/usr/include/linbox/solutions/charpoly.h is in liblinbox-dev 1.3.2-1.1.
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* Copyright (C) 2005 Clement Pernet
*
* Written by Clement Pernet <clement.pernet@imag.fr>
*
* ========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_charpoly_H
#define __LINBOX_charpoly_H
#include "linbox/solutions/methods.h"
#include "linbox/util/debug.h"
#include "linbox/field/field-traits.h"
#include "linbox/matrix/blas-matrix.h"
#include "linbox/algorithms/blas-domain.h"
#ifdef __LINBOX_HAVE_GIVARO
// BBcharpoly without givaropolynomials is not yet implemented
#include "linbox/algorithms/bbcharpoly.h"
#endif
// Namespace in which all LinBox library code resides
namespace LinBox
{
// for specialization with respect to the DomainCategory
template< class Blackbox, class Polynomial, class MyMethod, class DomainCategory>
Polynomial &charpoly ( Polynomial &P,
const Blackbox &A,
const DomainCategory &tag,
const MyMethod &M);
/* //error handler for rational domain
template <class Blackbox, class Polynomial>
Polynomial &charpoly (Polynomial& P,
const Blackbox& A,
const RingCategories::RationalTag& tag,
const Method::Hybrid& M)
{
throw LinboxError("LinBox ERROR: charpoly is not yet defined over a rational domain");
}
*/
/** \brief ...using an optional Method parameter
\param P - the output characteristic polynomial. If the polynomial
is of degree d, this random access container has size d+1, the 0-th
entry is the constant coefficient and the d-th is 1 since the charpoly
is monic.
\param A - a blackbox matrix
Optional \param M - the method object. Generally, the default
object suffices and the algorithm used is determined by the class of M.
Basic methods are Method::Blackbox, Method::Elimination, and
Method::Hybrid (the default).
See methods.h for more options.
\return a reference to P.
*/
template <class Blackbox, class Polynomial, class MyMethod>
Polynomial &charpoly (Polynomial & P,
const Blackbox & A,
const MyMethod & M){
return charpoly( P, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), M);
}
/// \brief ...using default method
template<class Blackbox, class Polynomial>
Polynomial &charpoly (Polynomial & P,
const Blackbox & A)
{
return charpoly (P, A, Method::Hybrid());
}
// The charpoly with Hybrid Method
template<class Polynomial, class Blackbox>
Polynomial &charpoly (Polynomial &P,
const Blackbox & A,
const RingCategories::ModularTag & tag,
const Method::Hybrid & M)
{
// not yet a hybrid
//return charpoly(P, A, tag, Method::Blackbox(M));
return charpoly(P, A, tag, Method::BlasElimination(M));
}
// The charpoly with Hybrid Method
template<class Polynomial, class Domain>
Polynomial &charpoly (Polynomial &P,
const SparseMatrix<Domain> & A,
const RingCategories::ModularTag & tag,
const Method::Hybrid & M)
{
// not yet a hybrid
return charpoly(P, A, tag, Method::Blackbox(M));
}
// The charpoly with Hybrid Method
template<class Polynomial, class Domain>
Polynomial &charpoly (Polynomial &P,
const BlasMatrix<Domain> & A,
const RingCategories::ModularTag & tag,
const Method::Hybrid & M)
{
// not yet a hybrid
return charpoly(P, A, tag, Method::BlasElimination(M));
}
// The charpoly with Elimination Method
template<class Polynomial, class Blackbox>
Polynomial & charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::ModularTag & tag,
const Method::Elimination & M)
{
return charpoly(P, A, tag, Method::BlasElimination(M));
}
/** @brief Compute the characteristic polynomial over \f$\mathbf{Z}_p\f$.
