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

Subspace of (Z/2Z)^d_rank. More...

#include <subquotient.h>

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

[legend]List of all members.

Public Member Functions
	Subspace ()
	Subspace (size_t n)
	Subspace (const bitvector::BitVectorList< dim > &, size_t)
	Constructs the normal subspace generated by the collection of |BitVectors| |b|, each of which has rank |n|.
	~Subspace ()
const bitvector::BitVector< dim > &	basis (size_t j) const
const bitvector::BitVectorList< dim > &	basis () const
size_t	dimension () const
const size_t	rank () const
const bitset::BitSet< dim > &	support () const
bitvector::BitVector< dim >	toBasis (bitvector::BitVector< dim > v) const
	Expresses |v| in the subspace basis.
bitvector::BitVector< dim >	fromBasis (bitvector::BitVector< dim > v) const
	Interprets |v| in the subspace basis and returns external form.
bool	contains (const bitvector::BitVector< dim > &v) const
bool	contains (const bitvector::BitVectorList< dim > &m) const
void	representative (bitvector::BitVector< dim > &, const bitvector::BitVector< dim > &) const
	Put in |r| the canonical representative of |v| modulo our subspace.
void	mod_reduce (bitvector::BitVector< dim > &w) const
bitvector::BitVector< dim >	mod_image (const bitvector::BitVector< dim > &w) const
void	apply (const bitvector::BitMatrix< dim > &)
void	swap (Subspace &)
Private Attributes
size_t	d_rank
	Dimension of the ambient vector space.
bitvector::BitVectorList< dim >	d_basis
	Basis of our |Subspace| in reduced form.
bitset::BitSet< dim >	d_support
	|BitSet| flagging the positions of the leading nonzero bits in the basis of our |Subspace|.

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Detailed Description

template<size_t dim>
class atlas::subquotient::Subspace< dim >

Subspace of (Z/2Z)^d_rank.

Elements of the vector space are |BitVector|s of capacity |dim| and actual size |d_rank|. The subspace is recorded by its (unique) ordered canonical basis |d_basis|. This means its vectors are reduced (in the sense of row-reduced matrices); that is (in the binary case) in the position of the leading (nonzero) bit of each vector, the other vectors heve a bit $0$, and the vectors are ordered by increasing position of their leading bit.

The locations of the leading bits are flagged by the |BitSet| |d_support| (of capacity |d_rank|); the number of set bits in |d_support| is equal to the dimension |d_basis.size()| of the |Subspace|.

Definition at line 58 of file subquotient.h.

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Constructor & Destructor Documentation

template<size_t dim> atlas::subquotient::Subspace< dim >::Subspace (   )  [inline]

Definition at line 82 of file subquotient.h.

template<size_t dim> atlas::subquotient::Subspace< dim >::Subspace (  size_t  n  )  [inline, explicit]

Definition at line 84 of file subquotient.h.

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

Constructs the normal subspace generated by the collection of |BitVectors| |b|, each of which has rank |n|. Definition at line 35 of file subquotient_def.h. References atlas::subquotient::Subspace< dim >::d_basis, atlas::subquotient::Subspace< dim >::d_support, and atlas::dynkin::normalize().

template<size_t dim> atlas::subquotient::Subspace< dim >::~Subspace (   )  [inline]

Definition at line 88 of file subquotient.h.

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Member Function Documentation

template<size_t dim> void atlas::subquotient::Subspace< dim >::apply (  const bitvector::BitMatrix< dim > &  r  )

Synopsis: applies |r| to our subspace, normalizing the resulting subspace. Precondition: r is a matrix of the appropriate size (it could go to a space of another dimension, even.) Definition at line 91 of file subquotient_def.h. References atlas::bitvector::BitMatrix< dim >::apply(), atlas::bitvector::BitMatrix< dim >::numColumns(), atlas::bitvector::BitMatrix< dim >::numRows(), and atlas::subquotient::Subspace< dim >::swap().

template<size_t dim> const bitvector::BitVectorList<dim>& atlas::subquotient::Subspace< dim >::basis (   )  const [inline]

Definition at line 98 of file subquotient.h.

template<size_t dim> const bitvector::BitVector<dim>& atlas::subquotient::Subspace< dim >::basis (  size_t  j  )  const [inline]

Definition at line 93 of file subquotient.h.

template<size_t dim> bool atlas::subquotient::Subspace< dim >::contains (  const bitvector::BitVectorList< dim > &  m  )  const [inline]

Definition at line 143 of file subquotient.h.

