Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | Friends
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > Class Template Reference

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

#include <Matrix.h>

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

List of all members.

Public Types

enum  { Options }
enum  
enum  
enum  
enum  
enum  
enum  
typedef Eigen::Map< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, Aligned
AlignedMapType
typedef PlainObjectBase< MatrixBase
 Base class typedef.
typedef Base::CoeffReturnType CoeffReturnType
typedef VectorwiseOp< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, Vertical
ColwiseReturnType
typedef const Eigen::Map
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, Aligned
ConstAlignedMapType
typedef const VectorwiseOp
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, Vertical
ConstColwiseReturnType
typedef const Diagonal< const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
ConstDiagonalReturnType
typedef const Eigen::Map
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, Unaligned
ConstMapType
typedef const Reverse< const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, BothDirections
ConstReverseReturnType
typedef const VectorwiseOp
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, Horizontal
ConstRowwiseReturnType
typedef const VectorBlock
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
ConstSegmentReturnType
typedef Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::ColsAtCompileTime==1?SizeMinusOne:1,
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::ColsAtCompileTime==1?1:SizeMinusOne
ConstStartMinusOne
typedef const Transpose< const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
ConstTransposeReturnType
typedef Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > 
DenseType
typedef Diagonal< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
DiagonalReturnType
typedef
internal::add_const_on_value_type
< typename internal::eval
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::type >::type 
EvalReturnType
typedef CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar >, const
ConstStartMinusOne
HNormalizedReturnType
typedef Homogeneous< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, HomogeneousReturnTypeDirection
HomogeneousReturnType
typedef internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Index 
Index
 The type of indices.
typedef Eigen::Map< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, Unaligned
MapType
typedef
internal::packet_traits
< Scalar >::type 
PacketScalar
typedef Base::PlainObject PlainObject
 The plain matrix type corresponding to this expression.
typedef NumTraits< Scalar >::Real RealScalar
typedef Reverse< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, BothDirections
ReverseReturnType
typedef VectorwiseOp< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, Horizontal
RowwiseReturnType
typedef internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar 
Scalar
typedef VectorBlock< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
SegmentReturnType
typedef
internal::stem_function
< Scalar >::type 
StemFunction
typedef internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::StorageKind 
StorageKind

