SparseVector< _Scalar, _Flags, _Index > Class Template Reference

Detailed Description

template<typename _Scalar, int _Flags = 0, typename _Index = int>
class Eigen::SparseVector< _Scalar, _Flags, _Index >

a sparse vector class

Template Parameters

_Scalar

the scalar type, i.e. the type of the coefficients

See http://www.netlib.org/linalg/html_templates/node91.html for details on the storage scheme.

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

Inheritance diagram for SparseVector< _Scalar, _Flags, _Index >:

Public Member Functions
const CwiseBinaryOp < CustomBinaryOp, const SparseVector< _Scalar, _Options, _Index >, const OtherDerived >	binaryExpr (const Eigen::SparseMatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
Block< SparseVector< _Scalar, _Options, _Index > >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const SparseVector< _Scalar, _Options, _Index > >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< SparseVector< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol)
const Block< const SparseVector< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol) const
Block< SparseVector< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const SparseVector< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< SparseVector< _Scalar, _Options, _Index > >	bottomLeftCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index > >	bottomLeftCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner ()
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner () const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index > >	bottomRightCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index > >	bottomRightCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner ()
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner () const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner (Index cRows, Index cCols) const
RowsBlockXpr	bottomRows (Index n)
ConstRowsBlockXpr	bottomRows (Index n) const
NRowsBlockXpr< N >::Type	bottomRows (Index n=N)
ConstNRowsBlockXpr< N >::Type	bottomRows (Index n=N) const
internal::cast_return_type < SparseVector< _Scalar, _Options, _Index >, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < SparseVector< _Scalar, _Options, _Index > >::Scalar, NewType >, const SparseVector < _Scalar, _Options, _Index > > >::type	cast () const
Scalar &	coeffRef (Index i)
ColXpr	col (Index i)
ConstColXpr	col (Index i) const
ConjugateReturnType	conjugate () const
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > >	cwiseAbs () const
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > >	cwiseAbs2 () const
const CwiseBinaryOp < std::equal_to< Scalar > , const SparseVector< _Scalar, _Options, _Index >, const OtherDerived >	cwiseEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseScalarEqualReturnType	cwiseEqual (const Scalar &s) const
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > >	cwiseInverse () const
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const OtherDerived >	cwiseMax (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const ConstantReturnType >	cwiseMax (const Scalar &other) const
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const OtherDerived >	cwiseMin (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const ConstantReturnType >	cwiseMin (const Scalar &other) const
const CwiseBinaryOp < std::not_equal_to< Scalar > , const SparseVector< _Scalar, _Options, _Index >, const OtherDerived >	cwiseNotEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_product_op < typename SparseVector < _Scalar, _Options, _Index > ::Scalar, typename OtherDerived::Scalar >, const SparseVector< _Scalar, _Options, _Index >, const OtherDerived >	cwiseProduct (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const OtherDerived >	cwiseQuotient (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > >	cwiseSqrt () const
SparseVector< _Scalar, _Options, _Index > &	derived ()
const SparseVector< _Scalar, _Options, _Index > &	derived () const
const internal::eval < SparseVector< _Scalar, _Options, _Index > >::type	eval () const
SegmentReturnType	head (Index n)
ConstSegmentReturnType	head (Index n) const
FixedSegmentReturnType< N >::Type	head (Index n=N)
