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Eigen  3.2.5
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Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > Class Template Reference
[Core module]

The matrix class, also used for vectors and row-vectors. More...

Inheritance diagram for Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >:

List of all members.

Public Types

typedef PlainObjectBase< MatrixBase
 Base class typedef.
typedef internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Index 
Index
 The type of indices.
typedef Base::PlainObject PlainObject
 The plain matrix type corresponding to this expression.

Public Member Functions

ArrayWrapper< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
array ()
const CwiseBinaryOp
< CustomBinaryOp, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, BlockRows, BlockCols > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, BlockRows,
BlockCols > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, BlockRows, BlockCols > 
block (Index startRow, Index startCol) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, BlockRows,
BlockCols > 
block (Index startRow, Index startCol)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomLeftCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomLeftCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
bottomLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
bottomLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomRightCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomRightCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomRightCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
bottomRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
bottomRightCorner (Index cRows, Index cCols)
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
ConstRowsBlockXpr bottomRows (Index n) const
RowsBlockXpr bottomRows (Index n)
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
ConstColXpr col (Index i) const
ColXpr col (Index i)
ConjugateReturnType conjugate () const
void conservativeResize (Index size)
void conservativeResize (NoChange_t, Index nbCols)
void conservativeResize (Index nbRows, NoChange_t)
void conservativeResize (Index nbRows, Index nbCols)
void conservativeResizeLike (const DenseBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs () const
const CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs2 () const
const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
const CwiseBinaryOp
< std::equal_to< Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseInverse () const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMax (const Scalar &other) const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMin (const Scalar &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_product_op
< typename Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >::Scalar,
typename OtherDerived::Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseSqrt () const
Scalar * data ()
const Scalar * data () const
Index diagonalSize () const
EvalReturnType eval () const
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
FixedSegmentReturnType< N >::Type head (Index n=N)
ConstSegmentReturnType head (Index n) const
SegmentReturnType head (Index n)
NonConstImagReturnType imag ()
const ImagReturnType imag () const
Index innerSize () const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
lazyAssign (const DenseBase< OtherDerived > &other)
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
NColsBlockXpr< N >::Type leftCols (Index n=N)
ConstColsBlockXpr leftCols (Index n) const
ColsBlockXpr leftCols (Index n)
template<typename OtherDerived >
 Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
 Constructs a Dim x Dim rotation matrix from the rotation r.
template<typename OtherDerived >
 Matrix (const EigenBase< OtherDerived > &other)
 Copy constructor for generic expressions.
template<typename OtherDerived >
 Matrix (const ReturnByValue< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 Matrix (const Matrix &other)
 Copy constructor.
template<typename OtherDerived >
 Matrix (const MatrixBase< OtherDerived > &other)
 Constructor copying the value of the expression other.
 Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w)
 Constructs an initialized 4D vector with given coefficients.
 Matrix (const Scalar &x, const Scalar &y, const Scalar &z)
 Constructs an initialized 3D vector with given coefficients.
 Matrix (const Scalar &x, const Scalar &y)
 Constructs an initialized 2D vector with given coefficients.
 Matrix (Index rows, Index cols)
 Constructs an uninitialized matrix with rows rows and cols columns.
 Matrix (Index dim)
 Constructs a vector or row-vector with given dimension. This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
 Matrix ()
 Default constructor.
ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
ColsBlockXpr middleCols (Index startCol, Index numCols)
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
ConstRowsBlockXpr middleRows (Index startRow, Index n) const
RowsBlockXpr middleRows (Index startRow, Index n)
Index nonZeros () const
bool operator!= (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, const Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
operator* (const std::complex< Scalar > &scalar) const
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
const CwiseBinaryOp
< internal::scalar_sum_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
operator+ (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_difference_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
operator- (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_opposite_op
< typename internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar >, const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
operator- () const
const CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar >, const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
operator/ (const Scalar &scalar) const
template<typename OtherDerived >
Matrixoperator= (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
 Set a Dim x Dim rotation matrix from the rotation r.
template<typename OtherDerived >
Matrixoperator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
Matrixoperator= (const Matrix &other)
 Assigns matrices to each other.
bool operator== (const MatrixBase< OtherDerived > &other) const
Index outerSize () const
NonConstRealReturnType real ()
RealReturnType real () const
void resize (Index nbRows, NoChange_t)
void resize (NoChange_t, Index nbCols)
void resize (Index size)
void resize (Index nbRows, Index nbCols)
void resizeLike (const EigenBase< OtherDerived > &_other)
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
NColsBlockXpr< N >::Type rightCols (Index n=N)
ConstColsBlockXpr rightCols (Index n) const
ColsBlockXpr rightCols (Index n)
ConstRowXpr row (Index i) const
RowXpr row (Index i)
ConstFixedSegmentReturnType< N >
::Type 
segment (Index start, Index n=N) const
FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
ConstSegmentReturnType segment (Index start, Index n) const
SegmentReturnType segment (Index start, Index n)
void swap (PlainObjectBase< OtherDerived > &other)
void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
FixedSegmentReturnType< N >::Type tail (Index n=N)
ConstSegmentReturnType tail (Index n) const
SegmentReturnType tail (Index n)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topLeftCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topLeftCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
topLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
topLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topRightCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topRightCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topRightCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
topRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
topRightCorner (Index cRows, Index cCols)
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
NRowsBlockXpr< N >::Type topRows (Index n=N)
ConstRowsBlockXpr topRows (Index n) const
RowsBlockXpr topRows (Index n)
const CwiseUnaryOp
< CustomUnaryOp, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
const CwiseUnaryView
< CustomViewOp, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
CoeffReturnType value () const

