Detailed Description

template<typename _Scalar, int _Options, typename _Index>
class Eigen::SparseMatrix< _Scalar, _Options, _Index >

A versatible sparse matrix representation.

This class implements a more versatile variants of the common compressed row/column storage format. Each colmun's (resp. row) non zeros are stored as a pair of value with associated row (resp. colmiun) index. All the non zeros are stored in a single large buffer. Unlike the compressed format, there might be extra space inbetween the nonzeros of two successive colmuns (resp. rows) such that insertion of new non-zero can be done with limited memory reallocation and copies.

A call to the function makeCompressed() turns the matrix into the standard compressed format compatible with many library.

More details on this storage sceheme are given in the manual pages.

Template Parameters:

_Scalar	the scalar type, i.e. the type of the coefficients
_Options	Union of bit flags controlling the storage scheme. Currently the only possibility is ColMajor or RowMajor. The default is 0 which means column-major.
_Index	the type of the indices. It has to be a signed type (e.g., short, int, std::ptrdiff_t). Default is `int`.

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_SPARSEMATRIX_PLUGIN.

Inheritance diagram for SparseMatrix< _Scalar, _Options, _Index >:

List of all members.

Public Member Functions
const CwiseBinaryOp < CustomBinaryOp, const SparseMatrix< _Scalar, _Options, _Index >, const OtherDerived >	binaryExpr (const Eigen::SparseMatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
Block< SparseMatrix< _Scalar, _Options, _Index > >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index > >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< SparseMatrix< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol)
const Block< const SparseMatrix< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol) const
Block< SparseMatrix< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index >, BlockRows, BlockCols >	block (Index startRow, Index startCol, Index blockRows, Index blockCols) const
Block< SparseMatrix< _Scalar, _Options, _Index > >	bottomLeftCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index > >	bottomLeftCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner ()
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner () const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomLeftCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index > >	bottomRightCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index > >	bottomRightCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner ()
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner () const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	bottomRightCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _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 < SparseMatrix< _Scalar, _Options, _Index >, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < SparseMatrix< _Scalar, _Options, _Index > >::Scalar, NewType >, const SparseMatrix < _Scalar, _Options, _Index > > >::type	cast () const
Scalar	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
ColXpr	col (Index i)
ConstColXpr	col (Index i) const
Index	cols () const
ConjugateReturnType	conjugate () const
void	conservativeResize (Index rows, Index cols)
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > >	cwiseAbs () const
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > >	cwiseAbs2 () const
const CwiseBinaryOp < std::equal_to< Scalar > , const SparseMatrix< _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 SparseMatrix < _Scalar, _Options, _Index > >	cwiseInverse () const
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const OtherDerived >	cwiseMax (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const ConstantReturnType >	cwiseMax (const Scalar &other) const
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const OtherDerived >	cwiseMin (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const ConstantReturnType >	cwiseMin (const Scalar &other) const
const CwiseBinaryOp < std::not_equal_to< Scalar > , const SparseMatrix< _Scalar, _Options, _Index >, const OtherDerived >	cwiseNotEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_product_op < typename SparseMatrix < _Scalar, _Options, _Index > ::Scalar, typename OtherDerived::Scalar >, const SparseMatrix< _Scalar, _Options, _Index >, const OtherDerived >	cwiseProduct (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const OtherDerived >	cwiseQuotient (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > >	cwiseSqrt () const
SparseMatrix< _Scalar, _Options, _Index > &	derived ()
const SparseMatrix< _Scalar, _Options, _Index > &	derived () const
const Diagonal< const SparseMatrix >	diagonal () const
const internal::eval < SparseMatrix< _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 ()
const Index *	innerIndexPtr () const
Index *	innerIndexPtr ()
const Index *	innerNonZeroPtr () const
Index *	innerNonZeroPtr ()
Index	innerSize () const
Scalar &	insert (Index row, Index col)
bool	isCompressed () const
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
void	makeCompressed ()
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 SparseMatrix < _Scalar, _Options, _Index > >	operator* (const std::complex< Scalar > &scalar) const
const SparseDenseProductReturnType < SparseMatrix< _Scalar, _Options, _Index > , OtherDerived >::Type	operator* (const MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_sum_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const OtherDerived >	operator+ (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseBinaryOp < internal::scalar_difference_op < Scalar >, const SparseMatrix < _Scalar, _Options, _Index > , const OtherDerived >	operator- (const Eigen::SparseMatrixBase< OtherDerived > &other) const