ConstFixedSegmentReturnType< N > ::Type	head (Index n=N) const
const ImagReturnType	imag () const
NonConstImagReturnType	imag ()
bool	isVector () const
ColsBlockXpr	leftCols (Index n)
ConstColsBlockXpr	leftCols (Index n) const
NColsBlockXpr< N >::Type	leftCols (Index n=N)
ConstNColsBlockXpr< N >::Type	leftCols (Index n=N) const
ColsBlockXpr	middleCols (Index startCol, Index numCols)
ConstColsBlockXpr	middleCols (Index startCol, Index numCols) const
NColsBlockXpr< N >::Type	middleCols (Index startCol, Index n=N)
ConstNColsBlockXpr< N >::Type	middleCols (Index startCol, Index n=N) const
RowsBlockXpr	middleRows (Index startRow, Index n)
ConstRowsBlockXpr	middleRows (Index startRow, Index n) const
NRowsBlockXpr< N >::Type	middleRows (Index startRow, Index n=N)
ConstNRowsBlockXpr< N >::Type	middleRows (Index startRow, Index n=N) const
Index	nonZeros () const
const ScalarMultipleReturnType	operator* (const Scalar &scalar) const
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const SparseVector < _Scalar, _Options, _Index > >	operator* (const std::complex< Scalar > &scalar) const
const SparseDenseProductReturnType < SparseVector< _Scalar, _Options, _Index > , OtherDerived >::Type	operator* (const MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_sum_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const OtherDerived >	operator+ (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_difference_op < Scalar >, const SparseVector < _Scalar, _Options, _Index > , const OtherDerived >	operator- (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < SparseVector< _Scalar, _Options, _Index > >::Scalar > , const SparseVector< _Scalar, _Options, _Index > >	operator- () const
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < SparseVector< _Scalar, _Options, _Index > >::Scalar > , const SparseVector< _Scalar, _Options, _Index > >	operator/ (const Scalar &scalar) const
RealReturnType	real () const
NonConstRealReturnType	real ()
ColsBlockXpr	rightCols (Index n)
ConstColsBlockXpr	rightCols (Index n) const
NColsBlockXpr< N >::Type	rightCols (Index n=N)
ConstNColsBlockXpr< N >::Type	rightCols (Index n=N) const
RowXpr	row (Index i)
ConstRowXpr	row (Index i) const
SegmentReturnType	segment (Index start, Index n)
ConstSegmentReturnType	segment (Index start, Index n) const
FixedSegmentReturnType< N >::Type	segment (Index start, Index n=N)
ConstFixedSegmentReturnType< N > ::Type	segment (Index start, Index n=N) const
Index	size () const
Scalar	sum () const
void	swap (SparseVector &other)
SegmentReturnType	tail (Index n)
ConstSegmentReturnType	tail (Index n) const
FixedSegmentReturnType< N >::Type	tail (Index n=N)
ConstFixedSegmentReturnType< N > ::Type	tail (Index n=N) const
Block< SparseVector< _Scalar, _Options, _Index > >	topLeftCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index > >	topLeftCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner ()
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner () const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index > >	topRightCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index > >	topRightCorner (Index cRows, Index cCols) const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner ()
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner () const
Block< SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner (Index cRows, Index cCols)
const Block< const SparseVector< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner (Index cRows, Index cCols) const
RowsBlockXpr	topRows (Index n)
ConstRowsBlockXpr	topRows (Index n) const
NRowsBlockXpr< N >::Type	topRows (Index n=N)
ConstNRowsBlockXpr< N >::Type	topRows (Index n=N) const
SparseSymmetricPermutationProduct < SparseVector< _Scalar, _Options, _Index >, Upper|Lower >	twistedBy (const PermutationMatrix< Dynamic, Dynamic, Index > &perm) const
const CwiseUnaryOp < CustomUnaryOp, const SparseVector< _Scalar, _Options, _Index > >	unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
	Apply a unary operator coefficient-wise. More...
const CwiseUnaryView < CustomViewOp, const SparseVector< _Scalar, _Options, _Index > >	unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
	~SparseVector ()

