bool operator!= ( const MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
true if at least one pair of coefficients of *this and other are not exactly equal to each other.
Warning
When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
See Also
isApprox(), operator==
EIGEN_DEVICE_FUNC const ScalarMultipleReturnType operator* ( const Scalar &  scalar) const
inlineinherited
Returns
an expression of *this scaled by the scalar factor scalar
EIGEN_DEVICE_FUNC 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
inlineinherited

Overloaded for efficient real matrix times complex scalar value

const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> operator+ ( const Eigen::MatrixBase< OtherDerived > &  other) const
inherited
Returns
an expression of the sum of *this and other
Note
If you want to add a given scalar to all coefficients, see Cwise::operator+().
See Also
class CwiseBinaryOp, operator+=()
const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> operator- ( const Eigen::MatrixBase< OtherDerived > &  other) const
inherited
Returns
an expression of the difference of *this and other
Note
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See Also
class CwiseBinaryOp, operator-=()
EIGEN_DEVICE_FUNC 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
inlineinherited
Returns
an expression of the opposite of *this
EIGEN_DEVICE_FUNC 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
inlineinherited
Returns
an expression of *this divided by the scalar value scalar
CommaInitializer<Derived> operator<< ( const DenseBase< OtherDerived > &  other)
inlineinherited
CommaInitializer< Derived > operator<< ( const Scalar &  s)
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:

m1 << 1, 2, 3,
4, 5, 6,
7, 8, 9;
cout << m1 << endl << endl;
m2.block(0,0, 2,2) << 10, 11, 12, 13;
cout << m2 << endl << endl;
v1 << 14, 15;
m2 << v1.transpose(), 16,
v1, m1.block(1,1,2,2);
cout << m2 << endl;

Output:

1 2 3
4 5 6
7 8 9

10 11  0
12 13  0
 0  0  1

14 15 16
14  5  6
15  8  9
Note
According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
See Also
CommaInitializer::finished(), class CommaInitializer
Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>& operator= ( const RotationBase< OtherDerived, ColsAtCompileTime > &  r)

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

This is defined in the Geometry module.

#include <Eigen/Geometry>
EIGEN_DEVICE_FUNC Matrix& 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=.
EIGEN_DEVICE_FUNC Matrix& operator= ( const EigenBase< OtherDerived > &  other)
inline

Copies the generic expression other into *this.

bool operator== ( const MatrixBase< OtherDerived > &  other) const
inlineinherited
Returns
true if each coefficients of *this and other are all exactly equal.
Warning
When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
See Also
isApprox(), operator!=
EIGEN_DEVICE_FUNC Index outerSize ( ) const
inlineinherited
Returns
true if either the number of rows or the number of columns is equal to 1. In other words, this function returns
rows()==1 || cols()==1
See Also
rows(), cols(), IsVectorAtCompileTime.
Returns
the outer size.
Note
For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension with respect to the storage order, i.e., the number of columns for a column-major matrix, and the number of rows for a row-major matrix.

References DenseBase< Derived >::IsRowMajor, and DenseBase< Derived >::IsVectorAtCompileTime.

internal::traits< Derived >::Scalar prod ( ) const
inlineinherited
Returns
the product of all coefficients of *this

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the product of all the coefficients:" << endl << m.prod() << endl;

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Here is the product of all the coefficients:
0.0019
See Also
sum(), mean(), trace()

References Eigen::Dynamic.

const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  rows,
Index  cols 
)
inlinestaticinherited
Returns
a random matrix expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.

Warning
This function is not re-entrant.

This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.

Example:

cout << MatrixXi::Random(2,3) << endl;

Output:

 7  6  9
-2  6 -6

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.

See Also
DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  size)
inlinestaticinherited
Returns
a random vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

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.

Warning
This function is not re-entrant.

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.

