/usr/include/linbox/solutions/rank.h is in liblinbox-dev 1.3.2-1.1.
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* Copyright(C) LinBox
* ------------------------------------
*
* ========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_rank_H
#define __LINBOX_rank_H
//#include "linbox-config.h"
#include "linbox/field/modular.h"
#include "linbox/randiter/random-prime.h"
#include "linbox/algorithms/matrix-hom.h"
#include "linbox/blackbox/sparse.h"
#include "linbox/blackbox/diagonal.h"
#include "linbox/blackbox/diagonal-gf2.h"
#include "linbox/blackbox/compose.h"
#include "linbox/blackbox/permutation.h"
#include "linbox/blackbox/transpose.h"
#include "linbox/algorithms/blackbox-container-symmetrize.h"
#include "linbox/algorithms/blackbox-container-symmetric.h"
#include "linbox/algorithms/blackbox-container.h"
#include "linbox/algorithms/massey-domain.h"
#include "linbox/algorithms/gauss.h"
#include "linbox/algorithms/gauss-gf2.h"
#include "linbox/algorithms/blas-domain.h"
#include "linbox/algorithms/whisart_trace.h"
#include "linbox/matrix/blas-matrix.h"
#include "linbox/switch/cekstv.h"
#include "linbox/blackbox/butterfly.h"
#include "linbox/vector/vector-traits.h"
#include "linbox/solutions/trace.h"
#include "linbox/solutions/methods.h"
#include "linbox/util/debug.h"
// Namespace in which all LinBox library code resides
namespace LinBox
{
/**
* Compute the rank of a linear transform A over a field by selected method.
* \ingroup solutions
* For very large and/or very sparse matrices the Wiedemann method will be faster
* (and it is memory efficient).
* For some sparse matrices SparseElimination may outperform Wiedemann.
* For small or dense matrices BlasElimination will be faster.
* \param[out] r output rank of A.
* \param[in] A linear transform, member of any blackbox class.
* \param[in] M may be a \p Method::Wiedemann (the default), a \p Method::BlasElimination, or a \p Method::SparseElimination..
* \param tag UNDOC
* \return a reference to r.
*/
template <class Blackbox, class Method, class DomainCategory>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const DomainCategory &tag,
const Method &M);
// error hanlder for rational domain
template <class Blackbox, class Method>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::RationalTag &tag,
const Method &M)
{
commentator().start ("Rational Rank", "Rrank");
// Same mapping as the integer one
rank(r, A, RingCategories::IntegerTag(), M);
commentator().stop ("done", NULL, "Rrank");
return r;
}
/**
* Compute the rank of a linear transform A over a field.
* \ingroup solutions
* The default method is Wiedemann(), using diagonal preconditioning and
* the minpoly. For small or dense matrices BlasElimination will be faster.
* \param A linear transform, member of any blackbox class.
* \param[out] r rank of \p A
* \return \p r rank of \p A.
*/
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A)
{
return rank(r, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), Method::Hybrid());
}
/** Rank of \p A.
* \p A may be modified
* @param A matrix
* @param r rank
*/
template <class Matrix>
inline unsigned long &rankin (unsigned long &r,
Matrix &A)
{
return rankin(r, A, typename FieldTraits<typename Matrix::Field>::categoryTag(), Method::Elimination());
}
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Hybrid &m)
{ // this should become a BB/Blas hybrid in the style of Duran/Saunders/Wan.
if (useBB(A)) return rank(r, A, tag, Method::Blackbox(m ));
else return rank(r, A, tag, Method::Elimination( m ));
}
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &m)
{
typedef typename Blackbox::Field Field;
const Field& F = A.field();
integer a, b; F.characteristic(a); F.cardinality(b);
if (a == b && a < LinBox::BlasBound)
return rank(r, A, tag, Method::BlasElimination(m));
else
return rank(r, A, tag, Method::NonBlasElimination( m ));
}
template <class Field, class Vector>
inline unsigned long &rank (unsigned long &r,
const SparseMatrix<Field, Vector> &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &m)
{
return rank(r, A, tag, Method::SparseElimination(m));
}
// specialization of NonBlas for SparseMatrix
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::NonBlasElimination & m)
{
return rank(r, A, tag, Method::SparseElimination(m));
}
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Blackbox &m);
/**
* Compute the rank of a linear transform A over a field.
* \ingroup solutions
*
* The default method is \p Wiedemann(), using diagonal preconditioning and
* the minpoly. For small or dense matrices \p BlasElimination will be faster.
