A class to store and manipulate sparse vectors. More...

#include <sparse_vector.h>

Inheritance diagram for sparse_vector< BASIS, MAP >:

Public Types
typedef BASIS::RATIONAL	RATIONAL
	Import of the rational type from the BASIS class.
typedef MAP::key_type	KEY
	Import of the KEY type from the MAP class.
typedef MAP::mapped_type	SCALAR
	Import of the SCALAR type from the MAP class.
typedef MAP::iterator	iterator
	Import of the iterator type from the MAP type.
typedef MAP::const_iterator	const_iterator
	Import of the KEY constant iterator type from the MAP type.
Public Member Functions
void	swap (typename sparse_vector &rhs)
	Swap the vector instance controlled by *this with the one in the RHS.
	sparse_vector (void)
	Default constructor.
	sparse_vector (const sparse_vector &v)
	Copy constructor.
	sparse_vector (const KEY &k, const SCALAR &s=one)
	Unidimensional constructor.
sparse_vector	operator- (void) const
	Returns an instance of the additive inverse of the instance.
sparse_vector &	operator*= (const SCALAR &s)
	Multiplies the instance with scalar s.
Static Public Attributes
static const SCALAR	zero
	The zero scalar value.
static const SCALAR	one
	The +1 scalar value.
static const SCALAR	mone
	The -1 scalar value.
static BASIS	basis
	Static initialisation of the sparse_vector basis.

Detailed Description

template<class BASIS, class MAP>
class sparse_vector< BASIS, MAP >

A class to store and manipulate sparse vectors.

An instance of the sparse_vector class is just a MAP between KEY and SCALAR, with vector space operators. It is a vector of basis elements of type KEY, stored in a MAP class, associated to coefficients given by SCALAR instances. Each basis element refers to the static instance of type BASIS.

The MAP class must comes with a std::map<KEY, SCALAR> interface. The scalar type SCALAR correponds to MAP::mapped_type. By default, the MAP class is taken from the BASIS via the BASIS::MAP type, cf. forward declaration of the sparse_vector class in libalgebra.h.

The SCALAR type must comes with operators making it an associative algebra (non necessarily commutative) containing the integers (via a suitable constructor). Thus, operators *,+,- must be implemented.

There is a compatibility condition between the BASIS and MAP classes since the MAP::key_type type and the BASIS::KEY must be the same.