Eigen  3.3.3
Eigen::DenseBase< Derived > Class Template Reference

Detailed Description

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

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

This class is the base that is inherited by all dense objects (matrix, vector, arrays, and related expression types). The common Eigen API for dense objects is contained in this class.

Template Parameters:
Derivedis the derived type, e.g., a matrix type or an expression.

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

See also:
The class hierarchy
+ Inheritance diagram for Eigen::DenseBase< Derived >:

List of all members.

Public Types

enum  {
  RowsAtCompileTime,
  ColsAtCompileTime,
  SizeAtCompileTime,
  MaxRowsAtCompileTime,
  MaxColsAtCompileTime,
  MaxSizeAtCompileTime,
  IsVectorAtCompileTime,
  Flags,
  IsRowMajor
}
typedef Array< typename
internal::traits< Derived >
::Scalar, internal::traits
< Derived >::RowsAtCompileTime,
internal::traits< Derived >
::ColsAtCompileTime, AutoAlign|(internal::traits
< Derived >::Flags
&RowMajorBit?RowMajor:ColMajor),
internal::traits< Derived >
::MaxRowsAtCompileTime,
internal::traits< Derived >
::MaxColsAtCompileTime
PlainArray
typedef Matrix< typename
internal::traits< Derived >
::Scalar, internal::traits
< Derived >::RowsAtCompileTime,
internal::traits< Derived >
::ColsAtCompileTime, AutoAlign|(internal::traits
< Derived >::Flags
&RowMajorBit?RowMajor:ColMajor),
internal::traits< Derived >
::MaxRowsAtCompileTime,
internal::traits< Derived >
::MaxColsAtCompileTime
PlainMatrix
typedef internal::conditional
< internal::is_same< typename
internal::traits< Derived >
::XprKind, MatrixXpr >::value,
PlainMatrix, PlainArray >
::type 
PlainObject
 The plain matrix or array type corresponding to this expression.
typedef internal::traits
< Derived >::Scalar 
Scalar
typedef internal::traits
< Derived >::StorageIndex 
StorageIndex
 The type used to store indices.
typedef Scalar value_type