Example:

cout << VectorXi::Random(2) << endl;

Output:

 7
-2

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See Also
DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()
const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( )
inlinestaticinherited
Returns
a fixed-size random matrix or vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << 100 * Matrix2i::Random() << endl;

Output:

 700  600
-200  600

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

Warning
This function is not re-entrant.
See Also
DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)
EIGEN_DEVICE_FUNC RealReturnType real ( ) const
inlineinherited
Returns
a read-only expression of the real part of *this.
See Also
imag()
EIGEN_DEVICE_FUNC NonConstRealReturnType real ( )
inlineinherited
Returns
a non const expression of the real part of *this.
See Also
imag()
internal::result_of<Func(typename internal::traits<Derived>::Scalar)>::type redux ( const Func &  func) const
inlineinherited
Returns
the result of a full redux operation on the whole matrix or vector using func

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.

See Also
DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
const Replicate< Derived, RowFactor, ColFactor > replicate ( ) const
inlineinherited
Returns
an expression of the replication of *this

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "m.replicate<3,2>() = ..." << endl;
cout << m.replicate<3,2>() << endl;

Output:

Here is the matrix m:
 7  6  9
-2  6 -6
m.replicate<3,2>() = ...
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
 7  6  9  7  6  9
-2  6 -6 -2  6 -6
See Also
VectorwiseOp::replicate(), DenseBase::replicate(Index,Index), class Replicate
const Replicate< Derived, Dynamic, Dynamic > replicate ( Index  rowFactor,
Index  colFactor 
) const
inlineinherited
Returns
an expression of the replication of *this

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "v.replicate(2,5) = ..." << endl;
cout << v.replicate(2,5) << endl;

Output:

Here is the vector v:
 7
-2
 6
v.replicate(2,5) = ...
 7  7  7  7  7
-2 -2 -2 -2 -2
 6  6  6  6  6
 7  7  7  7  7
-2 -2 -2 -2 -2
 6  6  6  6  6
See Also
VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate
EIGEN_DEVICE_FUNC void resize ( Index  nbRows,
Index  nbCols 
)
inlineinherited

Resizes *this to a rows x cols matrix.

This method is intended for dynamic-size matrices, although it is legal to call it on any matrix as long as fixed dimensions are left unchanged. If you only want to change the number of rows and/or of columns, you can use resize(NoChange_t, Index), resize(Index, NoChange_t).

If the current number of coefficients of *this exactly matches the product rows * cols, then no memory allocation is performed and the current values are left unchanged. In all other cases, including shrinking, the data is reallocated and all previous values are lost.

Example:

MatrixXd m(2,3);
m << 1,2,3,4,5,6;
cout << "here's the 2x3 matrix m:" << endl << m << endl;
cout << "let's resize m to 3x2. This is a conservative resizing because 2*3==3*2." << endl;
m.resize(3,2);
cout << "here's the 3x2 matrix m:" << endl << m << endl;
cout << "now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:" << endl;
m.resize(2,2);
cout << m << endl;

Output:

here's the 2x3 matrix m:
1 2 3
4 5 6
let's resize m to 3x2. This is a conservative resizing because 2*3==3*2.
here's the 3x2 matrix m:
1 5
4 3
2 6
now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:
6.94e-310 2.12e-314
4.94e-324 4.94e-323
See Also
resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)

References Eigen::Dynamic.

EIGEN_DEVICE_FUNC void resize ( Index  size)
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:

VectorXd v(10);
v.resize(3);
w.resize(3); // this is legal, but has no effect
cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl;
cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl;

Output:

v: 3 rows, 1 cols
w: 1 rows, 3 cols
See Also
resize(Index,Index), resize(NoChange_t, Index), resize(Index, NoChange_t)

References Eigen::Dynamic.

EIGEN_DEVICE_FUNC void resize ( NoChange_t  ,
Index  nbCols 
)
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:

MatrixXd m(3,4);
m.resize(NoChange, 5);
cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;

Output:

m: 3 rows, 5 cols
See Also
resize(Index,Index)

References PlainObjectBase< Derived >::resize().

EIGEN_DEVICE_FUNC void resize ( Index  nbRows,
NoChange_t   
)
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:

MatrixXd m(3,4);
m.resize(5, NoChange);
cout << "m: " << m.rows() << " rows, " << m.cols() << " cols" << endl;

Output:

m: 5 rows, 4 cols
See Also
resize(Index,Index)

References PlainObjectBase< Derived >::resize().

EIGEN_DEVICE_FUNC void resizeLike ( const EigenBase< OtherDerived > &  _other)
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().