Static Public Member Functions

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 StridedMapType< Stride
< Outer, Inner > >::type 
Map (Scalar *data, Index rows, Index cols, 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 size, 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, const Stride< Outer, Inner > &stride)
static StridedConstMapType
< Stride< Outer, Inner >
>::type 
Map (const Scalar *data, const Stride< Outer, Inner > &stride)
static MapType Map (Scalar *data, Index rows, Index cols)
static ConstMapType Map (const Scalar *data, Index rows, Index cols)
static MapType Map (Scalar *data, Index size)
static ConstMapType Map (const Scalar *data, Index size)
static MapType Map (Scalar *data)
static ConstMapType Map (const Scalar *data)
static StridedAlignedMapType
< Stride< Outer, Inner >
>::type 
MapAligned (Scalar *data, Index rows, Index cols, 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 size, 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, const Stride< Outer, Inner > &stride)
static
StridedConstAlignedMapType
< Stride< Outer, Inner >
>::type 
MapAligned (const Scalar *data, const Stride< Outer, Inner > &stride)
static AlignedMapType MapAligned (Scalar *data, Index rows, Index cols)
static ConstAlignedMapType MapAligned (const Scalar *data, Index rows, Index cols)
static AlignedMapType MapAligned (Scalar *data, Index size)
static ConstAlignedMapType MapAligned (const Scalar *data, Index size)
static AlignedMapType MapAligned (Scalar *data)
static ConstAlignedMapType MapAligned (const Scalar *data)

Protected Member Functions

Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
_set (const DenseBase< OtherDerived > &other)
 Copies the value of the expression other into *this with automatic resizing.

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

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

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

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

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

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

 Eigen::VectorXd v(10);
 v[0] = 0.1;
 v[1] = 0.2;
 v(0) = 0.3;
 v(1) = 0.4;

 Eigen::MatrixXi m(10, 10);
 m(0, 1) = 1;
 m(0, 2) = 2;
 m(0, 3) = 3;

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

Some notes:

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

Member Typedef Documentation

typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Index Index [inherited]
typedef Base::PlainObject PlainObject

The plain matrix type corresponding to this expression.

This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.

Reimplemented from MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.


Constructor & Destructor Documentation

Matrix (  )  [inline]

Default constructor.

For fixed-size matrices, does nothing.

For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix is called a null matrix. This constructor is the unique way to create null matrices: resizing a matrix to 0 is not supported.

See also:
resize(Index,Index)
Matrix ( Index  dim  )  [inline, explicit]

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.

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.

Matrix ( const EigenBase< OtherDerived > &  other  )  [inline]

Copy constructor for generic expressions.

See also:
MatrixBase::operator=(const EigenBase<OtherDerived>&)
Matrix ( const RotationBase< OtherDerived, ColsAtCompileTime > &  r  )  [inline, explicit]

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

This is defined in the Geometry module.