Public Member Functions

bool all () const
bool allFinite () const
bool any () const
BlockXpr block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const ConstBlockXpr block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 This is the const version of block(Index,Index,Index,Index). */.
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol)
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol) const
 This is the const version of block<>(Index, Index). */.
template<int NRows, int NCols>
FixedBlockXpr< NRows, NCols >::Type block (Index startRow, Index startCol, Index blockRows, Index blockCols)
template<int NRows, int NCols>
const ConstFixedBlockXpr
< NRows, NCols >::Type 
block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
 This is the const version of block<>(Index, Index, Index, Index).
BlockXpr bottomLeftCorner (Index cRows, Index cCols)
const ConstBlockXpr bottomLeftCorner (Index cRows, Index cCols) const
 This is the const version of bottomLeftCorner(Index, Index).
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner ()
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner () const
 This is the const version of bottomLeftCorner<int, int>().
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomLeftCorner (Index cRows, Index cCols) const
 This is the const version of bottomLeftCorner<int, int>(Index, Index).
BlockXpr bottomRightCorner (Index cRows, Index cCols)
const ConstBlockXpr bottomRightCorner (Index cRows, Index cCols) const
 This is the const version of bottomRightCorner(Index, Index).
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner ()
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner () const
 This is the const version of bottomRightCorner<int, int>().
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type bottomRightCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
bottomRightCorner (Index cRows, Index cCols) const
 This is the const version of bottomRightCorner<int, int>(Index, Index).
RowsBlockXpr bottomRows (Index n)
ConstRowsBlockXpr bottomRows (Index n) const
 This is the const version of bottomRows(Index).
template<int N>
NRowsBlockXpr< N >::Type bottomRows (Index n=N)
template<int N>
ConstNRowsBlockXpr< N >::Type bottomRows (Index n=N) const
 This is the const version of bottomRows<int>().
ColXpr col (Index i)
ConstColXpr col (Index i) const
 This is the const version of col().
ConstColwiseReturnType colwise () const
ColwiseReturnType colwise ()
Index count () const
EvalReturnType eval () const
void fill (const Scalar &value)
template<unsigned int Added, unsigned int Removed>
EIGEN_DEPRECATED const Derived & flagged () const
const WithFormat< Derived > format (const IOFormat &fmt) const
bool hasNaN () const
SegmentReturnType head (Index n)
ConstSegmentReturnType head (Index n) const
 This is the const version of head(Index).
template<int N>
FixedSegmentReturnType< N >::Type head (Index n=N)
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
head (Index n=N) const
 This is the const version of head<int>().
Index innerSize () const
template<typename OtherDerived >
bool isApprox (const DenseBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isApproxToConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isConstant (const Scalar &value, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename 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
bool isZero (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
Derived & lazyAssign (const DenseBase< OtherDerived > &other)
ColsBlockXpr leftCols (Index n)
ConstColsBlockXpr leftCols (Index n) const
 This is the const version of leftCols(Index).
template<int N>
NColsBlockXpr< N >::Type leftCols (Index n=N)
template<int N>
ConstNColsBlockXpr< N >::Type leftCols (Index n=N) const
 This is the const version of leftCols<int>().
internal::traits< Derived >::Scalar maxCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
internal::traits< Derived >::Scalar maxCoeff (IndexType *index) const
Scalar mean () const
ColsBlockXpr middleCols (Index startCol, Index numCols)
ConstColsBlockXpr middleCols (Index startCol, Index numCols) const
 This is the const version of middleCols(Index,Index).
template<int N>
NColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N)
template<int N>
ConstNColsBlockXpr< N >::Type middleCols (Index startCol, Index n=N) const
 This is the const version of middleCols<int>().
RowsBlockXpr middleRows (Index startRow, Index n)
ConstRowsBlockXpr middleRows (Index startRow, Index n) const
 This is the const version of middleRows(Index,Index).
template<int N>
NRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N)
template<int N>
ConstNRowsBlockXpr< N >::Type middleRows (Index startRow, Index n=N) const
 This is the const version of middleRows<int>().
internal::traits< Derived >::Scalar minCoeff () const
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *row, IndexType *col) const
template<typename IndexType >
internal::traits< Derived >::Scalar minCoeff (IndexType *index) const
const NestByValue< Derived > nestByValue () const
Index nonZeros () const
CommaInitializer< Derived > operator<< (const Scalar &s)
template<typename OtherDerived >
CommaInitializer< Derived > operator<< (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
Derived & operator= (const DenseBase &other)
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
Index outerSize () const
Scalar prod () const
template<typename Func >
internal::traits< Derived >::Scalar redux (const Func &func) const
template<int RowFactor, int ColFactor>
const Replicate< Derived,
RowFactor, ColFactor > 
replicate () const
const Replicate< Derived,
Dynamic, Dynamic > 
replicate (Index rowFactor, Index colFactor) const
void resize (Index newSize)
void resize (Index rows, Index cols)
ReverseReturnType reverse ()
ConstReverseReturnType reverse () const
void reverseInPlace ()
ColsBlockXpr rightCols (Index n)
ConstColsBlockXpr rightCols (Index n) const
 This is the const version of rightCols(Index).
template<int N>
NColsBlockXpr< N >::Type rightCols (Index n=N)
template<int N>
ConstNColsBlockXpr< N >::Type rightCols (Index n=N) const
 This is the const version of rightCols<int>().
RowXpr row (Index i)
ConstRowXpr row (Index i) const
 This is the const version of row(). */.
ConstRowwiseReturnType rowwise () const
RowwiseReturnType rowwise ()
SegmentReturnType segment (Index start, Index n)
ConstSegmentReturnType segment (Index start, Index n) const
 This is the const version of segment(Index,Index).
template<int N>
FixedSegmentReturnType< N >::Type segment (Index start, Index n=N)
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
segment (Index start, Index n=N) const
 This is the const version of segment<int>(Index).
template<typename ThenDerived , typename ElseDerived >
const Select< Derived,
ThenDerived, ElseDerived > 
select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const
template<typename ThenDerived >
const Select< Derived,
ThenDerived, typename
ThenDerived::ConstantReturnType > 
select (const DenseBase< ThenDerived > &thenMatrix, const typename ThenDerived::Scalar &elseScalar) const
template<typename ElseDerived >
const Select< Derived,
typename
ElseDerived::ConstantReturnType,
ElseDerived > 
select (const typename ElseDerived::Scalar &thenScalar, const DenseBase< ElseDerived > &elseMatrix) const
Derived & setConstant (const Scalar &value)
Derived & setLinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector.
Derived & setLinSpaced (const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector.
Derived & setOnes ()
Derived & setRandom ()
Derived & setZero ()
Scalar sum () const
template<typename OtherDerived >
void swap (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
void swap (PlainObjectBase< OtherDerived > &other)
SegmentReturnType tail (Index n)
ConstSegmentReturnType tail (Index n) const
 This is the const version of tail(Index).
template<int N>
FixedSegmentReturnType< N >::Type tail (Index n=N)
template<int N>
ConstFixedSegmentReturnType< N >
::Type 
tail (Index n=N) const
 This is the const version of tail<int>.
BlockXpr topLeftCorner (Index cRows, Index cCols)
const ConstBlockXpr topLeftCorner (Index cRows, Index cCols) const
 This is the const version of topLeftCorner(Index, Index).
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner ()
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner () const
 This is the const version of topLeftCorner<int, int>().
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topLeftCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topLeftCorner (Index cRows, Index cCols) const
 This is the const version of topLeftCorner<int, int>(Index, Index).
BlockXpr topRightCorner (Index cRows, Index cCols)
const ConstBlockXpr topRightCorner (Index cRows, Index cCols) const
 This is the const version of topRightCorner(Index, Index).
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner ()
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner () const
 This is the const version of topRightCorner<int, int>().
template<int CRows, int CCols>
FixedBlockXpr< CRows, CCols >::Type topRightCorner (Index cRows, Index cCols)
template<int CRows, int CCols>
const ConstFixedBlockXpr
< CRows, CCols >::Type 
topRightCorner (Index cRows, Index cCols) const
 This is the const version of topRightCorner<int, int>(Index, Index).
RowsBlockXpr topRows (Index n)
ConstRowsBlockXpr topRows (Index n) const
 This is the const version of topRows(Index).
template<int N>
NRowsBlockXpr< N >::Type topRows (Index n=N)
template<int N>
ConstNRowsBlockXpr< N >::Type topRows (Index n=N) const
 This is the const version of topRows<int>().
TransposeReturnType transpose ()
ConstTransposeReturnType transpose () const
void transposeInPlace ()
CoeffReturnType value () const
template<typename Visitor >
void visit (Visitor &func) const

