Ejemplo n.º 1
0
BitMatrix<dim> subquotientMap
(const Subquotient<dim>& source,
 const Subquotient<dim>& dest,
 const BitMatrix<dim>& m)
{
    assert(m.numColumns()==source.rank());
    assert(m.numRows()==dest.rank());

    BitMatrix<dim> result(dest.dimension(),0);

    // restrict m to source.space()
    for (RankFlags::iterator it=source.support().begin(); it(); ++it)
    {
        SmallBitVector v = m*source.space().basis(*it);
        assert(v.size()==dest.rank());

        /*
        // go to canonical representative modulo destination subspace
        dest.denominator().mod_reduce(v);
        assert(v.size()==dest.rank());

        // get coordinates in canonical basis
        v.slice(dest.space().support());  // express |v| in basis of |d_space|
        assert(v.size()==dest.space().dimension());

        v.slice(dest.support());
        */

        v=dest.toBasis(v);
        assert(v.size()==dest.dimension()); // dimension of the subquotient

        result.addColumn(v);
    }
    return result;
}
Ejemplo n.º 2
0
void Subspace<dim>::apply(const BitMatrix<dim>& r)
{
    assert(r.numColumns()==d_rank);

    BitVectorList<dim> b;
    b.reserve(dimension());

    for (size_t j = 0; j<dimension(); ++j)
    {
        b.push_back(r*d_basis[j]);
        assert(b.back().size()==r.numRows());
    }

    Subspace<dim> ns(b,r.numRows()); // construct (and normalize) new subspace
    swap(ns); // and install it in our place
}
Ejemplo n.º 3
0
/*!
  \brief Constructs the normalised subspace generated by the columns of
  a |BitMatrix|, i.e., the image of that matrix
*/
template<size_t dim> Subspace<dim>::
Subspace(const BitMatrix<dim>& M)
    : d_basis(M.image())
    , d_support()
    , d_rank(M.numRows())
{
// change |d_basis| to a normalised form, and set |d_support|:
    bitvector::Gauss_Jordan(d_support,d_basis);
}