 #include <Eigen/Geometry> 

References RotationBase< Derived, _Dim >::toRotationMatrix().


Member Function Documentation

Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set ( const DenseBase< OtherDerived > &  other  )  [inline, protected, inherited]

Copies the value of the expression other into *this with automatic resizing.

*this might be resized to match the dimensions of other. If *this was a null matrix (not already initialized), it will be initialized.

Note that copying a row-vector into a vector (and conversely) is allowed. The resizing, if any, is then done in the appropriate way so that row-vectors remain row-vectors and vectors remain vectors.

See also:
operator=(const MatrixBase<OtherDerived>&), _set_noalias()
ArrayWrapper<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array (  )  [inline, inherited]
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
const CwiseBinaryOp<CustomBinaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const [inline, inherited]
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()
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) [inline, inherited]
Returns:
an expression of a block in *this.
Template Parameters:
BlockRows number of rows in block as specified at compile-time
BlockCols number of columns in block as specified at compile-time
Parameters:
startRow the first row in the block
startCol the first column in the block
blockRows number of rows in block as specified at run-time
blockCols number of columns in block as specified at run-time

This function is mainly useful for blocks where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, blockRows should equal BlockRows unless BlockRows is Dynamic, and the same for the number of columns.

Example:

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;

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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) [inline, inherited]
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:
startRow the first row in the block
startCol the first column in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block<2,2>(1,1):" << endl << m.block<2,2>(1,1) << endl;
m.block<2,2>(1,1).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
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)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) [inline, inherited]
Returns:
a dynamic-size expression of a block in *this.
Parameters:
startRow the first row in the block
startCol the first column in the block
blockRows the number of rows in the block
blockCols the number of columns in the block

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.block(1, 1, 2, 2):" << endl << m.block(1, 1, 2, 2) << endl;
m.block(1, 1, 2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
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)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
an expression of a bottom-left corner of *this.
Template Parameters:
CRows number of rows in corner as specified at compile-time
CCols number of columns in corner as specified at compile-time
Parameters:
cRows number of rows in corner as specified at run-time
cCols number of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

Matrix4i m = Matrix4i::Random();
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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner (  )  const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomLeftCorner (  )  [inline, inherited]
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:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner<2,2>():" << endl;
cout << m.bottomLeftCorner<2,2>() << endl;
m.bottomLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomLeftCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
a dynamic-size expression of a bottom-left corner of *this.
Parameters:
cRows the number of rows in the corner
cCols the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomLeftCorner(2, 2):" << endl;
cout << m.bottomLeftCorner(2, 2) << endl;
m.bottomLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
an expression of a bottom-right corner of *this.
Template Parameters:
CRows number of rows in corner as specified at compile-time
CCols number of columns in corner as specified at compile-time
Parameters:
cRows number of rows in corner as specified at run-time
cCols number of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

Matrix4i m = Matrix4i::Random();
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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner (  )  const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> bottomRightCorner (  )  [inline, inherited]
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:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner<2,2>():" << endl;
cout << m.bottomRightCorner<2,2>() << endl;
m.bottomRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomRightCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > bottomRightCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
a dynamic-size expression of a bottom-right corner of *this.
Parameters:
cRows the number of rows in the corner
cCols the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.bottomRightCorner(2, 2):" << endl;
cout << m.bottomRightCorner(2, 2) << endl;
m.bottomRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type bottomRows ( Index  n = N  )  const [inline, inherited]

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

NRowsBlockXpr<N>::Type bottomRows ( Index  n = N  )  [inline, inherited]
Returns:
a block consisting of the bottom rows of *this.
Template Parameters:
N the number of rows in the block as specified at compile-time
Parameters:
n the number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

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)
ConstRowsBlockXpr bottomRows ( Index  n  )  const [inline, inherited]

This is the const version of bottomRows(Index).

RowsBlockXpr bottomRows ( Index  n  )  [inline, inherited]
Returns:
a block consisting of the bottom rows of *this.
Parameters:
n the number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
internal::cast_return_type<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar, NewType>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > >::type cast (  )  const [inline, inherited]
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
ConstColXpr col ( Index  i  )  const [inline, inherited]

This is the const version of col().

