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.

SparseChains encode non zero coefficients of (sparse) chains.

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

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

Has models
: CGAL::OSM::Sparse_chain<Ring, ChainTypeFlag>

See also: Ring; SparseMatrix

Types
typedef Ring	CoefficientType
	Type of coefficients stored in the matrix (a model of `Ring`).

typedef int	ChainTypeFlag
	Matrix and chain type (either OSM::ROW or OSM::COLUMN).

typedef unspecified_type	iterator
	SparseChain iterator type.

typedef unspecified_type	const_iterator
	SparseChain constant iterator type.

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

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

	SparseChain (const Sparse_chain &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
	Iterator to the end of the chain.

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

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

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

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

Sparse_chain &	*operator=** (const CoefficientType &lambda)
	Applies factor on each coefficients of `this`.

Sparse_chain	transpose ()
	Transposes a SparseChain.

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

Sparse_chain	operator- (const Sparse_chain &first, const Sparse_chain &second)
	Subtracts two chains together.

Sparse_chain	operator* (const CoefficientType &lambda, const Sparse_chain &chain)
	Applies factor on each coefficients.

Sparse_chain	operator* (const Sparse_chain &_chain, const CoefficientType &lambda)
	Applies factor on each coefficients.

Sparse_matrix< CoefficientType, COLUMN >	operator* (const Sparse_chain< CoefficientType, COLUMN > &column, const Sparse_chain< CoefficientType, ROW > &row)
	Performs matrix multiplication between two chains (COLUMN x ROW) and return a COLUMN matrix.

Sparse_matrix< CoefficientType, ROW >	operator% (const Sparse_chain< CoefficientType, COLUMN > &column, const Sparse_chain< CoefficientType, ROW > &row)
	Performs matrix multiplication between two chains (COLUMN x ROW) and return a ROW matrix.

CoefficientType	operator* (const Sparse_chain< CoefficientType, ROW > &row, const Sparse_chain< CoefficientType, COLUMN > &column)
	Performs dot product between two chains (ROW x COLUMN).

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

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

CoefficientType	get_coef (size_t index) const
	Gets the value of a coefficient of the chain.

void	set_coef (size_t index, CoefficientType 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.

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

Sparse_chain &	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.

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

Sparse_chain	operator/ (const Sparse_chain &chain, size_t indices)
	Gets a subchain from the chain.

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

Constructor & Destructor Documentation

◆ SparseChain() [1/2]

SparseChain::SparseChain ( size_t chainSize )

Creates new empty sparse chain of given size.

Constructor with size, initializes an empty sparse chain.

◆ SparseChain() [2/2]

SparseChain::SparseChain ( const Sparse_chain & other )

Creates new sparse chain by copy.

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

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 iterator to the end of the chain.

The function returns a constant iterator to the ending of the chain.

◆ end() [1/2]

const_iterator SparseChain::end ( ) const

noexcept

Constant iterator to the end of the chain.

The function returns a constant iterator to the ending of the chain.

◆ end() [2/2]

iterator SparseChain::end ( )

noexcept

Iterator to the end of the chain.

The function returns an iterator to the ending of the chain.

◆ nullify()

void SparseChain::nullify ( )

Removes all coefficients from the chain.

The function comes to set all coefficients to zero.

◆ operator+=()

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

Adds a chain to this.

Add a chain to this. Chains must have the same CoefficientType and the same ChainTypeFlag.

◆ operator-=()

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

Subtracts a chain from this.

Subtract a chain from this. Chains must have the same CoefficientType and the same ChainTypeFlag.

◆ operator/=() [1/2]

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

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]

Sparse_chain & 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 CoefficientType.

◆ transpose()

Sparse_chain SparseChain::transpose ( )

Transposes a SparseChain.

The result is a chain with ChainTypeFlag switched between COLUMN and ROW.

Friends And Related Function Documentation

◆ operator%

Sparse_matrix< CoefficientType, ROW > operator%	(	const Sparse_chain< CoefficientType, COLUMN > &	column,
		const Sparse_chain< CoefficientType, ROW > &	row
	)

friend

Performs matrix multiplication between two chains (COLUMN x ROW) and return a ROW matrix.

Generate a row-based matrix from the matrix multiplication and return it. Chains must have the same CoefficientType.

◆ operator* [1/2]

Sparse_matrix< CoefficientType, COLUMN > operator*	(	const Sparse_chain< CoefficientType, COLUMN > &	column,
		const Sparse_chain< CoefficientType, ROW > &	row
	)

friend

Performs matrix multiplication between two chains (COLUMN x ROW) and return a COLUMN matrix.

Generate a column-based matrix from the matrix multiplication and return it. Chains must have the same CoefficientType.

◆ operator* [2/2]

CoefficientType operator*	(	const Sparse_chain< CoefficientType, ROW > &	row,
		const Sparse_chain< CoefficientType, COLUMN > &	column
	)

friend

Performs dot product between two chains (ROW x COLUMN).

Chains must have the same CoefficientType.

◆ operator+

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

friend

Adds two chains together.

Add two chains and return the result in a new matrix. Chains must have the same CoefficientType and the same ChainTypeFlag.

◆ operator-

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

friend

Subtracts two chains together.

Subtract two chains and return the result in a new matrix. Chains must have the same CoefficientType and the same ChainTypeFlag.

◆ operator/ [1/2]

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

friend

Gets a subchain from the chain.

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

◆ operator/ [2/2]

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

friend

Gets a subchain 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() [1/2]

◆ SparseChain() [2/2]

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]