Public Member Functions

const AdjointReturnType adjoint () const
void adjointInPlace ()
bool all (void) const
bool any (void) const
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
void applyOnTheRight (const EigenBase< OtherDerived > &other)
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
ArrayWrapper< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
array ()
const ArrayWrapper< const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
array () const
const DiagonalWrapper< const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
asDiagonal () const
const PermutationWrapper
< const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
asPermutation () const
Basebase ()
const Basebase () const
const CwiseBinaryOp
< CustomBinaryOp, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
Block< 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 > > 
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)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, BlockRows, BlockCols > 
block (Index startRow, Index startCol) const
RealScalar blueNorm () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
bottomLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
bottomLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomLeftCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomLeftCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
bottomRightCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
bottomRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
bottomRightCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
bottomRightCorner () const
RowsBlockXpr bottomRows (Index n)
ConstRowsBlockXpr bottomRows (Index n) const
NRowsBlockXpr< N >::Type bottomRows ()
ConstNRowsBlockXpr< N >::Type bottomRows () const
internal::cast_return_type
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const CwiseUnaryOp
< internal::scalar_cast_op
< typename internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar, NewType >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > >::type 
cast () const
const Scalarcoeff (Index row, Index col) const
const Scalarcoeff (Index index) const
ScalarcoeffRef (Index row, Index col)
ScalarcoeffRef (Index index)
const ScalarcoeffRef (Index row, Index col) const
const ScalarcoeffRef (Index index) const
ColXpr col (Index i)
ConstColXpr col (Index i) const
const ColPivHouseholderQR
< PlainObject
colPivHouseholderQr () const
Index cols () const
ConstColwiseReturnType colwise () const
ColwiseReturnType colwise ()
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
ConjugateReturnType conjugate () const
void conservativeResize (Index rows, Index cols)
void conservativeResize (Index rows, NoChange_t)
void conservativeResize (NoChange_t, Index cols)
void conservativeResize (Index size)
void conservativeResizeLike (const DenseBase< OtherDerived > &other)
const
MatrixFunctionReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
cos () const
const
MatrixFunctionReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
cosh () const
Index count () const
cross_product_return_type
< OtherDerived >::type 
cross (const MatrixBase< OtherDerived > &other) const
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs () const
const CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseAbs2 () const
const CwiseBinaryOp
< std::equal_to< Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< std::binder1st
< std::equal_to< Scalar >
>, const Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
cwiseEqual (const Scalar &s) const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseInverse () const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMax (const Scalar &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const ConstantReturnType > 
cwiseMin (const Scalar &other) const
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, const OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
cwiseSqrt () const
const Scalardata () const
Scalardata ()
Scalar determinant () const
DiagonalReturnType diagonal ()
const ConstDiagonalReturnType diagonal () const
DiagonalIndexReturnType< Index >
::Type 
diagonal ()
ConstDiagonalIndexReturnType
< Index >::Type 
diagonal () const
DiagonalIndexReturnType
< Dynamic >::Type 
diagonal (Index index)
ConstDiagonalIndexReturnType
< Dynamic >::Type 
diagonal (Index index) const
Index diagonalSize () const
internal::scalar_product_traits
< typename internal::traits
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > >::Scalar, typename
internal::traits< OtherDerived >
::Scalar >::ReturnType 
dot (const MatrixBase< OtherDerived > &other) const
const EIGEN_CWISE_PRODUCT_RETURN_TYPE (Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, OtherDerived) cwiseProduct(const Eigen
EigenvaluesReturnType eigenvalues () const
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
EvalReturnType eval () const
void evalTo (Dest &) const
const
MatrixExponentialReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
exp () const
void fill (const Scalar &value)
const Flagged< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >, Added,
Removed > 
flagged () const
const ForceAlignedAccess
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
forceAlignedAccess () const
ForceAlignedAccess< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
forceAlignedAccess ()
internal::add_const_on_value_type
< typename
internal::conditional< Enable,
ForceAlignedAccess< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>, Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > & >::type >::type 
forceAlignedAccessIf () const
internal::conditional< Enable,
ForceAlignedAccess< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>, Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > & >::type 
forceAlignedAccessIf ()
const WithFormat< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
format (const IOFormat &fmt) const
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
const FullPivLU< PlainObjectfullPivLu () const
SegmentReturnType head (Index size)
DenseBase::ConstSegmentReturnType head (Index size) const
FixedSegmentReturnType< Size >
::Type 
head ()
ConstFixedSegmentReturnType
< Size >::Type 
head () const
const HNormalizedReturnType hnormalized () const
HomogeneousReturnType homogeneous () const
const HouseholderQR< PlainObjecthouseholderQr () const
RealScalar hypotNorm () const
const ImagReturnType imag () const
NonConstImagReturnType imag ()
Index innerSize () const
Index innerStride () const
const internal::inverse_impl
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
inverse () const
bool isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isIdentity (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isMuchSmallerThan (const RealScalar &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUnitary (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
lazyAssign (const DenseBase< OtherDerived > &other)
const LazyProductReturnType
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, OtherDerived >
::Type 
lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObjectldlt () const
ColsBlockXpr leftCols (Index n)
ConstColsBlockXpr leftCols (Index n) const
NColsBlockXpr< N >::Type leftCols ()
ConstNColsBlockXpr< N >::Type leftCols () const
const LLT< PlainObjectllt () const
const
MatrixLogarithmReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
log () const
RealScalar lpNorm () const
const PartialPivLU< PlainObjectlu () const
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
 Matrix ()
 Default constructor.
 Matrix (internal::constructor_without_unaligned_array_assert)
 Matrix (Index dim)
 Constructs a vector or row-vector with given dimension. This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
 Matrix (Index rows, Index cols)
 Constructs an uninitialized matrix with rows rows and cols columns.
 Matrix (const Scalar &x, const Scalar &y)
 Constructs an initialized 2D vector with given coefficients.
 Matrix (const Scalar &x, const Scalar &y, const Scalar &z)
 Constructs an initialized 3D vector with given coefficients.
 Matrix (const Scalar &x, const Scalar &y, const Scalar &z, const Scalar &w)
 Constructs an initialized 4D vector with given coefficients.
 Matrix (const Scalar *data)
template<typename OtherDerived >
 Matrix (const MatrixBase< OtherDerived > &other)
 Constructor copying the value of the expression other.
 Matrix (const Matrix &other)
 Copy constructor.
template<typename OtherDerived >
 Matrix (const ReturnByValue< OtherDerived > &other)
 Copy constructor with in-place evaluation.
template<typename OtherDerived >
 Matrix (const EigenBase< OtherDerived > &other)
 Copy constructor for generic expressions.
MatrixBase< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > & 
matrix ()
const MatrixBase< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > & 
matrix () const
template<typename OtherDerived >
 Matrix (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
 Constructs a Dim x Dim rotation matrix from the rotation r.
const
MatrixFunctionReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
matrixFunction (StemFunction f) const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
maxCoeff () const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
maxCoeff (IndexType *row, IndexType *col) const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
maxCoeff (IndexType *index) const
Scalar mean () const
ColsBlockXpr middleCols (Index startCol, Index numCols)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
NColsBlockXpr< N >::Type middleCols (Index startCol)
ConstNColsBlockXpr< N >::Type middleCols (Index startCol) const
RowsBlockXpr middleRows (Index startRow, Index numRows)
ConstRowsBlockXpr middleRows (Index startRow, Index numRows) const
NRowsBlockXpr< N >::Type middleRows (Index startRow)
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow) const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
minCoeff () const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
minCoeff (IndexType *row, IndexType *col) const
internal::traits< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
>::Scalar 
minCoeff (IndexType *index) const
const NestByValue< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
nestByValue () const
NoAlias< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >
, Eigen::MatrixBase
noalias ()
Index nonZeros () const
RealScalar norm () const
void normalize ()
const PlainObject normalized () const
bool operator!= (const MatrixBase< OtherDerived > &other) const
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
const ScalarMultipleReturnType operator* (const RealScalar &scalar) const
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, const Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
operator* (const std::complex< Scalar > &scalar) const
const ProductReturnType
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, OtherDerived >
::Type 
operator* (const MatrixBase< OtherDerived > &other) const
const DiagonalProduct< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, DiagonalDerived, OnTheRight
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
ScalarMultipleReturnType operator* (const UniformScaling< Scalar > &s) const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator*= (const EigenBase< OtherDerived > &other)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator*= (const Scalar &other)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator+= (const MatrixBase< OtherDerived > &other)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator+= (const EigenBase< OtherDerived > &other)
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
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator-= (const MatrixBase< OtherDerived > &other)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator-= (const EigenBase< OtherDerived > &other)
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
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator/= (const Scalar &other)
CommaInitializer< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
operator<< (const Scalar &s)
CommaInitializer< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
operator<< (const DenseBase< OtherDerived > &other)
Matrixoperator= (const Matrix &other)
 Assigns matrices to each other.
template<typename OtherDerived >
Matrixoperator= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
Matrixoperator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
template<typename OtherDerived >
Matrixoperator= (const ReturnByValue< OtherDerived > &func)
template<typename OtherDerived >
Matrixoperator= (const RotationBase< OtherDerived, ColsAtCompileTime > &r)
 Set a Dim x Dim rotation matrix from the rotation r.
bool operator== (const MatrixBase< OtherDerived > &other) const
RealScalar operatorNorm () const
Index outerSize () const
Index outerStride () const
PacketScalar packet (Index row, Index col) const
PacketScalar packet (Index index) const
const PartialPivLU< PlainObjectpartialPivLu () const
Scalar prod () const
RealReturnType real () const
NonConstRealReturnType real ()
const Replicate< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, RowFactor, ColFactor > 
replicate () const
const Replicate< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, Dynamic, Dynamic
replicate (Index rowFacor, Index colFactor) const
void resize (Index rows, Index cols)
void resize (Index size)
void resize (NoChange_t, Index cols)
void resize (Index rows, NoChange_t)
void resizeLike (const EigenBase< OtherDerived > &_other)
ReverseReturnType reverse ()
ConstReverseReturnType reverse () const
void reverseInPlace ()
ColsBlockXpr rightCols (Index n)
ConstColsBlockXpr rightCols (Index n) const
NColsBlockXpr< N >::Type rightCols ()
ConstNColsBlockXpr< N >::Type rightCols () const
RowXpr row (Index i)
ConstRowXpr row (Index i) const
Index rows () const
ConstRowwiseReturnType rowwise () const
RowwiseReturnType rowwise ()
SegmentReturnType segment (Index start, Index size)
DenseBase::ConstSegmentReturnType segment (Index start, Index size) const
FixedSegmentReturnType< Size >
::Type 
segment (Index start)
ConstFixedSegmentReturnType
< Size >::Type 
segment (Index start) const
const Select< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >
, ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
const Select< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >
, ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const
const Select< Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols >, typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
SelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView ()
ConstSelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView () const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setConstant (const Scalar &value)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setConstant (Index size, const Scalar &value)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setConstant (Index rows, Index cols, const Scalar &value)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setIdentity ()
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setIdentity (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setLinSpaced (Index size, const Scalar &low, const Scalar &high)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setLinSpaced (const Scalar &low, const Scalar &high)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setOnes ()
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setOnes (Index size)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setOnes (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setRandom ()
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setRandom (Index size)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setRandom (Index rows, Index cols)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setZero ()
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setZero (Index size)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
setZero (Index rows, Index cols)
const
MatrixFunctionReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
sin () const
const
MatrixFunctionReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
sinh () const
const SparseView< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const
const
MatrixSquareRootReturnValue
< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
sqrt () const
RealScalar squaredNorm () const
RealScalar stableNorm () const
Scalar sum () const
template<typename OtherDerived >
void swap (MatrixBase< OtherDerived > const &other)
void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
void swap (PlainObjectBase< OtherDerived > &other)
SegmentReturnType tail (Index size)
DenseBase::ConstSegmentReturnType tail (Index size) const
FixedSegmentReturnType< Size >
::Type 
tail ()
ConstFixedSegmentReturnType
< Size >::Type 
tail () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
topLeftCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
topLeftCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topLeftCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topLeftCorner () const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols > > 
topRightCorner (Index cRows, Index cCols)
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
topRightCorner (Index cRows, Index cCols) const
Block< Matrix< _Scalar, _Rows,
_Cols, _Options, _MaxRows,
_MaxCols >, CRows, CCols > 
topRightCorner ()
const Block< const Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols >
, CRows, CCols > 
topRightCorner () const
RowsBlockXpr topRows (Index n)
ConstRowsBlockXpr topRows (Index n) const
NRowsBlockXpr< N >::Type topRows ()
ConstNRowsBlockXpr< N >::Type topRows () const
Scalar trace () const
Eigen::Transpose< Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
transpose ()
ConstTransposeReturnType transpose () const
void transposeInPlace ()
TriangularViewReturnType< Mode >
::Type 
triangularView ()
ConstTriangularViewReturnType
< Mode >::Type 
triangularView () const
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
PlainObject unitOrthogonal (void) const
CoeffReturnType value () const
void visit (Visitor &func) const
void writePacket (Index row, Index col, const PacketScalar &x)
void writePacket (Index index, const PacketScalar &x)