ColXpr col ( Index  i  )  [inline, inherited]
Returns:
an expression of the i-th column of *this. Note that the numbering starts at 0.

Example:

Matrix3d m = Matrix3d::Identity();
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
ConjugateReturnType conjugate (  )  const [inline, inherited]
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()
void conservativeResize ( Index  size  )  [inline, inherited]

Resizes the vector to size while retaining old values.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.. This method does not work for partially dynamic matrices when the static dimension is anything other than 1. For example it will not work with Matrix<double, 2, Dynamic>.

When values are appended, they will be uninitialized.

void conservativeResize ( NoChange_t  ,
Index  nbCols 
) [inline, inherited]

Resizes the matrix to rows x cols while leaving old values untouched.

As opposed to conservativeResize(Index rows, Index cols), this version leaves the number of rows unchanged.

In case the matrix is growing, new columns will be uninitialized.

void conservativeResize ( Index  nbRows,
NoChange_t   
) [inline, inherited]

Resizes the matrix to rows x cols while leaving old values untouched.

As opposed to conservativeResize(Index rows, Index cols), this version leaves the number of columns unchanged.

In case the matrix is growing, new rows will be uninitialized.

void conservativeResize ( Index  nbRows,
Index  nbCols 
) [inline, inherited]

Resizes the matrix to rows x cols while leaving old values untouched.

The method is intended for matrices of dynamic size. If you only want to change the number of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or conservativeResize(Index, NoChange_t).

Matrices are resized relative to the top-left element. In case values need to be appended to the matrix they will be uninitialized.

void conservativeResizeLike ( const DenseBase< OtherDerived > &  other  )  [inline, inherited]

Resizes the matrix to rows x cols of other, while leaving old values untouched.

The method is intended for matrices of dynamic size. If you only want to change the number of rows and/or of columns, you can use conservativeResize(NoChange_t, Index) or conservativeResize(Index, NoChange_t).

Matrices are resized relative to the top-left element. In case values need to be appended to the matrix they will copied from other.

const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs (  )  const [inline, inherited]
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()
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseAbs2 (  )  const [inline, inherited]
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()
const CwiseScalarEqualReturnType cwiseEqual ( const Scalar &  s  )  const [inline, inherited]
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
const CwiseBinaryOp<std::equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseEqual ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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()
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseInverse (  )  const [inline, inherited]
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()
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMax ( const Scalar &  other  )  const [inline, inherited]
Returns:
an expression of the coefficient-wise max of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const ConstantReturnType> cwiseMin ( const Scalar &  other  )  const [inline, inherited]
Returns:
an expression of the coefficient-wise min of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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()
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseNotEqual ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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()
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 [inline, inherited]
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
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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()
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cwiseSqrt (  )  const [inline, inherited]
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()
Scalar* data (  )  [inline, inherited]
Returns:
a pointer to the data array of this matrix
const Scalar* data (  )  const [inline, inherited]
Returns:
a const pointer to the data array of this matrix
Index diagonalSize (  )  const [inline, inherited]
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.
EvalReturnType eval (  )  const [inline, inherited]
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.

ConstFixedSegmentReturnType<N>::Type head ( Index  n = N  )  const [inline, inherited]

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

FixedSegmentReturnType<N>::Type head ( Index  n = N  )  [inline, inherited]
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:
N the number of coefficients in the segment as specified at compile-time
Parameters:
n the number of coefficients in the segment as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.head(2):" << endl << v.head<2>() << endl;
v.head<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6
See also:
class Block
ConstSegmentReturnType head ( Index  n  )  const [inline, inherited]

This is the const version of head(Index).

SegmentReturnType head ( Index  n  )  [inline, inherited]
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:
n the number of coefficients in the segment

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.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)
NonConstImagReturnType imag (  )  [inline, inherited]
Returns:
a non const expression of the imaginary part of *this.
See also:
real()
const ImagReturnType imag (  )  const [inline, inherited]
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()
Index innerSize (  )  const [inline, inherited]
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.
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & lazyAssign ( const DenseBase< OtherDerived > &  other  )  [inline, inherited]
See also:
MatrixBase::lazyAssign()

Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

ConstNColsBlockXpr<N>::Type leftCols ( Index  n = N  )  const [inline, inherited]

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

NColsBlockXpr<N>::Type leftCols ( Index  n = N  )  [inline, inherited]
Returns:
a block consisting of the left columns of *this.
Template Parameters:
N the number of columns in the block as specified at compile-time
Parameters:
n the number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

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)
ConstColsBlockXpr leftCols ( Index  n  )  const [inline, inherited]

This is the const version of leftCols(Index).

