Definition

The concept SparseChain describes the requirements for sparse vectors (called sparse chains in homology) optimized for topological computations. More precisely, SparseChain provides all the operations on chains required by the SparseMatrix concept.

SparseChain encodes non zero coefficients of a sparse vector.

SparseChain can be either row or column vectors. The following constants, called StorageFormat, encode the direction of sparse chains (and sparse matrices).

CGAL::OSM::COLUMN for column-major chains and matrices (which is the default),
CGAL::OSM::ROW for row-major chains and matrices.

Has models
: CGAL::OSM::Sparse_chain<CoefficientRing, StorageFormat>

See also: IntegralDomainWithoutDivision; SparseMatrix

Types
typedef unspecified_type	Coefficient_ring
	Type of coefficients stored in the matrix (a model of `IntegralDomainWithoutDivision`).

typedef int	Storage_format
	Matrix and chain storage format (either CGAL::OSM::ROW or CGAL::OSM::COLUMN).

typedef unspecified_type	iterator
	Sparse chain iterator type.

typedef unspecified_type	const_iterator
	Sparse chain constant iterator type.

Creation, filling
	SparseChain ()
	Creates new empty sparse chain.

	SparseChain (size_t chainSize)
	Creates new empty sparse chain (ie. zero-chain) of given size.

	SparseChain (const SparseChain &other)
	Creates new sparse chain by copy.

SparseChain &	operator= (const SparseChain &other)
	Assigns to other chain.

Matrix informations and iterators
size_t	dimension () const
	Returns the dimension of the basis (that is, size of the chain).

iterator	begin () noexcept
	Iterator to the beginning of the chain.

const_iterator	begin () const noexcept
	Constant iterator to the beginning of the chain.

const_iterator	cbegin () const noexcept
	Constant iterator to the beginning of the chain.

iterator	end () noexcept
	Past-the-end iterator of the chain.

const_iterator	end () const noexcept
	Constant past-the-end iterator of the chain.

const_iterator	cend () const noexcept
	Constant past-the-end iterator of the chain.

Linear algebra operators
SparseChain &	operator+= (const SparseChain &_other)
	Adds a chain to `this`.

SparseChain &	operator-= (const SparseChain &_other)
	Subtracts a chain from `this`.

SparseChain &	*operator=** (const Coefficient_ring &lambda)
	Applies multiplication on each coefficient of `this`.

SparseChain	transpose ()
	Transposes a sparse chain.

SparseChain	operator+ (const SparseChain &first, const SparseChain &second)
	Adds two chains together.

SparseChain	operator- (const SparseChain &first, const SparseChain &second)
	Subtracts a chain from another chain.

SparseChain	operator* (const Coefficient_ring &lambda, const SparseChain &chain)
	Applies multiplication on each coefficient.

SparseChain	operator* (const SparseChain &_chain, const Coefficient_ring &lambda)
	Applies multiplication on each coefficient.

SparseMatrix	operator* (const SparseChain &column, const SparseChain &row)
	Performs matrix multiplication between a column chain and a row chain and returns a column-based matrix.

SparseMatrix	operator% (const Sparse_chain &column, const Sparse_chain &row)
	Performs matrix multiplication between a column chain and a row chain and returns a row-based matrix.

Coefficient_ring	operator* (const Sparse_chain &row, const Sparse_chain &column)
	Performs dot product between a row chain and a column chain.

Access and modifications
bool	operator== (const SparseChain &other_chain)
	Compares two chains.

Coefficient_ring	operator[] (size_t index)
	Gets the value of a coefficient of the chain.

Coefficient_ring	get_coefficient (size_t index) const
	Gets the value of a coefficient of the chain.

void	set_coefficient (size_t index, Coefficient_ring d)
	Sets a given coefficient of the chain.

bool	is_null (size_t index) const
	Checks if a coefficient of the chain is null.

bool	is_null () const
	Checks if the chain is null.

SparseChain &	operator/= (const std::vector< size_t > &indices)
	Restricts the chain to a sub-chain by removing indices.

SparseChain &	operator/= (size_t index)
	Restricts the chain to a sub-chain by removing a given index.

void	nullify ()
	Removes all coefficients from the chain.

bool	is_column () const
	Checks if chain is a column.

bool	is_row () const
	Checks if chain is a row.

SparseChain	operator/ (const SparseChain &chain, const std::vector< size_t > &indices)
	Gets a sub-chain from the chain.

SparseChain	operator/ (const SparseChain &chain, size_t indices)
	Gets a sub-chain from the chain.

Output
std::ostream &	operator<< (std::ostream &stream, const SparseChain &chain)
	Inserts `chain` in the output stream.

Constructor & Destructor Documentation

◆ SparseChain() [1/3]

SparseChain::SparseChain ( )

Creates new empty sparse chain.

Creates a sparse chain encoding an empty linear combination of cells.

◆ SparseChain() [2/3]

SparseChain::SparseChain ( size_t chainSize )

Creates new empty sparse chain (ie. zero-chain) of given size.

Constructor with size, initializes an empty sparse chain encoding a linear combination of cells with all coefficients null.

◆ SparseChain() [3/3]

SparseChain::SparseChain ( const SparseChain & other )

Creates new sparse chain by copy.

