/usr/include/linbox/solutions/rank.h is in liblinbox-dev 1.1.6~rc0-4.1.
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/* linbox/solutions/rank.h
* ------------------------------------
* See COPYING for license information.
*/
#ifndef __RANK_H
#define __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/compose.h"
#include "linbox/blackbox/permutation.h"
#include "linbox/blackbox/transpose.h"
#include "linbox/blackbox/blas-blackbox.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/blas-domain.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.
For very large and/or very sparse matrices the Wiedemann method will be faster
(and is memory efficient).
For some sparse matrices SparseElimination may outperform Wiedemann.
For small or dense matrices BlasElimination will be faster.
\param r - output rank of A.
\param - input A linear transform, member of any blackbox class.
\param - input M may be a Method::Wiedemann (the default), a Method::BlasElimination, or a Method::SparseElimination..
\returns reference to r.
\ingroup solutions
*/
template <class Blackbox, class Method, class DomainCategory>
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>
unsigned long &rank (unsigned long &r,
const Blackbox &A,
const RingCategories::RationalTag &tag,
const Method &M){
throw LinboxError("LinBox ERROR: rank is not yet defined over a rational domain");
}
/**
Compute the rank of a linear transform A over a field.
The default method is Wiedemann(), using diagonal preconditioning and
the minpoly. For small or dense matrices BlasElimination will be faster.
\returns <em>r</em> rank of A.
\param A linear transform, member of any blackbox class.
\ingroup solutions
*/
template <class Blackbox>
unsigned long &rank (unsigned long &r,
const Blackbox &A)
{ return rank(r, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), Method::Hybrid());
}
/** A may be modified
*/
template <class Matrix>
unsigned long &rankin (unsigned long &r,
Matrix &A)
{ return rankin(r, A, typename FieldTraits<typename Matrix::Field>::categoryTag(), Method::Elimination());
}
template <class Blackbox>
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>
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>
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>
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>
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.
The default method is Wiedemann(), using diagonal preconditioning and
the minpoly. For small or dense matrices BlasElimination will be faster.
\returns <em>r</em> rank of A.
\param A linear transform, member of any blackbox class.
\ingroup solutions
*/
template <class Blackbox, class Method>
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>
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]));
Diagonal<Field> D1 (F, d1);
Compose<Diagonal<Field>,Blackbox > B1 (&D1, &A);
typedef Compose<Compose<Diagonal<Field>,Blackbox >, Diagonal<Field> > BlackBox1;
BlackBox1 B (&B1, &D1);
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", "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 = 2*(unsigned long)floor( log( (double)A.rowdim() ) );
bool tryagain = (! F.areEqual( t, p2 ));
while( tryagain ) {
commentator.stop ("fail", NULL, "trace");
// 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);
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 B (&B1, &D1);
BlackboxContainerSymmetric<Field, BlackBox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, BlackBox1> > WD (&TF, M.earlyTermThreshold ());
WD.pseudo_minpoly (phi, rk);
commentator.report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Permuted pseudo Minpoly degree: " << res << std::endl;
commentator.start ("Monte Carlo certification", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
trace(t, B);
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> TF (&PAP, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, BlackBoxBAB> > WD (&TF, M.earlyTermThreshold ());
WD.pseudo_minpoly (phi, rk);
commentator.report(Commentator::LEVEL_ALWAYS,INTERNAL_DESCRIPTION) << "Butterfly pseudo Minpoly degree: " << res << std::endl;
commentator.start ("Monte Carlo certification", "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 (F, d1), D2 (F, d2);
Transpose<Blackbox> AT (&A);
Compose<Diagonal<Field>,Transpose<Blackbox> > B1 (&D1, &AT);
Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> > B2 (&B1, &D2);
Compose<Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> >, Blackbox> B3 (&B2, &A);
// Here there is an extra diagonal computation
// The probability of success is also divided by two, as
// D2^2 contains only squares and squares are half the total elements
typedef Compose<Compose<Compose<Compose<Diagonal<Field>,Transpose<Blackbox> >, Diagonal<Field> >, Blackbox>, Diagonal<Field> > Blackbox1;
Blackbox1 B (&B3, &D1);
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", "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 = 2*(unsigned long)floor( log( (double)A.rowdim() ) );
bool tryagain = (! F.areEqual( t, p2 ));
while( tryagain ) {
commentator.stop ("fail", NULL, "trace");
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() );
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", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
trace(t, B);
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", "trace");
if (phi.size() >= 2) F.neg(p2, phi[ phi.size()-2]);
trace(t, B);
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>
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>
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>
unsigned long &rankin (unsigned long &r,
Blackbox &A,
const RingCategories::IntegerTag &tag,
const Method::SparseElimination &M)
{
commentator.start ("Integer Rank", "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;
FBlackbox * Ap;
MatrixHom::map(Ap, A, Field(*genprime) );
commentator.report (Commentator::LEVEL_ALWAYS,INTERNAL_WARNING) << "Integer Rank is done modulo " << mmodulus << std::endl;
rankin(r, *Ap, RingCategories::ModularTag(), M);
delete Ap;
commentator.stop ("done", NULL, "irank");
return r;
}
template <class Field>
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;
}
// Change of representation to be able to call the sparse elimination
template <class Blackbox>
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;
MatrixHom::map(SpA, A, A.field());
rankin(r, *SpA, tag, M);
delete SpA;
return r;
}
// M may be <code>Method::BlasElimination()</code>.
template <class Blackbox>
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<typename Field::Element> 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>
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>
unsigned long &rankin (unsigned long &r,
BlasBlackbox<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<typename Field::Element>& >(A));
commentator.stop ("done", NULL, "blasbbrank");
return r;
}
template <class Blackbox, class MyMethod>
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( (long) floor (log((double)mmodulus) ) );
++genprime;
typedef typename Blackbox::template rebind< Field >::other FBlackbox;
FBlackbox * Ap;
MatrixHom::map(Ap, A, Field(*genprime) );
commentator.report (Commentator::LEVEL_ALWAYS,INTERNAL_WARNING) << "Integer Rank is done modulo " << mmodulus << std::endl;
rank(r, *Ap, RingCategories::ModularTag(), M);
delete Ap;
commentator.stop ("done", NULL, "iirank");
return r;
}
} // LinBox
#ifdef __LINBOX_HAVE_GIVARO
#define LINBOX_EXTENSION_DEGREE_MAX 20
#include "linbox/field/givaro-extension.h"
namespace LinBox {
template <class Blackbox>
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)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;
MatrixHom::map(Ap, A, EF );
rank(r, *Ap, tag, Method::Wiedemann(m));
}
} else {
unsigned long extend = (unsigned long)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;
MatrixHom::map(Ap, A, EF );
rank(r, *Ap, 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>
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 // __RANK_H
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