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < SparseMatrix< _Scalar, _Options, _Index > >::Scalar > , const SparseMatrix< _Scalar, _Options, _Index > >	operator- () const
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < SparseMatrix< _Scalar, _Options, _Index > >::Scalar > , const SparseMatrix< _Scalar, _Options, _Index > >	operator/ (const Scalar &scalar) const
const Index *	outerIndexPtr () const
Index *	outerIndexPtr ()
Index	outerSize () const
void	prune (const Scalar &reference, const RealScalar &epsilon=NumTraits< RealScalar >::dummy_precision())
template<typename KeepFunc >
void	prune (const KeepFunc &keep=KeepFunc())
RealReturnType	real () const
NonConstRealReturnType	real ()
void	reserve (Index reserveSize)
template<class SizesType >
void	reserve (const SizesType &reserveSizes)
void	resize (Index rows, Index cols)
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
Index	rows () 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
template<typename InputIterators >
void	setFromTriplets (const InputIterators &begin, const InputIterators &end)
void	setIdentity ()
void	setZero ()
Index	size () const
	SparseMatrix ()
	SparseMatrix (Index rows, Index cols)
template<typename OtherDerived >
	SparseMatrix (const SparseMatrixBase< OtherDerived > &other)
template<typename OtherDerived , unsigned int UpLo>
	SparseMatrix (const SparseSelfAdjointView< OtherDerived, UpLo > &other)
	SparseMatrix (const SparseMatrix &other)
template<typename OtherDerived >
	SparseMatrix (const ReturnByValue< OtherDerived > &other)
	Copy constructor with in-place evaluation.
void	swap (SparseMatrix &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< SparseMatrix< _Scalar, _Options, _Index > >	topLeftCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index > >	topLeftCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner ()
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner () const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topLeftCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index > >	topRightCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _Scalar, _Options, _Index > >	topRightCorner (Index cRows, Index cCols) const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner ()
const Block< const SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner () const
Block< SparseMatrix< _Scalar, _Options, _Index >, CRows, CCols >	topRightCorner (Index cRows, Index cCols)
const Block< const SparseMatrix< _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 < SparseMatrix< _Scalar, _Options, _Index >, Upper\|Lower >	twistedBy (const PermutationMatrix< Dynamic, Dynamic, Index > &perm) const
const CwiseUnaryOp < CustomUnaryOp, const SparseMatrix< _Scalar, _Options, _Index > >	unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
	Apply a unary operator coefficient-wise.
const CwiseUnaryView < CustomViewOp, const SparseMatrix< _Scalar, _Options, _Index > >	unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
void	uncompress ()
const Scalar *	valuePtr () const
Scalar *	valuePtr ()
	~SparseMatrix ()
Friends
const DenseSparseProductReturnType < OtherDerived, SparseMatrix < _Scalar, _Options, _Index > >::Type	operator* (const MatrixBase< OtherDerived > &lhs, const SparseMatrix< _Scalar, _Options, _Index > &rhs)

Constructor & Destructor Documentation

SparseMatrix ( ) [inline]

Default constructor yielding an empty 0 x 0 matrix

SparseMatrix	(	Index	rows,
		Index	cols
	)		`[inline]`

Constructs a rows x cols empty matrix

SparseMatrix ( const SparseMatrixBase< OtherDerived > & other ) [inline]

Constructs a sparse matrix from the sparse expression other

SparseMatrix ( const SparseSelfAdjointView< OtherDerived, UpLo > & other ) [inline]

Constructs a sparse matrix from the sparse selfadjoint view other

SparseMatrix ( const SparseMatrix< _Scalar, _Options, _Index > & other ) [inline]

Copy constructor (it performs a deep copy)

~SparseMatrix ( ) [inline]

Destructor

Member Function Documentation

const CwiseBinaryOp<CustomBinaryOp, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> binaryExpr	(	const Eigen::SparseMatrixBase< OtherDerived > &	other,
		const CustomBinaryOp &	func = `CustomBinaryOp()`
	)		const `[inline, inherited]`

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

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

Here is an example illustrating the use of custom functors:

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

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

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

Output:

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

See also:: class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()

Block<SparseMatrix< _Scalar, _Options, _Index > > block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

Output:

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

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

See also:: class Block, block(Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > > block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol
	)		`[inline, inherited]`

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

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

Parameters:

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

Example:

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

Output:

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

Note:

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

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		`[inline, inherited]`

Returns:: an expression of a block in *this.