ColsBlockXpr leftCols ( Index  n  )  [inline, inherited]
Returns:
a block consisting of the left columns of *this.
Parameters:
n the number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol,
Index  n = N 
) const [inline, inherited]

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

NColsBlockXpr<N>::Type middleCols ( Index  startCol,
Index  n = N 
) [inline, inherited]
Returns:
a block consisting of a range of columns of *this.
Template Parameters:
N the number of columns in the block as specified at compile-time
Parameters:
startCol the index of the first column in the block
n the number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

#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)
ConstColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) const [inline, inherited]

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

ColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) [inline, inherited]
Returns:
a block consisting of a range of columns of *this.
Parameters:
startCol the index of the first column in the block
numCols the number of columns in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(1..3,:) =\n" << A.middleCols(1,3) << endl;
    return 0;
}

Output:

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

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type middleRows ( Index  startRow,
Index  n = N 
) const [inline, inherited]

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

NRowsBlockXpr<N>::Type middleRows ( Index  startRow,
Index  n = N 
) [inline, inherited]
Returns:
a block consisting of a range of rows of *this.
Template Parameters:
N the number of rows in the block as specified at compile-time
Parameters:
startRow the index of the first row in the block
n the number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

#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)
ConstRowsBlockXpr middleRows ( Index  startRow,
Index  n 
) const [inline, inherited]

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

RowsBlockXpr middleRows ( Index  startRow,
Index  n 
) [inline, inherited]
Returns:
a block consisting of a range of rows of *this.
Parameters:
startRow the index of the first row in the block
n the number of rows in the block

Example:

#include <Eigen/Core>
#include <iostream>

using namespace Eigen;
using namespace std;

int main(void)
{
    int const N = 5;
    MatrixXi A(N,N);
    A.setRandom();
    cout << "A =\n" << A << '\n' << endl;
    cout << "A(2..3,:) =\n" << A.middleRows(2,2) << endl;
    return 0;
}

Output:

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

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
Index nonZeros (  )  const [inline, inherited]
Returns:
the number of nonzero coefficients which is in practice the number of stored coefficients.
bool operator!= ( const MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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==
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator* ( const std::complex< Scalar > &  scalar  )  const [inline, inherited]

Overloaded for efficient real matrix times complex scalar value

const ScalarMultipleReturnType operator* ( const Scalar &  scalar  )  const [inline, inherited]
Returns:
an expression of *this scaled by the scalar factor scalar
const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , const OtherDerived> operator+ ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline, 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 [inline, 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-=()
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator- (  )  const [inline, inherited]
Returns:
an expression of the opposite of *this
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator/ ( const Scalar &  scalar  )  const [inline, inherited]
Returns:
an expression of *this divided by the scalar value scalar
Matrix< _Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols > & operator= ( const RotationBase< OtherDerived, ColsAtCompileTime > &  r  )  [inline]

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

This is defined in the Geometry module.

 #include <Eigen/Geometry> 

References RotationBase< Derived, _Dim >::toRotationMatrix().

Matrix& operator= ( const EigenBase< OtherDerived > &  other  )  [inline]

Copies the generic expression other into *this.

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

Returns:
a reference to *this.

Reimplemented from PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

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=.
bool operator== ( const MatrixBase< OtherDerived > &  other  )  const [inline, inherited]
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!=
Index outerSize (  )  const [inline, inherited]
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.
NonConstRealReturnType real (  )  [inline, inherited]
Returns:
a non const expression of the real part of *this.
See also:
imag()
RealReturnType real (  )  const [inline, inherited]
Returns:
a read-only expression of the real part of *this.
See also:
imag()
void resize ( Index  nbRows,
NoChange_t   
) [inline, inherited]

Resizes the matrix, changing only the number of rows. For the parameter of type NoChange_t, just pass the special value NoChange as in the example below.