* \return \p r rank of \p A.
* \param A linear transform, member of any blackbox class.
* @param[out] r rank of \p A
* @param M method (see ???)
*/
template <class Blackbox, class Method>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const Method &M)
{ return rank(r, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), M);
}
/// M may be <code>Method::Wiedemann()</code>.
template <class Blackbox>
inline unsigned long &rank (unsigned long &res,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Wiedemann &M)
// This is too much for solutions. It belongs in algorithms
{
typedef typename Blackbox::Field Field;
const Field F = A.field();
typename Field::RandIter iter (F);
if (M.symmetric()) {
commentator().start ("Symmetric Rank", "srank");
std::vector<typename Field::Element> d1;
size_t i;
VectorWrapper::ensureDim (d1, A.coldim ());
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
typedef Compose<Compose<Diagonal<Field>,Blackbox >, Diagonal<Field> > BlackBox1;
Diagonal<Field> D0 (F, d1);
Compose<Diagonal<Field>,Blackbox > B0 (&D0, &A);
BlackBox1 B (&B0, &D0);
BlackboxContainerSymmetric<Field, BlackBox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, BlackBox1> > WD (&TF, M.earlyTermThreshold ());
std::vector<typename Field::Element> phi;
WD.pseudo_minpoly (phi, res);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Pseudo Minpoly degree: " << res << std::endl;
commentator().start ("Monte Carlo certification (1)", "trace");
typename Field::Element t, p2; F.init(p2, 0UL);
trace(t, B);
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
int nbperm = 0; unsigned long rk;
int logn = (int)(2*(unsigned long)floor( log( (double)A.rowdim() ) ));
bool tryagain = (! F.areEqual( t, p2 ));
while( tryagain ) {
commentator().stop ("fail", NULL, "trace");
#if 0
Permutation<Field> P(A.rowdim(), F);
for (i = 0; i < A.rowdim (); ++i)
P.permute( rand() % A.rowdim() , rand() % A.rowdim() );
for (i = 0; i < A.rowdim (); ++i)
P.permute( rand() % A.rowdim() , rand() % A.rowdim() );
Transpose< Permutation<Field> > TP(&P);
typedef Compose< Permutation<Field>, Blackbox > BlackboxP;
typedef Compose< Compose< Permutation<Field>, Blackbox >, Transpose< Permutation<Field> > > BlackboxPAP;
BlackboxP PA(&P, &A);
BlackboxPAP BP( &PA , &TP );
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
Diagonal<Field> D1 (F, d1);
Compose<Diagonal<Field>,BlackboxPAP > B1 (&D1, &BP);
typedef Compose<Compose<Diagonal<Field>,BlackboxPAP >, Diagonal<Field> > BlackBox2;
BlackBox2 B (&B1, &D1);
#endif
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
Diagonal<Field> D1 (F, d1);
Compose<Diagonal<Field>,Blackbox > B1 (&D1, &A);
BlackBox1 B2 (&B1, &D1);
BlackboxContainerSymmetric<Field, BlackBox1> TF1 (&B2, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, BlackBox1> > WD1 (&TF1, M.earlyTermThreshold ());
WD1.pseudo_minpoly (phi, rk);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Permuted pseudo Minpoly degree: " << res << std::endl;
commentator().start ("Monte Carlo certification (2)", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
trace(t, B2);
tryagain = (! F.areEqual( t, p2 ));
if (res > rk)
tryagain = true;
else
res = rk;
if( ++nbperm > logn) break;
}
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "symm permutations : " << nbperm << std::endl;
nbperm = 0;
while(tryagain) {
commentator().stop ("fail", NULL, "trace");
// F.write( F.write( commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION)
// << "end trace: ", t) << ", p2: ", p2) << std::endl;
typename Field::RandIter r (F);
typename CekstvSwitch<Field>::Factory factory (r);
typedef Butterfly<Field, CekstvSwitch<Field> > ButterflyP;
ButterflyP P (F, A.rowdim(), factory);
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
Diagonal<Field> D1 (F, d1);
typedef Compose< ButterflyP, Diagonal<Field> > ButD;
ButD PD(&P, &D1);
Transpose< ButD > TP (&PD);
Compose< ButD, Blackbox > B1( &PD, &A);
typedef Compose< Compose< ButD, Blackbox > , Transpose< ButD > > BlackBoxBAB;
BlackBoxBAB PAP(&B1, &TP);
BlackboxContainerSymmetric<Field, BlackBoxBAB> TF1 (&PAP, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, BlackBoxBAB> > WD1 (&TF1, M.earlyTermThreshold ());