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , BlockRows, BlockCols> block	(	Index	startRow,
		Index	startCol,
		Index	blockRows,
		Index	blockCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > > bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > > bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( ) [inline, inherited]

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner ( ) const [inline, inherited]

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomLeftCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > > bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > > bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( ) [inline, inherited]

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner ( ) const [inline, inherited]

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> bottomRightCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

RowsBlockXpr bottomRows ( Index n ) [inline, inherited]

Returns:: a block consisting of the bottom rows of *this.

Parameters:

n	the number of rows in the block

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

This is the const version of bottomRows(Index).

NRowsBlockXpr<N>::Type bottomRows ( Index n = N ) [inline, inherited]

Returns:: a block consisting of the bottom rows of *this.

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

internal::cast_return_type<SparseMatrix< _Scalar, _Options, _Index > ,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<SparseMatrix< _Scalar, _Options, _Index > >::Scalar, NewType>, const SparseMatrix< _Scalar, _Options, _Index > > >::type cast ( ) const [inline, inherited]

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

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

See also:: class CwiseUnaryOp

Scalar coeff	(	Index	row,
		Index	col
	)		const `[inline]`

Returns:: the value of the matrix at position i, j This function returns Scalar(0) if the element is an explicit zero

Scalar& coeffRef	(	Index	row,
		Index	col
	)		`[inline]`

Returns:: a non-const reference to the value of the matrix at position i, j

If the element does not exist then it is inserted via the insert(Index,Index) function which itself turns the matrix into a non compressed form if that was not the case.

This is a O(log(nnz_j)) operation (binary search) plus the cost of insert(Index,Index) function if the element does not already exist.

ColXpr col ( Index i ) [inline, inherited]

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

Example:

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

Output:

1 4 0
0 5 0
0 6 1

See also:: row(), class Block

Referenced by SparseMatrix< Scalar, RowMajor >::coeff(), and SparseMatrix< Scalar, RowMajor >::coeffRef().

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

This is the const version of col().

Index cols ( void ) const [inline]

Returns:: the number of columns of the matrix

Reimplemented from SparseMatrixBase< SparseMatrix< _Scalar, _Options, _Index > >.

Referenced by SparseMatrix< Scalar, RowMajor >::coeff(), SparseMatrix< Scalar, RowMajor >::coeffRef(), SparseQR< _MatrixType, _OrderingType >::cols(), SparseMatrix< Scalar, RowMajor >::conservativeResize(), SparseMatrix< Scalar, RowMajor >::insert(), SparseMatrix< Scalar, RowMajor >::resize(), and SparseMatrix< Scalar, RowMajor >::setIdentity().

ConjugateReturnType conjugate ( ) const [inline, inherited]

Returns:: an expression of the complex conjugate of *this.

See also:: adjoint()

void conservativeResize	(	Index	rows,
		Index	cols
	)		`[inline]`

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

See also:: resizeNonZeros(Index), reserve(), setZero()

const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > cwiseAbs ( ) const [inline, inherited]

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

Example:

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

Output:

2 4 6
5 1 0

See also:: cwiseAbs2()

const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > cwiseAbs2 ( ) const [inline, inherited]

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

Example:

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

Output:

 4 16 36
25  1  0

See also:: cwiseAbs()

const CwiseBinaryOp<std::equal_to<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> cwiseEqual ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

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

Example:

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

Output:

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

See also:: cwiseNotEqual(), isApprox(), isMuchSmallerThan()

const CwiseScalarEqualReturnType cwiseEqual ( const Scalar & s ) const [inline, inherited]

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

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

See also:: cwiseEqual(const MatrixBase<OtherDerived> &) const

const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > cwiseInverse ( ) const [inline, inherited]

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

Example:

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

Output:

  0.5     2     1
0.333     4     1

See also:: cwiseProduct()

const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> cwiseMax ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

Example:

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

Output:

4
3
4

See also:: class CwiseBinaryOp, min()

const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const ConstantReturnType> cwiseMax ( const Scalar & other ) const [inline, inherited]

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

See also:: class CwiseBinaryOp, min()

const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> cwiseMin ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

Example:

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

Output:

2
2
3

See also:: class CwiseBinaryOp, max()

const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const ConstantReturnType> cwiseMin ( const Scalar & other ) const [inline, inherited]

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

See also:: class CwiseBinaryOp, min()

const CwiseBinaryOp<std::not_equal_to<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> cwiseNotEqual ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

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

Example:

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

Output:

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

See also:: cwiseEqual(), isApprox(), isMuchSmallerThan()

const CwiseBinaryOp<internal::scalar_product_op<typename SparseMatrix< _Scalar, _Options, _Index > ::Scalar, typename OtherDerived ::Scalar >, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived > cwiseProduct ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

Example:

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

Output:

See also:: class CwiseBinaryOp, cwiseAbs2

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > , const OtherDerived> cwiseQuotient ( const Eigen::SparseMatrixBase< OtherDerived > & other ) const [inline, inherited]

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

Example:

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

Output:

 0.5
 1.5
1.33

See also:: class CwiseBinaryOp, cwiseProduct(), cwiseInverse()

const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > cwiseSqrt ( ) const [inline, inherited]

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

Example:

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

Output:

   1
1.41
   2

See also:: cwisePow(), cwiseSquare()

SparseMatrix< _Scalar, _Options, _Index > & derived ( ) [inline, inherited]

Returns:: a reference to the derived object

const SparseMatrix< _Scalar, _Options, _Index > & derived ( ) const [inline, inherited]

Returns:: a const reference to the derived object

const Diagonal<const SparseMatrix> diagonal ( ) const [inline]

Returns:: a const expression of the diagonal coefficients

const internal::eval<SparseMatrix< _Scalar, _Options, _Index > >::type eval ( ) const [inline, inherited]

Returns:: the matrix or vector obtained by evaluating this expression.

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

SegmentReturnType head ( Index n ) [inline, inherited]

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

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

Parameters:

n	the number of coefficients in the segment

Example:

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

Output:

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

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

See also:: class Block, block(Index,Index)

ConstSegmentReturnType head ( Index n ) const [inline, inherited]

This is the const version of head(Index).

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

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

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

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

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

const ImagReturnType imag ( ) const [inline, inherited]

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

See also:: real()

NonConstImagReturnType imag ( ) [inline, inherited]

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

See also:: real()

const Index* innerIndexPtr ( ) const [inline]

Returns:: a const pointer to the array of inner indices. This function is aimed at interoperability with other libraries.

See also:: valuePtr(), outerIndexPtr()

Index* innerIndexPtr ( ) [inline]

Returns:: a non-const pointer to the array of inner indices. This function is aimed at interoperability with other libraries.

See also:: valuePtr(), outerIndexPtr()

const Index* innerNonZeroPtr ( ) const [inline]

Returns:: a const pointer to the array of the number of non zeros of the inner vectors. This function is aimed at interoperability with other libraries.

Warning:: it returns the null pointer 0 in compressed mode

Index* innerNonZeroPtr ( ) [inline]

Returns:: a non-const pointer to the array of the number of non zeros of the inner vectors. This function is aimed at interoperability with other libraries.

Warning:: it returns the null pointer 0 in compressed mode

Index innerSize ( ) const [inline]

Returns:: the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major)

Reimplemented from SparseMatrixBase< SparseMatrix< _Scalar, _Options, _Index > >.

Scalar& insert	(	Index	row,
		Index	col
	)		`[inline]`

Returns:: a reference to a novel non zero coefficient with coordinates row x col. The non zero coefficient must not already exist.

If the matrix *this is in compressed mode, then *this is turned into uncompressed mode while reserving room for 2 non zeros per inner vector. It is strongly recommended to first call reserve(const SizesType &) to reserve a more appropriate number of elements per inner vector that better match your scenario.

This function performs a sorted insertion in O(1) if the elements of each inner vector are inserted in increasing inner index order, and in O(nnz_j) for a random insertion.