DenseBase< Derived >::ReverseReturnType reverse ( )
inlineinherited
Returns
an expression of the reverse of *this.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the reverse of m:" << endl << m.reverse() << endl;
cout << "Here is the coefficient (1,0) in the reverse of m:" << endl
<< m.reverse()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 4." << endl;
m.reverse()(1,0) = 4;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  6 -3  1
-2  9  6  0
 6 -6 -5  3
Here is the reverse of m:
 3 -5 -6  6
 0  6  9 -2
 1 -3  6  7
Here is the coefficient (1,0) in the reverse of m:
0
Let us overwrite this coefficient with the value 4.
Now the matrix m is:
 7  6 -3  1
-2  9  6  4
 6 -6 -5  3
const DenseBase< Derived >::ConstReverseReturnType reverse ( ) const
inlineinherited

This is the const version of reverse().

void reverseInPlace ( )
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:

  • less error prone: doing the same operation with .reverse() requires special care:
    m = m.reverse().eval();
  • this API allows to avoid creating a temporary (the current implementation creates a temporary, but that could be avoided using swap)
  • it allows future optimizations (cache friendliness, etc.)
See Also
reverse()
EIGEN_DEVICE_FUNC ColsBlockXpr rightCols ( Index  n)
inlineinherited
Returns
a block consisting of the right columns of *this.
Parameters
nthe number of columns in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols(2):" << endl;
cout << a.rightCols(2) << endl;
a.rightCols(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstColsBlockXpr rightCols ( Index  n) const
inlineinherited

This is the const version of rightCols(Index).

EIGEN_DEVICE_FUNC NColsBlockXpr<N>::Type rightCols ( Index  n = N)
inlineinherited
Returns
a block consisting of the right columns of *this.
Template Parameters
Nthe number of columns in the block as specified at compile-time
Parameters
nthe 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:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.rightCols<2>():" << endl;
cout << a.rightCols<2>() << endl;
a.rightCols<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols<2>():
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNColsBlockXpr<N>::Type rightCols ( Index  n = N) const
inlineinherited

This is the const version of rightCols<int>().

EIGEN_DEVICE_FUNC RowXpr row ( Index  i)
inlineinherited
Returns
an expression of the i-th row of *this. Note that the numbering starts at 0.

Example:

m.row(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

1 0 0
4 5 6
0 0 1
See Also
col(), class Block

Referenced by VectorwiseOp< ExpressionType, Direction >::cross(), and Transform< Scalar, Dim, Mode, _Options >::pretranslate().

EIGEN_DEVICE_FUNC ConstRowXpr row ( Index  i) const
inlineinherited

This is the const version of row().

const DenseBase< Derived >::ConstRowwiseReturnType rowwise ( ) const
inlineinherited
Returns
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << endl;
cout << "Here is the maximum absolute value of each row:"
<< endl << m.cwiseAbs().rowwise().maxCoeff() << endl;

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Here is the sum of each row:
 0.948
  1.15
-0.483
Here is the maximum absolute value of each row:
 0.68
0.823
0.605
See Also
colwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Referenced by Eigen::umeyama().

DenseBase< Derived >::RowwiseReturnType rowwise ( )
inlineinherited
Returns
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See Also
colwise(), class VectorwiseOp, Reductions, visitors and broadcasting
EIGEN_DEVICE_FUNC SegmentReturnType segment ( Index  start,
Index  n 
)
inlineinherited
Returns
a dynamic-size expression of a segment (i.e. a vector block) in *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.

Parameters
startthe first coefficient in the segment
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl;
v.segment(1, 2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment(1, 2):
-2  6
Now the vector v is:
7 0 0 6
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See Also
class Block, segment(Index)
EIGEN_DEVICE_FUNC ConstSegmentReturnType segment ( Index  start,
Index  n 
) const
inlineinherited

This is the const version of segment(Index,Index).