*
* Compute the characteristic polynomial of a matrix using dense
* elimination methods
* @param P Polynomial where to store the result
* @param A Blackbox representing the matrix
* @param tag
* @param M
*/
template < class Polynomial, class Blackbox >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::ModularTag & tag,
const Method::BlasElimination & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
BlasMatrix< typename Blackbox::Field > BBB (A);
BlasMatrixDomain< typename Blackbox::Field > BMD (BBB.field());
return BMD.charpoly (P, static_cast<BlasMatrix<typename Blackbox::Field> >(BBB));
}
}
#include "linbox/algorithms/matrix-hom.h"
#include "linbox/algorithms/rational-cra2.h"
#include "linbox/algorithms/varprec-cra-early-multip.h"
#include "linbox/algorithms/charpoly-rational.h"
namespace LinBox
{
template <class Blackbox, class MyMethod>
struct IntegerModularCharpoly {
const Blackbox &A;
const MyMethod &M;
IntegerModularCharpoly(const Blackbox& b, const MyMethod& n) :
A(b), M(n)
{}
template<typename Polynomial, typename Field>
Polynomial& operator()(Polynomial& P, const Field& F) const
{
typedef typename Blackbox::template rebind<Field>::other FBlackbox;
FBlackbox Ap(A, F);
return charpoly( P, Ap, typename FieldTraits<Field>::categoryTag(), M);
// integer p;
// F.characteristic(p);
// std::cerr<<"Charpoly(A) mod "<<p<<" = "<<P;
}
};
template < class Blackbox, class Polynomial >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::IntegerTag & tag,
const Method::Hybrid & M)
{
commentator().start ("Integer Charpoly", "Icharpoly");
if ( (A.rowdim() < 1000) && (A.coldim() <1000) )
charpoly(P, A, tag, Method::BlasElimination(M) );
else
charpoly(P, A, tag, Method::Blackbox(M) );
commentator().stop ("done", NULL, "Icharpoly");
return P;
}
//#if 0
#if defined(__LINBOX_HAVE_NTL) && defined(__LINBOX_HAVE_GIVARO)
}
#include "linbox/algorithms/cia.h"
namespace LinBox
{
#if 0
// The charpoly with Hybrid Method
template<class Blackbox, class Polynomial>
Polynomial &charpoly (Polynomial &P,
const Blackbox &A,
const RingCategories::IntegerTag &tag,
const Method::Hybrid &M)
{
// not yet a hybrid
return charpoly(P, A, tag, Method::Blackbox(M));
}
#endif
template < class IntRing, class Polynomial >
Polynomial& charpoly (Polynomial & P,
const BlasMatrix<IntRing> & A,
const RingCategories::IntegerTag & tag,
const Method::Hybrid & M)
{
commentator().start ("BlasMatrix Integer Charpoly", "Icharpoly");
charpoly(P, A, tag, Method::BlasElimination(M) );
commentator().stop ("done", NULL, "Icharpoly");
return P;
}
#if 0
template < class IntRing, class Polynomial >
Polynomial& charpoly (Polynomial & P,
const BlasMatrix<IntRing> & A,
const RingCategories::IntegerTag & tag,
const Method::Hybrid & M)
{
commentator().start ("BlasMatrix Integer Charpoly", "Icharpoly");
charpoly(P, A, tag, Method::BlasElimination(M) );
commentator().stop ("done", NULL, "Icharpoly");
return P;
}
#endif
/** @brief Compute the characteristic polynomial over {\bf Z}
*
* Compute the characteristic polynomial of a matrix using dense
* elimination methods
* @param P Polynomial where to store the result
* @param A \ref Black-Box representing the matrix
*/
template < class Polynomial, class Blackbox >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::IntegerTag & tag,
const Method::BlasElimination & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
typename GivPolynomialRing<typename Blackbox::Field>::Element Pg;
return P = cia (Pg, A, M);
}
/** Compute the characteristic polynomial over {\bf Z}
*
* Compute the characteristic polynomial of a matrix, represented via
* a blackBox.
*
* @param P Polynomial where to store the result
* @param A \ref Black-Box representing the matrix
*/
template < class Polynomial, class Blackbox/*, class Categorytag*/ >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::IntegerTag & tag,
const Method::Blackbox & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
typename GivPolynomialRing<typename Blackbox::Field>::Element Pg;
return P = BBcharpoly::blackboxcharpoly (Pg, A, tag, M);
}
#else // no NTL or no Givaro (??)
