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Eigen  3.2.5
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MatrixBase< Derived > Class Template Reference
[Core module]

Base class for all dense matrices, vectors, and expressions. More...

Inheritance diagram for MatrixBase< Derived >:

List of all members.

Public Types

enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime,
  MaxRowsAtCompileTime,
  MaxColsAtCompileTime,
  MaxSizeAtCompileTime,
  IsVectorAtCompileTime,
  Flags,
  IsRowMajor ,
  CoeffReadCost
}
typedef internal::traits
< Derived >::Index 
Index
 The type of indices.
typedef Matrix< typename
internal::traits< Derived >
::Scalar, internal::traits
< Derived >::RowsAtCompileTime,
internal::traits< Derived >
::ColsAtCompileTime, AutoAlign|(internal::traits
< Derived >::Flags
&RowMajorBit?RowMajor:ColMajor),
internal::traits< Derived >
::MaxRowsAtCompileTime,
internal::traits< Derived >
::MaxColsAtCompileTime > 
PlainObject
 The plain matrix type corresponding to this expression.

Public Member Functions

const AdjointReturnType adjoint () const
void adjointInPlace ()
bool all (void) const
bool allFinite () const
bool any (void) const
template<typename EssentialPart >
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename EssentialPart >
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename OtherScalar >
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherDerived >
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
template<typename OtherScalar >
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherDerived >
void applyOnTheRight (const EigenBase< OtherDerived > &other)
ArrayWrapper< Derived > array ()
const DiagonalWrapper< const
Derived > 
asDiagonal () const
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp
< CustomBinaryOp, const
Derived, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
template<int BlockRows, int BlockCols>
const Block< const Derived,
BlockRows, BlockCols > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows,
BlockCols > 
block (Index startRow, Index startCol, Index blockRows, Index blockCols)
template<int BlockRows, int BlockCols>
const Block< const Derived,
BlockRows, BlockCols > 
block (Index startRow, Index startCol) const
template<int BlockRows, int BlockCols>
Block< Derived, BlockRows,
BlockCols > 
block (Index startRow, Index startCol)
const Block< const Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< Derived > block (Index startRow, Index startCol, Index blockRows, Index blockCols)
RealScalar blueNorm () const
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomLeftCorner () const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomLeftCorner ()
const Block< const Derived > bottomLeftCorner (Index cRows, Index cCols) const
Block< Derived > bottomLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
bottomRightCorner () const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > bottomRightCorner ()
const Block< const Derived > bottomRightCorner (Index cRows, Index cCols) const
Block< Derived > bottomRightCorner (Index cRows, Index cCols)
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
template<int N>
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
ConstRowsBlockXpr bottomRows (Index n) const
RowsBlockXpr bottomRows (Index n)
template<typename NewType >
internal::cast_return_type
< Derived, const CwiseUnaryOp
< internal::scalar_cast_op
< typename internal::traits
< Derived >::Scalar, NewType >
, const Derived > >::type 
cast () const
ConstColXpr col (Index i) const
ColXpr col (Index i)
const ColPivHouseholderQR
< PlainObject
colPivHouseholderQr () const
ColwiseReturnType colwise ()
ConstColwiseReturnType colwise () const
template<typename ResultType >
void computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
template<typename ResultType >
void computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const
ConjugateReturnType conjugate () const
Index count () const
template<typename OtherDerived >
cross_product_return_type
< OtherDerived >::type 
cross (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, const Derived > 
cwiseAbs () const
const CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, const Derived > 
cwiseAbs2 () const
const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, const Derived > 
cwiseInverse () const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Derived,
const ConstantReturnType > 
cwiseMax (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Derived,
const ConstantReturnType > 
cwiseMin (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_product_op
< typename Derived::Scalar,
typename OtherDerived::Scalar >
, const Derived, const
OtherDerived > 
cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, const Derived > 
cwiseSqrt () const
Scalar determinant () const
ConstDiagonalDynamicIndexReturnType diagonal (Index index) const
DiagonalDynamicIndexReturnType diagonal (Index index)
ConstDiagonalReturnType diagonal () const
DiagonalReturnType diagonal ()
Index diagonalSize () const
template<typename OtherDerived >
internal::scalar_product_traits
< typename internal::traits
< Derived >::Scalar, typename
internal::traits< OtherDerived >
::Scalar >::ReturnType 
dot (const MatrixBase< OtherDerived > &other) const
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix.
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
EvalReturnType eval () const
void fill (const Scalar &value)
template<unsigned int Added, unsigned int Removed>
const Flagged< Derived, Added,
Removed > 
flagged () const
ForceAlignedAccess< Derived > forceAlignedAccess ()
const ForceAlignedAccess< Derived > forceAlignedAccess () const
template<bool Enable>
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type 
forceAlignedAccessIf ()
template<bool Enable>
internal::add_const_on_value_type
< typename
internal::conditional< Enable,
ForceAlignedAccess< Derived >
, Derived & >::type >::type 
forceAlignedAccessIf () const
const WithFormat< Derived > format (const IOFormat &fmt) const
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
const FullPivLU< PlainObjectfullPivLu () const
bool hasNaN () const
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
template<int N>
FixedSegmentReturnType< N >::Type head (Index n=N)
ConstSegmentReturnType head (Index n) const
SegmentReturnType head (Index n)
const HNormalizedReturnType hnormalized () const
HomogeneousReturnType homogeneous () const
const HouseholderQR< PlainObjecthouseholderQr () const
RealScalar hypotNorm () const
NonConstImagReturnType imag ()
const ImagReturnType imag () const
Index innerSize () const
const internal::inverse_impl
< Derived > 
inverse () const
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename Derived >
bool isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, const RealScalar &prec) const
template<typename OtherDerived >
bool isMuchSmallerThan (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isOnes (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
template<typename OtherDerived >
const LazyProductReturnType
< Derived, OtherDerived >
::Type 
lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObjectldlt () const
template<int N>
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
template<int N>
NColsBlockXpr< N >::Type leftCols (Index n=N)
ConstColsBlockXpr leftCols (Index n) const
ColsBlockXpr leftCols (Index n)
const LLT< PlainObjectllt () const
template<int p>
RealScalar lpNorm () const
const PartialPivLU< PlainObjectlu () const
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
internal::traits< Derived >::Scalar maxCoeff () const
Scalar mean () const
template<int N>
ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
template<int N>
NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
ColsBlockXpr middleCols (Index startCol, Index numCols)
template<int N>
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
template<int N>
NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
ConstRowsBlockXpr middleRows (Index startRow, Index n) const
RowsBlockXpr middleRows (Index startRow, Index n)
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
internal::traits< Derived >::Scalar minCoeff () const
const NestByValue< Derived > nestByValue () const
NoAlias< Derived,
Eigen::MatrixBase
noalias ()
Index nonZeros () const
RealScalar norm () const
void normalize ()
const PlainObject normalized () const
template<typename OtherDerived >
bool operator!= (const MatrixBase< OtherDerived > &other) const
ScalarMultipleReturnType operator* (const UniformScaling< Scalar > &s) const
template<typename DiagonalDerived >
const DiagonalProduct< Derived,
DiagonalDerived, OnTheRight > 
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
template<typename OtherDerived >
const ProductReturnType
< Derived, OtherDerived >
::Type 
operator* (const MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, const Derived > 
operator* (const std::complex< Scalar > &scalar) const
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
template<typename OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_sum_op
< Scalar >, const Derived,
const OtherDerived > 
operator+ (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_difference_op
< Scalar >, const Derived,
const OtherDerived > 
operator- (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseUnaryOp
< internal::scalar_opposite_op
< typename internal::traits
< Derived >::Scalar >, const
Derived > 
operator- () const
template<typename OtherDerived >
Derived & operator-= (const MatrixBase< OtherDerived > &other)
const CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Derived >::Scalar >, const
Derived > 
operator/ (const Scalar &scalar) const
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
CommaInitializer< Derived > operator<< (const Scalar &s)
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
Derived & operator= (const MatrixBase &other)
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
RealScalar operatorNorm () const
 Computes the L2 operator norm.
Index outerSize () const
const PartialPivLU< PlainObjectpartialPivLu () const
Scalar prod () const
NonConstRealReturnType real ()
RealReturnType real () const
const ReplicateReturnType replicate (Index rowFacor, Index colFactor) const
template<int RowFactor, int ColFactor>
const Replicate< Derived,
RowFactor, ColFactor > 
replicate () const
void resize (Index nbRows, Index nbCols)
void resize (Index newSize)
ConstReverseReturnType reverse () const
ReverseReturnType reverse ()
void reverseInPlace ()
template<int N>
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
template<int N>
NColsBlockXpr< N >::Type rightCols (Index n=N)
ConstColsBlockXpr rightCols (Index n) const
ColsBlockXpr rightCols (Index n)
ConstRowXpr row (Index i) const
RowXpr row (Index i)
RowwiseReturnType rowwise ()
ConstRowwiseReturnType rowwise () const
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
segment (Index start, Index n=N) const
template<int N>
FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
ConstSegmentReturnType segment (Index start, Index n) const
SegmentReturnType segment (Index start, Index n)
template<typename ElseDerived >
const Select< Derived,
typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
template<typename ThenDerived >
const Select< Derived,
ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const
template<typename ThenDerived , typename ElseDerived >
const Select< Derived,
ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
Derived & setConstant (const Scalar &value)
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
Derived & setIdentity ()
Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
Derived & setOnes ()
Derived & setRandom ()
Derived & setZero ()
RealScalar squaredNorm () const
RealScalar stableNorm () const
Scalar sum () const
template<typename OtherDerived >
void swap (PlainObjectBase< OtherDerived > &other)
template<typename OtherDerived >
void swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase)
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
template<int N>
FixedSegmentReturnType< N >::Type tail (Index n=N)
ConstSegmentReturnType tail (Index n) const
SegmentReturnType tail (Index n)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topLeftCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topLeftCorner () const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topLeftCorner ()
const Block< const Derived > topLeftCorner (Index cRows, Index cCols) const
Block< Derived > topLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topRightCorner (Index cRows, Index cCols) const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const Block< const Derived,
CRows, CCols > 
topRightCorner () const
template<int CRows, int CCols>
Block< Derived, CRows, CCols > topRightCorner ()
const Block< const Derived > topRightCorner (Index cRows, Index cCols) const
Block< Derived > topRightCorner (Index cRows, Index cCols)
template<int N>
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
template<int N>
NRowsBlockXpr< N >::Type topRows (Index n=N)
ConstRowsBlockXpr topRows (Index n) const
RowsBlockXpr topRows (Index n)
Scalar trace () const
ConstTransposeReturnType transpose () const
Eigen::Transpose< Derived > transpose ()
void transposeInPlace ()
template<unsigned int Mode>
ConstTriangularViewReturnType
< Mode >::Type 
triangularView () const
template<unsigned int Mode>
TriangularViewReturnType< Mode >
::Type 
triangularView ()
template<typename CustomUnaryOp >
const CwiseUnaryOp
< CustomUnaryOp, const Derived > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
template<typename CustomViewOp >
const CwiseUnaryView
< CustomViewOp, const Derived > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
PlainObject unitOrthogonal (void) const
CoeffReturnType value () const
template<typename Visitor >
void visit (Visitor &func) const

Static Public Member Functions

static const ConstantReturnType Constant (const Scalar &value)
static const ConstantReturnType Constant (Index size, const Scalar &value)
static const ConstantReturnType Constant (Index rows, Index cols, const Scalar &value)
static const IdentityReturnType Identity (Index rows, Index cols)
static const IdentityReturnType Identity ()
static const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
 Sets a linearly space vector.
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index size, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, Derived > 
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
static const ConstantReturnType Ones ()
static const ConstantReturnType Ones (Index size)
static const ConstantReturnType Ones (Index rows, Index cols)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Derived > 
Random ()
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Derived > 
Random (Index size)
static const CwiseNullaryOp
< internal::scalar_random_op
< Scalar >, Derived > 
Random (Index rows, Index cols)
static const BasisReturnType Unit (Index i)
static const BasisReturnType Unit (Index size, Index i)
static const BasisReturnType UnitW ()
static const BasisReturnType UnitX ()
static const BasisReturnType UnitY ()
static const BasisReturnType UnitZ ()
static const ConstantReturnType Zero ()
static const ConstantReturnType Zero (Index size)
static const ConstantReturnType Zero (Index rows, Index cols)

Detailed Description

template<typename Derived>
class Eigen::MatrixBase< Derived >

Base class for all dense matrices, vectors, and expressions.