WD1.pseudo_minpoly (phi, rk);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Butterfly pseudo Minpoly degree: " << res << std::endl;
commentator().start ("Monte Carlo certification (3)", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
trace(t, PAP);
tryagain = (! F.areEqual( t, p2 ));
if (res > rk)
tryagain = true;
else
res = rk;
++nbperm;
}
// F.write( F.write( commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION)
// << "end trace: ", t) << ", p2: ", p2) << std::endl;
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "butterflies : " << nbperm << std::endl;
commentator().stop ("success", NULL, "trace");
commentator().stop ("done", NULL, "srank");
return res;
}
else {
commentator().start ("Rank", "wrank");
std::vector<typename Field::Element> d1, d2;
size_t i;
VectorWrapper::ensureDim (d1, A.coldim ());
VectorWrapper::ensureDim (d2, A.rowdim ());
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
for (i = 0; i < A.rowdim (); i++)
do iter.random (d2[i]); while (F.isZero (d2[i]));
Diagonal<Field> D1_i (F, d1), D2_i (F, d2);
Transpose<Blackbox> AT_i (&A);
Compose<Diagonal<Field>,Transpose<Blackbox> > B1_i (&D1_i, &AT_i);
Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> > B2_i (&B1_i, &D2_i);
Compose<Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> >, Blackbox> B3_i (&B2_i, &A);
// Here there is an extra diagonal computation
// The probability of success is also divided by two, as
// D2_i^2 contains only squares and squares are half the total elements
typedef Compose<Compose<Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> >, Blackbox>, Diagonal<Field> > Blackbox0;
Blackbox0 B_i (&B3_i, &D1_i);
BlackboxContainerSymmetric<Field, Blackbox0> TF_i (&B_i, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, Blackbox0> > WD (&TF_i, M.earlyTermThreshold ());
std::vector<typename Field::Element> phi;
WD.pseudo_minpoly (phi, res);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Pseudo Minpoly degree: " << res << std::endl;
commentator().start ("Monte Carlo certification (4)", "trace");
typename Field::Element t, p2; F.init(p2, 0UL);
// trace(t, B_i);
WhisartTraceTranspose(t, F, D1_i, A, D2_i);
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
int nbperm = 0; unsigned long rk;
int logn = (int)(2*(unsigned long)floor( log( (double)A.rowdim() ) ));
bool tryagain = (! F.areEqual( t, p2 ));
while( tryagain ) {
commentator().stop ("fail", NULL, "trace");
Permutation<Field> P((int)A.rowdim(), F);
for (i = 0; i < A.rowdim (); ++i)
P.permute( rand() % A.rowdim() , rand() % A.rowdim() );
for (i = 0; i < A.rowdim (); ++i)
P.permute( rand() % A.rowdim() , rand() % A.rowdim() );
typedef Compose< Permutation<Field>, Blackbox > BlackboxP;
BlackboxP BP(&P, &A);
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
for (i = 0; i < A.rowdim (); i++)
do iter.random (d2[i]); while (F.isZero (d2[i]));
Diagonal<Field> D1 (F, d1), D2 (F, d2);
Transpose<BlackboxP> AT (&BP);
Compose<Diagonal<Field>,Transpose<BlackboxP> > B1 (&D1, &AT);
Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> > B2 (&B1, &D2);
Compose<Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> >, BlackboxP> B3 (&B2, &BP);
typedef Compose<Compose<Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> >, BlackboxP>, Diagonal<Field> > Blackbox1;
Blackbox1 B (&B3, &D1);
BlackboxContainerSymmetric<Field, Blackbox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, Blackbox1> > MD (&TF, M.earlyTermThreshold ());
MD.pseudo_minpoly (phi, rk);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Permuted pseudo Minpoly degree: " << rk << std::endl;
commentator().start ("Monte Carlo certification (5)", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
// trace(t, B);
WhisartTraceTranspose(t, F, D1, BP, D2);
tryagain = (! F.areEqual( t, p2 ));
if (res > rk)
tryagain = true;
else
res = rk;
if( ++nbperm > logn) break;
}
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "permutations : " << nbperm << std::endl;
nbperm = 0;
while(tryagain) {
commentator().stop ("fail", NULL, "trace");
typename Field::RandIter r (F);
typename CekstvSwitch<Field>::Factory factory (r);
typedef Butterfly<Field, CekstvSwitch<Field> > ButterflyP;
