Detailed Description

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

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.
_StorageIndex	the type of the indices. It has to be a signed type (e.g., short, int, std::ptrdiff_t). Default is `int`.

Warning:: In Eigen 3.2, the undocumented type SparseMatrix::Index was improperly defined as the storage index type (e.g., int), whereas it is now (starting from Eigen 3.3) deprecated and always defined as Eigen::Index. Codes making use of SparseMatrix::Index, might thus likely have to be changed to use SparseMatrix::StorageIndex instead.

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

Inheritance diagram for Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >:

List of all members.

Public Member Functions
Scalar	coeff (Index row, Index col) const
Scalar &	coeffRef (Index row, Index col)
Index	cols () const
void	conservativeResize (Index rows, Index cols)
const ConstDiagonalReturnType	diagonal () const
DiagonalReturnType	diagonal ()
const StorageIndex *	innerIndexPtr () const
StorageIndex *	innerIndexPtr ()
const StorageIndex *	innerNonZeroPtr () const
StorageIndex *	innerNonZeroPtr ()
Index	innerSize () const
Scalar &	insert (Index row, Index col)
void	makeCompressed ()
const StorageIndex *	outerIndexPtr () const
StorageIndex *	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())
void	reserve (Index reserveSize)
template<class SizesType >
void	reserve (const SizesType &reserveSizes)
void	resize (Index rows, Index cols)
Index	rows () const
template<typename InputIterators >
void	setFromTriplets (const InputIterators &begin, const InputIterators &end)
template<typename InputIterators , typename DupFunctor >
void	setFromTriplets (const InputIterators &begin, const InputIterators &end, DupFunctor dup_func)
void	setIdentity ()
void	setZero ()
	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.
template<typename OtherDerived >
	SparseMatrix (const DiagonalBase< OtherDerived > &other)
	Copy constructor with in-place evaluation.
Scalar	sum () const
void	swap (SparseMatrix &other)
void	uncompress ()
const Scalar *	valuePtr () const
Scalar *	valuePtr ()
	~SparseMatrix ()

Constructor & Destructor Documentation

template<typename _Scalar, int _Options, typename _StorageIndex>

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix ( ) [inline]

Default constructor yielding an empty 0 x 0 matrix

template<typename _Scalar, int _Options, typename _StorageIndex>

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix	(	Index	rows,
		Index	cols
	)		`[inline]`

Constructs a rows x cols empty matrix

template<typename _Scalar, int _Options, typename _StorageIndex>

template<typename OtherDerived >

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix ( const SparseMatrixBase< OtherDerived > & other ) [inline]

Constructs a sparse matrix from the sparse expression other

template<typename _Scalar, int _Options, typename _StorageIndex>

template<typename OtherDerived , unsigned int UpLo>

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix ( const SparseSelfAdjointView< OtherDerived, UpLo > & other ) [inline]

Constructs a sparse matrix from the sparse selfadjoint view other

template<typename _Scalar, int _Options, typename _StorageIndex>

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix ( const SparseMatrix< _Scalar, _Options, _StorageIndex > & other ) [inline]

Copy constructor (it performs a deep copy)

template<typename _Scalar, int _Options, typename _StorageIndex>

Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::~SparseMatrix ( ) [inline]

Destructor

Member Function Documentation

template<typename _Scalar, int _Options, typename _StorageIndex>

Scalar Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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

template<typename _Scalar, int _Options, typename _StorageIndex>

Scalar& Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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.

template<typename _Scalar, int _Options, typename _StorageIndex>

Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::cols ( void ) const [inline]

Returns:: the number of columns of the matrix

Reimplemented from Eigen::SparseMatrixBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::conservativeResize	(	Index	rows,
		Index	cols
	)		`[inline]`

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

If the sizes of the matrix are decreased, then the matrix is turned to uncompressed-mode and the storage of the out of bounds coefficients is kept and reserved. Call makeCompressed() to pack the entries and squeeze extra memory.

See also:: reserve(), setZero(), makeCompressed()

template<typename _Scalar, int _Options, typename _StorageIndex>

const ConstDiagonalReturnType Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::diagonal ( ) const [inline]

Returns:: a const expression of the diagonal coefficients.

template<typename _Scalar, int _Options, typename _StorageIndex>

DiagonalReturnType Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::diagonal ( ) [inline]

Returns:: a read-write expression of the diagonal coefficients.

