/usr/include/linbox/solutions/smith-form.h is in liblinbox-dev 1.3.2-1.1build2.
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*
*
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*/
#ifndef __LINBOX_smith_form_H
#define __LINBOX_smith_form_H
#include <list>
#include <vector>
#include "linbox/util/error.h"
#include "linbox/algorithms/matrix-hom.h"
#ifdef __LINBOX_HAVE_NTL
#include "linbox/algorithms/smith-form-adaptive.h"
#endif
#include "linbox/field/PID-integer.h"
//#include "linbox/algorithms/smith-form.h"
//#include "linbox/algorithms/smith-form-local.h"
namespace LinBox
{
template<class I1, class Lp>
void distinct (I1 a, I1 b, Lp& c)
{ typename I1::value_type e;
size_t count = 0;
if (a != b) {e = *a; ++a; count = 1;}
else return;
while (a != b)
{ if (*a == e)
++count;
else
{ c.push_back(typename Lp::value_type(e, count));
e = *a; count = 1;
}
++a;
}
c.push_back(typename Lp::value_type(e, count));
return;
}
/** Compute the Smith form of A.
* \ingroup solutions
*
* The Smith form of a linear operator A, represented as a
* black box, is computed over a representation of \f$Z\f$ or \f$Z_m\f$.
*
* @param[out] S a list of invariant/repcount pairs.
* @param A Matrix of which to compute the Smith form
* @param M may be a \p Method::Hybrid (default), which uses the
algorithms/smith-form-adaptive.
@todo Other methods will be provided later.
For now see the examples/smith.C
for ways to call other smith form algorithms.
*/
template <class Output, class Blackbox, class MyMethod>
Output &smithForm(Output & S,
const Blackbox &A,
const MyMethod &M)
{
smithForm(S, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), M);
return S;
}
// for specialization with respect to the DomainCategory
template< class Output, class Blackbox, class SmithMethod, class DomainCategory>
Output &smithForm(Output & S,
const Blackbox &A,
const DomainCategory &tag,
const SmithMethod &M)
{
throw LinBoxError( "Smith form solution implemented only for NTL.\n Please reconfigure LinBox with NTL enabled.");
}
// The smithForm with default Method
template<class Output, class Blackbox>
Output &smithForm(Output& S,
const Blackbox& A)
{
smithForm(S, A, Method::Hybrid());
return S;
}
#if 0
// The smithForm for ModularTag
template<class Output, class Blackbox, class MyMethod>
Output &smithForm(Output & S,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const MyMethod& M)
{
typename Blackbox::Field F = A.field();
integer p, c; F.characteristic(p); F.cardinality(c);
if (probab_prime(p) && p == c)
{ size_t r; rank(r, A);
S.resize(0);
size_t n = (A.rowdim() > A.coldim() ? A.coldim() : A.rowdim())-r;
if (r > 0) S.push_back( std::pair<size_t, integer>(r, 1) );
if (n > 0) S.push_back( std::pair<size_t, integer>(n, 0) );
}
else
{
integr x; size_t c;
for(x = p, c = 0; divides(2, x); x /= 2, ++c);
if (x == 1 && c <= 32) // (a low power of 2)
{
List L;
LocalSmith<Local2_32> SmithForm;
SmithForm( L, M, R );
distinct(L.begin(), L.end(), S);
}
// if (a odd prime power) call local-smith
else
{
IliopoulosElimination::smithIn (M);
typedef std::list< PIR::Element > List;
List L;
for (size_t i = 0; i < M.rowdim(); ++i) L.push_back(M[i][i]);
distinct(L.begin(), L.end(), S);
}
}
return S;
}
#endif
#ifdef __LINBOX_HAVE_NTL
template<>
std::list<std::pair<integer, size_t> > &
smithForm(std::list<std::pair<integer, size_t> >& S,
const BlasMatrix<PID_integer> &A,
const RingCategories::IntegerTag &tag,
const Method::Hybrid & M)
{
std::vector<integer> v (A.rowdim() < A.coldim() ? A.rowdim() : A.coldim());
SmithFormAdaptive::smithForm(v, A);
distinct(v.begin(), v.end(), S);
return S;
}
#endif
#if 0
// The smithForm with BlackBox Method
template<class Output, class Blackbox>
Output &smithForm(Output & S,
const Blackbox &A,
const RingCategories::IntegerTag &tag,
const Method::Blackbox &M)
{
// this will be binary search smith form (EGV')
}
#endif
} // end of LinBox namespace
#endif // __LINBOX_smith_form_H
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