atlas::subquotient::Subspace< dim > Class Template Reference

#include <Atlas.h>

Collaboration diagram for atlas::subquotient::Subspace< dim >:

Public Member Functions
	Subspace ()
	Subspace (size_t n)
	Subspace (const BitVectorList< dim > &, size_t)
	Constructs the normalised subspace generated by the collection of |BitVectors| |b|, each of which has rank |n|. More...
	Subspace (const BitMatrix< dim > &)
	Constructs the normalised subspace generated by the columns of a |BitMatrix|, i.e., the image of that matrix. More...
const BitVector< dim > &	basis (size_t j) const
const BitVectorList< dim > &	basis () const
size_t	dimension () const
const size_t	rank () const
const BitSet< dim > &	support () const
BitVectorList< dim >	basis_perp () const
BitSet< dim >	support_perp () const
BitVector< dim >	toBasis (BitVector< dim > v) const
	Expresses |v| in the subspace basis. More...
BitVector< dim >	fromBasis (const BitVector< dim > &v) const
	Interprets |v| in the subspace basis and returns external form. More...
bool	contains (const BitVector< dim > &v) const
bool	contains (const BitVectorList< dim > &m) const
BitVector< dim >	representative (const BitVector< dim > &) const
	Return canonical representative of |v| modulo our subspace. More...
BitVector< dim >	mod_image (const BitVector< dim > &w) const
void	mod_reduce (BitVector< dim > &w) const
void	apply (const BitMatrix< dim > &)
void	swap (Subspace &)

Private Attributes
BitVectorList< dim >	d_basis
	reduced echelon basis More...
BitSet< dim >	d_support
	pivot (leading nonzero bit) positions More...
unsigned short int	d_rank
	Dimension of the ambient vector space. More...

Constructor & Destructor Documentation

template<size_t dim>

atlas::subquotient::Subspace< dim >::Subspace ( )

inline

template<size_t dim>

atlas::subquotient::Subspace< dim >::Subspace ( size_t  n )

inlineexplicit

template<size_t dim>

atlas::subquotient::Subspace< dim >::Subspace	(	const BitVectorList< dim > &	b,
		size_t	n
	)

Constructs the normalised subspace generated by the collection of |BitVectors| |b|, each of which has rank |n|.

template<size_t dim>

atlas::subquotient::Subspace< dim >::Subspace

(

const BitMatrix< dim > &

M

)

Constructs the normalised subspace generated by the columns of a |BitMatrix|, i.e., the image of that matrix.

Member Function Documentation

template<size_t dim>

void atlas::subquotient::Subspace< dim >::apply

(

const BitMatrix< dim > &

r

)

Synopsis: applies |r| to our subspace, normalizing the resulting subspace.

Precondition: r is a matrix of the appropriate column size (it could go to a space of another dimension, even.)

template<size_t dim>

const BitVector<dim>& atlas::subquotient::Subspace< dim >::basis ( size_t  j ) const

inline

template<size_t dim>

const BitVectorList<dim>& atlas::subquotient::Subspace< dim >::basis ( ) const

inline

template<size_t dim>

BitVectorList< dim > atlas::subquotient::Subspace< dim >::basis_perp

(

)

const

template<size_t dim>

bool atlas::subquotient::Subspace< dim >::contains

(

const BitVector< dim > &

v

)

const

template<size_t dim>

bool atlas::subquotient::Subspace< dim >::contains

(

const BitVectorList< dim > &

m

)

const

template<size_t dim>

size_t atlas::subquotient::Subspace< dim >::dimension ( ) const

inline

template<size_t dim>

BitVector<dim> atlas::subquotient::Subspace< dim >::fromBasis ( const BitVector< dim > &  v ) const

inline

Interprets |v| in the subspace basis and returns external form.

template<size_t dim>

BitVector<dim> atlas::subquotient::Subspace< dim >::mod_image ( const BitVector< dim > &  w ) const

inline

template<size_t dim>

void atlas::subquotient::Subspace< dim >::mod_reduce ( BitVector< dim > &  w ) const

inline

template<size_t dim>

const size_t atlas::subquotient::Subspace< dim >::rank ( ) const

inline

template<size_t dim>

BitVector< dim > atlas::subquotient::Subspace< dim >::representative

(

const BitVector< dim > &

v

)

const

Return canonical representative of |v| modulo our subspace.

This representative is characterized by the vanishing of its bits in positions |d_support| (the leading bits of the canonical basis of our subspace). Note that we are making no reference to the space from which our subspace is divided out; this could be the whole space $(Z/2Z)^n$ (in any case |r| is expressed in its canonical basis) or some subspace containing our subspace.

The algorithm projects v onto the subspace, the result |pv| being expressed in the canonical basis of the subspace: the coordinates of pv are just the entries of |v| in the coordinates flagged by |d_support|. Then |w| is computed as the corresponding |BitVector| in $(Z/2Z)^n$, given by combining the canonical basis with coefficients from |pv|. Finally we set |r=v-w|.

template<size_t dim>

const BitSet<dim>& atlas::subquotient::Subspace< dim >::support ( ) const

inline

template<size_t dim>

BitSet<dim> atlas::subquotient::Subspace< dim >::support_perp ( ) const

inline

template<size_t dim>

void atlas::subquotient::Subspace< dim >::swap

(

Subspace< dim > &

source

)

template<size_t dim>

BitVector<dim> atlas::subquotient::Subspace< dim >::toBasis ( BitVector< dim >  v ) const

inline

Expresses |v| in the subspace basis.

Member Data Documentation

template<size_t dim>

BitVectorList<dim> atlas::subquotient::Subspace< dim >::d_basis

private

reduced echelon basis

template<size_t dim>

unsigned short int atlas::subquotient::Subspace< dim >::d_rank

private

Dimension of the ambient vector space.

template<size_t dim>

BitSet<dim> atlas::subquotient::Subspace< dim >::d_support

private

pivot (leading nonzero bit) positions

---

The documentation for this class was generated from the following files:

• /home/ran/atlas_project/latest_branch_07182016/sources/Atlas.h
• /home/ran/atlas_project/latest_branch_07182016/sources/structure/subquotient.h
• /home/ran/atlas_project/latest_branch_07182016/sources/structure/subquotient.cpp