Static Public Member Functions

static const ConstantReturnType Constant (Index rows, Index cols, const Scalar &value)
static const ConstantReturnType Constant (Index size, const Scalar &value)
static const ConstantReturnType Constant (const Scalar &value)
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (Index size, const Scalar &low, const Scalar &high)
 Sets a linearly spaced vector.
static const
SequentialLinSpacedReturnType 
LinSpaced (Sequential_t, const Scalar &low, const Scalar &high)
static const
RandomAccessLinSpacedReturnType 
LinSpaced (const Scalar &low, const Scalar &high)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, PlainObject
NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, PlainObject
NullaryExpr (Index size, const CustomNullaryOp &func)
template<typename CustomNullaryOp >
static const CwiseNullaryOp
< CustomNullaryOp, PlainObject
NullaryExpr (const CustomNullaryOp &func)
static const ConstantReturnType Ones (Index rows, Index cols)
static const ConstantReturnType Ones (Index size)
static const ConstantReturnType Ones ()
static const RandomReturnType Random (Index rows, Index cols)
static const RandomReturnType Random (Index size)
static const RandomReturnType Random ()
static const ConstantReturnType Zero (Index rows, Index cols)
static const ConstantReturnType Zero (Index size)
static const ConstantReturnType Zero ()

Protected Member Functions

 DenseBase ()

Related Functions

(Note that these are not member functions.)

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

Member Typedef Documentation

template<typename Derived>
typedef Array<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime, AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor), internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime > Eigen::DenseBase< Derived >::PlainArray

The plain array type corresponding to this expression.

See also:
PlainObject
template<typename Derived>
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 > Eigen::DenseBase< Derived >::PlainMatrix

The plain matrix type corresponding to this expression.

See also:
PlainObject
template<typename Derived>
typedef internal::conditional<internal::is_same<typename internal::traits<Derived>::XprKind,MatrixXpr >::value, PlainMatrix, PlainArray>::type Eigen::DenseBase< Derived >::PlainObject

The plain matrix or array 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 Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >, Eigen::MatrixBase< Derived >, Eigen::MatrixBase< MatrixWrapper< ExpressionType > >, Eigen::MatrixBase< Homogeneous< MatrixType, _Direction > >, Eigen::MatrixBase< Solve< Decomposition, RhsType > >, and Eigen::Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.

template<typename Derived>
typedef internal::traits<Derived>::Scalar Eigen::DenseBase< Derived >::Scalar

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

Reimplemented from Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >.

template<typename Derived>
typedef internal::traits<Derived>::StorageIndex Eigen::DenseBase< Derived >::StorageIndex

The type used to store indices.

This typedef is relevant for types that store multiple indices such as PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index

See also:
Preprocessor directives, Eigen::Index, SparseMatrixBase.
template<typename Derived>
typedef Scalar Eigen::DenseBase< Derived >::value_type

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

It is an alias for the Scalar type


Member Enumeration Documentation

template<typename Derived>
anonymous enum
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.