Static Public Member Functions

static const ConstantReturnType Constant (Index rows, Index cols, const Scalar &value)
static const ConstantReturnType Constant (Index size, const Scalar &value)
static const ConstantReturnType Constant (const Scalar &value)
static const IdentityReturnType Identity ()
static const IdentityReturnType Identity (Index rows, Index cols)
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (Index size, const Scalar &low, const Scalar &high)
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
static const CwiseNullaryOp
< CustomNullaryOp, Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
static const CwiseNullaryOp
< CustomNullaryOp, Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
NullaryExpr (Index size, const CustomNullaryOp &func)
static const CwiseNullaryOp
< CustomNullaryOp, Matrix
< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > > 
NullaryExpr (const CustomNullaryOp &func)
static const ConstantReturnType Ones (Index rows, Index cols)
static const ConstantReturnType Ones (Index size)
static const ConstantReturnType Ones ()
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
Random (Index rows, Index cols)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
Random (Index size)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Matrix< _Scalar,
_Rows, _Cols, _Options,
_MaxRows, _MaxCols > > 
Random ()
static const BasisReturnType Unit (Index size, Index i)
static const BasisReturnType Unit (Index i)
static const BasisReturnType UnitW ()
static const BasisReturnType UnitX ()
static const BasisReturnType UnitY ()
static const BasisReturnType UnitZ ()
static const ConstantReturnType Zero (Index rows, Index cols)
static const ConstantReturnType Zero (Index size)
static 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

void _init2 (Index rows, Index cols, typename internal::enable_if< Base::SizeAtCompileTime!=2, T0 >::type *=0)
void _init2 (const Scalar &x, const Scalar &y, typename internal::enable_if< Base::SizeAtCompileTime==2, T0 >::type *=0)
void _resize_to_match (const EigenBase< OtherDerived > &other)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
_set (const DenseBase< OtherDerived > &other)
 Copies the value of the expression other into *this with automatic resizing.
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
_set_noalias (const DenseBase< OtherDerived > &other)
void _set_selector (const OtherDerived &other, const internal::true_type &)
void _set_selector (const OtherDerived &other, const internal::false_type &)
void _swap (DenseBase< OtherDerived > const &other)
void checkTransposeAliasing (const OtherDerived &other) const
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator+= (const ArrayBase< OtherDerived > &)
Matrix< _Scalar, _Rows, _Cols,
_Options, _MaxRows, _MaxCols > & 
operator-= (const ArrayBase< OtherDerived > &)

Protected Attributes

DenseStorage< Scalar,
Base::MaxSizeAtCompileTime,
Base::RowsAtCompileTime,
Base::ColsAtCompileTime,
Options
m_storage

Friends

const ScalarMultipleReturnType operator* (const Scalar &scalar, const StorageBaseType &matrix)
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 StorageBaseType &matrix)

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:
_ScalarNumeric 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:
_OptionsA 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:

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 Eigen::Map<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Aligned> AlignedMapType [inherited]
typedef Base::CoeffReturnType CoeffReturnType [inherited]
typedef VectorwiseOp<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Vertical> ColwiseReturnType [inherited]
typedef const Eigen::Map<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Aligned> ConstAlignedMapType [inherited]
typedef const VectorwiseOp<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Vertical> ConstColwiseReturnType [inherited]
typedef const Diagonal<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstDiagonalReturnType [inherited]
typedef const Eigen::Map<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Unaligned> ConstMapType [inherited]
typedef const Reverse<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections> ConstReverseReturnType [inherited]
typedef const VectorwiseOp<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Horizontal> ConstRowwiseReturnType [inherited]
typedef const VectorBlock<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstSegmentReturnType [inherited]
typedef Block<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::ColsAtCompileTime==1 ? 1 : SizeMinusOne> ConstStartMinusOne [inherited]
typedef const Transpose<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > ConstTransposeReturnType [inherited]
typedef Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > DenseType [inherited]
typedef Diagonal<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > DiagonalReturnType [inherited]
typedef internal::add_const_on_value_type<typename internal::eval<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::type>::type EvalReturnType [inherited]
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar>, const ConstStartMinusOne > HNormalizedReturnType [inherited]
typedef Homogeneous<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , HomogeneousReturnTypeDirection> HomogeneousReturnType [inherited]
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Index Index [inherited]
typedef Eigen::Map<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Unaligned> MapType [inherited]
typedef internal::packet_traits<Scalar>::type PacketScalar [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 > >.

typedef NumTraits<Scalar>::Real RealScalar [inherited]
typedef Reverse<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , BothDirections> ReverseReturnType [inherited]
typedef VectorwiseOp<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Horizontal> RowwiseReturnType [inherited]
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar Scalar [inherited]
typedef VectorBlock<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > SegmentReturnType [inherited]
typedef internal::stem_function<Scalar>::type StemFunction [inherited]
typedef internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::StorageKind StorageKind [inherited]

Member Enumeration Documentation

anonymous enum
Enumerator:
Options 
anonymous enum [inherited]
anonymous enum [inherited]
anonymous enum [inherited]
anonymous enum [inherited]
anonymous enum [inherited]
anonymous enum [inherited]

Constructor & Destructor Documentation

Matrix ( ) [inline, explicit]

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 ( internal::constructor_without_unaligned_array_assert  ) [inline]
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 Scalar x,
const Scalar y 
)

Constructs an initialized 2D vector with given coefficients.

Matrix ( const Scalar x,
const Scalar y,
const Scalar z 
) [inline]

Constructs an initialized 3D vector with given coefficients.

Matrix ( const Scalar x,
const Scalar y,
const Scalar z,
const Scalar w 
) [inline]

Constructs an initialized 4D vector with given coefficients.

Matrix ( const Scalar data) [inline, explicit]
Matrix ( const MatrixBase< OtherDerived > &  other) [inline]

Constructor copying the value of the expression other.

Matrix ( const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &  other) [inline]

Copy constructor.

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

Copy constructor with in-place evaluation.

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

Copy constructor for generic expressions.

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

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

This is defined in the Geometry module.

 #include <Eigen/Geometry> 

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


Member Function Documentation

void _init2 ( Index  rows,
Index  cols,
typename internal::enable_if< Base::SizeAtCompileTime!=2, T0 >::type *  = 0 
) [inline, protected, inherited]
void _init2 ( const Scalar x,
const Scalar y,
typename internal::enable_if< Base::SizeAtCompileTime==2, T0 >::type *  = 0 
) [inline, protected, inherited]
void _resize_to_match ( const EigenBase< OtherDerived > &  other) [inline, protected, inherited]
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()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & _set_noalias ( const DenseBase< OtherDerived > &  other) [inline, protected, inherited]
void _set_selector ( const OtherDerived &  other,
const internal::true_type &   
) [inline, protected, inherited]
void _set_selector ( const OtherDerived &  other,
const internal::false_type &   
) [inline, protected, inherited]
void _swap ( DenseBase< OtherDerived > const &  other) [inline, protected, inherited]
const AdjointReturnType adjoint ( ) const [inherited]
Returns:
an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

Matrix2cf m = Matrix2cf::Random();
cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;

Output:

Here is the 2x2 complex matrix m:
 (-0.211,0.68) (-0.605,0.823)
 (0.597,0.566)  (0.536,-0.33)
Here is the adjoint of m:
(-0.211,-0.68) (0.597,-0.566)
(-0.605,-0.823)   (0.536,0.33)
Warning:
If you want to replace a matrix by its own adjoint, do NOT do this:
 m = m.adjoint(); // bug!!! caused by aliasing effect
Instead, use the adjointInPlace() method:
 m.adjointInPlace();
which gives Eigen good opportunities for optimization, or alternatively you can also do:
 m = m.adjoint().eval();
See also:
adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op
void adjointInPlace ( ) [inherited]

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

 m.adjointInPlace();

has the same effect on m as doing

 m = m.adjoint().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 adjoint. If you just need the adjoint of a matrix, use adjoint().

Note:
if the matrix is not square, then *this must be a resizable matrix.
See also:
transpose(), adjoint(), transposeInPlace()
bool all ( void  ) const [inherited]
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<()
bool any ( void  ) const [inherited]
Returns:
true if at least one coefficient is true
See also:
all()
void applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
) [inherited]

Apply the elementary reflector H given by $ H = I - tau v v^*$ with $ v^T = [1 essential^T] $ from the left to a vector or matrix.

On input:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()
void applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
) [inherited]

Apply the elementary reflector H given by $ H = I - tau v v^*$ with $ v^T = [1 essential^T] $ from the right to a vector or matrix.

On input:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()
void applyOnTheLeft ( const EigenBase< OtherDerived > &  other) [inherited]

replaces *this by *this * other.

Referenced by Eigen::internal::real_2x2_jacobi_svd().

void applyOnTheLeft ( Index  p,
Index  q,
const JacobiRotation< OtherScalar > &  j 
) [inherited]

This is defined in the Jacobi module.