Copy constructor, initialize a sparse chain from an existing sparse chain of same storage format.

Member Function Documentation

◆ begin() [1/2]

const_iterator SparseChain::begin ( ) const

noexcept

Constant iterator to the beginning of the chain.

The function returns a constant iterator to the first non zero index.

◆ begin() [2/2]

iterator SparseChain::begin ( )

noexcept

Iterator to the beginning of the chain.

The function returns an iterator to the first non zero index.

◆ cbegin()

const_iterator SparseChain::cbegin ( ) const

noexcept

Constant iterator to the beginning of the chain.

The function returns a constant iterator to the first non zero index.

◆ cend()

const_iterator SparseChain::cend ( ) const

noexcept

Constant past-the-end iterator of the chain.

The function returns a constant iterator past the endi of the chain.

◆ end() [1/2]

const_iterator SparseChain::end ( ) const

noexcept

Constant past-the-end iterator of the chain.

The function returns a constant iterator past the end of the chain.

◆ end() [2/2]

iterator SparseChain::end ( )

noexcept

Past-the-end iterator of the chain.

The function returns an iterator past the end of the chain.

◆ nullify()

void SparseChain::nullify ( )

Removes all coefficients from the chain.

The function comes to set all coefficients to zero.

◆ operator+=()

SparseChain & SparseChain::operator+= ( const SparseChain & _other )

Adds a chain to this.

Add a chain to this. Chains must have the same Coefficient_ring and the same storage format.

◆ operator-=()

SparseChain & SparseChain::operator-= ( const SparseChain & _other )

Subtracts a chain from this.

Subtract a chain from this. Chains must have the same Coefficient_ring and the same storage format.

◆ operator/=() [1/2]

SparseChain & SparseChain::operator/= ( const std::vector< size_t > & indices )

Restricts the chain to a sub-chain by removing indices.

Removes all indices provided in the vector from the chain. Return a reference to the modified chain.

◆ operator/=() [2/2]

SparseChain & SparseChain::operator/= ( size_t index )

Restricts the chain to a sub-chain by removing a given index.

Removes the index provided from the chain. Return a reference to the modified chain.

◆ operator=()

SparseChain & SparseChain::operator= ( const SparseChain & other )

Assigns to other chain.

Assign to other chain coefficient-wise, equivalent to copying it.

SparseChain must have the same Coefficient_ring.

◆ transpose()

SparseChain SparseChain::transpose ( )

Transposes a sparse chain.

The result is a chain with storage format switched between column and row.

Friends And Related Function Documentation

◆ operator%

SparseMatrix operator%	(	const Sparse_chain &	column,
		const Sparse_chain &	row
	)

friend

Performs matrix multiplication between a column chain and a row chain and returns a row-based matrix.

Generate a row-based matrix from the matrix multiplication and return it.

Precondition: chains must have the same Coefficient_ring.; column.is_column() and row.is_row() must be true

◆ operator* [1/2]

Coefficient_ring operator*	(	const Sparse_chain &	row,
		const Sparse_chain &	column
	)

friend

Performs dot product between a row chain and a column chain.

Precondition: chains must have the same Coefficient_ring.; row.is_row() and column.is_column() must be true

◆ operator* [2/2]

SparseMatrix operator*	(	const SparseChain &	column,
		const SparseChain &	row
	)

friend

Performs matrix multiplication between a column chain and a row chain and returns a column-based matrix.

Generate a column-based matrix from the matrix multiplication and return it.

Precondition: chains must have the same Coefficient_ring.; column.is_column() and row.is_row() must be true

◆ operator+

SparseChain operator+	(	const SparseChain &	first,
		const SparseChain &	second
	)

friend

Adds two chains together.

Add two chains and return the result in a new matrix. Chains must have the same Coefficient_ring and the same storage format.

◆ operator-

SparseChain operator-	(	const SparseChain &	first,
		const SparseChain &	second
	)

friend

Subtracts a chain from another chain.

Subtract two chains and return the result in a new matrix. Chains must have the same Coefficient_ring and the same storage format.

◆ operator/ [1/2]

SparseChain operator/	(	const SparseChain &	chain,
		const std::vector< size_t > &	indices
	)

friend

Gets a sub-chain from the chain.

Return a new chain where all coefficients of indices provided in the vector are removed.

◆ operator/ [2/2]

SparseChain operator/	(	const SparseChain &	chain,
		size_t	indices
	)

friend

Gets a sub-chain from the chain.

Return a new chain where the coefficients at a given index is removed.

Definition

Types

Creation, filling

Matrix informations and iterators

Linear algebra operators

Access and modifications

Output

Constructor & Destructor Documentation

◆ SparseChain() [1/3]

◆ SparseChain() [2/3]

◆ SparseChain() [3/3]

Member Function Documentation

◆ begin() [1/2]

◆ begin() [2/2]

◆ cbegin()

◆ cend()

◆ end() [1/2]

◆ end() [2/2]

◆ nullify()

◆ operator+=()

◆ operator-=()

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ transpose()

Friends And Related Function Documentation

◆ operator%

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator+

◆ operator-

◆ operator/ [1/2]

◆ operator/ [2/2]