Constructor & Destructor Documentation

template<typename Derived>
Eigen::DenseBase< Derived >::DenseBase ( ) [inline, protected]

Default constructor. Do nothing.


Member Function Documentation

template<typename Derived >
bool Eigen::DenseBase< Derived >::all ( ) const [inline]
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<()
template<typename Derived >
bool Eigen::DenseBase< Derived >::allFinite ( ) const [inline]
Returns:
true if *this contains only finite numbers, i.e., no NaN and no +/-INF values.
See also:
hasNaN()
template<typename Derived >
bool Eigen::DenseBase< Derived >::any ( ) const [inline]
Returns:
true if at least one coefficient is true
See also:
all()
template<typename Derived>
BlockXpr Eigen::DenseBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) [inline]
Returns:
a dynamic-size expression of a block in *this.
Parameters:
startRowthe first row in the block
startColthe first column in the block
blockRowsthe number of rows in the block
blockColsthe number of columns in the block

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note:
Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.
See also:
class Block, block(Index,Index)
template<typename Derived>
template<int NRows, int NCols>
FixedBlockXpr<NRows,NCols>::Type Eigen::DenseBase< Derived >::block ( Index  startRow,
Index  startCol 
) [inline]
Returns:
a fixed-size expression of a block in *this.

The template parameters NRows and NCols are the number of rows and columns in the block.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9
Note:
since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:
 m.template block<3,3>(1,1); 
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int NRows, int NCols>
FixedBlockXpr<NRows,NCols>::Type Eigen::DenseBase< Derived >::block ( Index  startRow,
Index  startCol,
Index  blockRows,
Index  blockCols 
) [inline]
Returns:
an expression of a block in *this.
Template Parameters:
NRowsnumber of rows in block as specified at compile-time
NColsnumber of columns in block as specified at compile-time
Parameters:
startRowthe first row in the block
startColthe first column in the block
blockRowsnumber of rows in block as specified at run-time
blockColsnumber of columns in block as specified at run-time

This function is mainly useful for blocks where the number of rows is specified at compile-time and the number of columns is specified at run-time, or vice versa. The compile-time and run-time information should not contradict. In other words, blockRows should equal NRows unless NRows 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)
template<typename Derived>
BlockXpr Eigen::DenseBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
a dynamic-size expression of a bottom-left corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::bottomLeftCorner ( ) [inline]
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)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::bottomLeftCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
an expression of a bottom-left corner of *this.
Template Parameters:
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters:
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

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

Example:

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
template<typename Derived>
BlockXpr Eigen::DenseBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
a dynamic-size expression of a bottom-right corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::bottomRightCorner ( ) [inline]
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)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::bottomRightCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
an expression of a bottom-right corner of *this.
Template Parameters:
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters:
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

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

Example:

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
template<typename Derived>
RowsBlockXpr Eigen::DenseBase< Derived >::bottomRows ( Index  n) [inline]
Returns:
a block consisting of the bottom rows of *this.
Parameters:
nthe number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::DenseBase< Derived >::bottomRows ( Index  n = N) [inline]
Returns:
a block consisting of the bottom rows of *this.
Template Parameters:
Nthe number of rows in the block as specified at compile-time
Parameters:
nthe number of rows in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
ColXpr Eigen::DenseBase< Derived >::col ( Index  i) [inline]
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
template<typename Derived>
ConstColwiseReturnType Eigen::DenseBase< Derived >::colwise ( ) const [inline]
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
template<typename Derived >
DenseBase< Derived >::ColwiseReturnType Eigen::DenseBase< Derived >::colwise ( ) [inline]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant ( Index  rows,
Index  cols,
const Scalar value 
) [inline, static]
Returns:
an expression of a constant matrix of value value

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

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

The template parameter CustomNullaryOp is the type of the functor.

See also:
class CwiseNullaryOp
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant ( Index  size,
const Scalar value 
) [inline, static]
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
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Constant ( const Scalar value) [inline, static]
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
template<typename Derived >
Eigen::Index Eigen::DenseBase< Derived >::count ( ) const [inline]
Returns:
the number of coefficients which evaluate to true
See also:
all(), any()
template<typename Derived>
EvalReturnType Eigen::DenseBase< Derived >::eval ( ) const [inline]
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.