ButterflyP P (F, A.rowdim(), factory);
typedef Compose< ButterflyP, Blackbox > BlackboxP;
BlackboxP BP(&P, &A);
for (i = 0; i < A.coldim (); i++)
do iter.random (d1[i]); while (F.isZero (d1[i]));
for (i = 0; i < A.rowdim (); i++)
do iter.random (d2[i]); while (F.isZero (d2[i]));
Diagonal<Field> D1 (F, d1), D2 (F, d2);
Transpose<BlackboxP> AT (&BP);
Compose<Diagonal<Field>,Transpose<BlackboxP> > B1 (&D1, &AT);
Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> > B2 (&B1, &D2);
Compose<Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> >, BlackboxP> B3 (&B2, &BP);
typedef Compose<Compose<Compose<Compose<Diagonal<Field>,Transpose<BlackboxP> >, Diagonal<Field> >, BlackboxP>, Diagonal<Field> > Blackbox1;
Blackbox1 B (&B3, &D1);
BlackboxContainerSymmetric<Field, Blackbox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, Blackbox1> > MD (&TF, M.earlyTermThreshold ());
MD.pseudo_minpoly (phi, rk);
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Butterfly pseudo Minpoly degree: " << rk << std::endl;
commentator().start ("Monte Carlo certification (6)", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
// trace(t, B);
WhisartTraceTranspose(t, F, D1, BP, D2);
tryagain = (! F.areEqual( t, p2 ));
if (res > rk)
tryagain = true;
else
res = rk;
++nbperm;
}
commentator().report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "butterflies : " << nbperm << std::endl;
commentator().stop ("success", NULL, "trace");
commentator().stop ("done", NULL, "wrank");
return res;
}
}
/// M may be <code>Method::SparseElimination()</code>.
template <class Field>
inline unsigned long &rank (unsigned long &r,
const SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &M)
{
// We make a copy as these data will be destroyed
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> A1 (A);
return rankin(r, A1, tag, M);
}
template <class Field, class Method>
inline unsigned long &rankin (unsigned long &r,
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> &A,
const Method &M)
{
return rankin(r, A, typename FieldTraits<Field>::categoryTag(), M);
}
template <class Blackbox, class Ring>
inline unsigned long &rankin (unsigned long &r,
Blackbox &A,
const RingCategories::IntegerTag &tag,
const Method::SparseElimination &M)
{
commentator().start ("Integer Rank inplace", "irank");
typedef Modular<double> Field;
integer mmodulus;
FieldTraits<Field>::maxModulus(mmodulus);
RandomPrimeIterator genprime( (long) floor (log((double)mmodulus) ) );
++genprime;
typedef typename Blackbox::template rebind< Field >::other FBlackbox;
Field Fp(*genprime);
FBlackbox Ap(A, Fp);
commentator().report (Commentator::LEVEL_ALWAYS,INTERNAL_WARNING) << "Integer Rank is done modulo " << *genprime << std::endl;
rankin(r, Ap, RingCategories::ModularTag(), M);
commentator().stop ("done", NULL, "irank");
return r;
}
template <class Field>
inline unsigned long &rankin (unsigned long &r,
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &M)
{
commentator().start ("Sparse Elimination Rank", "serank");
GaussDomain<Field> GD ( A.field() );
GD.rankin (r, A, M.strategy ());
commentator().stop ("done", NULL, "serank");
return r;
}
/// specialization to \f$ \mathbf{F}_2 \f$
inline unsigned long &rankin (unsigned long &r,
GaussDomain<GF2>::Matrix &A,
const Method::SparseElimination &)//M
{
commentator().start ("Sparse Elimination Rank over GF2", "serankmod2");
GaussDomain<GF2> GD ( A.field() );
GD.rankin (r, A, Specifier::PIVOT_LINEAR);
commentator().stop ("done", NULL, "serankmod2");
return r;
}
/// specialization to \f$ \mathbf{F}_2 \f$
inline unsigned long &rankin (unsigned long &r,
GaussDomain<GF2>::Matrix &A,
const RingCategories::ModularTag &,//tag
const Method::SparseElimination &M)
{
return rankin(r, A, M);
}
// Change of representation to be able to call the sparse elimination
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &M)
{
typedef typename Blackbox::Field Field;
typedef SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> SparseBB;
SparseBB SpA(A.field(), A.rowdim(), A.coldim() );
MatrixHom::map(SpA, A, A.field());
return rankin(r, SpA, tag, M);
}
// M may be <code>Method::BlasElimination()</code>.