Example:

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

Output:

m: 5 rows, 4 cols
See also:
resize(Index,Index)
void resize ( NoChange_t  ,
Index  nbCols 
) [inline, inherited]

Resizes the matrix, changing only the number of columns. For the parameter of type NoChange_t, just pass the special value NoChange as in the example below.

Example:

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

Output:

m: 3 rows, 5 cols
See also:
resize(Index,Index)
void resize ( Index  size  )  [inline, inherited]

Resizes *this to a vector of length size

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.. This method does not work for partially dynamic matrices when the static dimension is anything other than 1. For example it will not work with Matrix<double, 2, Dynamic>.

Example:

VectorXd v(10);
v.resize(3);
RowVector3d w;
w.resize(3); // this is legal, but has no effect
cout << "v: " << v.rows() << " rows, " << v.cols() << " cols" << endl;
cout << "w: " << w.rows() << " rows, " << w.cols() << " cols" << endl;

Output:

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

Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

void resize ( Index  nbRows,
Index  nbCols 
) [inline, inherited]

Resizes *this to a rows x cols matrix.

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

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

Example:

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

Output:

here's the 2x3 matrix m:
1 2 3
4 5 6
let's resize m to 3x2. This is a conservative resizing because 2*3==3*2.
here's the 3x2 matrix m:
1 5
4 3
2 6
now let's resize m to size 2x2. This is NOT a conservative resizing, so it becomes uninitialized:
1.58e-307         0
2.65e-269         0
See also:
resize(Index) for vectors, resize(NoChange_t, Index), resize(Index, NoChange_t)

Reimplemented from DenseBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

void resizeLike ( const EigenBase< OtherDerived > &  _other  )  [inline, inherited]

Resizes *this to have the same dimensions as other. Takes care of doing all the checking that's needed.

Note that copying a row-vector into a vector (and conversely) is allowed. The resizing, if any, is then done in the appropriate way so that row-vectors remain row-vectors and vectors remain vectors.

ConstNColsBlockXpr<N>::Type rightCols ( Index  n = N  )  const [inline, inherited]

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

NColsBlockXpr<N>::Type rightCols ( Index  n = N  )  [inline, inherited]
Returns:
a block consisting of the right columns of *this.
Template Parameters:
N the number of columns in the block as specified at compile-time
Parameters:
n the number of columns in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

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)
ConstColsBlockXpr rightCols ( Index  n  )  const [inline, inherited]

This is the const version of rightCols(Index).

ColsBlockXpr rightCols ( Index  n  )  [inline, inherited]
Returns:
a block consisting of the right columns of *this.
Parameters:
n the number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstRowXpr row ( Index  i  )  const [inline, inherited]

This is the const version of row().

RowXpr row ( Index  i  )  [inline, inherited]
Returns:
an expression of the i-th row of *this. Note that the numbering starts at 0.

Example:

Matrix3d m = Matrix3d::Identity();
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
ConstFixedSegmentReturnType<N>::Type segment ( Index  start,
Index  n = N 
) const [inline, inherited]

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

FixedSegmentReturnType<N>::Type segment ( Index  start,
Index  n = N 
) [inline, inherited]
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:
N the number of coefficients in the segment as specified at compile-time
Parameters:
start the index of the first element in the segment
n the number of coefficients in the segment as specified at compile-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment<2>(1):" << endl << v.segment<2>(1) << endl;
v.segment<2>(2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment<2>(1):
-2  6
Now the vector v is:
 7 -2  0  0
See also:
class Block
ConstSegmentReturnType segment ( Index  start,
Index  n 
) const [inline, inherited]

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

SegmentReturnType segment ( Index  start,
Index  n 
) [inline, inherited]
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:
start the first coefficient in the segment
n the number of coefficients in the segment

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.segment(1, 2):" << endl << v.segment(1, 2) << endl;
v.segment(1, 2).setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment(1, 2):
-2  6
Now the vector v is:
7 0 0 6
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)
void swap ( PlainObjectBase< OtherDerived > &  other  )  [inline, inherited]

swaps *this with the matrix or array other.

void swap ( const DenseBase< OtherDerived > &  other,
int  = OtherDerived::ThisConstantIsPrivateInPlainObjectBase 
) [inline, inherited]

swaps *this with the expression other.