EIGEN_DEVICE_FUNC FixedSegmentReturnType<N>::Type segment ( Index  start,
Index  n = N 
)
inlineinherited
Returns
a fixed-size expression of a segment (i.e. a vector block) in *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.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
startthe index of the first element in the segment
nthe 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:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl;
v.segment<2>(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment<2>(1):
-2  6
Now the vector v is:
 7 -2  0  0
See Also
class Block
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType<N>::Type segment ( Index  start,
Index  n = N 
) const
inlineinherited

This is the const version of segment<int>(Index).

const Select< Derived, ThenDerived, ElseDerived > select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const
inlineinherited
Returns
a matrix where each coefficient (i,j) is equal to thenMatrix(i,j) if *this(i,j), and elseMatrix(i,j) otherwise.

Example:

MatrixXi m(3, 3);
m << 1, 2, 3,
4, 5, 6,
7, 8, 9;
m = (m.array() >= 5).select(-m, m);
cout << m << endl;

Output:

 1  2  3
 4 -5 -6
-7 -8 -9
See Also
class Select
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > select ( const DenseBase< ThenDerived > &  thenMatrix,
const typename ThenDerived::Scalar &  elseScalar 
) const
inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.

See Also
DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > select ( const typename ElseDerived::Scalar &  thenScalar,
const DenseBase< ElseDerived > &  elseMatrix 
) const
inlineinherited

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.

See Also
DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
Derived & setConstant ( const Scalar &  val)
inlineinherited

Sets all coefficients in this expression to value.

See Also
fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
Derived & setLinSpaced ( Index  newSize,
const Scalar &  low,
const Scalar &  high 
)
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:

VectorXf v;
v.setLinSpaced(5,0.5f,1.5f);
cout << v << endl;

Output:

 0.5
0.75
   1
1.25
 1.5
See Also
CwiseNullaryOp
Derived & setLinSpaced ( const Scalar &  low,
const Scalar &  high 
)
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.

See Also
setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
Derived & setOnes ( )
inlineinherited

Sets all coefficients in this expression to one.

Example:

m.row(1).setOnes();
cout << m << endl;

Output:

 7  9 -5 -3
 1  1  1  1
 6 -3  0  9
 6  6  3  9
See Also
class CwiseNullaryOp, Ones()
Derived & setRandom ( )
inlineinherited

Sets all coefficients in this expression to random values.

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

Warning
This function is not re-entrant.

Example:

m.col(1).setRandom();
cout << m << endl;

Output:

 0  7  0  0
 0 -2  0  0
 0  6  0  0
 0  6  0  0
See Also
class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)
Derived & setZero ( )
inlineinherited

Sets all coefficients in this expression to zero.

Example:

m.row(1).setZero();
cout << m << endl;

Output:

 7  9 -5 -3
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See Also
class CwiseNullaryOp, Zero()
internal::traits< Derived >::Scalar sum ( ) const
inlineinherited
Returns
the sum of all coefficients of *this
See Also
trace(), prod(), mean()

References Eigen::Dynamic.

EIGEN_DEVICE_FUNC void swap ( const DenseBase< OtherDerived > &  other,
int  = OtherDerived::ThisConstantIsPrivateInPlainObjectBase 
)
inlineinherited

swaps *this with the expression other.

EIGEN_DEVICE_FUNC void swap ( PlainObjectBase< OtherDerived > &  other)
inlineinherited

swaps *this with the matrix or array other.

EIGEN_DEVICE_FUNC SegmentReturnType tail ( Index  n)
inlineinherited
Returns
a dynamic-size expression of the last coefficients of *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.

Parameters
nthe number of coefficients in the segment

Example:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail(2) << endl;
v.tail(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
Note
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See Also
class Block, block(Index,Index)
EIGEN_DEVICE_FUNC ConstSegmentReturnType tail ( Index  n) const
inlineinherited

This is the const version of tail(Index).

EIGEN_DEVICE_FUNC FixedSegmentReturnType<N>::Type tail ( Index  n = N)
inlineinherited
Returns
a fixed-size expression of the last coefficients of *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.

Template Parameters
Nthe number of coefficients in the segment as specified at compile-time
Parameters
nthe 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:

cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl;
v.tail<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
See Also
class Block
EIGEN_DEVICE_FUNC ConstFixedSegmentReturnType<N>::Type tail ( Index  n = N) const
inlineinherited

This is the const version of tail<int>.