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::BlasElimination &M)
{
commentator().start ("Blas Rank", "blasrank");
typedef typename Blackbox::Field Field;
const Field F = A.field();
integer a, b; F.characteristic(a); F.cardinality(b);
linbox_check( a == b );
linbox_check( a < LinBox::BlasBound);
BlasMatrix<Field> B(A);
BlasMatrixDomain<Field> D(F);
r = D.rank(B);
commentator().stop ("done", NULL, "blasrank");
return r;
}
// is this used?
// A is modified.
template <class Matrix>
inline unsigned long &rankin (unsigned long &r,
Matrix &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &M)
{
typedef typename Matrix::Field Field;
const Field F = A.field();
GaussDomain<Field> GD (F);
GD.rankin( r, A, M.strategy ());
return r;
}
/// A is modified.
template <class Field>
inline unsigned long &rankin (unsigned long &r,
BlasMatrix<Field> &A,
const RingCategories::ModularTag &tag,
const Method::BlasElimination &M)
{
commentator().start ("BlasBB Rank", "blasbbrank");
const Field F = A.field();
BlasMatrixDomain<Field> D(F);
r = D.rankin(static_cast< BlasMatrix<Field>& >(A));
commentator().stop ("done", NULL, "blasbbrank");
return r;
}
template <class Blackbox, class MyMethod>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::IntegerTag &tag,
const MyMethod &M)
{
commentator().start ("Integer Rank", "iirank");
typedef Modular<double> Field;
integer mmodulus;
FieldTraits<Field>::maxModulus(mmodulus);
RandomPrimeIterator genprime( (unsigned) floor (log((double)mmodulus) ) );
++genprime;
typedef typename Blackbox::template rebind< Field >::other FBlackbox;
Field Fp(*genprime);
FBlackbox Ap(A, Fp );
commentator().report (Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Integer Rank is done modulo " << *genprime << std::endl;
rank(r, Ap, RingCategories::ModularTag(), M);
commentator().stop ("done", NULL, "iirank");
return r;
}
} // LinBox
#ifdef __LINBOX_HAVE_GIVARO
#ifndef LINBOX_EXTENSION_DEGREE_MAX
#define LINBOX_EXTENSION_DEGREE_MAX 19
#endif
#include "linbox/field/givaro.h"
namespace LinBox
{
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Blackbox & m)
{
commentator().start ("BB Rank", "extend");
if (m.certificate()) {
typedef typename Blackbox::Field Field;
const Field& F = A.field();
integer a,c; F.cardinality(a); F.characteristic(c);
if (a != c) {
unsigned long extend = (unsigned long)Givaro::FF_EXPONENT_MAX(a,(integer)LINBOX_EXTENSION_DEGREE_MAX);
if (extend > 1) {
commentator().report (Commentator::LEVEL_ALWAYS,INTERNAL_WARNING) << "Extension of degree " << extend << std::endl;
GivaroExtension<Field> EF( F, extend);
typedef typename Blackbox::template rebind< GivaroExtension<Field> >::other FBlackbox;
FBlackbox Ap(A, EF);
rank(r, Ap, tag, Method::Wiedemann(m));
}
else
rank(r, A, tag, Method::Wiedemann(m));
}
else {
unsigned long extend = (unsigned long)Givaro::FF_EXPONENT_MAX(c,(integer)LINBOX_EXTENSION_DEGREE_MAX);
if (extend > 1) {
commentator().report (Commentator::LEVEL_ALWAYS,INTERNAL_WARNING) << "Word size extension : " << extend << std::endl;
GivaroGfq EF( (unsigned long)c, extend);
typedef typename Blackbox::template rebind< GivaroGfq >::other FBlackbox;
FBlackbox Ap(A, EF);
rank(r, Ap, tag, Method::Wiedemann(m));
}
else
rank(r, A, tag, Method::Wiedemann(m));
}
}
else
rank(r, A, tag, Method::Wiedemann(m));
commentator().stop ("done", NULL, "extend");
return r;
}
}
#else
namespace LinBox
{
template <class Blackbox>
inline unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Blackbox & m)
{
return rank(r, A, tag, Method::Wiedemann(m));
}
}
#endif
#endif // __LINBOX_rank_H
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,:0,t0,+0,=s
// Local Variables:
// mode: C++
// tab-width: 8
// indent-tabs-mode: nil
// c-basic-offset: 8
// End:
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