Warning:
Be carefull with eval() and the auto C++ keyword, as detailed in this page .
template<typename Derived >
void Eigen::DenseBase< Derived >::fill ( const Scalar val) [inline]

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

See also:
setConstant(), Constant(), class CwiseNullaryOp
template<typename Derived>
template<unsigned int Added, unsigned int Removed>
EIGEN_DEPRECATED const Derived& Eigen::DenseBase< Derived >::flagged ( ) const [inline]
Deprecated:
it now returns *this
template<typename Derived>
const WithFormat<Derived> Eigen::DenseBase< Derived >::format ( const IOFormat fmt) const [inline]
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
template<typename Derived >
bool Eigen::DenseBase< Derived >::hasNaN ( ) const [inline]
Returns:
true is *this contains at least one Not A Number (NaN).
See also:
allFinite()
template<typename Derived>
SegmentReturnType Eigen::DenseBase< Derived >::head ( Index  n) [inline]
Returns:
a dynamic-size expression of the first coefficients of *this.

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

Parameters:
nthe number of coefficients in the segment

Example:

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)
template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::DenseBase< Derived >::head ( Index  n = N) [inline]
Returns:
a fixed-size expression of the first coefficients of *this.

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

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

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

Example:

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
template<typename Derived>
Index Eigen::DenseBase< Derived >::innerSize ( ) const [inline]
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.
template<typename Derived >
template<typename OtherDerived >
bool Eigen::DenseBase< Derived >::isApprox ( const DenseBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
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
template<typename Derived >
bool Eigen::DenseBase< Derived >::isApproxToConstant ( const Scalar val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns:
true if all coefficients in this matrix are approximately equal to val, to within precision prec
template<typename Derived >
bool Eigen::DenseBase< Derived >::isConstant ( const Scalar val,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const

This is just an alias for isApproxToConstant().

Returns:
true if all coefficients in this matrix are approximately equal to value, to within precision prec
template<typename Derived>
template<typename Derived >
bool Eigen::DenseBase< Derived >::isMuchSmallerThan ( const typename NumTraits< Scalar >::Real &  other,
const RealScalar &  prec 
) const
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
template<typename Derived >
template<typename OtherDerived >
bool Eigen::DenseBase< Derived >::isMuchSmallerThan ( const DenseBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
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
template<typename Derived >
bool Eigen::DenseBase< Derived >::isOnes ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
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()
template<typename Derived >
bool Eigen::DenseBase< Derived >::isZero ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
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()
template<typename Derived >
template<typename OtherDerived >
Derived & Eigen::DenseBase< Derived >::lazyAssign ( const DenseBase< OtherDerived > &  other) [inline]
template<typename Derived>
ColsBlockXpr Eigen::DenseBase< Derived >::leftCols ( Index  n) [inline]
Returns:
a block consisting of the left columns of *this.
Parameters:
nthe number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::DenseBase< Derived >::leftCols ( Index  n = N) [inline]
Returns:
a block consisting of the left columns of *this.
Template Parameters:
Nthe number of columns in the block as specified at compile-time
Parameters:
nthe number of columns in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived >
const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced ( Sequential_t  ,
Index  size,
const Scalar low,
const Scalar high 
) [inline, static]
Deprecated:
because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)
See also:
LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&)
template<typename Derived >
const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced ( Index  size,
const Scalar low,
const Scalar high 
) [inline, static]

Sets a linearly spaced 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

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

cout << "Even spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,4).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,8).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,15).transpose() << endl;
cout << "Uneven spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,7).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,9).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,16).transpose() << endl;

Output:

Even spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
Uneven spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
See also:
setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
template<typename Derived >
const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced ( Sequential_t  ,
const Scalar low,
const Scalar high 
) [inline, static]
Deprecated:
because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)
See also:
LinSpaced(Scalar,Scalar)
template<typename Derived >
const DenseBase< Derived >::RandomAccessLinSpacedReturnType Eigen::DenseBase< Derived >::LinSpaced ( const Scalar low,
const Scalar high 
) [inline, static]

Sets a linearly spaced 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

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

cout << "Even spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,4).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,8).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,15).transpose() << endl;
cout << "Uneven spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,7).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,9).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,16).transpose() << endl;

Output:

Even spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
Uneven spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
See also:
setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
Special version for fixed size types which does not require the size parameter.

template<typename Derived >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::maxCoeff ( ) const [inline]
Returns:
the maximum of all coefficients of *this.
Warning:
the result is undefined if *this contains NaN.
template<typename Derived >
template<typename IndexType >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::maxCoeff ( IndexType *  rowId,
IndexType *  colId 
) const
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::visit(), DenseBase::maxCoeff()
template<typename Derived >
template<typename IndexType >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::maxCoeff ( IndexType *  index) const
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()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::mean ( ) const [inline]
Returns:
the mean of all coefficients of *this
See also:
trace(), prod(), sum()
template<typename Derived>
ColsBlockXpr Eigen::DenseBase< Derived >::middleCols ( Index  startCol,
Index  numCols 
) [inline]
Returns:
a block consisting of a range of columns of *this.
Parameters:
startColthe index of the first column in the block
numColsthe number of columns in the block