Constructor & Destructor Documentation

~SparseVector ( )

inline

Destructor

Member Function Documentation

const CwiseBinaryOp<CustomBinaryOp, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> binaryExpr ( const Eigen::SparseMatrixBase< OtherDerived > &  other, const CustomBinaryOp &  func = CustomBinaryOp()  ) const

inlineinherited

Returns

an expression of a custom coefficient-wise operator func of *this and other

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

Here is an example illustrating the use of custom functors:

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

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

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

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)

See Also

class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()

Block<SparseVector< _Scalar, _Options, _Index > > block ( Index  startRow, Index  startCol, Index  blockRows, Index  blockCols  )

inlineinherited

Returns

a dynamic-size expression of a block in *this.

Parameters

startRow	the first row in the block
startCol	the first column in the block
blockRows	the number of rows in the block
blockCols	the number of columns in the block

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block(1, 1, 2, 2):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9

Note

Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size matrix, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See Also

class Block, block(Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > > block ( Index  startRow, Index  startCol, Index  blockRows, Index  blockCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , BlockRows, BlockCols> block ( Index  startRow, Index  startCol  )

inlineinherited

Returns

a fixed-size expression of a block in *this.

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

Parameters

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.block<2,2>(1,1):
-6  1
-3  0
Now the matrix m is:
 7  9 -5 -3
-2  0  0  0
 6  0  0  9
 6  6  3  9

Note

since block is a templated member, the keyword template has to be used if the matrix type is also a template parameter:

m.template block<3,3>(1,1); 

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , BlockRows, BlockCols> block ( Index  startRow, Index  startCol  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , BlockRows, BlockCols> block ( Index  startRow, Index  startCol, Index  blockRows, Index  blockCols  )

inlineinherited

Returns

an expression of a block in *this.

Template Parameters

BlockRows	number of rows in block as specified at compile-time
BlockCols	number of columns in block as specified at compile-time

Parameters

startRow	the first row in the block
startCol	the first column in the block
blockRows	number of rows in block as specified at run-time
blockCols	number of columns in block as specified at run-time

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

Example:

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

Output:

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

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , BlockRows, BlockCols> block ( Index  startRow, Index  startCol, Index  blockRows, Index  blockCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > > bottomLeftCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

a dynamic-size expression of a bottom-left corner of *this.

Parameters

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner(2, 2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > > bottomLeftCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( )

inlineinherited

Returns

an expression of a fixed-size bottom-left corner of *this.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,2>():
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

an expression of a bottom-left corner of *this.

Template Parameters

CRows	number of rows in corner as specified at compile-time
CCols	number of columns in corner as specified at compile-time

Parameters

cRows	number of rows in corner as specified at run-time
cCols	number of columns in corner as specified at run-time

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomLeftCorner<2,Dynamic>(2,2):
 6 -3
 6  6
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  9
 0  0  3  9

See Also

class Block

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > > bottomRightCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

a dynamic-size expression of a bottom-right corner of *this.

Parameters

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner(2, 2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > > bottomRightCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( )

inlineinherited

Returns

an expression of a fixed-size bottom-right corner of *this.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,2>():
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

an expression of a bottom-right corner of *this.

Template Parameters

CRows	number of rows in corner as specified at compile-time
CCols	number of columns in corner as specified at compile-time

Parameters

cRows	number of rows in corner as specified at run-time
cCols	number of columns in corner as specified at run-time

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.bottomRightCorner<2,Dynamic>(2,2):
0 9
3 9
Now the matrix m is:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  0
 6  6  0  0

See Also

class Block

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

RowsBlockXpr bottomRows ( Index  n )

inlineinherited

Returns

a block consisting of the bottom rows of *this.

Parameters

n	the number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows(2):
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0

See Also

class Block, block(Index,Index,Index,Index)

ConstRowsBlockXpr bottomRows ( Index  n ) const

inlineinherited

This is the const version of bottomRows(Index).

NRowsBlockXpr<N>::Type bottomRows ( Index  n = N )

inlineinherited

Returns

a block consisting of the bottom rows of *this.

Template Parameters

N	the number of rows in the block as specified at compile-time

Parameters

n	the number of rows in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.bottomRows<2>():
 6 -3  0  9
 6  6  3  9
Now the array a is:
 7  9 -5 -3
-2 -6  1  0
 0  0  0  0
 0  0  0  0

See Also

class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type bottomRows ( Index  n = N ) const

inlineinherited

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

internal::cast_return_type<SparseVector< _Scalar, _Options, _Index > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<SparseVector< _Scalar, _Options, _Index > >::Scalar, NewType>, const SparseVector< _Scalar, _Options, _Index > > >::type cast ( ) const

inlineinherited

Returns

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

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

See Also

class CwiseUnaryOp

Scalar& coeffRef ( Index  i )

inline

Returns

a reference to the coefficient value at given index i This operation involes a log(rho*size) binary search. If the coefficient does not exist yet, then a sorted insertion into a sequential buffer is performed.

This insertion might be very costly if the number of nonzeros above i is large.

ColXpr col ( Index  i )

inlineinherited

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

ConstColXpr col ( Index  i ) const

inlineinherited

This is the const version of col().

ConjugateReturnType conjugate ( ) const

inlineinherited

Returns

an expression of the complex conjugate of *this.

