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Eigen
3.3.7
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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.
_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 . |
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
.
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 () | |
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const Map< const Array< Scalar, Dynamic, 1 > > | coeffs () const |
Map< Array< Scalar, Dynamic, 1 > > | coeffs () |
const StorageIndex * | innerIndexPtr () const |
StorageIndex * | innerIndexPtr () |
const StorageIndex * | innerNonZeroPtr () const |
StorageIndex * | innerNonZeroPtr () |
bool | isCompressed () const |
Index | nonZeros () const |
const StorageIndex * | outerIndexPtr () const |
StorageIndex * | outerIndexPtr () |
const Scalar * | valuePtr () const |
Scalar * | valuePtr () |
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const CwiseBinaryOp < CustomBinaryOp, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | binaryExpr (const Eigen::SparseMatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
BlockXpr | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const ConstBlockXpr | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
This is the const version of block(Index,Index,Index,Index). */. | |
FixedBlockXpr< NRows, NCols >::Type | block (Index startRow, Index startCol) |
const ConstFixedBlockXpr < NRows, NCols >::Type | block (Index startRow, Index startCol) const |
This is the const version of block<>(Index, Index). */. | |
FixedBlockXpr< NRows, NCols >::Type | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
const ConstFixedBlockXpr < NRows, NCols >::Type | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
This is the const version of block<>(Index, Index, Index, Index). | |
BlockXpr | bottomLeftCorner (Index cRows, Index cCols) |
const ConstBlockXpr | bottomLeftCorner (Index cRows, Index cCols) const |
This is the const version of bottomLeftCorner(Index, Index). | |
FixedBlockXpr< CRows, CCols >::Type | bottomLeftCorner () |
const ConstFixedBlockXpr < CRows, CCols >::Type | bottomLeftCorner () const |
This is the const version of bottomLeftCorner<int, int>(). | |
FixedBlockXpr< CRows, CCols >::Type | bottomLeftCorner (Index cRows, Index cCols) |
const ConstFixedBlockXpr < CRows, CCols >::Type | bottomLeftCorner (Index cRows, Index cCols) const |
This is the const version of bottomLeftCorner<int, int>(Index, Index). | |
BlockXpr | bottomRightCorner (Index cRows, Index cCols) |
const ConstBlockXpr | bottomRightCorner (Index cRows, Index cCols) const |
This is the const version of bottomRightCorner(Index, Index). | |
FixedBlockXpr< CRows, CCols >::Type | bottomRightCorner () |
const ConstFixedBlockXpr < CRows, CCols >::Type | bottomRightCorner () const |
This is the const version of bottomRightCorner<int, int>(). | |
FixedBlockXpr< CRows, CCols >::Type | bottomRightCorner (Index cRows, Index cCols) |
const ConstFixedBlockXpr < CRows, CCols >::Type | bottomRightCorner (Index cRows, Index cCols) const |
This is the const version of bottomRightCorner<int, int>(Index, Index). | |
RowsBlockXpr | bottomRows (Index n) |
ConstRowsBlockXpr | bottomRows (Index n) const |
This is the const version of bottomRows(Index). | |
NRowsBlockXpr< N >::Type | bottomRows (Index n=N) |
ConstNRowsBlockXpr< N >::Type | bottomRows (Index n=N) const |
This is the const version of bottomRows<int>(). | |
CastXpr< NewType >::Type | cast () const |
ColXpr | col (Index i) |
ConstColXpr | col (Index i) const |
This is the const version of col(). | |
Index | cols () const |
ConjugateReturnType | conjugate () const |
const CwiseAbsReturnType | cwiseAbs () const |
const CwiseAbs2ReturnType | cwiseAbs2 () const |
const CwiseBinaryOp < std::equal_to< Scalar > , const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | cwiseEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseScalarEqualReturnType | cwiseEqual (const Scalar &s) const |
const CwiseInverseReturnType | cwiseInverse () const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar, Scalar >, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | cwiseMax (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_max_op < Scalar, Scalar >, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const ConstantReturnType > | cwiseMax (const Scalar &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar, Scalar >, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | cwiseMin (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_min_op < Scalar, Scalar >, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const ConstantReturnType > | cwiseMin (const Scalar &other) const |
const CwiseBinaryOp < std::not_equal_to< Scalar > , const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | cwiseNotEqual (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_product_op < SparseMatrix< _Scalar, _Options, _StorageIndex > ::Scalar, OtherDerived::Scalar > , const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | cwiseProduct (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar >, const SparseMatrix < _Scalar, _Options, _StorageIndex >, const OtherDerived > | cwiseQuotient (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseSignReturnType | cwiseSign () const |