This class is the base that is inherited by all matrix, vector, and related expression types. Most of the Eigen API is contained in this class, and its base classes. Other important classes for the Eigen API are Matrix, and VectorwiseOp.

Note that some methods are defined in other modules such as the LU module LU module for all functions related to matrix inversions.

Template Parameters:
Derived is the derived type, e.g. a matrix type, or an expression, etc.

When writing a function taking Eigen objects as argument, if you want your function to take as argument any matrix, vector, or expression, just let it take a MatrixBase argument. As an example, here is a function printFirstRow which, given a matrix, vector, or expression x, prints the first row of x.

    template<typename Derived>
    void printFirstRow(const Eigen::MatrixBase<Derived>& x)
    {
      cout << x.row(0) << endl;
    }

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_MATRIXBASE_PLUGIN.

See also:
The class hierarchy

Member Typedef Documentation

typedef internal::traits<Derived>::Index Index [inherited]

The type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also:
Preprocessor directives.
typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime, AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor), internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime > 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 in Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.


Member Enumeration Documentation

anonymous enum [inherited]
Enumerator:
RowsAtCompileTime 

The number of rows at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also:
MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime
ColsAtCompileTime 

The number of columns at compile-time. This is just a copy of the value provided by the Derived type. If a value is not known at compile-time, it is set to the Dynamic constant.

See also:
MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime
SizeAtCompileTime 

This is equal to the number of coefficients, i.e. the number of rows times the number of columns, or to Dynamic if this is not known at compile-time.

See also:
RowsAtCompileTime, ColsAtCompileTime
MaxRowsAtCompileTime 

This value is equal to the maximum possible number of rows that this expression might have. If this expression might have an arbitrarily high number of rows, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
MaxColsAtCompileTime 

This value is equal to the maximum possible number of columns that this expression might have. If this expression might have an arbitrarily high number of columns, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
MaxSizeAtCompileTime 

This value is equal to the maximum possible number of coefficients that this expression might have. If this expression might have an arbitrarily high number of coefficients, this value is set to Dynamic.

This value is useful to know when evaluating an expression, in order to determine whether it is possible to avoid doing a dynamic memory allocation.

See also:
SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
IsVectorAtCompileTime 

This is set to true if either the number of rows or the number of columns is known at compile-time to be equal to 1. Indeed, in that case, we are dealing with a column-vector (if there is only one column) or with a row-vector (if there is only one row).

Flags 

This stores expression Flags flags which may or may not be inherited by new expressions constructed from this one. See the list of flags.

IsRowMajor 

True if this expression has row-major storage order.

CoeffReadCost 

This is a rough measure of how expensive it is to read one coefficient from this expression.


Member Function Documentation

const MatrixBase< Derived >::AdjointReturnType adjoint (  )  const [inline]
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

References DenseBase< Derived >::transpose().

Referenced by MatrixBase< Derived >::adjointInPlace().

void adjointInPlace (  )  [inline]

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. This excludes (non-square) fixed-size matrices, block-expressions and maps.
See also:
transpose(), adjoint(), transposeInPlace()

References MatrixBase< Derived >::adjoint().

bool all ( void   )  const [inline, 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<()

References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.

Referenced by DenseBase< Derived >::hasNaN().

bool allFinite (  )  const [inline, inherited]
Returns:
true if *this contains only finite numbers, i.e., no NaN and no +/-INF values.
See also:
hasNaN()

References DenseBase< Derived >::hasNaN().

bool any ( void   )  const [inline, inherited]
Returns:
true if at least one coefficient is true
See also:
all()

References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.

void applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar &  tau,
Scalar *  workspace 
) [inline]

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:
essential the essential part of the vector v
tau the scaling factor of the Householder transformation
workspace a pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()

References DenseBase< Derived >::row().

void applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar &  tau,
Scalar *  workspace 
) [inline]

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:
essential the essential part of the vector v
tau the scaling factor of the Householder transformation
workspace a pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()

References DenseBase< Derived >::col().

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

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()

References DenseBase< Derived >::row().

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

replaces *this by other * *this.

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A.applyOnTheLeft(B); 
cout << "After applyOnTheLeft, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After applyOnTheLeft, A = 
-0.211  0.823  0.536
 0.566 -0.605 -0.444
  0.68  0.597  -0.33
void applyOnTheRight ( const EigenBase< OtherDerived > &  other  )  [inline]

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

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566
ArrayWrapper<Derived> array (  )  [inline]
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
const DiagonalWrapper< const Derived > asDiagonal (  )  const [inline]
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()

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::fromPositionOrientationScale(), Transform< _Scalar, _Dim, _Mode, _Options >::prescale(), and Transform< _Scalar, _Dim, _Mode, _Options >::scale().

const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const [inline]
Returns:
an expression of a custom coefficient-wise operator func of *this and other

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

Here is an example illustrating the use of custom functors:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template binary functor
template<typename Scalar> struct MakeComplexOp {
  EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)
  typedef complex<Scalar> result_type;
  complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
  cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;
  return 0;
}

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)
See also:
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
const Block<const Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) const [inline, inherited]

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

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

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

Example:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;
m.block<2, Dynamic>(1, 1, 2, 3).setZero();
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the block:" << endl << m.block<2, Dynamic>(1, 1, 2, 3) << endl;
m.block<2, Dynamic>(1, 1, 2, 3).setZero();
cout << "Now the matrix m is:" << endl << m << endl;
See also:
class Block, block(Index,Index,Index,Index)
const Block<const Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) const [inline, inherited]

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

Block<Derived, BlockRows, BlockCols> block ( Index  startRow,
Index  startCol 
) [inline, inherited]
Returns:
a fixed-size expression of a block in *this.