ConstFixedSegmentReturnType<N>::Type tail ( Index  n = N  )  const [inline, inherited]

This is the const version of tail<int>.

FixedSegmentReturnType<N>::Type tail ( Index  n = N  )  [inline, inherited]
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:
N the number of coefficients in the segment as specified at compile-time
Parameters:
n the number of coefficients in the segment as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.tail(2):" << endl << v.tail<2>() << endl;
v.tail<2>().setZero();
cout << "Now the vector v is:" << endl << v << endl;

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0
See also:
class Block
ConstSegmentReturnType tail ( Index  n  )  const [inline, inherited]

This is the const version of tail(Index).

SegmentReturnType tail ( Index  n  )  [inline, inherited]
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:
n the number of coefficients in the segment

Example:

RowVector4i v = RowVector4i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "Here is v.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)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
an expression of a top-left corner of *this.
Template Parameters:
CRows number of rows in corner as specified at compile-time
CCols number of columns in corner as specified at compile-time
Parameters:
cRows number of rows in corner as specified at run-time
cCols number of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

Matrix4i m = Matrix4i::Random();
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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner (  )  const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topLeftCorner (  )  [inline, inherited]
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:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner<2,2>():" << endl;
cout << m.topLeftCorner<2,2>() << endl;
m.topLeftCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,2>():
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topLeftCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
a dynamic-size expression of a top-left corner of *this.
Parameters:
cRows the number of rows in the corner
cCols the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topLeftCorner(2, 2):" << endl;
cout << m.topLeftCorner(2, 2) << endl;
m.topLeftCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
an expression of a top-right corner of *this.
Template Parameters:
CRows number of rows in corner as specified at compile-time
CCols number of columns in corner as specified at compile-time
Parameters:
cRows number of rows in corner as specified at run-time
cCols number of columns in corner as specified at run-time

This function is mainly useful for corners where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, cRows should equal CRows unless CRows is Dynamic, and the same for the number of columns.

Example:

Matrix4i m = Matrix4i::Random();
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 Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner (  )  const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , CRows, CCols> topRightCorner (  )  [inline, inherited]
Returns:
an expression of a fixed-size top-right corner of *this.
Template Parameters:
CRows the number of rows in the corner
CCols the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner<2,2>():" << endl;
cout << m.topRightCorner<2,2>() << endl;
m.topRightCorner<2,2>().setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,2>():
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block<int,int>(Index,Index)
const Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topRightCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

Block<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > topRightCorner ( Index  cRows,
Index  cCols 
) [inline, inherited]
Returns:
a dynamic-size expression of a top-right corner of *this.
Parameters:
cRows the number of rows in the corner
cCols the number of columns in the corner

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.topRightCorner(2, 2):" << endl;
cout << m.topRightCorner(2, 2) << endl;
m.topRightCorner(2, 2).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstNRowsBlockXpr<N>::Type topRows ( Index  n = N  )  const [inline, inherited]

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

NRowsBlockXpr<N>::Type topRows ( Index  n = N  )  [inline, inherited]
Returns:
a block consisting of the top rows of *this.
Template Parameters:
N the number of rows in the block as specified at compile-time
Parameters:
n the number of rows in the block as specified at run-time

The compile-time and run-time information should not contradict. In other words, n should equal N unless N is Dynamic.

Example:

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)
ConstRowsBlockXpr topRows ( Index  n  )  const [inline, inherited]

This is the const version of topRows(Index).

RowsBlockXpr topRows ( Index  n  )  [inline, inherited]
Returns:
a block consisting of the top rows of *this.
Parameters:
n the number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
const CwiseUnaryOp<CustomUnaryOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp()  )  const [inline, inherited]

Apply a unary operator coefficient-wise.

Parameters:
[in] func Functor implementing the unary operator
Template Parameters:
CustomUnaryOp Type 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
const CwiseUnaryView<CustomViewOp, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()  )  const [inline, inherited]
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
CoeffReturnType value (  )  const [inline, inherited]
Returns:
the unique coefficient of a 1x1 expression

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