 #include <Eigen/Jacobi> 

Applies the rotation in the plane j to the rows p and q of *this, i.e., it computes B = J * B, with $ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) $.

See also:
class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
void applyOnTheRight ( const EigenBase< OtherDerived > &  other) [inherited]

replaces *this by *this * other. It is equivalent to MatrixBase::operator*=()

void applyOnTheRight ( Index  p,
Index  q,
const JacobiRotation< OtherScalar > &  j 
) [inherited]

Applies the rotation in the plane j to the columns p and q of *this, i.e., it computes B = B * J with $ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) $.

See also:
class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()
ArrayWrapper<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array ( ) [inline, inherited]
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
const ArrayWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > array ( ) const [inline, inherited]
const DiagonalWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > asDiagonal ( ) const [inherited]
Returns:
a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients

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 << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;

Output:

2 0 0
0 5 0
0 0 6
See also:
class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
const PermutationWrapper<const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > asPermutation ( ) const [inherited]
Base& base ( ) [inline, inherited]
const Base& base ( ) const [inline, inherited]
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 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-=()
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+=()
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()
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:
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:

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 > > 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 
) [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:
startRowthe first row in the block
startColthe 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 > , BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const [inline, inherited]

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

RealScalar blueNorm ( ) const [inherited]
Returns:
the l2 norm of *this using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.

For architecture/scalar types without vectorization, this version is much faster than stableNorm(). Otherwise the stableNorm() is faster.

See also:
norm(), stableNorm(), hypotNorm()
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:
cRowsthe number of rows in the corner
cColsthe 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 > > 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 > , 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 > , CRows, CCols> bottomLeftCorner ( ) const [inline, inherited]

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

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:
cRowsthe number of rows in the corner
cColsthe 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)
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 > , 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 > , CRows, CCols> bottomRightCorner ( ) const [inline, inherited]

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

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

This is the const version of bottomRows(Index).

NRowsBlockXpr<N>::Type bottomRows ( ) [inline, inherited]
Returns:
a block consisting of the bottom rows of *this.
Template 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)
ConstNRowsBlockXpr<N>::Type bottomRows ( ) const [inline, inherited]

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

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
void checkTransposeAliasing ( const OtherDerived &  other) const [protected, inherited]
const Scalar& coeff ( Index  row,
Index  col 
) const [inline, inherited]
const Scalar& coeff ( Index  index) const [inline, inherited]
Scalar& coeffRef ( Index  row,
Index  col 
) [inline, inherited]
Scalar& coeffRef ( Index  index) [inline, inherited]
const Scalar& coeffRef ( Index  row,
Index  col 
) const [inline, inherited]
const Scalar& coeffRef ( Index  index) const [inline, inherited]
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

Referenced by IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::_solve_sparse().

ConstColXpr col ( Index  i) const [inline, inherited]

This is the const version of col().

const ColPivHouseholderQR<PlainObject> colPivHouseholderQr ( ) const [inherited]
Returns:
the column-pivoting Householder QR decomposition of *this.
See also:
class ColPivHouseholderQR
Index cols ( void  ) const [inline, inherited]
ConstColwiseReturnType colwise ( ) const [inherited]
Returns:
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Matrix3d m = Matrix3d::Random();
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, Tutorial page 7 - Reductions, visitors and broadcasting
ColwiseReturnType colwise ( ) [inherited]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
rowwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
void computeInverseAndDetWithCheck ( ResultType &  inverse,
typename ResultType::Scalar &  determinant,
bool invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 

Computation of matrix inverse and determinant, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Parameters:
inverseReference to the matrix in which to store the inverse.
determinantReference to the variable in which to store the inverse.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
double determinant;
m.computeInverseAndDetWithCheck(inverse,determinant,invertible);
cout << "Its determinant is " << determinant << endl;
if(invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
}
else {
  cout << "It is not invertible." << 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
Its determinant is 0.209
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
inverse(), computeInverseWithCheck()
void computeInverseWithCheck ( ResultType &  inverse,
bool invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 

Computation of matrix inverse, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Parameters:
inverseReference to the matrix in which to store the inverse.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
m.computeInverseWithCheck(inverse,invertible);
if(invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
}
else {
  cout << "It is not invertible." << 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
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
inverse(), computeInverseAndDetWithCheck()
ConjugateReturnType conjugate ( ) const [inline, inherited]
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()
void conservativeResize ( Index  rows,
Index  cols 
) [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 conservativeResize ( Index  rows,
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 ( NoChange_t  ,
Index  cols 
) [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  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 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.

static const ConstantReturnType Constant ( Index  rows,
Index  cols,
const Scalar value 
) [static, inherited]
Returns:
an expression of a constant matrix of value value

The parameters rows and cols 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 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
static const ConstantReturnType Constant ( Index  size,
const Scalar value 
) [static, inherited]
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
static const ConstantReturnType Constant ( const Scalar value) [static, inherited]
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
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cos ( ) const [inherited]
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > cosh ( ) const [inherited]
Index count ( ) const [inherited]
Returns:
the number of coefficients which evaluate to true
See also:
all(), any()
cross_product_return_type<OtherDerived>::type cross ( const MatrixBase< OtherDerived > &  other) const [inherited]

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Returns:
the cross product of *this and other

Here is a very good explanation of cross-product: http://xkcd.com/199/

See also:
MatrixBase::cross3()
PlainObject cross3 ( const MatrixBase< OtherDerived > &  other) const [inherited]

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Returns:
the cross product of *this and other using only the x, y, and z coefficients

The size of *this and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.

See also:
MatrixBase::cross()
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 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<std::binder1st<std::equal_to<Scalar> >, const Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > 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 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 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_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_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<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<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_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()
const Scalar* data ( ) const [inline, inherited]
Returns:
a const pointer to the data array of this matrix

Referenced by PardisoImpl< Derived >::_solve().

Scalar* data ( ) [inline, inherited]
Returns:
a pointer to the data array of this matrix
Scalar determinant ( ) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the determinant of this matrix
DiagonalReturnType diagonal ( ) [inherited]
Returns:
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the main diagonal of m:" << endl
     << m.diagonal() << endl;

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here are the coefficients on the main diagonal of m:
7
9
-5
See also:
class Diagonal
Returns:
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal<1>().transpose() << endl
     << m.diagonal<-2>().transpose() << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also:
MatrixBase::diagonal(), class Diagonal
const ConstDiagonalReturnType diagonal ( ) const [inherited]

This is the const version of diagonal().

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

DiagonalIndexReturnType<Index>::Type diagonal ( ) [inherited]
ConstDiagonalIndexReturnType<Index>::Type diagonal ( ) const [inherited]
DiagonalIndexReturnType<Dynamic>::Type diagonal ( Index  index) [inherited]
Returns:
an expression of the DiagIndex-th sub or super diagonal of the matrix *this

*this is not required to be square.

The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal(1).transpose() << endl
     << m.diagonal(-2).transpose() << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also:
MatrixBase::diagonal(), class Diagonal
ConstDiagonalIndexReturnType<Dynamic>::Type diagonal ( Index  index) const [inherited]

This is the const version of diagonal(Index).

Index diagonalSize ( ) const [inline, inherited]
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.
internal::scalar_product_traits<typename internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType dot ( const MatrixBase< OtherDerived > &  other) const [inherited]
Returns:
the dot product of *this with other.

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:
If the scalar type is complex numbers, then this function returns the hermitian (sesquilinear) dot product, conjugate-linear in the first variable and linear in the second variable.
See also:
squaredNorm(), norm()
const EIGEN_CWISE_PRODUCT_RETURN_TYPE ( Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >  ,
OtherDerived   
) 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
EigenvaluesReturnType eigenvalues ( ) const [inherited]

Computes the eigenvalues of a matrix.

Returns:
Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

 #include <Eigen/Eigenvalues> 

This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).

The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.