const CwiseSqrtReturnType | cwiseSqrt () const |
const internal::eval < SparseMatrix< _Scalar, _Options, _StorageIndex > >::type | eval () const |
SegmentReturnType | head (Index n) |
ConstSegmentReturnType | head (Index n) const |
This is the const version of head(Index). | |
FixedSegmentReturnType< N >::Type | head (Index n=N) |
ConstFixedSegmentReturnType< N > ::Type | head (Index n=N) const |
This is the const version of head<int>(). | |
const ImagReturnType | imag () const |
NonConstImagReturnType | imag () |
Index | innerSize () const |
bool | isVector () const |
ColsBlockXpr | leftCols (Index n) |
ConstColsBlockXpr | leftCols (Index n) const |
This is the const version of leftCols(Index). | |
NColsBlockXpr< N >::Type | leftCols (Index n=N) |
ConstNColsBlockXpr< N >::Type | leftCols (Index n=N) const |
This is the const version of leftCols<int>(). | |
ColsBlockXpr | middleCols (Index startCol, Index numCols) |
ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
This is the const version of middleCols(Index,Index). | |
NColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) |
ConstNColsBlockXpr< N >::Type | middleCols (Index startCol, Index n=N) const |
This is the const version of middleCols<int>(). | |
RowsBlockXpr | middleRows (Index startRow, Index n) |
ConstRowsBlockXpr | middleRows (Index startRow, Index n) const |
This is the const version of middleRows(Index,Index). | |
NRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) |
ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow, Index n=N) const |
This is the const version of middleRows<int>(). | |
const CwiseBinaryOp < internal::scalar_boolean_and_op, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | operator&& (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < internal::scalar_product_op < Scalar, T >, SparseMatrix < _Scalar, _Options, _StorageIndex >, Constant< T > > | operator* (const T &scalar) const |
const CwiseBinaryOp< sum < Scalar >, const SparseMatrix < _Scalar, _Options, _StorageIndex >, const OtherDerived > | operator+ (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const CwiseBinaryOp < difference< Scalar >, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | operator- (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
const NegativeReturnType | operator- () const |
const CwiseBinaryOp < internal::scalar_quotient_op < Scalar, T >, SparseMatrix < _Scalar, _Options, _StorageIndex >, Constant< T > > | operator/ (const T &scalar) const |
const CwiseBinaryOp < internal::scalar_boolean_or_op, const SparseMatrix< _Scalar, _Options, _StorageIndex > , const OtherDerived > | operator|| (const Eigen::SparseMatrixBase< OtherDerived > &other) const |
Index | outerSize () const |
RealReturnType | real () const |
NonConstRealReturnType | real () |
ColsBlockXpr | rightCols (Index n) |
ConstColsBlockXpr | rightCols (Index n) const |
This is the const version of rightCols(Index). | |
NColsBlockXpr< N >::Type | rightCols (Index n=N) |
ConstNColsBlockXpr< N >::Type | rightCols (Index n=N) const |
This is the const version of rightCols<int>(). | |
RowXpr | row (Index i) |
ConstRowXpr | row (Index i) const |
This is the const version of row(). */. | |
Index | rows () const |
SegmentReturnType | segment (Index start, Index n) |
ConstSegmentReturnType | segment (Index start, Index n) const |
This is the const version of segment(Index,Index). | |
FixedSegmentReturnType< N >::Type | segment (Index start, Index n=N) |
ConstFixedSegmentReturnType< N > ::Type | segment (Index start, Index n=N) const |
This is the const version of segment<int>(Index). | |
Index | size () const |
SegmentReturnType | tail (Index n) |
ConstSegmentReturnType | tail (Index n) const |
This is the const version of tail(Index). | |
FixedSegmentReturnType< N >::Type | tail (Index n=N) |
ConstFixedSegmentReturnType< N > ::Type | tail (Index n=N) const |
This is the const version of tail<int>. | |
BlockXpr | topLeftCorner (Index cRows, Index cCols) |
const ConstBlockXpr | topLeftCorner (Index cRows, Index cCols) const |
This is the const version of topLeftCorner(Index, Index). | |
FixedBlockXpr< CRows, CCols >::Type | topLeftCorner () |
const ConstFixedBlockXpr < CRows, CCols >::Type | topLeftCorner () const |
This is the const version of topLeftCorner<int, int>(). | |
FixedBlockXpr< CRows, CCols >::Type | topLeftCorner (Index cRows, Index cCols) |
const ConstFixedBlockXpr < CRows, CCols >::Type | topLeftCorner (Index cRows, Index cCols) const |
This is the const version of topLeftCorner<int, int>(Index, Index). | |
BlockXpr | topRightCorner (Index cRows, Index cCols) |
const ConstBlockXpr | topRightCorner (Index cRows, Index cCols) const |
This is the const version of topRightCorner(Index, Index). | |
FixedBlockXpr< CRows, CCols >::Type | topRightCorner () |
const ConstFixedBlockXpr < CRows, CCols >::Type | topRightCorner () const |
This is the const version of topRightCorner<int, int>(). | |