Referenced by SparseMatrix< Scalar, RowMajor >::coeffRef().

bool isCompressed ( ) const [inline]

Returns:: whether *this is in compressed form.

Referenced by SparseMatrix< Scalar, RowMajor >::insert(), SparseMatrix< Scalar, RowMajor >::makeCompressed(), and SparseMatrix< Scalar, RowMajor >::reserve().

bool isVector ( ) const [inline, inherited]

Returns:

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

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

See also:: rows(), cols(), IsVectorAtCompileTime.

ColsBlockXpr leftCols ( Index n ) [inline, inherited]

Returns:: a block consisting of the left columns of *this.

Parameters:

n	the number of columns in the block

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

This is the const version of leftCols(Index).

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

Returns:: a block consisting of the left columns of *this.

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

void makeCompressed ( ) [inline]

Turns the matrix into the compressed format.

Referenced by SparseMatrix< Scalar, RowMajor >::prune().

ColsBlockXpr middleCols	(	Index	startCol,
		Index	numCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

NColsBlockXpr<N>::Type middleCols	(	Index	startCol,
		Index	n = `N`
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

RowsBlockXpr middleRows	(	Index	startRow,
		Index	n
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

NRowsBlockXpr<N>::Type middleRows	(	Index	startRow,
		Index	n = `N`
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

using namespace Eigen;
using namespace std;

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

Output:

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

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

See also:: class Block, block(Index,Index,Index,Index)

ConstNRowsBlockXpr<N>::Type middleRows	(	Index	startRow,
		Index	n = `N`
	)		const `[inline, inherited]`

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

Index nonZeros ( ) const [inline]

Returns:: the number of non zero coefficients

Reimplemented from SparseMatrixBase< SparseMatrix< _Scalar, _Options, _Index > >.

const ScalarMultipleReturnType operator* ( const Scalar & scalar ) const [inline, inherited]

Returns:: an expression of *this scaled by the scalar factor scalar

const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const SparseMatrix< _Scalar, _Options, _Index > > operator* ( const std::complex< Scalar > & scalar ) const [inline, inherited]

Overloaded for efficient real matrix times complex scalar value

const SparseDenseProductReturnType<SparseMatrix< _Scalar, _Options, _Index > ,OtherDerived>::Type operator* ( const MatrixBase< OtherDerived > & other ) const [inline, inherited]

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

const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const SparseMatrix< _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 SparseMatrix< _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<SparseMatrix< _Scalar, _Options, _Index > >::Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > operator- ( ) const [inline, inherited]

Returns:: an expression of the opposite of *this

const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<SparseMatrix< _Scalar, _Options, _Index > >::Scalar>, const SparseMatrix< _Scalar, _Options, _Index > > operator/ ( const Scalar & scalar ) const [inline, inherited]

Returns:: an expression of *this divided by the scalar value scalar

const Index* outerIndexPtr ( ) const [inline]

Returns:: a const pointer to the array of the starting positions of the inner vectors. This function is aimed at interoperability with other libraries.

See also:: valuePtr(), innerIndexPtr()

Index* outerIndexPtr ( ) [inline]

Returns:: a non-const pointer to the array of the starting positions of the inner vectors. This function is aimed at interoperability with other libraries.

See also:: valuePtr(), innerIndexPtr()

Index outerSize ( ) const [inline]

Returns:: the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major)

Reimplemented from SparseMatrixBase< SparseMatrix< _Scalar, _Options, _Index > >.

Referenced by SparseMatrix< Scalar, RowMajor >::insert(), and SparseMatrix< Scalar, RowMajor >::resize().

void prune	(	const Scalar &	reference,
		const RealScalar &	epsilon = `NumTraits<RealScalar>::dummy_precision()`
	)		`[inline]`

Suppresses all nonzeros which are much smaller than reference under the tolerence epsilon

Referenced by SparseMatrix< Scalar, RowMajor >::prune().

void prune ( const KeepFunc & keep = KeepFunc() ) [inline]

Turns the matrix into compressed format, and suppresses all nonzeros which do not satisfy the predicate keep. The functor type KeepFunc must implement the following function:

 bool operator() (const Index& row, const Index& col, const Scalar& value) const;

See also:: prune(Scalar,RealScalar)

RealReturnType real ( ) const [inline, inherited]

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

See also:: imag()

NonConstRealReturnType real ( ) [inline, inherited]

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

See also:: imag()

void reserve ( Index reserveSize ) [inline]

Preallocates reserveSize non zeros.