See Also

adjoint()

const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > > cwiseAbs ( ) const

inlineinherited

Returns

an expression of the coefficient-wise absolute value of *this

Example:

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

Output:

2 4 6
5 1 0

See Also

cwiseAbs2()

const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > > cwiseAbs2 ( ) const

inlineinherited

Returns

an expression of the coefficient-wise squared absolute value of *this

Example:

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

Output:

 4 16 36
25  1  0

See Also

cwiseAbs()

const CwiseBinaryOp<std::equal_to<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> cwiseEqual ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise == operator of *this and other

Warning

this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

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

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3

See Also

cwiseNotEqual(), isApprox(), isMuchSmallerThan()

const CwiseScalarEqualReturnType cwiseEqual ( const Scalar &  s ) const

inlineinherited

Returns

an expression of the coefficient-wise == operator of *this and a scalar s

Warning

this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

See Also

cwiseEqual(const MatrixBase<OtherDerived> &) const

const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > > cwiseInverse ( ) const

inlineinherited

Returns

an expression of the coefficient-wise inverse of *this.

Example:

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

Output:

  0.5     2     1
0.333     4     1

See Also

cwiseProduct()

const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> cwiseMax ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise max of *this and other

Example:

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

Output:

4
3
4

See Also

class CwiseBinaryOp, min()

const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const ConstantReturnType> cwiseMax ( const Scalar &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise max of *this and scalar other

See Also

class CwiseBinaryOp, min()

const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> cwiseMin ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise min of *this and other

Example:

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

Output:

2
2
3

See Also

class CwiseBinaryOp, max()

const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const ConstantReturnType> cwiseMin ( const Scalar &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise min of *this and scalar other

See Also

class CwiseBinaryOp, min()

const CwiseBinaryOp<std::not_equal_to<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> cwiseNotEqual ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise != operator of *this and other

Warning

this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

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

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1

See Also

cwiseEqual(), isApprox(), isMuchSmallerThan()

const CwiseBinaryOp<internal::scalar_product_op<typename SparseVector< _Scalar, _Options, _Index > ::Scalar, typename OtherDerived ::Scalar >, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived > cwiseProduct ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the Schur product (coefficient wise product) of *this and other

Example:

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

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25

See Also

class CwiseBinaryOp, cwiseAbs2

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> cwiseQuotient ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inlineinherited

Returns

an expression of the coefficient-wise quotient of *this and other

Example:

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

Output:

 0.5
 1.5
1.33

See Also

class CwiseBinaryOp, cwiseProduct(), cwiseInverse()

const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const SparseVector< _Scalar, _Options, _Index > > cwiseSqrt ( ) const

inlineinherited

Returns

an expression of the coefficient-wise square root of *this.

Example:

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

Output:

   1
1.41
   2

See Also

cwisePow(), cwiseSquare()

SparseVector< _Scalar, _Options, _Index > & derived ( )

inlineinherited

Returns

a reference to the derived object

const SparseVector< _Scalar, _Options, _Index > & derived ( ) const

inlineinherited

Returns

a const reference to the derived object

const internal::eval<SparseVector< _Scalar, _Options, _Index > >::type eval ( ) const

inlineinherited

Returns

the matrix or vector obtained by evaluating this expression.

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

SegmentReturnType head ( Index  n )

inlineinherited

Returns

a dynamic-size expression of the first coefficients of *this.

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

Parameters

n	the number of coefficients in the segment

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6

Note

Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See Also

class Block, block(Index,Index)

ConstSegmentReturnType head ( Index  n ) const

inlineinherited

This is the const version of head(Index).

FixedSegmentReturnType<N>::Type head ( Index  n = N )

inlineinherited

Returns

a fixed-size expression of the first coefficients of *this.

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

Template Parameters

N	the number of coefficients in the segment as specified at compile-time

Parameters

n	the number of coefficients in the segment as specified at run-time

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

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.head(2):
 7 -2
Now the vector v is:
0 0 6 6

See Also

class Block

ConstFixedSegmentReturnType<N>::Type head ( Index  n = N ) const

inlineinherited

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

const ImagReturnType imag ( ) const

inlineinherited

Returns

an read-only expression of the imaginary part of *this.

See Also

real()

NonConstImagReturnType imag ( )

inlineinherited

Returns

a non const expression of the imaginary part of *this.

See Also

real()

bool isVector ( ) const

inlineinherited

Returns

true if either the number of rows or the number of columns is equal to 1. In other words, this function returns

rows()==1 || cols()==1 

See Also

rows(), cols(), IsVectorAtCompileTime.

