/usr/include/linbox/solutions/det.h is in liblinbox-dev 1.3.2-1.1build2.
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* Copyright (C) 2001, 2002 LinBox
* Time-stamp: <04 Oct 11 16:42:52 Jean-Guillaume.Dumas@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========
*/
/*! @file solutions/det.h
* @ingroup solutions
* @brief NO DOC
*/
#ifndef __LINBOX_det_H
#define __LINBOX_det_H
#include "linbox/blackbox/diagonal.h"
#include "linbox/blackbox/compose.h"
#include "linbox/solutions/methods.h"
#include "linbox/solutions/getentry.h"
#include "linbox/matrix/blas-matrix.h"
#include "linbox/algorithms/blackbox-container.h"
#include "linbox/algorithms/blackbox-container-symmetric.h"
#include "linbox/algorithms/massey-domain.h"
#include "linbox/algorithms/blas-domain.h"
#include "linbox/algorithms/gauss.h"
#include "linbox/vector/vector-traits.h"
#include "linbox/util/prime-stream.h"
#include "linbox/util/debug.h"
#include "linbox/util/mpicpp.h"
// Namespace in which all LinBox library code resides
namespace LinBox
{
/** \brief Compute the determinant of A.
*
* The determinant of a linear operator A, represented as a
* black box, is computed over the ring or field of A.
*
* @param d Field element into which to store the result
* @param A Black box of which to compute the determinant
* @param tag optional tag. Specifies Integer, Rational or modular ring/field
* @param M optional method. The default is Method::Hybrid(), Other options
include Blackbox, Elimination, Wiedemann, BlasElimination and SparseElimination.
Sometimes it helps to indicate properties of the matrix in the method object
(for instance symmetry). See class Method for details.
\ingroup solutions
*/
template< class Blackbox, class DetMethod, class DomainCategory>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const DomainCategory &tag,
const DetMethod &Meth);
// The det where A can be modified in place
// Default is to use the generic det (might copy)
template< class Blackbox, class DetMethod, class DomainCategory>
typename Blackbox::Field::Element &detin (typename Blackbox::Field::Element &d,
Blackbox &A,
const DomainCategory &tag,
const DetMethod &Meth)
{
return det(d, A, tag, Meth);
}
// The det with default Method
template<class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A)
{
return det(d, A, Method::Hybrid());
}
// The det where A can be modified in place
template<class Blackbox>
typename Blackbox::Field::Element &detin (typename Blackbox::Field::Element &d,
Blackbox &A)
{
return detin(d, A, Method::Hybrid());
}
// The det with category specializer
template <class Blackbox, class MyMethod>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const MyMethod &Meth)
{
return det(d, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), Meth);
}
// The in place det with category specializer
template <class Blackbox, class MyMethod>
typename Blackbox::Field::Element &detin (typename Blackbox::Field::Element &d,
Blackbox &A,
const MyMethod &Meth)
{
return detin(d, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), Meth);
}
// The det with Hybrid Method
template<class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Hybrid &Meth)
{
// not yet a hybrid
if (useBB(A))
return det(d, A, tag, Method::Blackbox(Meth));
else
return det(d, A, tag, Method::Elimination(Meth));
}
template<class Blackbox>
typename Blackbox::Field::Element &detin (typename Blackbox::Field::Element &d,
Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Hybrid &Meth)
{
// not yet a hybrid
/*
if (useBB(A))
return det(d, A, tag, Method::Blackbox(Meth));
else
*/
return detin(d, A, tag, Method::Elimination(Meth));
}
// The det with Hybrid Method on BlasMatrix
template<class Field>
typename Field::Element &det (typename Field::Element &d,
const BlasMatrix<Field> &A,
const RingCategories::ModularTag &tag,
const Method::Hybrid &Meth)
{
return det(d, A, tag, Method::Elimination(Meth));
}
template<class Field>
typename Field::Element &detin (typename Field::Element &d,
BlasMatrix<Field> &A,
const RingCategories::ModularTag &tag,
const Method::Hybrid &Meth)
{
return detin(d, A, tag, Method::Elimination(Meth));
}
// Forward declaration saves us from including blackbox/toeplitz.h
template<class A, class B> class Toeplitz;
// Toeplitz determinant
template<class CField, class PField >
typename CField::Element& det(typename CField::Element & res,
const Toeplitz<CField,PField> & A )
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
return A.det(res);
}
template<class CField, class PField >
typename CField::Element& detin(typename CField::Element & res,
Toeplitz<CField,PField> & A )
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
return A.det(res);
}
// The det with BlackBox Method
template<class Blackbox>
typename Blackbox::Field::Element &det (
typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Blackbox &Meth)
{
return det(d, A, tag, Method::Wiedemann(Meth));
}
// The det with Wiedemann, finite field.