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

Parameters:
startRow the first row in the block
startCol the first column in the block

Example:

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

Output:

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

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

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, block(Index,Index)
NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm (  )  const [inline]
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()
const Block<const Derived, CRows, CCols> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

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

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,Dynamic>(2,2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block
const Block<const Derived, CRows, CCols> bottomLeftCorner (  )  const [inline, inherited]

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

Block<Derived, 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 Derived> bottomLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

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

Example:

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

Output:

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

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

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

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,Dynamic>(2,2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block
const Block<const Derived, CRows, CCols> bottomRightCorner (  )  const [inline, inherited]

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

Block<Derived, 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 Derived> bottomRightCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

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

Example:

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

Output:

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

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

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

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
ConstRowsBlockXpr bottomRows ( Index  n  )  const [inline, inherited]

This is the const version of bottomRows(Index).

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type cast (  )  const [inline]
Returns:
an expression of *this with the Scalar type casted to NewScalar.

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

See also:
class CwiseUnaryOp
ConstColXpr col ( Index  i  )  const [inline, inherited]

This is the const version of col().

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

Example:

Matrix3d m = Matrix3d::Identity();
m.col(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

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

Referenced by MatrixBase< Derived >::applyHouseholderOnTheRight(), and MatrixBase< Derived >::applyOnTheRight().

const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > colPivHouseholderQr (  )  const [inline]
Returns:
the column-pivoting Householder QR decomposition of *this.
See also:
class ColPivHouseholderQR

References DenseBase< Derived >::eval().

DenseBase< Derived >::ColwiseReturnType colwise (  )  [inline, inherited]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting
const DenseBase< Derived >::ConstColwiseReturnType colwise (  )  const [inline, 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, Reductions, visitors and broadcasting

Referenced by Eigen::umeyama().

void computeInverseAndDetWithCheck ( ResultType &  inverse,
typename ResultType::Scalar &  determinant,
bool &  invertible,
const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

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:
inverse Reference to the matrix in which to store the inverse.
determinant Reference to the variable in which to store the determinant.
invertible Reference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThreshold Optional 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()

References DenseBase< Derived >::RowsAtCompileTime.

Referenced by MatrixBase< Derived >::computeInverseWithCheck().

void computeInverseWithCheck ( ResultType &  inverse,
bool &  invertible,
const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

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:
inverse Reference to the matrix in which to store the inverse.
invertible Reference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThreshold Optional 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()

References MatrixBase< Derived >::computeInverseAndDetWithCheck().

ConjugateReturnType conjugate (  )  const [inline]
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()
const DenseBase< Derived >::ConstantReturnType Constant ( const Scalar &  value  )  [inline, 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

References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.

const DenseBase< Derived >::ConstantReturnType Constant ( Index  size,
const Scalar &  value 
) [inline, 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

References DenseBase< Derived >::NullaryExpr().

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

The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.

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

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp

References DenseBase< Derived >::NullaryExpr().

Referenced by DenseBase< Derived >::Ones(), DenseBase< Derived >::select(), DenseBase< Derived >::setConstant(), and DenseBase< Derived >::Zero().

DenseBase< Derived >::Index count (  )  const [inline, inherited]
Returns:
the number of coefficients which evaluate to true
See also:
all(), any()
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross ( const MatrixBase< OtherDerived > &  other  )  const [inline]

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()
MatrixBase< Derived >::PlainObject cross3 ( const MatrixBase< OtherDerived > &  other  )  const [inline]

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 Derived> cwiseAbs (  )  const [inline]
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()

Referenced by MatrixBase< Derived >::hypotNorm(), and SelfAdjointView< MatrixType, UpLo >::operatorNorm().

const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> cwiseAbs2 (  )  const [inline]
Returns:
an expression of the coefficient-wise squared absolute value of *this

Example:

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

Output:

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

Example:

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

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3
See also:
cwiseNotEqual(), isApprox(), isMuchSmallerThan()
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> cwiseInverse (  )  const [inline]
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 Derived, const ConstantReturnType> cwiseMax ( const Scalar &  other  )  const [inline]
Returns:
an expression of the coefficient-wise max of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
Returns:
an expression of the coefficient-wise max of *this and other

Example:

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

Output:

4
3
4
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType> cwiseMin ( const Scalar &  other  )  const [inline]
Returns:
an expression of the coefficient-wise min of *this and scalar other
See also:
class CwiseBinaryOp, min()
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
Returns:
an expression of the coefficient-wise min of *this and other

Example:

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

Output:

2
2
3
See also:
class CwiseBinaryOp, max()
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> cwiseNotEqual ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
Returns:
an expression of the coefficient-wise != operator of *this and other
Warning:
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

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

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1
See also:
cwiseEqual(), isApprox(), isMuchSmallerThan()
const CwiseBinaryOp<internal::scalar_product_op<typename Derived ::Scalar, typename OtherDerived ::Scalar >, const Derived , const OtherDerived > cwiseProduct ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
Returns:
an expression of the Schur product (coefficient wise product) of *this and other

Example:

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

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25
See also:
class CwiseBinaryOp, cwiseAbs2
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
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 Derived> cwiseSqrt (  )  const [inline]
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()
internal::traits< Derived >::Scalar determinant (  )  const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the determinant of this matrix
MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType diagonal ( Index  index  )  const [inline]

This is the const version of diagonal(Index).

MatrixBase< Derived >::DiagonalDynamicIndexReturnType diagonal ( Index  index  )  [inline]
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
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type diagonal (  )  const [inline]

This is the const version of diagonal().

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

MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal (  )  [inline]
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

Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::conjugate(), and AngleAxis< _Scalar >::toRotationMatrix().

Index diagonalSize (  )  const [inline]
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot ( const MatrixBase< OtherDerived > &  other  )  const [inline]
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()
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues (  )  const [inline]

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:
(-5.31e-17,0)
        (3,0)
        (0,0)
See also:
EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()

Referenced by MatrixBase< Derived >::operatorNorm().

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.