The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
VectorXcd eivals = ones.eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

The eigenvalues of the 3x3 matrix of ones are:
(-2.98e-17,0)
(3,0)
(1.81e-32,0)
See also:
EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()
Matrix<Scalar,3,1> eulerAngles ( Index  a0,
Index  a1,
Index  a2 
) const [inherited]

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Returns:
the Euler-angles of the rotation matrix *this using the convention defined by the triplet (a0,a1,a2)

Each of the three parameters a0,a1,a2 represents the respective rotation axis as an integer in {0,1,2}. For instance, in:

 Vector3f ea = mat.eulerAngles(2, 0, 2); 

"2" represents the z axis and "0" the x axis, etc. The returned angles are such that we have the following equality:

 mat == AngleAxisf(ea[0], Vector3f::UnitZ())
      * AngleAxisf(ea[1], Vector3f::UnitX())
      * AngleAxisf(ea[2], Vector3f::UnitZ()); 

This corresponds to the right-multiply conventions (with right hand side frames).

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.

void evalTo ( Dest &  ) const [inline, inherited]
const MatrixExponentialReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > exp ( ) const [inherited]
void fill ( const Scalar value) [inherited]

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

See also:
setConstant(), Constant(), class CwiseNullaryOp
const Flagged<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , Added, Removed> flagged ( ) const [inherited]
Returns:
an expression of *this with added and removed flags

This is mostly for internal use.

See also:
class Flagged
const ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > forceAlignedAccess ( ) const [inline, inherited]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(),class ForceAlignedAccess

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

ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > forceAlignedAccess ( ) [inline, inherited]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(), class ForceAlignedAccess

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

internal::add_const_on_value_type<typename internal::conditional<Enable,ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &>::type>::type forceAlignedAccessIf ( ) const [inline, inherited]
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

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

internal::conditional<Enable,ForceAlignedAccess<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > &>::type forceAlignedAccessIf ( ) [inline, inherited]
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

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

const WithFormat<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > format ( const IOFormat fmt) const [inline, inherited]
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
Returns:
the full-pivoting Householder QR decomposition of *this.
See also:
class FullPivHouseholderQR
const FullPivLU<PlainObject> fullPivLu ( ) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU
SegmentReturnType head ( Index  size) [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:
sizethe number of coefficients in the block

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)
DenseBase::ConstSegmentReturnType head ( Index  size) const [inherited]

This is the const version of head(Index).

FixedSegmentReturnType<Size>::Type head ( ) [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.

The template parameter Size is the number of coefficients in the block

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
ConstFixedSegmentReturnType<Size>::Type head ( ) const [inherited]

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

const HNormalizedReturnType hnormalized ( ) const [inherited]

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Returns:
an expression of the homogeneous normalized vector of *this

Example:

Output:

See also:
VectorwiseOp::hnormalized()
HomogeneousReturnType homogeneous ( ) const [inherited]

This is defined in the Geometry module.

 #include <Eigen/Geometry> 
Returns:
an expression of the equivalent homogeneous vector

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

Example:

Output:

See also:
class Homogeneous
const HouseholderQR<PlainObject> householderQr ( ) const [inherited]
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR
RealScalar hypotNorm ( ) const [inherited]
Returns:
the l2 norm of *this avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
See also:
norm(), stableNorm()
static const IdentityReturnType Identity ( ) [static, inherited]
Returns:
an expression of the identity matrix (not necessarily square).

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

Example:

cout << Matrix<double, 3, 4>::Identity() << endl;

Output:

1 0 0 0
0 1 0 0
0 0 1 0
See also:
Identity(Index,Index), setIdentity(), isIdentity()

Referenced by main().

static const IdentityReturnType Identity ( Index  rows,
Index  cols 
) [static, inherited]
Returns:
an expression of the identity matrix (not necessarily square).

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 Identity() should be used instead.

Example:

cout << MatrixXd::Identity(4, 3) << endl;

Output:

1 0 0
0 1 0
0 0 1
0 0 0
See also:
Identity(), setIdentity(), isIdentity()
const ImagReturnType imag ( ) const [inline, inherited]
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()
NonConstImagReturnType imag ( ) [inline, inherited]
Returns:
a non const 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.
Index innerStride ( ) const [inline]
const internal::inverse_impl<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > inverse ( ) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the matrix inverse of this matrix.

For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.

Note:
This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following:
  • for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
  • for the general case, use class FullPivLU.
Example:
Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << 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
Its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
computeInverseAndDetWithCheck()
bool isApprox ( const DenseBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) 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 value,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const [inherited]
Returns:
true if all coefficients in this matrix are approximately equal to value, to within precision prec
bool isConstant ( const Scalar value,
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 isDiagonal ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const [inherited]
Returns:
true if *this is approximately equal to a diagonal matrix, within the precision given by prec.

Example:

Matrix3d m = 10000 * Matrix3d::Identity();
m(0,2) = 1;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl;
cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;

Output:

Here's the matrix m:
1e+04     0     1
    0 1e+04     0
    0     0 1e+04
m.isDiagonal() returns: 0
m.isDiagonal(1e-3) returns: 1
See also:
asDiagonal()
bool isIdentity ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const [inherited]
Returns:
true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.

Example:

Matrix3d m = Matrix3d::Identity();
m(0,2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isIdentity() returns: " << m.isIdentity() << endl;
cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
bool isLowerTriangular ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const [inherited]
Returns:
true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
See also:
isUpperTriangular()
bool isMuchSmallerThan ( const RealScalar other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const [inherited]
bool isMuchSmallerThan ( const DenseBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) 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 ( 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:

Matrix3d m = Matrix3d::Ones();
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 isOrthogonal ( const MatrixBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const [inherited]
Returns:
true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

Vector3d v(1,0,0);
Vector3d w(1e-4,0,1);
cout << "Here's the vector v:" << endl << v << endl;
cout << "Here's the vector w:" << endl << w << endl;
cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl;
cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;

Output:

Here's the vector v:
1
0
0
Here's the vector w:
0.0001
0
1
v.isOrthogonal(w) returns: 0
v.isOrthogonal(w,1e-3) returns: 1
bool isUnitary ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const [inherited]
Returns:
true if *this is approximately an unitary matrix, within the precision given by prec. In the case where the Scalar type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
Note:
This can be used to check whether a family of vectors forms an orthonormal basis. Indeed, m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.

Example:

Matrix3d m = Matrix3d::Identity();
m(0,2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isUnitary() returns: " << m.isUnitary() << endl;
cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isUnitary() returns: 0
m.isUnitary(1e-3) returns: 1
bool isUpperTriangular ( RealScalar  prec = NumTraits<Scalar>::dummy_precision()) const [inherited]
Returns:
true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
See also:
isLowerTriangular()
bool isZero ( 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:

Matrix3d m = Matrix3d::Zero();
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()
JacobiSVD<PlainObject> jacobiSvd ( unsigned int  computationOptions = 0) const [inherited]

This is defined in the SVD module.

 #include <Eigen/SVD> 
Returns:
the singular value decomposition of *this computed by two-sided Jacobi transformations.
See also:
class JacobiSVD
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & lazyAssign ( const DenseBase< OtherDerived > &  other) [inline, inherited]
See also:
MatrixBase::lazyAssign()
const LazyProductReturnType<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,OtherDerived>::Type lazyProduct ( const MatrixBase< OtherDerived > &  other) const [inherited]
Returns:
an expression of the matrix product of *this and other without implicit evaluation.

The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.

Warning:
This version of the matrix product can be much much slower. So use it only if you know what you are doing and that you measured a true speed improvement.
See also:
operator*(const MatrixBase&)
const LDLT<PlainObject> ldlt ( ) const [inherited]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky> 
Returns:
the Cholesky decomposition with full pivoting without square root of *this
ColsBlockXpr leftCols ( Index  n) [inline, inherited]
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)

Referenced by PardisoImpl< PardisoLU< MatrixType > >::_solve_sparse(), and PastixBase< PastixLU< _MatrixType > >::_solve_sparse().

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

This is the const version of leftCols(Index).