ColsBlockXpr leftCols ( Index  n )

inlineinherited

Returns

a block consisting of the left columns of *this.

Parameters

n	the number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols(2):
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9

See Also

class Block, block(Index,Index,Index,Index)

ConstColsBlockXpr leftCols ( Index  n ) const

inlineinherited

This is the const version of leftCols(Index).

NColsBlockXpr<N>::Type leftCols ( Index  n = N )

inlineinherited

Returns

a block consisting of the left columns of *this.

Template Parameters

N	the number of columns in the block as specified at compile-time

Parameters

n	the number of columns in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.leftCols<2>():
 7  9
-2 -6
 6 -3
 6  6
Now the array a is:
 0  0 -5 -3
 0  0  1  0
 0  0  0  9
 0  0  3  9

See Also

class Block, block(Index,Index,Index,Index)

ConstNColsBlockXpr<N>::Type leftCols ( Index  n = N ) const

inlineinherited

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

ColsBlockXpr middleCols ( Index  startCol, Index  numCols  )

inlineinherited

Returns

a block consisting of a range of columns of *this.

Parameters

startCol	the index of the first column in the block
numCols	the number of columns in the block

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(1..3,:) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2

See Also

class Block, block(Index,Index,Index,Index)

ConstColsBlockXpr middleCols ( Index  startCol, Index  numCols  ) const

inlineinherited

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

NColsBlockXpr<N>::Type middleCols ( Index  startCol, Index  n = N  )

inlineinherited

Returns

a block consisting of a range of columns of *this.

Template Parameters

N	the number of columns in the block as specified at compile-time

Parameters

startCol	the index of the first column in the block
n	the number of columns in the block as specified at run-time

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(:,1..3) =
-6  0  9
-3  3  3
 6 -3  5
-5  0 -8
 1  9  2

See Also

class Block, block(Index,Index,Index,Index)

ConstNColsBlockXpr<N>::Type middleCols ( Index  startCol, Index  n = N  ) const

inlineinherited

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

RowsBlockXpr middleRows ( Index  startRow, Index  n  )

inlineinherited

Returns

a block consisting of a range of rows of *this.

Parameters

startRow	the index of the first row in the block
n	the number of rows in the block

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(2..3,:) =
 6  6 -3  5 -8
 6 -5  0 -8  6

See Also

class Block, block(Index,Index,Index,Index)

ConstRowsBlockXpr middleRows ( Index  startRow, Index  n  ) const

inlineinherited

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

NRowsBlockXpr<N>::Type middleRows ( Index  startRow, Index  n = N  )

inlineinherited

Returns

a block consisting of a range of rows of *this.

Template Parameters

N	the number of rows in the block as specified at compile-time

Parameters

startRow	the index of the first row in the block
n	the number of rows in the block as specified at run-time

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

A(1..3,:) =
-2 -3  3  3 -5
 6  6 -3  5 -8
 6 -5  0 -8  6

See Also

class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type middleRows ( Index  startRow, Index  n = N  ) const

inlineinherited

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

Index nonZeros ( ) const

inline

Returns

the number of non zero coefficients

const ScalarMultipleReturnType operator* ( const Scalar &  scalar ) const

inlineinherited

Returns

an expression of *this scaled by the scalar factor scalar

const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const SparseVector< _Scalar, _Options, _Index > > operator* ( const std::complex< Scalar > &  scalar ) const

inlineinherited

Overloaded for efficient real matrix times complex scalar value

const SparseDenseProductReturnType<SparseVector< _Scalar, _Options, _Index > ,OtherDerived>::Type operator* ( const MatrixBase< OtherDerived > &  other ) const

inlineinherited

sparse * dense (returns a dense object unless it is an outer product)

const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> operator+ ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inherited

Returns

an expression of the sum of *this and other

Note

If you want to add a given scalar to all coefficients, see Cwise::operator+().

See Also

class CwiseBinaryOp, operator+=()

const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const SparseVector< _Scalar, _Options, _Index > , const OtherDerived> operator- ( const Eigen::SparseMatrixBase< OtherDerived > &  other ) const

inherited

Returns

an expression of the difference of *this and other

Note

If you want to substract a given scalar from all coefficients, see Cwise::operator-().