Referenced by MatrixBase< Derived >::colPivHouseholderQr(), MatrixBase< Derived >::fullPivHouseholderQr(), MatrixBase< Derived >::fullPivLu(), MatrixBase< Derived >::householderQr(), MatrixBase< Derived >::lu(), MatrixBase< Derived >::operatorNorm(), and MatrixBase< Derived >::partialPivLu().

void fill ( const Scalar &  val  )  [inline, inherited]

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

See also:
setConstant(), Constant(), class CwiseNullaryOp

References DenseBase< Derived >::setConstant().

const Flagged< Derived, Added, Removed > flagged (  )  const [inline, inherited]
Returns:
an expression of *this with added and removed flags

This is mostly for internal use.

See also:
class Flagged
ForceAlignedAccess< Derived > forceAlignedAccess (  )  [inline]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

const ForceAlignedAccess< Derived > forceAlignedAccess (  )  const [inline]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(),class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf (  )  [inline]
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

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

Reimplemented from DenseBase< Derived >.

const WithFormat< Derived > 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
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr (  )  const [inline]
Returns:
the full-pivoting Householder QR decomposition of *this.
See also:
class FullPivHouseholderQR

References DenseBase< Derived >::eval().

const FullPivLU< typename MatrixBase< Derived >::PlainObject > fullPivLu (  )  const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU

References DenseBase< Derived >::eval().

bool hasNaN (  )  const [inline, inherited]
Returns:
true is *this contains at least one Not A Number (NaN).
See also:
allFinite()

References DenseBase< Derived >::all().

Referenced by DenseBase< Derived >::allFinite().

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

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

FixedSegmentReturnType<N>::Type head ( Index  n = N  )  [inline, inherited]
Returns:
a fixed-size expression of the first coefficients of *this.

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

Template Parameters:
N the number of coefficients in the segment as specified at compile-time
Parameters:
n the number of coefficients in the segment as specified at run-time

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

Example:

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

Output:

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

This is the const version of head(Index).

SegmentReturnType head ( Index  n  )  [inline, inherited]
Returns:
a dynamic-size expression of the first coefficients of *this.

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

Parameters:
n the number of coefficients in the segment

Example:

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

Output:

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

Referenced by MatrixBase< Derived >::stableNorm().

const MatrixBase< Derived >::HNormalizedReturnType hnormalized (  )  const [inline]

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()

References DenseBase< Derived >::ColsAtCompileTime.

MatrixBase< Derived >::HomogeneousReturnType homogeneous (  )  const [inline]

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< typename MatrixBase< Derived >::PlainObject > householderQr (  )  const [inline]
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR

References DenseBase< Derived >::eval().

NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm (  )  const [inline]
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()

References MatrixBase< Derived >::cwiseAbs().

const MatrixBase< Derived >::IdentityReturnType Identity ( Index  nbRows,
Index  nbCols 
) [inline, static]
Returns:
an expression of the identity matrix (not necessarily square).

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

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

References DenseBase< Derived >::NullaryExpr().

const MatrixBase< Derived >::IdentityReturnType Identity (  )  [inline, static]
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()

References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.

NonConstImagReturnType imag (  )  [inline]
Returns:
a non const expression of the imaginary part of *this.
See also:
real()
const ImagReturnType imag (  )  const [inline]
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()
Index innerSize (  )  const [inline, inherited]
Returns:
the inner size.
Note:
For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension with respect to the storage order, i.e., the number of rows for a column-major matrix, and the number of columns for a row-major matrix.
const internal::inverse_impl< Derived > inverse (  )  const [inline]

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: 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()

Referenced by Hyperplane< _Scalar, _AmbientDim, _Options >::transform().

bool isApprox ( const DenseBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const [inline, 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

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::isApprox().

bool isApproxToConstant ( const Scalar &  val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const [inline, inherited]
Returns:
true if all coefficients in this matrix are approximately equal to val, to within precision prec
bool isConstant ( const Scalar &  val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const [inline, 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 ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline]
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 ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline]
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 ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline]
Returns:
true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
See also:
isUpperTriangular()
bool isMuchSmallerThan ( const typename NumTraits< Scalar >::Real &  other,
const RealScalar &  prec 
) const [inline, inherited]
Returns:
true if the norm of *this is much smaller than other, within the precision determined by prec.
Note:
The fuzzy compares are done multiplicatively. A vector $ v $ is considered to be much smaller than $ x $ within precision $ p $ if

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

For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.

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

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

For matrices, the comparison is done using the Hilbert-Schmidt norm.
See also:
isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
bool isOnes ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline, 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,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const [inline]
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 ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline]
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 ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline]
Returns:
true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
See also:
isLowerTriangular()
bool isZero ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()  )  const [inline, 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< typename MatrixBase< Derived >::PlainObject > jacobiSvd ( unsigned int  computationOptions = 0  )  const [inline]

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
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct ( const MatrixBase< OtherDerived > &  other  )  const [inline]
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< typename MatrixBase< Derived >::PlainObject > ldlt (  )  const [inline]

This is defined in the Cholesky module.

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

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

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

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

Example:

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

Output:

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

This is the const version of leftCols(Index).

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( const Scalar &  low,
const Scalar &  high 
) [inline, 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
Special version for fixed size types which does not require the size parameter.

References DenseBase< Derived >::NullaryExpr().

const DenseBase< Derived >::SequentialLinSpacedReturnType LinSpaced ( Sequential_t  ,
const Scalar &  low,
const Scalar &  high 
) [inline, 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
Special version for fixed size types which does not require the size parameter.

References DenseBase< Derived >::NullaryExpr().

const DenseBase< Derived >::RandomAccessLinSpacedReturnType LinSpaced ( Index  size,
const Scalar &  low,
const Scalar &  high 
) [inline, 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

References DenseBase< Derived >::NullaryExpr().

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

References DenseBase< Derived >::NullaryExpr().

const LLT< typename MatrixBase< Derived >::PlainObject > llt (  )  const [inline]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky> 
Returns:
the LLT decomposition of *this
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm (  )  const [inline]
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< Derived >.

const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu (  )  const [inline]

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

References DenseBase< Derived >::eval().

void makeHouseholder ( EssentialPart &  essential,
Scalar &  tau,
RealScalar &  beta 
) const [inline]

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:
essential the essential part of the vector v
tau the scaling factor of the Householder transformation
beta the result of H * *this
See also:
MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

References MatrixBase< Derived >::real(), and DenseBase< Derived >::tail().