Precondition: the matrix must be in compressed mode.

Referenced by SparseMatrix< Scalar, RowMajor >::insert().

void reserve ( const SizesType & reserveSizes ) [inline]

Preallocates reserveSize[j] non zeros for each column (resp. row) j.

This function turns the matrix in non-compressed mode

void resize	(	Index	rows,
		Index	cols
	)		`[inline]`

Resizes the matrix to a rows x cols matrix and initializes it to zero.

See also:: resizeNonZeros(Index), reserve(), setZero()

Referenced by SparseMatrix< Scalar, RowMajor >::conservativeResize(), and SparseMatrix< Scalar, RowMajor >::SparseMatrix().

ColsBlockXpr rightCols ( Index n ) [inline, inherited]

Returns:: a block consisting of the right columns of *this.

Parameters:

n	the number of columns in the block

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

This is the const version of rightCols(Index).

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

Returns:: a block consisting of the right columns of *this.

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

RowXpr row ( Index i ) [inline, inherited]

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

Example:

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

Output:

1 0 0
4 5 6
0 0 1

See also:: col(), class Block

Referenced by SparseMatrix< Scalar, RowMajor >::coeff(), and SparseMatrix< Scalar, RowMajor >::coeffRef().

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

This is the const version of row().

Index rows ( void ) const [inline]

Returns:: the number of rows of the matrix

Reimplemented from SparseMatrixBase< SparseMatrix< _Scalar, _Options, _Index > >.

Referenced by SparseMatrix< Scalar, RowMajor >::coeff(), SparseMatrix< Scalar, RowMajor >::coeffRef(), SparseMatrix< Scalar, RowMajor >::conservativeResize(), SparseMatrix< Scalar, RowMajor >::insert(), SparseMatrix< Scalar, RowMajor >::resize(), SparseQR< _MatrixType, _OrderingType >::rows(), and SparseMatrix< Scalar, RowMajor >::setIdentity().

SegmentReturnType segment	(	Index	start,
		Index	n
	)		`[inline, inherited]`

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

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

Parameters:

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

Example:

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

Output:

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

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

See also:: class Block, segment(Index)

ConstSegmentReturnType segment	(	Index	start,
		Index	n
	)		const `[inline, inherited]`

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

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

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

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

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

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

void setFromTriplets	(	const InputIterators &	begin,
		const InputIterators &	end
	)

Fill the matrix *this with the list of triplets defined by the iterator range begin - end.

A triplet is a tuple (i,j,value) defining a non-zero element. The input list of triplets does not have to be sorted, and can contains duplicated elements. In any case, the result is a sorted and compressed sparse matrix where the duplicates have been summed up. This is a O(n) operation, with n the number of triplet elements. The initial contents of *this is destroyed. The matrix *this must be properly resized beforehand using the SparseMatrix(Index,Index) constructor, or the resize(Index,Index) method. The sizes are not extracted from the triplet list.

The InputIterators value_type must provide the following interface:

 Scalar value() const; // the value
 Scalar row() const;   // the row index i
 Scalar col() const;   // the column index j

See for instance the Eigen::Triplet template class.

Here is a typical usage example:

    typedef Triplet<double> T;
    std::vector<T> tripletList;
    triplets.reserve(estimation_of_entries);
    for(...)
    {
      // ...
      tripletList.push_back(T(i,j,v_ij));
    }
    SparseMatrixType m(rows,cols);
    m.setFromTriplets(tripletList.begin(), tripletList.end());
    // m is ready to go!

Warning:: The list of triplets is read multiple times (at least twice). Therefore, it is not recommended to define an abstract iterator over a complex data-structure that would be expensive to evaluate. The triplets should rather be explicitely stored into a std::vector for instance.

void setIdentity ( ) [inline]

Sets *this to the identity matrix. This function also turns the matrix into compressed mode, and drop any reserved memory.

void setZero ( ) [inline]

Removes all non zeros but keep allocated memory

Index size ( ) const [inline, inherited]

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

See also:: rows(), cols().

