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Eigen  3.3.71
Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex > Class Template Reference

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
_Scalarthe scalar type, i.e. the type of the coefficients
_OptionsUnion of bit flags controlling the storage scheme. Currently the only possibility is ColMajor or RowMajor. The default is 0 which means column-major.
_StorageIndexthe 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 >:

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)
 
DiagonalReturnType diagonal ()
 
const ConstDiagonalReturnType diagonal () const
 
StorageIndex * innerIndexPtr ()
 
const StorageIndex * innerIndexPtr () const
 
StorageIndex * innerNonZeroPtr ()
 
const StorageIndex * innerNonZeroPtr () const
 
Index innerSize () const
 
Scalar & insert (Index row, Index col)
 
bool isCompressed () const
 
void makeCompressed ()
 
Index nonZeros () const
 
StorageIndex * outerIndexPtr ()
 
const StorageIndex * outerIndexPtr () const
 
Index outerSize () const
 
template<typename KeepFunc >
void prune (const KeepFunc &keep=KeepFunc())
 
void prune (const Scalar &reference, const RealScalar &epsilon=NumTraits< RealScalar >::dummy_precision())
 
template<class SizesType >
void reserve (const SizesType &reserveSizes)
 
void reserve (Index reserveSize)
 
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 ()
 
template<typename OtherDerived >
 SparseMatrix (const DiagonalBase< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 
template<typename OtherDerived >
 SparseMatrix (const ReturnByValue< OtherDerived > &other)
 Copy constructor with in-place evaluation.
 
 SparseMatrix (const SparseMatrix &other)
 
template<typename OtherDerived >
 SparseMatrix (const SparseMatrixBase< OtherDerived > &other)
 
template<typename OtherDerived , unsigned int UpLo>
 SparseMatrix (const SparseSelfAdjointView< OtherDerived, UpLo > &other)
 
 SparseMatrix (Index rows, Index cols)
 
Scalar sum () const
 
void swap (SparseMatrix &other)
 
void uncompress ()
 
Scalar * valuePtr ()
 
const Scalar * valuePtr () const
 
 ~SparseMatrix ()
 
- Public Member Functions inherited from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >
Map< Array< Scalar, Dynamic, 1 > > coeffs ()
 
const Map< const Array< Scalar, Dynamic, 1 > > coeffs () const
 
StorageIndex * innerIndexPtr ()
 
const StorageIndex * innerIndexPtr () const
 
StorageIndex * innerNonZeroPtr ()
 
const StorageIndex * innerNonZeroPtr () const
 
bool isCompressed () const
 
Index nonZeros () const
 
StorageIndex * outerIndexPtr ()
 
const StorageIndex * outerIndexPtr () const
 
Scalar * valuePtr ()
 
const Scalar * valuePtr () const
 

Additional Inherited Members

- Protected Member Functions inherited from Eigen::SparseCompressedBase< SparseMatrix< _Scalar, _Options, _StorageIndex > >
 SparseCompressedBase ()
 

Constructor & Destructor Documentation

◆ SparseMatrix() [1/5]

template<typename _Scalar , int _Options, typename _StorageIndex >
Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::SparseMatrix ( )
inline

Default constructor yielding an empty 0 x 0 matrix

◆ SparseMatrix() [2/5]

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

◆ SparseMatrix() [3/5]

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

◆ SparseMatrix() [4/5]

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

◆ SparseMatrix() [5/5]

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)

◆ ~SparseMatrix()

template<typename _Scalar , int _Options, typename _StorageIndex >
Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::~SparseMatrix ( )
inline

Destructor

Member Function Documentation

◆ coeff()

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

◆ coeffRef()

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.

◆ cols()

template<typename _Scalar , int _Options, typename _StorageIndex >
Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::cols ( ) const
inline
Returns
the number of columns of the matrix

◆ conservativeResize()

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()

◆ diagonal() [1/2]

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.

◆ diagonal() [2/2]

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.

◆ innerIndexPtr() [1/2]

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()

◆ innerIndexPtr() [2/2]

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()

◆ innerNonZeroPtr() [1/2]

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

◆ innerNonZeroPtr() [2/2]

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

◆ innerSize()

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)

◆ insert()

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.

◆ isCompressed()

template<typename _Scalar , int _Options, typename _StorageIndex >
bool Eigen::SparseCompressedBase::isCompressed
inline
Returns
whether *this is in compressed form.

◆ makeCompressed()

template<typename _Scalar , int _Options, typename _StorageIndex >
void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::makeCompressed ( )
inline

Turns the matrix into the compressed format.

◆ nonZeros()

template<typename _Scalar , int _Options, typename _StorageIndex >
Index Eigen::SparseCompressedBase::nonZeros
inline
Returns
the number of non zero coefficients

◆ outerIndexPtr() [1/2]

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()

◆ outerIndexPtr() [2/2]

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()

◆ outerSize()

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)

◆ prune() [1/2]

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)

◆ prune() [2/2]

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

◆ reserve() [1/2]

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.

◆ reserve() [2/2]

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.

◆ resize()

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()

◆ rows()

template<typename _Scalar , int _Options, typename _StorageIndex >
Index Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::rows ( ) const
inline
Returns
the number of rows of the matrix

◆ setFromTriplets() [1/2]

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.

◆ setFromTriplets() [2/2]

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; });

◆ setIdentity()

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.

◆ setZero()

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()

◆ sum()

template<typename _Scalar , int _Options, typename _Index >
internal::traits< SparseMatrix< _Scalar, _Options, _Index > >::Scalar Eigen::SparseMatrix< _Scalar, _Options, _Index >::sum

Overloaded for performance

◆ swap()

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.

◆ uncompress()

template<typename _Scalar , int _Options, typename _StorageIndex >
void Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::uncompress ( )
inline

Turns the matrix into the uncompressed mode

◆ valuePtr() [1/2]

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()

◆ valuePtr() [2/2]

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()

The documentation for this class was generated from the following files:
Eigen::SparseMatrix::cols
Index cols() const
Definition: SparseMatrix.h:138
Eigen::PlainObjectBase::data
const Scalar * data() const
Definition: PlainObjectBase.h:255
Eigen::SparseMatrix::rows
Index rows() const
Definition: SparseMatrix.h:136
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33