Referenced by MatrixBase< Derived >::makeHouseholderInPlace().

void makeHouseholderInPlace ( Scalar &  tau,
RealScalar &  beta 
) [inline]

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:
tau the scaling factor of the Householder transformation
beta the result of H * *this
See also:
MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

References MatrixBase< Derived >::makeHouseholder().

internal::traits< Derived >::Scalar maxCoeff ( IndexType *  index  )  const [inline, inherited]
Returns:
the maximum of all coefficients of *this and puts in *index its location.
Warning:
the result is undefined if *this contains NaN.
See also:
DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()

References DenseBase< Derived >::RowsAtCompileTime, and DenseBase< Derived >::visit().

internal::traits< Derived >::Scalar maxCoeff ( IndexType *  rowPtr,
IndexType *  colPtr 
) const [inline, inherited]
Returns:
the maximum of all coefficients of *this and puts in *row and *col its location.
Warning:
the result is undefined if *this contains NaN.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()

References DenseBase< Derived >::visit().

internal::traits< Derived >::Scalar maxCoeff (  )  const [inline, inherited]
Returns:
the maximum of all coefficients of *this.
Warning:
the result is undefined if *this contains NaN.
internal::traits< Derived >::Scalar mean (  )  const [inline, inherited]
Returns:
the mean of all coefficients of *this
See also:
trace(), prod(), sum()
ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol,
Index  n = N 
) const [inline, inherited]

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

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
ConstColsBlockXpr middleCols ( Index  startCol,
Index  numCols 
) const [inline, inherited]

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

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

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
internal::traits< Derived >::Scalar minCoeff ( IndexType *  index  )  const [inline, inherited]
Returns:
the minimum of all coefficients of *this and puts in *index its location.
Warning:
the result is undefined if *this contains NaN.
See also:
DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::minCoeff()

References DenseBase< Derived >::RowsAtCompileTime, and DenseBase< Derived >::visit().

internal::traits< Derived >::Scalar minCoeff ( IndexType *  rowId,
IndexType *  colId 
) const [inline, inherited]
Returns:
the minimum of all coefficients of *this and puts in *row and *col its location.
Warning:
the result is undefined if *this contains NaN.
See also:
DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visitor(), DenseBase::minCoeff()

References DenseBase< Derived >::visit().

internal::traits< Derived >::Scalar minCoeff (  )  const [inline, inherited]
Returns:
the minimum of all coefficients of *this.
Warning:
the result is undefined if *this contains NaN.
const NestByValue< Derived > nestByValue (  )  const [inline, inherited]
Returns:
an expression of the temporary version of *this.
NoAlias< Derived, MatrixBase > noalias (  )  [inline]
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
Index nonZeros (  )  const [inline, inherited]
Returns:
the number of nonzero coefficients which is in practice the number of stored coefficients.
NumTraits< typename internal::traits< Derived >::Scalar >::Real norm (  )  const [inline]
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()

References MatrixBase< Derived >::squaredNorm().

Referenced by MatrixBase< Derived >::normalize().

void normalize (  )  [inline]

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()

References MatrixBase< Derived >::norm().

const MatrixBase< Derived >::PlainObject normalized (  )  const [inline]
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()

Referenced by QuaternionBase< Derived >::setFromTwoVectors().

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( const CustomNullaryOp &  func  )  [inline, 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

References DenseBase< Derived >::ColsAtCompileTime, and DenseBase< Derived >::RowsAtCompileTime.

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
) [inline, 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

References DenseBase< Derived >::RowsAtCompileTime.

const CwiseNullaryOp< CustomNullaryOp, Derived > NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
) [inline, 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

Referenced by DenseBase< Derived >::Constant(), MatrixBase< Derived >::Identity(), DenseBase< Derived >::LinSpaced(), DenseBase< Derived >::Random(), and DenseBase< Derived >::setLinSpaced().

const DenseBase< Derived >::ConstantReturnType Ones (  )  [inline, 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

References DenseBase< Derived >::Constant().

const DenseBase< Derived >::ConstantReturnType Ones ( Index  newSize  )  [inline, static, inherited]
Returns:
an expression of a vector where all coefficients equal one.

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

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

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

Example:

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

Output:

6 6 6 6
1
1
See also:
Ones(), Ones(Index,Index), isOnes(), class Ones

References DenseBase< Derived >::Constant().

const DenseBase< Derived >::ConstantReturnType Ones ( Index  nbRows,
Index  nbCols 
) [inline, static, inherited]
Returns:
an expression of a matrix where all coefficients equal one.

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

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

Example:

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

Output:

1 1 1
1 1 1
See also:
Ones(), Ones(Index), isOnes(), class Ones

References DenseBase< Derived >::Constant().

bool operator!= ( const MatrixBase< OtherDerived > &  other  )  const [inline]
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==
MatrixBase< Derived >::ScalarMultipleReturnType operator* ( const UniformScaling< Scalar > &  s  )  const [inline]

Concatenates a linear transformation matrix and a uniform scaling

const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* ( const DiagonalBase< DiagonalDerived > &  a_diagonal  )  const [inline]
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.
const ProductReturnType< Derived, OtherDerived >::Type operator* ( const MatrixBase< OtherDerived > &  other  )  const [inline]
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 CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> operator* ( const std::complex< Scalar > &  scalar  )  const [inline]

Overloaded for efficient real matrix times complex scalar value

const ScalarMultipleReturnType operator* ( const Scalar &  scalar  )  const [inline]
Returns:
an expression of *this scaled by the scalar factor scalar
Derived & operator*= ( const EigenBase< OtherDerived > &  other  )  [inline]

replaces *this by *this * other.

Returns:
a reference to *this

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566
const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Derived, const OtherDerived> operator+ ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
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+=()
Derived & operator+= ( const MatrixBase< OtherDerived > &  other  )  [inline]

replaces *this by *this + other.