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::DenseBase< Derived >::middleCols ( Index  startCol,
Index  n = N 
) [inline]
Returns:
a block consisting of a range of columns of *this.
Template Parameters:
Nthe number of columns in the block as specified at compile-time
Parameters:
startColthe index of the first column in the block
nthe number of columns in the block as specified at run-time

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
RowsBlockXpr Eigen::DenseBase< Derived >::middleRows ( Index  startRow,
Index  n 
) [inline]
Returns:
a block consisting of a range of rows of *this.
Parameters:
startRowthe index of the first row in the block
nthe number of rows in the block

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::DenseBase< Derived >::middleRows ( Index  startRow,
Index  n = N 
) [inline]
Returns:
a block consisting of a range of rows of *this.
Template Parameters:
Nthe number of rows in the block as specified at compile-time
Parameters:
startRowthe index of the first row in the block
nthe number of rows in the block as specified at run-time

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::minCoeff ( ) const [inline]
Returns:
the minimum of all coefficients of *this.
Warning:
the result is undefined if *this contains NaN.
template<typename Derived >
template<typename IndexType >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::minCoeff ( IndexType *  rowId,
IndexType *  colId 
) const
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::visit(), DenseBase::minCoeff()
template<typename Derived >
template<typename IndexType >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::minCoeff ( IndexType *  index) const
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::visit(), DenseBase::minCoeff()
template<typename Derived >
const NestByValue< Derived > Eigen::DenseBase< Derived >::nestByValue ( ) const [inline]
Returns:
an expression of the temporary version of *this.
template<typename Derived>
Index Eigen::DenseBase< Derived >::nonZeros ( ) const [inline]
Returns:
the number of nonzero coefficients which is in practice the number of stored coefficients.
template<typename Derived >
template<typename CustomNullaryOp >
const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr ( Index  rows,
Index  cols,
const CustomNullaryOp &  func 
) [inline, static]
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
template<typename Derived >
template<typename CustomNullaryOp >
const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr ( Index  size,
const CustomNullaryOp &  func 
) [inline, static]
Returns:
an expression of a matrix defined by a custom functor func

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

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

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

The template parameter CustomNullaryOp is the type of the functor.

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

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

using namespace Eigen;

int main() {
  std::default_random_engine generator;
  std::poisson_distribution<int> distribution(4.1);
  auto poisson = [&] () {return distribution(generator);};

  RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson );
  std::cout << v << "\n";
}

Output:

2 3 1 4 3 4 4 3 2 3
See also:
class CwiseNullaryOp
template<typename Derived >
template<typename CustomNullaryOp >
const CwiseNullaryOp< CustomNullaryOp, typename DenseBase< Derived >::PlainObject > Eigen::DenseBase< Derived >::NullaryExpr ( const CustomNullaryOp &  func) [inline, static]
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
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones ( Index  rows,
Index  cols 
) [inline, static]
Returns:
an expression of a matrix where all coefficients equal one.

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

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

Example:

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

Output:

1 1 1
1 1 1
See also:
Ones(), Ones(Index), isOnes(), class Ones
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones ( Index  newSize) [inline, static]
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
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Ones ( ) [inline, static]
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
template<typename Derived >
CommaInitializer< Derived > Eigen::DenseBase< Derived >::operator<< ( const Scalar s) [inline]

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
template<typename Derived >
template<typename OtherDerived >
CommaInitializer< Derived > Eigen::DenseBase< Derived >::operator<< ( const DenseBase< OtherDerived > &  other) [inline]
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::operator= ( const DenseBase< 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)

template<typename Derived >
template<typename OtherDerived >
Derived & Eigen::DenseBase< Derived >::operator= ( const EigenBase< OtherDerived > &  other)
template<typename Derived>
Index Eigen::DenseBase< Derived >::outerSize ( ) const [inline]
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.
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::prod ( ) const [inline]
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()
template<typename Derived >
const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random ( Index  rows,
Index  cols 
) [inline, static]
Returns:
a random matrix expression

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

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

Warning:
This function is not re-entrant.

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

Example:

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

Output:

 7  6  9
-2  6 -6

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

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

See also:
DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()
template<typename Derived >
const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random ( Index  size) [inline, static]
Returns:
a random vector expression

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

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

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

Warning:
This function is not re-entrant.