EIGEN_DEVICE_FUNC Block<Derived> topLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a top-left corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner(2, 2):" << endl;
cout << m.topLeftCorner(2, 2) << endl;
m.topLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived> topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topLeftCorner(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived, CRows, CCols> topLeftCorner ( )
inlineinherited
Returns
an expression of a fixed-size top-left corner of *this.

The template parameters CRows and CCols are the number of rows and columns in the corner.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,2>():" << endl;
cout << m.topLeftCorner<2,2>() << endl;
m.topLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,2>():
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived, CRows, CCols> topLeftCorner ( ) const
inlineinherited

This is the const version of topLeftCorner<int, int>().

Block<Derived, CRows, CCols> topLeftCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a top-left corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber 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:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,Dynamic>(2,2):" << endl;
cout << m.topLeftCorner<2,Dynamic>(2,2) << endl;
m.topLeftCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,Dynamic>(2,2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See Also
class Block
const Block<const Derived, CRows, CCols> topLeftCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topLeftCorner<int, int>(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived> topRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
a dynamic-size expression of a top-right corner of *this.
Parameters
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner(2, 2):" << endl;
cout << m.topRightCorner(2, 2) << endl;
m.topRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived> topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topRightCorner(Index, Index).

EIGEN_DEVICE_FUNC Block<Derived, CRows, CCols> topRightCorner ( )
inlineinherited
Returns
an expression of a fixed-size top-right corner of *this.
Template Parameters
CRowsthe number of rows in the corner
CColsthe number of columns in the corner

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,2>():" << endl;
cout << m.topRightCorner<2,2>() << endl;
m.topRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,2>():
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block<int,int>(Index,Index)
EIGEN_DEVICE_FUNC const Block<const Derived, CRows, CCols> topRightCorner ( ) const
inlineinherited

This is the const version of topRightCorner<int, int>().

Block<Derived, CRows, CCols> topRightCorner ( Index  cRows,
Index  cCols 
)
inlineinherited
Returns
an expression of a top-right corner of *this.
Template Parameters
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters
cRowsnumber of rows in corner as specified at run-time
cColsnumber 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:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,Dynamic>(2,2):" << endl;
cout << m.topRightCorner<2,Dynamic>(2,2) << endl;
m.topRightCorner<2,Dynamic>(2,2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,Dynamic>(2,2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See Also
class Block
const Block<const Derived, CRows, CCols> topRightCorner ( Index  cRows,
Index  cCols 
) const
inlineinherited

This is the const version of topRightCorner<int, int>(Index, Index).

EIGEN_DEVICE_FUNC RowsBlockXpr topRows ( Index  n)
inlineinherited
Returns
a block consisting of the top rows of *this.
Parameters
nthe number of rows in the block

Example:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows(2):" << endl;
cout << a.topRows(2) << endl;
a.topRows(2).setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstRowsBlockXpr topRows ( Index  n) const
inlineinherited

This is the const version of topRows(Index).

EIGEN_DEVICE_FUNC NRowsBlockXpr<N>::Type topRows ( Index  n = N)
inlineinherited
Returns
a block consisting of the top rows of *this.
Template Parameters
Nthe number of rows in the block as specified at compile-time
Parameters
nthe 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:

Array44i a = Array44i::Random();
cout << "Here is the array a:" << endl << a << endl;
cout << "Here is a.topRows<2>():" << endl;
cout << a.topRows<2>() << endl;
a.topRows<2>().setZero();
cout << "Now the array a is:" << endl << a << endl;

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See Also
class Block, block(Index,Index,Index,Index)
EIGEN_DEVICE_FUNC ConstNRowsBlockXpr<N>::Type topRows ( Index  n = N) const
inlineinherited

This is the const version of topRows<int>().

Transpose< Derived > transpose ( )
inlineinherited
Returns
an expression of the transpose of *this.