NColsBlockXpr<N>::Type leftCols ( ) [inline, inherited]
Returns:
a block consisting of the left columns of *this.
Template 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)
ConstNColsBlockXpr<N>::Type leftCols ( ) const [inline, inherited]

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

static const SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
Index  size,
const Scalar low,
const Scalar high 
) [static, inherited]

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
static const RandomAccessLinSpacedReturnType LinSpaced ( Index  size,
const Scalar low,
const Scalar high 
) [static, inherited]

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
static const SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
const Scalar low,
const Scalar high 
) [static, inherited]
Special version for fixed size types which does not require the size parameter.

static const RandomAccessLinSpacedReturnType LinSpaced ( const Scalar low,
const Scalar high 
) [static, inherited]
Special version for fixed size types which does not require the size parameter.

const LLT<PlainObject> llt ( ) const [inherited]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky> 
Returns:
the LLT decomposition of *this
const MatrixLogarithmReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > log ( ) const [inherited]
RealScalar lpNorm ( ) const [inherited]
Returns:
the $ \ell^p $ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values of the coefficients of *this. If p is the special value Eigen::Infinity, this function returns the $ \ell^\infty $ norm, that is the maximum of the absolute values of the coefficients of *this.
See also:
norm()

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

const PartialPivLU<PlainObject> lu ( ) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 

Synonym of partialPivLu().

Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU
void makeHouseholder ( EssentialPart &  essential,
Scalar tau,
RealScalar beta 
) const [inherited]

Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $

On output:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
betathe result of H * *this
See also:
MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()
void makeHouseholderInPlace ( Scalar tau,
RealScalar beta 
) [inherited]

Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $

The essential part of the vector v is stored in *this.

On output:

Parameters:
tauthe scaling factor of the Householder transformation
betathe result of H * *this
See also:
MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()
static ConstMapType Map ( const Scalar data) [inline, static, inherited]
static MapType Map ( Scalar data) [inline, static, inherited]
static ConstMapType Map ( const Scalar data,
Index  size 
) [inline, static, inherited]
static MapType Map ( Scalar data,
Index  size 
) [inline, static, inherited]
static ConstMapType Map ( const Scalar data,
Index  rows,
Index  cols 
) [inline, static, inherited]
static MapType Map ( Scalar data,
Index  rows,
Index  cols 
) [inline, static, inherited]
static StridedConstMapType<Stride<Outer, Inner> >::type Map ( const Scalar data,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedMapType<Stride<Outer, Inner> >::type Map ( Scalar data,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedConstMapType<Stride<Outer, Inner> >::type Map ( const Scalar data,
Index  size,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedMapType<Stride<Outer, Inner> >::type Map ( Scalar data,
Index  size,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedConstMapType<Stride<Outer, Inner> >::type Map ( const Scalar data,
Index  rows,
Index  cols,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedMapType<Stride<Outer, Inner> >::type Map ( Scalar data,
Index  rows,
Index  cols,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static ConstAlignedMapType MapAligned ( const Scalar data) [inline, static, inherited]
static AlignedMapType MapAligned ( Scalar data) [inline, static, inherited]
static ConstAlignedMapType MapAligned ( const Scalar data,
Index  size 
) [inline, static, inherited]
static AlignedMapType MapAligned ( Scalar data,
Index  size 
) [inline, static, inherited]
static ConstAlignedMapType MapAligned ( const Scalar data,
Index  rows,
Index  cols 
) [inline, static, inherited]
static AlignedMapType MapAligned ( Scalar data,
Index  rows,
Index  cols 
) [inline, static, inherited]
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( const Scalar data,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( Scalar data,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( const Scalar data,
Index  size,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( Scalar data,
Index  size,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedConstAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( const Scalar data,
Index  rows,
Index  cols,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
static StridedAlignedMapType<Stride<Outer, Inner> >::type MapAligned ( Scalar data,
Index  rows,
Index  cols,
const Stride< Outer, Inner > &  stride 
) [inline, static, inherited]
MatrixBase<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >& matrix ( ) [inline, inherited]
const MatrixBase<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >& matrix ( ) const [inline, inherited]
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > matrixFunction ( StemFunction  f) const [inherited]
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff ( ) const [inherited]
Returns:
the maximum of all coefficients of *this
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff ( IndexType *  row,
IndexType *  col 
) const [inherited]
Returns:
the maximum of all coefficients of *this and puts in *row and *col its location.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar maxCoeff ( IndexType *  index) const [inherited]
Returns:
the maximum of all coefficients of *this and puts in *index its location.
See also:
DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()
Scalar mean ( ) const [inherited]
Returns:
the mean of all coefficients of *this
See also:
trace(), prod(), sum()
ColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) [inline, inherited]
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)
ConstColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) const [inline, inherited]

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

NColsBlockXpr<N>::Type middleCols ( Index  startCol) [inline, inherited]
Returns:
a block consisting of a range of columns of *this.
Template Parameters:
Nthe number of columns in the block
Parameters:
startColthe index of the first column 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<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)
ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol) const [inline, inherited]

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

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

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

NRowsBlockXpr<N>::Type middleRows ( Index  startRow) [inline, inherited]
Returns:
a block consisting of a range of rows of *this.
Template Parameters:
Nthe number of rows in the block
Parameters:
startRowthe index of the first row 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.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)
ConstNRowsBlockXpr<N>::Type middleRows ( Index  startRow) const [inline, inherited]

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

internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff ( ) const [inherited]
Returns:
the minimum of all coefficients of *this
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff ( IndexType *  row,
IndexType *  col 
) const [inherited]
Returns:
the minimum of all coefficients of *this and puts in *row and *col its location.
See also:
DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()
internal::traits<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::Scalar minCoeff ( IndexType *  index) const [inherited]
Returns:
the minimum of all coefficients of *this and puts in *index its location.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()
const NestByValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > nestByValue ( ) const [inline, inherited]
Returns:
an expression of the temporary version of *this.
NoAlias<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,Eigen::MatrixBase > noalias ( ) [inherited]
Returns:
a pseudo expression of *this with an operator= assuming no aliasing between *this and the source expression.

More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.

Here are some examples where noalias is usefull:

 D.noalias()  = A * B;
 D.noalias() += A.transpose() * B;
 D.noalias() -= 2 * A * B.adjoint();

On the other hand the following example will lead to a wrong result:

 A.noalias() = A * B;

because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:

 A = A * B;
See also:
class NoAlias

Referenced by Eigen::internal::apply_block_householder_on_the_left().

Index nonZeros ( ) const [inline, inherited]
Returns:
the number of nonzero coefficients which is in practice the number of stored coefficients.
RealScalar norm ( ) const [inherited]
Returns:
, for vectors, the l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.
See also:
dot(), squaredNorm()
void normalize ( void  ) [inherited]

Normalizes the vector, i.e. divides it by its own norm.

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

See also:
norm(), normalized()
const PlainObject normalized ( ) const [inherited]
Returns:
an expression of the quotient of *this by its own norm.

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

See also:
norm(), normalize()
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
) [static, inherited]
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
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
) [static, inherited]
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.

See also:
class CwiseNullaryOp
static const CwiseNullaryOp<CustomNullaryOp, Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > NullaryExpr ( const CustomNullaryOp &  func) [static, inherited]
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
static const ConstantReturnType Ones ( Index  rows,
Index  cols 
) [static, inherited]
Returns:
an expression of a matrix where all coefficients equal one.

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 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
static const ConstantReturnType Ones ( Index  size) [static, inherited]
Returns:
an expression of a vector where all coefficients equal one.

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 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
static const ConstantReturnType Ones ( ) [static, inherited]
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 [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 ScalarMultipleReturnType operator* ( const Scalar scalar) const [inline, inherited]
Returns:
an expression of *this scaled by the scalar factor scalar
const ScalarMultipleReturnType operator* ( const RealScalar scalar) const [inherited]
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 ProductReturnType<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,OtherDerived>::Type operator* ( const MatrixBase< OtherDerived > &  other) const [inherited]
Returns:
the matrix product of *this and other.
Note:
If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
See also:
lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
const DiagonalProduct<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , DiagonalDerived, OnTheRight> operator* ( const DiagonalBase< DiagonalDerived > &  diagonal) const [inherited]
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.
ScalarMultipleReturnType operator* ( const UniformScaling< Scalar > &  s) const [inherited]

Concatenates a linear transformation matrix and a uniform scaling

Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator*= ( const EigenBase< OtherDerived > &  other) [inherited]

replaces *this by *this * other.