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

Example:

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

Output:

 7
-2

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

See also:
DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()
template<typename Derived >
const DenseBase< Derived >::RandomReturnType Eigen::DenseBase< Derived >::Random ( ) [inline, static]
Returns:
a fixed-size random matrix or vector expression

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

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

Example:

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

Output:

 700  600
-200  600

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

Warning:
This function is not re-entrant.
See also:
DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)
template<typename Derived>
template<typename Func >
internal::traits<Derived>::Scalar Eigen::DenseBase< Derived >::redux ( const Func &  func) const
Returns:
the result of a full redux operation on the whole matrix or vector using func

The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current C++98 and C++11 functor styles are handled.

See also:
DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
template<typename Derived >
template<int RowFactor, int ColFactor>
const Replicate< Derived, RowFactor, ColFactor > Eigen::DenseBase< Derived >::replicate ( ) const
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
template<typename Derived>
const Replicate<Derived, Dynamic, Dynamic> Eigen::DenseBase< Derived >::replicate ( Index  rowFactor,
Index  colFactor 
) const [inline]
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
template<typename Derived>
void Eigen::DenseBase< Derived >::resize ( Index  newSize) [inline]

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

template<typename Derived>
void Eigen::DenseBase< Derived >::resize ( Index  rows,
Index  cols 
) [inline]

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

template<typename Derived >
DenseBase< Derived >::ReverseReturnType Eigen::DenseBase< Derived >::reverse ( ) [inline]
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
template<typename Derived>
ConstReverseReturnType Eigen::DenseBase< Derived >::reverse ( ) const [inline]

This is the const version of reverse().

template<typename Derived >
void Eigen::DenseBase< Derived >::reverseInPlace ( ) [inline]

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 benefits:

  • less error prone: doing the same operation with .reverse() requires special care:
     m = m.reverse().eval(); 
    
  • this API enables reverse operations without the need for a temporary
  • it allows future optimizations (cache friendliness, etc.)
See also:
VectorwiseOp::reverseInPlace(), reverse()
template<typename Derived>
ColsBlockXpr Eigen::DenseBase< Derived >::rightCols ( Index  n) [inline]
Returns:
a block consisting of the right columns of *this.
Parameters:
nthe number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NColsBlockXpr<N>::Type Eigen::DenseBase< Derived >::rightCols ( Index  n = N) [inline]
Returns:
a block consisting of the right columns of *this.
Template Parameters:
Nthe number of columns in the block as specified at compile-time
Parameters:
nthe number of columns in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols<2>():
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
RowXpr Eigen::DenseBase< Derived >::row ( Index  i) [inline]
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
template<typename Derived>
ConstRowwiseReturnType Eigen::DenseBase< Derived >::rowwise ( ) const [inline]
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
template<typename Derived >
DenseBase< Derived >::RowwiseReturnType Eigen::DenseBase< Derived >::rowwise ( ) [inline]
Returns:
a writable VectorwiseOp wrapper of *this providing additional partial reduction operations
See also:
colwise(), class VectorwiseOp, Reductions, visitors and broadcasting
template<typename Derived>
SegmentReturnType Eigen::DenseBase< Derived >::segment ( Index  start,
Index  n 
) [inline]
Returns:
a dynamic-size expression of a segment (i.e. a vector block) in *this.

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

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

Example:

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

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

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

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

Example:

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
template<typename Derived >
template<typename ThenDerived , typename ElseDerived >
const Select< Derived, ThenDerived, ElseDerived > Eigen::DenseBase< Derived >::select ( const DenseBase< ThenDerived > &  thenMatrix,
const DenseBase< ElseDerived > &  elseMatrix 
) const [inline]
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
template<typename Derived >
template<typename ThenDerived >
const Select< Derived, ThenDerived, typename ThenDerived::ConstantReturnType > Eigen::DenseBase< Derived >::select ( const DenseBase< ThenDerived > &  thenMatrix,
const typename ThenDerived::Scalar &  elseScalar 
) const [inline]

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
template<typename Derived >
template<typename ElseDerived >
const Select< Derived, typename ElseDerived::ConstantReturnType, ElseDerived > Eigen::DenseBase< Derived >::select ( const typename ElseDerived::Scalar &  thenScalar,
const DenseBase< ElseDerived > &  elseMatrix 
) const [inline]

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
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setConstant ( const Scalar val) [inline]

Sets all coefficients in this expression to value val.

See also:
fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setLinSpaced ( Index  newSize,
const Scalar low,
const Scalar high 
) [inline]

Sets a linearly spaced 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

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also:
LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setLinSpaced ( const Scalar low,
const Scalar high 
) [inline]

Sets a linearly spaced vector.

The function fills *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.

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also:
LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setOnes ( ) [inline]

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()
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setRandom ( ) [inline]

Sets all coefficients in this expression to random values.