Example:

cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the transpose of m:" << endl << m.transpose() << endl;
cout << "Here is the coefficient (1,0) in the transpose of m:" << endl
<< m.transpose()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 0." << endl;
m.transpose()(1,0) = 0;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  6
-2  6
Here is the transpose of m:
 7 -2
 6  6
Here is the coefficient (1,0) in the transpose of m:
6
Let us overwrite this coefficient with the value 0.
Now the matrix m is:
 7  0
-2  6
Warning
If you want to replace a matrix by its own transpose, do NOT do this:
* m = m.transpose(); // bug!!! caused by aliasing effect
*
Instead, use the transposeInPlace() method:
* m.transposeInPlace();
*
which gives Eigen good opportunities for optimization, or alternatively you can also do:
* m = m.transpose().eval();
*
See Also
transposeInPlace(), adjoint()
DenseBase< Derived >::ConstTransposeReturnType transpose ( ) const
inlineinherited

This is the const version of transpose().

Make sure you read the warning for transpose() !

See Also
transposeInPlace(), adjoint()
void transposeInPlace ( )
inlineinherited

This is the "in place" version of transpose(): it replaces *this by its own transpose. Thus, doing

* m.transposeInPlace();
*

has the same effect on m as doing

* m = m.transpose().eval();
*

and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.

Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().

Note
if the matrix is not square, then *this must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.
See Also
transpose(), adjoint(), adjointInPlace()

References Eigen::Dynamic.

EIGEN_DEVICE_FUNC const CwiseUnaryOp<CustomUnaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp()) const
inlineinherited

Apply a unary operator coefficient-wise.

Parameters
[in]funcFunctor implementing the unary operator
Template Parameters
CustomUnaryOpType of func
Returns
An expression of a custom coefficient-wise unary operator func of *this

The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define function to be applied coefficient-wise
double ramp(double x)
{
if (x > 0)
return x;
else
return 0;
}
int main(int, char**)
{
Matrix4d m1 = Matrix4d::Random();
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
  0.68  0.823      0      0
     0      0  0.108 0.0268
 0.566      0      0  0.904
 0.597  0.536  0.258  0.832

Genuine functors allow for more possibilities, for instance it may contain a state.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
Matrix4d m1 = Matrix4d::Random();
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See Also
class CwiseUnaryOp, class CwiseBinaryOp
EIGEN_DEVICE_FUNC const CwiseUnaryView<CustomViewOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()) const
inlineinherited
Returns
an expression of a custom coefficient-wise unary operator func of *this

The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
Scalar m_inf, m_sup;
};
int main(int, char**)
{
Matrix4d m1 = Matrix4d::Random();
cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See Also
class CwiseUnaryOp, class CwiseBinaryOp
EIGEN_DEVICE_FUNC CoeffReturnType value ( ) const
inlineinherited
Returns
the unique coefficient of a 1x1 expression
void visit ( Visitor &  visitor) const
inherited

Applies the visitor visitor to the whole coefficients of the matrix or vector.

The template parameter Visitor is the type of the visitor and provides the following interface:

* struct MyVisitor {
* // called for the first coefficient
* void init(const Scalar& value, Index i, Index j);
* // called for all other coefficients
* void operator() (const Scalar& value, Index i, Index j);
* };
*
Note
compared to one or two for loops, visitors offer automatic unrolling for small fixed size matrix.
See Also
minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()

References Eigen::Dynamic.

const DenseBase< Derived >::ConstantReturnType Zero ( Index  nbRows,
Index  nbCols 
)
inlinestaticinherited
Returns
an expression of a zero matrix.

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.

This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.

Example:

cout << MatrixXi::Zero(2,3) << endl;

Output:

0 0 0
0 0 0
See Also
Zero(), Zero(Index)
const DenseBase< Derived >::ConstantReturnType Zero ( Index  size)
inlinestaticinherited
Returns
an expression of a zero vector.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

Example:

cout << RowVectorXi::Zero(4) << endl;
cout << VectorXf::Zero(2) << endl;

Output:

0 0 0 0
0
0
See Also
Zero(), Zero(Index,Index)
const DenseBase< Derived >::ConstantReturnType Zero ( )
inlinestaticinherited
Returns
an expression of a fixed-size zero matrix or vector.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << Matrix2d::Zero() << endl;
cout << RowVector4i::Zero() << endl;

Output:

0 0
0 0
0 0 0 0
See Also
Zero(Index), Zero(Index,Index)

Friends And Related Function Documentation

std::ostream & operator<< ( std::ostream &  s,
const DenseBase< Derived > &  m 
)
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.

See Also
DenseBase::format()

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