FixedBlockXpr< CRows, CCols >::Type | topRightCorner (Index cRows, Index cCols) |
const ConstFixedBlockXpr < CRows, CCols >::Type | topRightCorner (Index cRows, Index cCols) const |
This is the const version of topRightCorner<int, int>(Index, Index). | |
RowsBlockXpr | topRows (Index n) |
ConstRowsBlockXpr | topRows (Index n) const |
This is the const version of topRows(Index). | |
NRowsBlockXpr< N >::Type | topRows (Index n=N) |
ConstNRowsBlockXpr< N >::Type | topRows (Index n=N) const |
This is the const version of topRows<int>(). | |
SparseSymmetricPermutationProduct < SparseMatrix< _Scalar, _Options, _StorageIndex > , Upper|Lower > | twistedBy (const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &perm) const |
const CwiseUnaryOp < CustomUnaryOp, const SparseMatrix< _Scalar, _Options, _StorageIndex > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
Apply a unary operator coefficient-wise. More... | |
const CwiseUnaryView < CustomViewOp, const SparseMatrix< _Scalar, _Options, _StorageIndex > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
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Index | cols () const |
SparseMatrix< _Scalar, _Options, _StorageIndex > & | derived () |
const SparseMatrix< _Scalar, _Options, _StorageIndex > & | derived () const |
Index | rows () const |
Index | size () const |
Additional Inherited Members | |
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typedef internal::traits < SparseMatrix< _Scalar, _Options, _StorageIndex > >::StorageIndex | StorageIndex |
typedef Scalar | value_type |
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typedef Eigen::Index | Index |
The interface type of indices. More... | |
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SparseCompressedBase () | |
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Default constructor yielding an empty 0
x
0
matrix
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Constructs a rows x
cols empty matrix
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Constructs a sparse matrix from the sparse expression other
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Constructs a sparse matrix from the sparse selfadjoint view other
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Copy constructor (it performs a deep copy)
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Destructor
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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.
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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.
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SparseMatrix< _Scalar, _Options, _StorageIndex >::Scalar & Eigen::SparseMatrix< _Scalar, _Options, _StorageIndex >::insert | ( | Index | row, |
Index | col | ||
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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.
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Turns the matrix into the compressed format.
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Suppresses all nonzeros which are much smaller than reference under the tolerence epsilon
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Preallocates reserveSize non zeros.
Precondition: the matrix must be in compressed mode.
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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:
for i
in the [0,this->outerSize()[ range. Typical choices include std::vector<int>, Eigen::VectorXi, Eigen::VectorXi::Constant, etc.
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void Eigen::SparseMatrix< Scalar, _Options, _StorageIndex >::setFromTriplets | ( | const InputIterators & | begin, |
const InputIterators & | end | ||
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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:
See for instance the Eigen::Triplet template class.
Here is a typical usage example:
void Eigen::SparseMatrix< Scalar, _Options, _StorageIndex >::setFromTriplets | ( | const InputIterators & | begin, |
const InputIterators & | end, | ||
DupFunctor | dup_func | ||
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The same as setFromTriplets but when duplicates are met the functor dup_func is applied:
Here is a C++11 example keeping the latest entry only:
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Sets *this to the identity matrix. This function also turns the matrix into compressed mode, and drop any reserved memory.
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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
after resizing it.
internal::traits< SparseMatrix< _Scalar, _Options, _Index > >::Scalar Eigen::SparseMatrix< _Scalar, _Options, _Index >::sum | ( | ) | const |
Overloaded for performance
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Swaps the content of two sparse matrices of the same type. This is a fast operation that simply swaps the underlying pointers and parameters.
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Turns the matrix into the uncompressed mode
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