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

Warning:
This function is not re-entrant.

Example:

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)
template<typename Derived >
Derived & Eigen::DenseBase< Derived >::setZero ( ) [inline]

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()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::DenseBase< Derived >::sum ( ) const [inline]
Returns:
the sum of all coefficients of *this

If *this is empty, then the value 0 is returned.

See also:
trace(), prod(), mean()
template<typename Derived>
template<typename OtherDerived >
void Eigen::DenseBase< Derived >::swap ( const DenseBase< OtherDerived > &  other) [inline]

swaps *this with the expression other.

template<typename Derived>
template<typename OtherDerived >
void Eigen::DenseBase< Derived >::swap ( PlainObjectBase< OtherDerived > &  other) [inline]

swaps *this with the matrix or array other.

template<typename Derived>
SegmentReturnType Eigen::DenseBase< Derived >::tail ( Index  n) [inline]
Returns:
a dynamic-size expression of the last coefficients of *this.

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

Parameters:
nthe number of coefficients in the segment

Example:

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)
template<typename Derived>
template<int N>
FixedSegmentReturnType<N>::Type Eigen::DenseBase< Derived >::tail ( Index  n = N) [inline]
Returns:
a fixed-size expression of the last coefficients of *this.

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

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

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

Example:

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
template<typename Derived>
BlockXpr Eigen::DenseBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
a dynamic-size expression of a top-left corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::topLeftCorner ( ) [inline]
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)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::topLeftCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
an expression of a top-left corner of *this.
Template Parameters:
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters:
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

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

Example:

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
template<typename Derived>
BlockXpr Eigen::DenseBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
a dynamic-size expression of a top-right corner of *this.
Parameters:
cRowsthe number of rows in the corner
cColsthe number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::topRightCorner ( ) [inline]
Returns:
an expression of a fixed-size top-right corner of *this.
Template Parameters:
CRowsthe number of rows in the corner
CColsthe number of columns in the corner

Example:

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)
template<typename Derived>
template<int CRows, int CCols>
FixedBlockXpr<CRows,CCols>::Type Eigen::DenseBase< Derived >::topRightCorner ( Index  cRows,
Index  cCols 
) [inline]
Returns:
an expression of a top-right corner of *this.
Template Parameters:
CRowsnumber of rows in corner as specified at compile-time
CColsnumber of columns in corner as specified at compile-time
Parameters:
cRowsnumber of rows in corner as specified at run-time
cColsnumber of columns in corner as specified at run-time

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

Example:

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
template<typename Derived>
RowsBlockXpr Eigen::DenseBase< Derived >::topRows ( Index  n) [inline]
Returns:
a block consisting of the top rows of *this.
Parameters:
nthe number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived>
template<int N>
NRowsBlockXpr<N>::Type Eigen::DenseBase< Derived >::topRows ( Index  n = N) [inline]
Returns:
a block consisting of the top rows of *this.
Template Parameters:
Nthe number of rows in the block as specified at compile-time
Parameters:
nthe number of rows in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9
See also:
class Block, block(Index,Index,Index,Index)
template<typename Derived >
Transpose< Derived > Eigen::DenseBase< Derived >::transpose ( ) [inline]
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()
template<typename Derived >
DenseBase< Derived >::ConstTransposeReturnType Eigen::DenseBase< Derived >::transpose ( ) const [inline]

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also:
transposeInPlace(), adjoint()
template<typename Derived >
void Eigen::DenseBase< Derived >::transposeInPlace ( ) [inline]

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()
template<typename Derived>
CoeffReturnType Eigen::DenseBase< Derived >::value ( ) const [inline]
Returns:
the unique coefficient of a 1x1 expression
template<typename Derived >
template<typename Visitor >
void Eigen::DenseBase< Derived >::visit ( Visitor &  visitor) const

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()
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero ( Index  rows,
Index  cols 
) [inline, static]
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)
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero ( Index  size) [inline, static]
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)
template<typename Derived >
const DenseBase< Derived >::ConstantReturnType Eigen::DenseBase< Derived >::Zero ( ) [inline, static]
Returns:
an expression of a fixed-size zero matrix or vector.

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

Example:

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

Output:

0 0
0 0
0 0 0 0
See also:
Zero(Index), Zero(Index,Index)

Friends And Related Function Documentation

template<typename Derived >
std::ostream & operator<< ( std::ostream &  s,
const DenseBase< Derived > &  m 
) [related]

Outputs the matrix, to the given stream.

If you wish to print the matrix with a format different than the default, use DenseBase::format().

It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.

See also:
DenseBase::format()

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