Returns:
a reference to *this
const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const Derived, const OtherDerived> operator- ( const Eigen::MatrixBase< OtherDerived > &  other  )  const [inline]
Returns:
an expression of the difference of *this and other
Note:
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See also:
class CwiseBinaryOp, operator-=()
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> operator- (  )  const [inline]
Returns:
an expression of the opposite of *this
Derived & operator-= ( const MatrixBase< OtherDerived > &  other  )  [inline]

replaces *this by *this - other.

Returns:
a reference to *this
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> operator/ ( const Scalar &  scalar  )  const [inline]
Returns:
an expression of *this divided by the scalar value scalar
CommaInitializer< Derived > operator<< ( const DenseBase< OtherDerived > &  other  )  [inline, inherited]
CommaInitializer< Derived > operator<< ( const Scalar &  s  )  [inline, 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
Note:
According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.
See also:
CommaInitializer::finished(), class CommaInitializer
Derived & 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 DenseBase< Derived >.

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

References EigenBase< Derived >::derived().

Derived & operator= ( const MatrixBase< Derived > &  other  )  [inline]

Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)

Reimplemented from DenseBase< Derived >.

bool operator== ( const MatrixBase< OtherDerived > &  other  )  const [inline]
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!=
MatrixBase< Derived >::RealScalar operatorNorm (  )  const [inline]

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()

References MatrixBase< Derived >::eigenvalues(), and DenseBase< Derived >::eval().

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.
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > partialPivLu (  )  const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU

References DenseBase< Derived >::eval().

internal::traits< Derived >::Scalar prod (  )  const [inline, 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()

References DenseBase< Derived >::SizeAtCompileTime.

const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random (  )  [inline, 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)

References DenseBase< Derived >::ColsAtCompileTime, DenseBase< Derived >::NullaryExpr(), and DenseBase< Derived >::RowsAtCompileTime.

Referenced by DenseBase< Derived >::setRandom().

const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  size  )  [inline, 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()

References DenseBase< Derived >::NullaryExpr().

const CwiseNullaryOp< internal::scalar_random_op< typename internal::traits< Derived >::Scalar >, Derived > Random ( Index  rows,
Index  cols 
) [inline, 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()

References DenseBase< Derived >::NullaryExpr().

NonConstRealReturnType real (  )  [inline]
Returns:
a non const expression of the real part of *this.
See also:
imag()
RealReturnType real (  )  const [inline]
Returns:
a read-only expression of the real part of *this.
See also:
imag()

Referenced by MatrixBase< Derived >::makeHouseholder(), and MatrixBase< Derived >::squaredNorm().

const DenseBase< Derived >::ReplicateReturnType replicate ( Index  rowFactor,
Index  colFactor 
) const [inline, 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
const Replicate< Derived, RowFactor, ColFactor > replicate (  )  const [inline, 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
void resize ( Index  nbRows,
Index  nbCols 
) [inline, inherited]

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

Reimplemented in ArrayWrapper< ExpressionType >, MatrixWrapper< ExpressionType >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

void resize ( Index  newSize  )  [inline, inherited]

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

Reimplemented in ArrayWrapper< ExpressionType >, MatrixWrapper< ExpressionType >, PlainObjectBase< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >.

const DenseBase< Derived >::ConstReverseReturnType reverse (  )  const [inline, inherited]

This is the const version of reverse().

DenseBase< Derived >::ReverseReturnType reverse (  )  [inline, 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
void reverseInPlace (  )  [inline, 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()
ConstNColsBlockXpr<N>::Type rightCols ( Index  n = N  )  const [inline, inherited]

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

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

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

Example:

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

Output:

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

This is the const version of rightCols(Index).

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

Example:

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

Output:

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

This is the const version of row().

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

Example:

Matrix3d m = Matrix3d::Identity();
m.row(1) = Vector3d(4,5,6);
cout << m << endl;

Output:

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

Referenced by MatrixBase< Derived >::applyHouseholderOnTheLeft(), MatrixBase< Derived >::applyOnTheLeft(), and Transform< _Scalar, _Dim, _Mode, _Options >::pretranslate().

DenseBase< Derived >::RowwiseReturnType rowwise (  )  [inline, inherited]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
colwise(), class VectorwiseOp, Reductions, visitors and broadcasting
const DenseBase< Derived >::ConstRowwiseReturnType rowwise (  )  const [inline, 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, Reductions, visitors and broadcasting

Referenced by Eigen::umeyama().

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

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

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

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

Template Parameters:
N the number of coefficients in the segment as specified at compile-time
Parameters:
start the index of the first element in the segment
n the number of coefficients in the segment as specified at compile-time

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

Example:

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

Output:

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

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

SegmentReturnType segment ( Index  start,
Index  n 
) [inline, inherited]
Returns:
a dynamic-size expression of a segment (i.e. a vector block) in *this.

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

Parameters:
start the first coefficient in the segment
n the number of coefficients in the segment

Example:

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

Output:

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

Referenced by MatrixBase< Derived >::stableNorm().

const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > select ( const 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

References DenseBase< Derived >::Constant().

const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > select ( const DenseBase< ThenDerived > &  thenMatrix,
const 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

References DenseBase< Derived >::Constant().

const Select< Derived, ThenDerived, ElseDerived > select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const [inline, 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
Derived & setConstant ( const Scalar &  val  )  [inline, 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()

References DenseBase< Derived >::Constant().

Referenced by DenseBase< Derived >::fill(), DenseBase< Derived >::setOnes(), and DenseBase< Derived >::setZero().

Derived & setIdentity ( Index  nbRows,
Index  nbCols 
) [inline]

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

Parameters:
nbRows the new number of rows
nbCols the 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()

References MatrixBase< Derived >::setIdentity().

Derived & setIdentity (  )  [inline]

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()

Referenced by Transform< _Scalar, _Dim, _Mode, _Options >::setIdentity(), and MatrixBase< Derived >::setIdentity().

Derived & setLinSpaced ( const Scalar &  low,
const Scalar &  high 
) [inline, 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

References DenseBase< Derived >::setLinSpaced().