}
#include "linbox/field/modular.h"
#include "linbox/algorithms/cra-domain.h"
#include "linbox/algorithms/cra-full-multip.h"
#include "linbox/algorithms/cra-early-multip.h"
#include "linbox/randiter/random-prime.h"
#include "linbox/algorithms/matrix-hom.h"
namespace LinBox
{
#if 0
#include "linbox/algorithms/rational-cra2.h"
#include "linbox/algorithms/varprec-cra-early-multip.h"
#include "linbox/algorithms/charpoly-rational.h"
namespace LinBox
{
template <class Blackbox, class MyMethod>
struct IntegerModularCharpoly {
const Blackbox &A;
const MyMethod &M;
IntegerModularCharpoly(const Blackbox& b, const MyMethod& n) :
A(b), M(n)
{}
template<typename Polynomial, typename Field>
Polynomial& operator()(Polynomial& P, const Field& F) const {
typedef typename Blackbox::template rebind<Field>::other FBlackbox;
FBlackbox * Ap;
MatrixHom::map(Ap, A, F);
charpoly( P, *Ap, typename FieldTraits<Field>::categoryTag(), M);
integer p;
F.characteristic(p);
//std::cerr<<"Charpoly(A) mod "<<p<<" = "<<P;
delete Ap;
return P;
}
};
#endif
template < class Polynomial,class Blackbox >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::IntegerTag & tag,
const Method::Blackbox & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
commentator().start ("Integer BlackBox Charpoly : No NTL installation -> chinese remaindering", "IbbCharpoly");
RandomPrimeIterator genprime( 26-(int)ceil(log((double)A.rowdim())*0.7213475205));
#if 0
typename Blackbox::ConstIterator it = A.Begin();
typename Blackbox::ConstIterator it_end = A.End();
integer max = 1,min=0;
while( it != it_end ){
// cerr<<"it="<<(*it)<<endl;
if (max < (*it))
max = *it;
if ( min > (*it))
min = *it;
it++;
}
if (max<-min)
max=-min;
size_t n=A.coldim();
double hadamarcp = n/2.0*(log(double(n))+2*log(double(max))+0.21163275)/log(2.0);
ChineseRemainder< FullMultipCRA<Modular<double> > > cra(hadamarcp);
#endif
ChineseRemainder< EarlyMultipCRA<Modular<double> > > cra(3UL);
IntegerModularCharpoly<Blackbox,Method::Blackbox> iteration(A, M);
cra.operator() (P, iteration, genprime);
commentator().stop ("done", NULL, "IbbCharpoly");
return P;
}
template < class Polynomial,class Blackbox >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::IntegerTag & tag,
const Method::BlasElimination & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
commentator().start ("Integer Dense Charpoly : No NTL installation -> chinese remaindering", "IbbCharpoly");
RandomPrimeIterator genprime( 26-(int)ceil(log((double)A.rowdim())*0.7213475205));
#if 0
typename Blackbox::ConstIterator it = A.Begin();
typename Blackbox::ConstIterator it_end = A.End();
integer max = 1,min=0;
while( it != it_end ){
// cerr<<"it="<<(*it)<<endl;
if (max < (*it))
max = *it;
if ( min > (*it))
min = *it;
it++;
}
if (max<-min)
max=-min;
size_t n=A.coldim();
double hadamarcp = n/2.0*(log(double(n))+2*log(double(max))+0.21163275)/log(2.0);
ChineseRemainder< FullMultipCRA<Modular<double> > > cra(hadamarcp);
#endif
ChineseRemainder< EarlyMultipCRA<Modular<double> > > cra(3UL);
IntegerModularCharpoly<Blackbox,Method::BlasElimination> iteration(A, M);
cra(P, iteration, genprime);
commentator().stop ("done", NULL, "IbbCharpoly");
return P;
}
#endif
/** Compute the characteristic polynomial over \f$\mathbf{Z}_p\f$.
*
* Compute the characteristic polynomial of a matrix, represented via
* a blackBox.
*
* @param P Polynomial where to store the result
* @param A Blackbox representing the matrix
* @param tag
* @param M
*/
template < class Polynomial, class Blackbox/*, class Categorytag*/ >
Polynomial& charpoly (Polynomial & P,
const Blackbox & A,
const RingCategories::ModularTag & tag,
const Method::Blackbox & M)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for characteristic polynomial computation\n");
#ifdef __LINBOX_HAVE_GIVARO
typename GivPolynomialRing<typename Blackbox::Field>::Element Pg;
return P = BBcharpoly::blackboxcharpoly (Pg, A, tag, M);
#else
return charpoly(P, A, tag, Method::BlasElimination());
#endif
}
template < class Blackbox, class Polynomial, class MyMethod>
Polynomial &charpoly (Polynomial& P, const Blackbox& A,
const RingCategories::RationalTag& tag, const MyMethod& M)
{
commentator().start ("Rational Charpoly", "Rcharpoly");
RandomPrimeIterator genprime( 26-(int)ceil(log((double)A.rowdim())*0.7213475205));
RationalRemainder2< VarPrecEarlyMultipCRA<Modular<double> > > rra(3UL);
IntegerModularCharpoly<Blackbox,MyMethod> iteration(A, M);
std::vector<Integer> PP; // use of integer due to non genericity of cra. PG 2005-08-04
Integer den;
rra(PP,den, iteration, genprime);
size_t i =0;
P.resize(PP.size());
for (typename Polynomial::iterator it= P.begin(); it != P.end(); ++it, ++i)
A.field().init(*it, PP[i],den);
commentator().stop ("done", NULL, "Rcharpoly");
return P;
}
} // end of LinBox namespace
#endif // __LINBOX_charpoly_H
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// mode: C++
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