Returns:
a reference to *this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator*= ( const Scalar other) [inline, inherited]
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= ( const MatrixBase< OtherDerived > &  other) [inherited]

replaces *this by *this + other.

Returns:
a reference to *this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= ( const EigenBase< OtherDerived > &  other) [inherited]
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator+= ( const ArrayBase< OtherDerived > &  ) [inline, protected, inherited]
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
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= ( const MatrixBase< OtherDerived > &  other) [inherited]

replaces *this by *this - other.

Returns:
a reference to *this
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= ( const EigenBase< OtherDerived > &  other) [inherited]
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & operator-= ( const ArrayBase< OtherDerived > &  ) [inline, protected, inherited]
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, _Options, _MaxRows, _MaxCols > & operator/= ( const Scalar other) [inline, inherited]
CommaInitializer<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator<< ( const Scalar s) [inherited]

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:

Matrix3i m1;
m1 << 1, 2, 3,
      4, 5, 6,
      7, 8, 9;
cout << m1 << endl << endl;
Matrix3i m2 = Matrix3i::Identity();
m2.block(0,0, 2,2) << 10, 11, 12, 13;
cout << m2 << endl << endl;
Vector2i v1;
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
See also:
CommaInitializer::finished(), class CommaInitializer
CommaInitializer<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > operator<< ( const DenseBase< OtherDerived > &  other) [inherited]
See also:
operator<<(const Scalar&)
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=.
Matrix& operator= ( const MatrixBase< OtherDerived > &  other) [inline]
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 ReturnByValue< OtherDerived > &  func) [inline]
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> 

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

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!=
RealScalar operatorNorm ( ) const [inherited]

Computes the L2 operator norm.

Returns:
Operator norm of the matrix.

This is defined in the Eigenvalues module.

 #include <Eigen/Eigenvalues> 

This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix $ A $ is defined to be

\[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \]

where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix $ A^*A $.

The current implementation uses the eigenvalues of $ A^*A $, as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.

Example:

MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
     << ones.operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3
See also:
SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()
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.
Index outerStride ( ) const [inline]
PacketScalar packet ( Index  row,
Index  col 
) const [inline, inherited]
PacketScalar packet ( Index  index) const [inline, inherited]
const PartialPivLU<PlainObject> partialPivLu ( ) const [inherited]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU
Scalar prod ( ) const [inherited]
Returns:
the product of all coefficients of *this

Example:

Matrix3d m = Matrix3d::Random();
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()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random ( Index  rows,
Index  cols 
) [static, inherited]
Returns:
a random matrix expression

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

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

Example:

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 also:
MatrixBase::setRandom(), MatrixBase::Random(Index), MatrixBase::Random()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random ( Index  size) [static, inherited]
Returns:
a random vector expression

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

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

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

Example:

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:
MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random()
static const CwiseNullaryOp<internal::scalar_random_op<Scalar>,Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random ( ) [static, inherited]
Returns:
a fixed-size random matrix or vector expression

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.

See also:
MatrixBase::setRandom(), MatrixBase::Random(Index,Index), MatrixBase::Random(Index)

Referenced by main().

RealReturnType real ( ) const [inline, inherited]
Returns:
a read-only expression of the real part of *this.
See also:
imag()
NonConstRealReturnType real ( ) [inline, inherited]
Returns:
a non const expression of the real part of *this.
See also:
imag()
const Replicate<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,RowFactor,ColFactor> replicate ( ) const [inherited]
Returns:
an expression of the replication of *this

Example:

MatrixXi m = MatrixXi::Random(2,3);
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<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,Dynamic,Dynamic> replicate ( Index  rowFacor,
Index  colFactor 
) const [inherited]
Returns:
an expression of the replication of *this

Example:

Vector3i v = Vector3i::Random();
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
void resize ( Index  rows,
Index  cols 
) [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 2
4 5
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 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 ( NoChange_t  ,
Index  cols 
) [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  rows,
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 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.

ReverseReturnType reverse ( ) [inherited]
Returns:
an expression of the reverse of *this.

Example:

MatrixXi m = MatrixXi::Random(3,4);
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
ConstReverseReturnType reverse ( ) const [inherited]

This is the const version of reverse().

void reverseInPlace ( ) [inherited]

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

This is the const version of rightCols(Index).

NColsBlockXpr<N>::Type rightCols ( ) [inline, inherited]
Returns:
a block consisting of the right columns of *this.
Template 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)
ConstNColsBlockXpr<N>::Type rightCols ( ) const [inline, inherited]

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

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
ConstRowXpr row ( Index  i) const [inline, inherited]

This is the const version of row().

Index rows ( void  ) const [inline, inherited]
ConstRowwiseReturnType rowwise ( ) const [inherited]
Returns:
a VectorwiseOp wrapper of *this providing additional partial reduction operations

Example:

Matrix3d m = Matrix3d::Random();
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, Tutorial page 7 - Reductions, visitors and broadcasting
RowwiseReturnType rowwise ( ) [inherited]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
colwise(), class VectorwiseOp, Tutorial page 7 - Reductions, visitors and broadcasting
SegmentReturnType segment ( Index  start,
Index  size 
) [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:
startthe first coefficient in the segment
sizethe 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)
DenseBase::ConstSegmentReturnType segment ( Index  start,
Index  size 
) const [inherited]

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

FixedSegmentReturnType<Size>::Type segment ( Index  start) [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.

The template parameter Size is the number of coefficients in the block

Parameters:
startthe index of the first element of the sub-vector

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
ConstFixedSegmentReturnType<Size>::Type segment ( Index  start) const [inherited]

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

const Select<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,ThenDerived,ElseDerived> select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const [inherited]
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<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > ,ThenDerived, typename ThenDerived::ConstantReturnType> select ( const DenseBase< ThenDerived > &  thenMatrix,
typename ThenDerived::Scalar  elseScalar 
) const [inline, inherited]

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<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > , typename ElseDerived::ConstantReturnType, ElseDerived > select ( typename ElseDerived::Scalar  thenScalar,
const DenseBase< ElseDerived > &  elseMatrix 
) const [inline, inherited]

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
SelfAdjointViewReturnType<UpLo>::Type selfadjointView ( ) [inherited]
ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView ( ) const [inherited]
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant ( const Scalar value) [inherited]

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()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant ( Index  size,
const Scalar value 
) [inherited]

Resizes to the given size, and sets all coefficients in this expression to the given value.

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

Example:

VectorXf v;
v.setConstant(3, 5);
cout << v << endl;

Output:

5
5
5
See also:
MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setConstant ( Index  rows,
Index  cols,
const Scalar value 
) [inherited]

Resizes to the given size, and sets all coefficients in this expression to the given value.

Parameters:
rowsthe new number of rows
colsthe new number of columns
valuethe value to which all coefficients are set

Example:

MatrixXf m;
m.setConstant(3, 3, 5);
cout << m << endl;

Output:

5 5 5
5 5 5
5 5 5
See also:
MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setIdentity ( ) [inherited]

Writes the identity expression (not necessarily square) into *this.

Example:

Matrix4i m = Matrix4i::Zero();
m.block<3,3>(1,0).setIdentity();
cout << m << endl;

Output:

0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setIdentity ( Index  rows,
Index  cols 
) [inherited]

Resizes to the given size, and writes the identity expression (not necessarily square) into *this.

Parameters:
rowsthe new number of rows
colsthe new number of columns

Example:

MatrixXf m;
m.setIdentity(3, 3);
cout << m << endl;

Output:

1 0 0
0 1 0
0 0 1
See also:
MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setLinSpaced ( Index  size,
const Scalar low,
const Scalar high 
) [inherited]

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).transpose();
cout << v << endl;

Output:

0.5
0.75
1
1.25
1.5
See also:
CwiseNullaryOp
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setLinSpaced ( const Scalar low,
const Scalar high 
) [inherited]

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
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes ( ) [inherited]

Sets all coefficients in this expression to one.