Warning:: If the diagonal entries are written, then all diagonal entries must already exist, otherwise an assertion will be raised.

template<typename _Scalar, int _Options, typename _StorageIndex>

const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::innerSize ( ) const [inline]

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

Reimplemented from Eigen::SparseMatrixBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar , int _Options, typename _StorageIndex >

SparseMatrix< _Scalar, _Options, _StorageIndex >::Scalar & Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::insert	(	Index	row,
		Index	col
	)

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 x this->innerSize() non zeros if reserve(Index) has not been called earlier. In this case, the insertion procedure is optimized for a sequential insertion mode where elements are assumed to be inserted by increasing outer-indices.

If that's not the case, then it is strongly recommended to either use a triplet-list to assemble the matrix, or to first call reserve(const SizesType &) to reserve the appropriate number of non-zero elements per inner vector.

Assuming memory has been appropriately reserved, 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.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::makeCompressed ( ) [inline]

Turns the matrix into the compressed format.

template<typename _Scalar, int _Options, typename _StorageIndex>

const StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

StorageIndex* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::outerSize ( ) const [inline]

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

Reimplemented from Eigen::SparseMatrixBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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

template<typename _Scalar, int _Options, typename _StorageIndex>

template<typename KeepFunc >

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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)

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::reserve ( Index reserveSize ) [inline]

Preallocates reserveSize non zeros.

Precondition: the matrix must be in compressed mode.

template<typename _Scalar, int _Options, typename _StorageIndex>

template<class SizesType >

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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.

The type SizesType must expose the following interface:

        typedef value_type;
        const value_type& operator[](i) const;

for i in the [0,this->outerSize()[ range. Typical choices include std::vector<int>, Eigen::VectorXi, Eigen::VectorXi::Constant, etc.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::resize	(	Index	rows,
		Index	cols
	)		`[inline]`

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

This function does not free the currently allocated memory. To release as much as memory as possible, call

 mat.data().squeeze();

after resizing it.

See also:: reserve(), setZero()

template<typename _Scalar, int _Options, typename _StorageIndex>

Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::rows ( void ) const [inline]

Returns:: the number of rows of the matrix

Reimplemented from Eigen::SparseMatrixBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename Scalar , int _Options, typename _StorageIndex >

template<typename InputIterators >

void Eigen::SparseMatrix< Scalar, _Options, _StorageIndex >::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.

template<typename Scalar , int _Options, typename _StorageIndex >

template<typename InputIterators , typename DupFunctor >

void Eigen::SparseMatrix< Scalar, _Options, _StorageIndex >::setFromTriplets	(	const InputIterators &	begin,
		const InputIterators &	end,
		DupFunctor	dup_func
	)

The same as setFromTriplets but when duplicates are met the functor dup_func is applied:

 value = dup_func(OldValue, NewValue)

Here is a C++11 example keeping the latest entry only:

 mat.setFromTriplets(triplets.begin(), triplets.end(), [] (const Scalar&,const Scalar &b) { return b; });

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::setIdentity ( ) [inline]

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

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::setZero ( ) [inline]

Removes all non zeros but keep allocated memory

This function does not free the currently allocated memory. To release as much as memory as possible, call

 mat.data().squeeze();

after resizing it.

See also:: resize(Index,Index), data()

template<typename _Scalar , int _Options, typename _Index >

internal::traits< SparseMatrix< _Scalar, _Options, _Index > >::Scalar Eigen::SparseMatrix< _Scalar, _Options, _Index >::sum ( ) const

Overloaded for performance

Reimplemented from Eigen::SparseMatrixBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::swap ( SparseMatrix< _Scalar, _Options, _StorageIndex > & 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.

template<typename _Scalar, int _Options, typename _StorageIndex>

void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::uncompress ( ) [inline]

Turns the matrix into the uncompressed mode

template<typename _Scalar, int _Options, typename _StorageIndex>

const Scalar* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

template<typename _Scalar, int _Options, typename _StorageIndex>

Scalar* Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::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()

Reimplemented from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >.

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

Detailed Description

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

Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation

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