Derived & setLinSpaced ( Index  newSize,
const Scalar &  low,
const Scalar &  high 
) [inline, 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);
cout << v << endl;

Output:

 0.5
0.75
   1
1.25
 1.5
See also:
CwiseNullaryOp

References DenseBase< Derived >::NullaryExpr().

Referenced by DenseBase< Derived >::setLinSpaced().

Derived & setOnes (  )  [inline, 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()

References DenseBase< Derived >::setConstant().

Derived & setRandom (  )  [inline, 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)

References DenseBase< Derived >::Random().

Derived & setZero (  )  [inline, 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()

References DenseBase< Derived >::setConstant().

NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm (  )  const [inline]
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()

References MatrixBase< Derived >::real().

Referenced by MatrixBase< Derived >::norm().

NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm (  )  const [inline]
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()

References Eigen::AlignedBit, Eigen::DirectAccessBit, DenseBase< Derived >::Flags, DenseBase< Derived >::head(), and DenseBase< Derived >::segment().

internal::traits< Derived >::Scalar sum (  )  const [inline, inherited]
Returns:
the sum of all coefficients of *this
See also:
trace(), prod(), mean()

References DenseBase< Derived >::SizeAtCompileTime.

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

swaps *this with the matrix or array other.

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

swaps *this with the expression other.

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

This is the const version of tail<int>.

FixedSegmentReturnType<N>::Type tail ( Index  n = N  )  [inline, inherited]
Returns:
a fixed-size expression of the last coefficients of *this.

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

Template Parameters:
N the number of coefficients in the segment as specified at compile-time
Parameters:
n the number of coefficients in the segment as specified at run-time

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

Example:

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

Output:

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

This is the const version of tail(Index).

SegmentReturnType tail ( Index  n  )  [inline, inherited]
Returns:
a dynamic-size expression of the last coefficients of *this.

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

Parameters:
n the number of coefficients in the segment

Example:

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

Output:

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

Referenced by MatrixBase< Derived >::makeHouseholder().

const Block<const Derived, CRows, CCols> topLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

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

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,Dynamic>(2,2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block
const Block<const Derived, CRows, CCols> topLeftCorner (  )  const [inline, inherited]

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

Block<Derived, 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 Derived> topLeftCorner ( Index  cRows,
Index  cCols 
) const [inline, inherited]

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

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

Example:

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

Output:

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

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

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

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,Dynamic>(2,2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block
const Block<const Derived, CRows, CCols> topRightCorner (  )  const [inline, inherited]

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

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

Example:

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

Output:

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

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

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

Example:

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

Output:

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

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

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

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
ConstRowsBlockXpr topRows ( Index  n  )  const [inline, inherited]

This is the const version of topRows(Index).

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
internal::traits< Derived >::Scalar trace (  )  const [inline]
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< Derived >.

DenseBase< Derived >::ConstTransposeReturnType transpose (  )  const [inline, inherited]

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also:
transposeInPlace(), adjoint()
Transpose< Derived > transpose (  )  [inline, 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()

Referenced by MatrixBase< Derived >::adjoint().

void transposeInPlace (  )  [inline, 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. This excludes (non-square) fixed-size matrices, block-expressions and maps.
See also:
transpose(), adjoint(), adjointInPlace()

References DenseBase< Derived >::ColsAtCompileTime, and DenseBase< Derived >::RowsAtCompileTime.

MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView (  )  const [inline]

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

MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView (  )  [inline]
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
const CwiseUnaryOp<CustomUnaryOp, const Derived> unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp()  )  const [inline]

Apply a unary operator coefficient-wise.

Parameters:
[in] func Functor implementing the unary operator
Template Parameters:
CustomUnaryOp Type of func
Returns:
An expression of a custom coefficient-wise unary operator func of *this

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define function to be applied coefficient-wise
double ramp(double x)
{
  if (x > 0)
    return x;
  else 
    return 0;
}

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random();
  cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
  return 0;
}

Output:

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

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
  CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
  const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
  Scalar m_inf, m_sup;
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random();
  cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
  return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also:
class CwiseUnaryOp, class CwiseBinaryOp
const CwiseUnaryView<CustomViewOp, const Derived> unaryViewExpr ( const CustomViewOp &  func = CustomViewOp()  )  const [inline]
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
const MatrixBase< Derived >::BasisReturnType Unit ( Index  i  )  [inline, static]
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()
const MatrixBase< Derived >::BasisReturnType Unit ( Index  newSize,
Index  i 
) [inline, static]
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()

Referenced by MatrixBase< Derived >::UnitW(), MatrixBase< Derived >::UnitX(), MatrixBase< Derived >::UnitY(), and MatrixBase< Derived >::UnitZ().

MatrixBase< Derived >::PlainObject unitOrthogonal ( void   )  const [inline]
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()
const MatrixBase< Derived >::BasisReturnType UnitW (  )  [inline, static]
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()

References MatrixBase< Derived >::Unit().

const MatrixBase< Derived >::BasisReturnType UnitX (  )  [inline, static]
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()

References MatrixBase< Derived >::Unit().

const MatrixBase< Derived >::BasisReturnType UnitY (  )  [inline, static]
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()

References MatrixBase< Derived >::Unit().

const MatrixBase< Derived >::BasisReturnType UnitZ (  )  [inline, static]
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()

References MatrixBase< Derived >::Unit().

CoeffReturnType value (  )  const [inline, inherited]
Returns:
the unique coefficient of a 1x1 expression
void visit ( Visitor &  visitor  )  const [inline, inherited]

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

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

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

References DenseBase< Derived >::CoeffReadCost, and DenseBase< Derived >::SizeAtCompileTime.

Referenced by DenseBase< Derived >::maxCoeff(), and DenseBase< Derived >::minCoeff().

const DenseBase< Derived >::ConstantReturnType Zero (  )  [inline, 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)

References DenseBase< Derived >::Constant().

const DenseBase< Derived >::ConstantReturnType Zero ( Index  size  )  [inline, 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)

References DenseBase< Derived >::Constant().

const DenseBase< Derived >::ConstantReturnType Zero ( Index  nbRows,
Index  nbCols 
) [inline, 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)

References DenseBase< Derived >::Constant().


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