See Also

class CwiseBinaryOp, operator-=()

const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<SparseVector< _Scalar, _Options, _Index > >::Scalar>, const SparseVector< _Scalar, _Options, _Index > > operator- ( ) const

inlineinherited

Returns

an expression of the opposite of *this

const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<SparseVector< _Scalar, _Options, _Index > >::Scalar>, const SparseVector< _Scalar, _Options, _Index > > operator/ ( const Scalar &  scalar ) const

inlineinherited

Returns

an expression of *this divided by the scalar value scalar

RealReturnType real ( ) const

inlineinherited

Returns

a read-only expression of the real part of *this.

See Also

imag()

NonConstRealReturnType real ( )

inlineinherited

Returns

a non const expression of the real part of *this.

See Also

imag()

ColsBlockXpr rightCols ( Index  n )

inlineinherited

Returns

a block consisting of the right columns of *this.

Parameters

n	the number of columns in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols(2):
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0

See Also

class Block, block(Index,Index,Index,Index)

ConstColsBlockXpr rightCols ( Index  n ) const

inlineinherited

This is the const version of rightCols(Index).

NColsBlockXpr<N>::Type rightCols ( Index  n = N )

inlineinherited

Returns

a block consisting of the right columns of *this.

Template Parameters

N	the number of columns in the block as specified at compile-time

Parameters

n	the number of columns in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.rightCols<2>():
-5 -3
 1  0
 0  9
 3  9
Now the array a is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  0
 6  6  0  0

See Also

class Block, block(Index,Index,Index,Index)

ConstNColsBlockXpr<N>::Type rightCols ( Index  n = N ) const

inlineinherited

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

RowXpr row ( Index  i )

inlineinherited

Returns

an expression of the i-th row of *this. Note that the numbering starts at 0.

Example:

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

Output:

1 0 0
4 5 6
0 0 1

See Also

col(), class Block

ConstRowXpr row ( Index  i ) const

inlineinherited

This is the const version of row().

SegmentReturnType segment ( Index  start, Index  n  )

inlineinherited

Returns

a dynamic-size expression of a segment (i.e. a vector block) in *this.

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

Parameters

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

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment(1, 2):
-2  6
Now the vector v is:
7 0 0 6

Note

Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See Also

class Block, segment(Index)

ConstSegmentReturnType segment ( Index  start, Index  n  ) const

inlineinherited

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

FixedSegmentReturnType<N>::Type segment ( Index  start, Index  n = N  )

inlineinherited

Returns

a fixed-size expression of a segment (i.e. a vector block) in *this

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

Template Parameters

N	the number of coefficients in the segment as specified at compile-time

Parameters

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

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

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.segment<2>(1):
-2  6
Now the vector v is:
 7 -2  0  0

See Also

class Block

ConstFixedSegmentReturnType<N>::Type segment ( Index  start, Index  n = N  ) const

inlineinherited

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

Index size ( ) const

inlineinherited

Returns

the number of coefficients, which is rows()*cols().

See Also

rows(), cols().

internal::traits< SparseVector< _Scalar, _Options, _Index > >::Scalar sum

(

)

const

Overloaded for performance

void swap ( SparseVector< _Scalar, _Flags, _Index > &  other )

inline

Swaps the values of *this and other. Overloaded for performance: this version performs a shallow swap by swaping pointers and attributes only.

See Also

SparseMatrixBase::swap()

SegmentReturnType tail ( Index  n )

inlineinherited

Returns

a dynamic-size expression of the last coefficients of *this.

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

Parameters

n	the number of coefficients in the segment

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0

Note

Even though the returned expression has dynamic size, in the case when it is applied to a fixed-size vector, it inherits a fixed maximal size, which means that evaluating it does not cause a dynamic memory allocation.

See Also

class Block, block(Index,Index)

ConstSegmentReturnType tail ( Index  n ) const

inlineinherited

This is the const version of tail(Index).

FixedSegmentReturnType<N>::Type tail ( Index  n = N )

inlineinherited

Returns

a fixed-size expression of the last coefficients of *this.

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

Template Parameters

N	the number of coefficients in the segment as specified at compile-time

Parameters

n	the number of coefficients in the segment as specified at run-time

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

Example:

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

Output:

Here is the vector v:
 7 -2  6  6
Here is v.tail(2):
6 6
Now the vector v is:
 7 -2  0  0

See Also

class Block

ConstFixedSegmentReturnType<N>::Type tail ( Index  n = N ) const

inlineinherited

This is the const version of tail<int>.