Example:

Matrix4i m = Matrix4i::Random();
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()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes ( Index  size) [inherited]

Resizes to the given size, and sets all coefficients in this expression to one.

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

Example:

VectorXf v;
v.setOnes(3);
cout << v << endl;

Output:

1
1
1
See also:
MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setOnes ( Index  rows,
Index  cols 
) [inherited]

Resizes to the given size, and sets all coefficients in this expression to one.

Parameters:
rowsthe new number of rows
colsthe new number of columns

Example:

MatrixXf m;
m.setOnes(3, 3);
cout << m << endl;

Output:

1 1 1
1 1 1
1 1 1
See also:
MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom ( ) [inherited]

Sets all coefficients in this expression to random values.

Example:

Matrix4i m = Matrix4i::Zero();
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)
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom ( Index  size) [inherited]

Resizes to the given size, and sets all coefficients in this expression to random values.

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

Example:

VectorXf v;
v.setRandom(3);
cout << v << endl;

Output:

0.68
-0.211
0.566
See also:
MatrixBase::setRandom(), setRandom(Index,Index), class CwiseNullaryOp, MatrixBase::Random()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setRandom ( Index  rows,
Index  cols 
) [inherited]

Resizes to the given size, and sets all coefficients in this expression to random values.

Parameters:
rowsthe new number of rows
colsthe new number of columns

Example:

MatrixXf m;
m.setRandom(3, 3);
cout << m << endl;

Output:

  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
See also:
MatrixBase::setRandom(), setRandom(Index), class CwiseNullaryOp, MatrixBase::Random()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero ( ) [inherited]

Sets all coefficients in this expression to zero.

Example:

Matrix4i m = Matrix4i::Random();
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()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero ( Index  size) [inherited]

Resizes to the given size, and sets all coefficients in this expression to zero.

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

Example:

VectorXf v;
v.setZero(3);
cout << v << endl;

Output:

0
0
0
See also:
DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero()
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero ( Index  rows,
Index  cols 
) [inherited]

Resizes to the given size, and sets all coefficients in this expression to zero.

Parameters:
rowsthe new number of rows
colsthe new number of columns

Example:

MatrixXf m;
m.setZero(3, 3);
cout << m << endl;

Output:

0 0 0
0 0 0
0 0 0
See also:
DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero()
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sin ( ) const [inherited]
const MatrixFunctionReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sinh ( ) const [inherited]
const SparseView<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sparseView ( const Scalar m_reference = Scalar(0),
typename NumTraits< Scalar >::Real  m_epsilon = NumTraits<Scalar>::dummy_precision() 
) const [inherited]
const MatrixSquareRootReturnValue<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > sqrt ( ) const [inherited]
RealScalar squaredNorm ( ) const [inherited]
Returns:
, for vectors, the squared l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this with itself.
See also:
dot(), norm()
RealScalar stableNorm ( ) const [inherited]
Returns:
the l2 norm of *this avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s 2 - compute $ s \Vert \frac{*this}{s} \Vert $ in a standard way

For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.

See also:
norm(), blueNorm(), hypotNorm()
Scalar sum ( ) const [inherited]
Returns:
the sum of all coefficients of *this
See also:
trace(), prod(), mean()
void swap ( MatrixBase< OtherDerived > const &  other) [inline]
void swap ( const DenseBase< OtherDerived > &  other,
int  = OtherDerived::ThisConstantIsPrivateInPlainObjectBase 
) [inline, inherited]

swaps *this with the expression other.

void swap ( PlainObjectBase< OtherDerived > &  other) [inline, inherited]

swaps *this with the matrix or array other.

SegmentReturnType tail ( Index  size) [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:
sizethe number of coefficients in the block

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)
DenseBase::ConstSegmentReturnType tail ( Index  size) const [inherited]

This is the const version of tail(Index).

FixedSegmentReturnType<Size>::Type tail ( ) [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.

The template parameter Size is the number of coefficients in the block

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
ConstFixedSegmentReturnType<Size>::Type tail ( ) const [inherited]

This is the const version of tail<int>.

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:
cRowsthe number of rows in the corner
cColsthe 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 > > 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 > , 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 > , CRows, CCols> topLeftCorner ( ) const [inline, inherited]

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

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:
cRowsthe number of rows in the corner
cColsthe 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)
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 > , CRows, CCols> topRightCorner ( ) [inline, inherited]
Returns:
an expression of a fixed-size top-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.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)
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>().

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

This is the const version of topRows(Index).

NRowsBlockXpr<N>::Type topRows ( ) [inline, inherited]
Returns:
a block consisting of the top rows of *this.
Template 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)
ConstNRowsBlockXpr<N>::Type topRows ( ) const [inline, inherited]

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

Scalar trace ( ) const [inherited]
Returns:
the trace of *this, i.e. the sum of the coefficients on the main diagonal.

*this can be any matrix, not necessarily square.

See also:
diagonal(), sum()

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

Eigen::Transpose<Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > transpose ( ) [inherited]
Returns:
an expression of the transpose of *this.

Example:

Matrix2i m = Matrix2i::Random();
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()
ConstTransposeReturnType transpose ( ) const [inherited]

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also:
transposeInPlace(), adjoint()
void transposeInPlace ( ) [inherited]

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.
See also:
transpose(), adjoint(), adjointInPlace()
TriangularViewReturnType<Mode>::Type triangularView ( ) [inherited]
Returns:
an expression of a triangular view extracted from the current matrix

The parameter Mode can have the following values: #Upper, #StrictlyUpper, #UnitUpper, #Lower, #StrictlyLower, #UnitLower.

Example:

#ifndef _MSC_VER
  #warning deprecated
#endif
/* deprecated
Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the upper-triangular matrix extracted from m:" << endl
     << m.part<Eigen::UpperTriangular>() << endl;
cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
     << m.part<Eigen::StrictlyUpperTriangular>() << endl;
cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
     << m.part<Eigen::UnitLowerTriangular>() << endl;
*/

Output:

See also:
class TriangularView
ConstTriangularViewReturnType<Mode>::Type triangularView ( ) const [inherited]

This is the const version of MatrixBase::triangularView()

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]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
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
static const BasisReturnType Unit ( Index  size,
Index  i 
) [static, inherited]
Returns:
an expression of the i-th unit (basis) vector.

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:
MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
static const BasisReturnType Unit ( Index  i) [static, inherited]
Returns:
an expression of the i-th unit (basis) vector.

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

This variant is for fixed-size vector only.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
PlainObject unitOrthogonal ( void  ) const [inherited]
Returns:
a unit vector which is orthogonal to *this

The size of *this must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this, i.e., (-y,x).normalized().

See also:
cross()
static const BasisReturnType UnitW ( ) [static, inherited]
Returns:
an expression of the W axis unit vector (0,0,0,1)

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:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
static const BasisReturnType UnitX ( ) [static, inherited]
Returns:
an expression of the X axis unit vector (1{,0}^*)

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:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
static const BasisReturnType UnitY ( ) [static, inherited]
Returns:
an expression of the Y axis unit vector (0,1{,0}^*)

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:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
static const BasisReturnType UnitZ ( ) [static, inherited]
Returns:
an expression of the Z axis unit vector (0,0,1{,0}^*)

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:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
CoeffReturnType value ( ) const [inline, inherited]
Returns:
the unique coefficient of a 1x1 expression
void visit ( Visitor &  func) 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()
void writePacket ( Index  row,
Index  col,
const PacketScalar x 
) [inline, inherited]
void writePacket ( Index  index,
const PacketScalar x 
) [inline, inherited]
static const ConstantReturnType Zero ( Index  rows,
Index  cols 
) [static, inherited]
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)
static const ConstantReturnType Zero ( Index  size) [static, inherited]
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)
static const ConstantReturnType Zero ( ) [static, inherited]
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

const ScalarMultipleReturnType operator* ( const Scalar scalar,
const StorageBaseType &  matrix 
) [friend, inherited]
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 StorageBaseType &  matrix 
) [friend, inherited]

Member Data Documentation

DenseStorage<Scalar, Base::MaxSizeAtCompileTime, Base::RowsAtCompileTime, Base::ColsAtCompileTime, Options> m_storage [protected, inherited]

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