template<size_t dim> bool atlas::subquotient::Subspace< dim >::contains (  const bitvector::BitVector< dim > &  v  )  const [inline]

Definition at line 140 of file subquotient.h. References atlas::bitvector::BitVector< dim >::isZero().

template<size_t dim> size_t atlas::subquotient::Subspace< dim >::dimension (   )  const [inline]

Definition at line 102 of file subquotient.h. Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::dimension(), atlas::subquotient::Subquotient< constants::RANK_MAX >::fromBasis(), and atlas::subquotient::Subquotient< constants::RANK_MAX >::toBasis().

template<size_t dim> bitvector::BitVector<dim> atlas::subquotient::Subspace< dim >::fromBasis (  bitvector::BitVector< dim >  v  )  const [inline]

Interprets |v| in the subspace basis and returns external form. Definition at line 129 of file subquotient.h. References atlas::bitvector::combination(), atlas::bitvector::BitVector< dim >::data(), atlas::lietype::rank(), and atlas::bitvector::BitVector< dim >::size(). Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::fromBasis().

template<size_t dim> bitvector::BitVector<dim> atlas::subquotient::Subspace< dim >::mod_image (  const bitvector::BitVector< dim > &  w  )  const [inline]

Definition at line 159 of file subquotient.h. Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::mod_image().

template<size_t dim> void atlas::subquotient::Subspace< dim >::mod_reduce (  bitvector::BitVector< dim > &  w  )  const [inline]

Definition at line 156 of file subquotient.h. Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::mod_reduce().

template<size_t dim> const size_t atlas::subquotient::Subspace< dim >::rank (   )  const [inline]

Definition at line 106 of file subquotient.h. Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::rank().

template<size_t dim> void atlas::subquotient::Subspace< dim >::representative (  bitvector::BitVector< dim > &  r, const bitvector::BitVector< dim > &  v )  const

Put in |r| the canonical representative of |v| modulo our subspace. This |r| 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 pv in the subspace expressed in the canonical basis of the subspace. The coordinates of pv are the entries of v in the coordinates flagged by d_support. Then w is the BitVector in (Z/2Z)^n given by combining the canonical basis with coefficients pv. Finally r is equal to v-w. Definition at line 66 of file subquotient_def.h. References atlas::bitvector::combination(), and atlas::lietype::rank(). Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::representative().

template<size_t dim> const bitset::BitSet<dim>& atlas::subquotient::Subspace< dim >::support (   )  const [inline]

Definition at line 110 of file subquotient.h. Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::significantBits().

template<size_t dim> void atlas::subquotient::Subspace< dim >::swap (  Subspace< dim > &   )

Definition at line 115 of file subquotient_def.h. References atlas::subquotient::Subspace< dim >::d_basis, atlas::subquotient::Subspace< dim >::d_rank, atlas::subquotient::Subspace< dim >::d_support, atlas::bitset::BitSet< n >::swap(), and atlas::bitvector::BitMatrix< dim >::swap(). Referenced by atlas::subquotient::Subspace< dim >::apply().

template<size_t dim> bitvector::BitVector<dim> atlas::subquotient::Subspace< dim >::toBasis (  bitvector::BitVector< dim >  v  )  const [inline]

Expresses |v| in the subspace basis. Definition at line 117 of file subquotient.h. References atlas::bitvector::BitVector< dim >::size(), and atlas::bitvector::BitVector< dim >::slice(). Referenced by atlas::subquotient::Subquotient< constants::RANK_MAX >::toBasis().

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Member Data Documentation

template<size_t dim> bitvector::BitVectorList<dim> atlas::subquotient::Subspace< dim >::d_basis [private]

Basis of our |Subspace| in reduced form. Definition at line 70 of file subquotient.h. Referenced by atlas::subquotient::Subspace< dim >::Subspace(), and atlas::subquotient::Subspace< dim >::swap().

template<size_t dim> size_t atlas::subquotient::Subspace< dim >::d_rank [private]

Dimension of the ambient vector space. Definition at line 65 of file subquotient.h. Referenced by atlas::subquotient::Subspace< dim >::swap().

template<size_t dim> bitset::BitSet<dim> atlas::subquotient::Subspace< dim >::d_support [private]

|BitSet| flagging the positions of the leading nonzero bits in the basis of our |Subspace|. Definition at line 75 of file subquotient.h. Referenced by atlas::subquotient::Subspace< dim >::Subspace(), and atlas::subquotient::Subspace< dim >::swap().

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

• /home/r0/dav/atlas.dir/atlas3/sources/structure/subquotient.h
• /home/r0/dav/atlas.dir/atlas3/sources/structure/subquotient_def.h

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