Block<SparseVector< _Scalar, _Options, _Index > > topLeftCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

a dynamic-size expression of a top-left corner of *this.

Parameters

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner(2, 2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > > topLeftCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( )

inlineinherited

Returns

an expression of a fixed-size top-left corner of *this.

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,2>():
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

an expression of a top-left corner of *this.

Template Parameters

CRows	number of rows in corner as specified at compile-time
CCols	number of columns in corner as specified at compile-time

Parameters

cRows	number of rows in corner as specified at run-time
cCols	number of columns in corner as specified at run-time

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topLeftCorner<2,Dynamic>(2,2):
 7  9
-2 -6
Now the matrix m is:
 0  0 -5 -3
 0  0  1  0
 6 -3  0  9
 6  6  3  9

See Also

class Block

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > > topRightCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

a dynamic-size expression of a top-right corner of *this.

Parameters

cRows	the number of rows in the corner
cCols	the number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner(2, 2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block(Index,Index,Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > > topRightCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( )

inlineinherited

Returns

an expression of a fixed-size top-right corner of *this.

Template Parameters

CRows	the number of rows in the corner
CCols	the number of columns in the corner

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,2>():
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block<int,int>(Index,Index)

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( ) const

inlineinherited

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

Block<SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( Index  cRows, Index  cCols  )

inlineinherited

Returns

an expression of a top-right corner of *this.

Template Parameters

CRows	number of rows in corner as specified at compile-time
CCols	number of columns in corner as specified at compile-time

Parameters

cRows	number of rows in corner as specified at run-time
cCols	number of columns in corner as specified at run-time

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

Example:

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

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is m.topRightCorner<2,Dynamic>(2,2):
-5 -3
 1  0
Now the matrix m is:
 7  9  0  0
-2 -6  0  0
 6 -3  0  9
 6  6  3  9

See Also

class Block

const Block<const SparseVector< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( Index  cRows, Index  cCols  ) const

inlineinherited

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

RowsBlockXpr topRows ( Index  n )

inlineinherited

Returns

a block consisting of the top rows of *this.

Parameters

n	the number of rows in the block

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows(2):
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block(Index,Index,Index,Index)

ConstRowsBlockXpr topRows ( Index  n ) const

inlineinherited

This is the const version of topRows(Index).

NRowsBlockXpr<N>::Type topRows ( Index  n = N )

inlineinherited

Returns

a block consisting of the top rows of *this.

Template Parameters

N	the number of rows in the block as specified at compile-time

Parameters

n	the number of rows in the block as specified at run-time

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

Example:

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

Output:

Here is the array a:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here is a.topRows<2>():
 7  9 -5 -3
-2 -6  1  0
Now the array a is:
 0  0  0  0
 0  0  0  0
 6 -3  0  9
 6  6  3  9

See Also

class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type topRows ( Index  n = N ) const

inlineinherited

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

SparseSymmetricPermutationProduct<SparseVector< _Scalar, _Options, _Index > ,Upper|Lower> twistedBy ( const PermutationMatrix< Dynamic, Dynamic, Index > &  perm ) const

inlineinherited

Returns

an expression of P H P^-1 where H is the matrix represented by *this

const CwiseUnaryOp<CustomUnaryOp, const SparseVector< _Scalar, _Options, _Index > > unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp() ) const

inlineinherited

Apply a unary operator coefficient-wise.

Parameters

[in]

func

Functor implementing the unary operator

Template Parameters

CustomUnaryOp

Type of func

Returns

An expression of a custom coefficient-wise unary operator func of *this

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

Example:

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

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

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

Output:

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

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

Example:

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

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

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

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5

See Also

class CwiseUnaryOp, class CwiseBinaryOp

const CwiseUnaryView<CustomViewOp, const SparseVector< _Scalar, _Options, _Index > > unaryViewExpr ( const CustomViewOp &  func = CustomViewOp() ) const

inlineinherited

Returns

an expression of a custom coefficient-wise unary operator func of *this

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

Example:

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

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

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

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5

See Also

class CwiseUnaryOp, class CwiseBinaryOp

---

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

• SparseUtil.h
• SparseVector.h
• SparseRedux.h