Reimplemented from EigenBase< SparseMatrix< _Scalar, _Options, _Index > >.

void swap ( SparseMatrix< _Scalar, _Options, _Index > & other ) [inline]

Swaps the content of two sparse matrices of the same type. This is a fast operation that simply swaps the underlying pointers and parameters.

Referenced by SparseMatrix< Scalar, RowMajor >::swap().

SegmentReturnType tail ( Index n ) [inline, inherited]

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

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

Parameters:

n	the number of coefficients in the segment

Example:

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

Output:

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

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

See also:: class Block, block(Index,Index)

ConstSegmentReturnType tail ( Index n ) const [inline, inherited]

This is the const version of tail(Index).

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

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

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

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

This is the const version of tail<int>.

Block<SparseMatrix< _Scalar, _Options, _Index > > topLeftCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > > topLeftCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( ) [inline, inherited]

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner ( ) const [inline, inherited]

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topLeftCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > > topRightCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Parameters:

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > > topRightCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( ) [inline, inherited]

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

Template Parameters:

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

Example:

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

Output:

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

See also:: class Block, block<int,int>(Index,Index)

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner ( ) const [inline, inherited]

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

Block<SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner	(	Index	cRows,
		Index	cCols
	)		`[inline, inherited]`

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

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block

const Block<const SparseMatrix< _Scalar, _Options, _Index > , CRows, CCols> topRightCorner	(	Index	cRows,
		Index	cCols
	)		const `[inline, inherited]`

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

RowsBlockXpr topRows ( Index n ) [inline, inherited]

Returns:: a block consisting of the top rows of *this.

Parameters:

n	the number of rows in the block

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

This is the const version of topRows(Index).

NRowsBlockXpr<N>::Type topRows ( Index n = N ) [inline, inherited]

Returns:: a block consisting of the top rows of *this.

Template Parameters:

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

Parameters:

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

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

Example:

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

Output:

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

See also:: class Block, block(Index,Index,Index,Index)

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

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

SparseSymmetricPermutationProduct<SparseMatrix< _Scalar, _Options, _Index > ,Upper|Lower> twistedBy ( const PermutationMatrix< Dynamic, Dynamic, Index > & perm ) const [inline, inherited]

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

const CwiseUnaryOp<CustomUnaryOp, const SparseMatrix< _Scalar, _Options, _Index > > unaryExpr ( const CustomUnaryOp & func = CustomUnaryOp() ) const [inline, inherited]

Apply a unary operator coefficient-wise.

Parameters:

[in] func Functor implementing the unary operator

Template Parameters:

CustomUnaryOp Type of func

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

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

Example:

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

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

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

Output:

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

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

Example:

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

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

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

Output:

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

See also:: class CwiseUnaryOp, class CwiseBinaryOp

const CwiseUnaryView<CustomViewOp, const SparseMatrix< _Scalar, _Options, _Index > > unaryViewExpr ( const CustomViewOp & func = CustomViewOp() ) const [inline, inherited]

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

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

Example:

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

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

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

Output:

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

See also:: class CwiseUnaryOp, class CwiseBinaryOp

void uncompress ( ) [inline]

Turns the matrix into the uncompressed mode

const Scalar* valuePtr ( ) const [inline]

Returns:: a const pointer to the array of values. This function is aimed at interoperability with other libraries.

See also:: innerIndexPtr(), outerIndexPtr()

Scalar* valuePtr ( ) [inline]

Returns:: a non-const pointer to the array of values. This function is aimed at interoperability with other libraries.

See also:: innerIndexPtr(), outerIndexPtr()

Friends And Related Function Documentation

const DenseSparseProductReturnType<OtherDerived,SparseMatrix< _Scalar, _Options, _Index > >::Type operator*	(	const MatrixBase< OtherDerived > &	lhs,
		const SparseMatrix< _Scalar, _Options, _Index > &	rhs
	)		`[friend, inherited]`

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

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

SparseMatrix.h

Detailed Description

template<typename _Scalar, int _Options, typename _Index> class Eigen::SparseMatrix< _Scalar, _Options, _Index >

Public Member Functions

Friends

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename _Scalar, int _Options, typename _Index>
class Eigen::SparseMatrix< _Scalar, _Options, _Index >