template <class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Wiedemann &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
typedef typename Blackbox::Field Field;
typedef std::vector<typename Field::Element> Polynomial;
Field F = A.field();
if(Meth.symmetric()) {
commentator().start ("Symmetric Wiedemann Determinant", "sdet");
linbox_check (A.coldim () == A.rowdim ());
Polynomial phi;
unsigned long deg;
typename Field::RandIter iter (F);
// Precondition here to separate the eigenvalues, so that
// minpoly (B) = charpoly (B) with high probability
// Here there is an extra diagonal computation
// The probability of success is also divided by two, as
// diag^2 contains only squares and squares are half the total elements
std::vector<typename Field::Element> diag (A.coldim ());
typename Field::Element pi;
size_t i;
size_t iternum = 1;
do {
F.init (pi, 1);
for (i = 0; i < A.coldim (); i++) {
do iter.random (diag[i]); while (F.isZero (diag[i]));
F.mulin (pi, diag[i]);
}
Diagonal<Field> D (F, diag);
Compose<Blackbox,Diagonal<Field> > B0 (&A, &D);
typedef Compose<Diagonal<Field>,Compose<Blackbox,Diagonal<Field> > > Blackbox1;
Blackbox1 B(&D, &B0);
BlackboxContainerSymmetric<Field, Blackbox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainerSymmetric<Field, Blackbox1> > WD (&TF, Meth.earlyTermThreshold ());
WD.minpoly (phi, deg);
// std::cout << "\tdet: iteration # " << iternum << "\tMinpoly deg= "
// << phi.size() << "\n" ;
// std::cout << "[" ;
// for(typename Polynomial::const_iterator refs = phi.begin();
// refs != phi.end() ;
// ++refs )
// std::cout << (*refs) << " " ;
// std::cout << "]" << std::endl;
++iternum;
} while ( (phi.size () < A.coldim () + 1) && ( !F.isZero (phi[0]) ) );
// Divided twice since multiplied twice by the diagonal matrix
F.div (d, phi[0], pi);
F.divin (d, pi);
if ( (deg & 1) == 1)
F.negin (d);
commentator().stop ("done", NULL, "sdet");
return d;
}
else {
commentator().start ("Wiedemann Determinant", "wdet");
linbox_check (A.coldim () == A.rowdim ());
Polynomial phi;
unsigned long deg;
typename Field::RandIter iter (F);
// Precondition here to separate the eigenvalues, so that
// minpoly (B) = charpoly (B) with high probability
std::vector<typename Field::Element> diag (A.coldim ());
typename Field::Element pi;
size_t i;
size_t iternum = 1;
do {
F.init (pi, 1);
for (i = 0; i < A.coldim (); i++) {
do iter.random (diag[i]); while (F.isZero (diag[i]));
F.mulin (pi, diag[i]);
}
Diagonal<Field> D (F, diag);
Compose<Blackbox,Diagonal<Field> > B (&A, &D);
typedef Compose<Blackbox,Diagonal<Field> > Blackbox1;
BlackboxContainer<Field, Blackbox1> TF (&B, F, iter);
MasseyDomain<Field, BlackboxContainer<Field, Blackbox1> > WD (&TF, Meth.earlyTermThreshold ());
WD.minpoly (phi, deg);
++iternum;
} while ( (phi.size () < A.coldim () + 1) && ( !F.isZero (phi[0]) ) );
F.div (d, phi[0], pi);
if ( (deg & 1) == 1)
F.negin (d);
commentator().stop ("done", NULL, "wdet");
return d;
}
}
// the det with Blas, finite field.
template <class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::BlasElimination &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
typedef typename Blackbox::Field Field;
Field F = A.field();
commentator().start ("Blas Determinant", "blasdet");
linbox_check (A.coldim () == A.rowdim ());
BlasMatrix<Field> B(A);
BlasMatrixDomain<Field> BMD(F);
d= BMD.detin(B);
commentator().stop ("done", NULL, "blasdet");
return d;
}
template <class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
typedef typename Blackbox::Field Field;
commentator().start ("Sparse Elimination Determinant", "SEDet");
// We make a copy as these data will be destroyed
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> A1 (A.field(), A.rowdim(), A.coldim());
typename Blackbox::Field::Element tmp;
for(size_t i = 0; i < A.rowdim() ; ++i)
for(size_t j = 0; j < A.coldim(); ++j)
A1.setEntry(i,j,getEntry(tmp, A, i, j));
GaussDomain<Field> GD ( A1.field() );
GD.detin (d, A1, Meth.strategy ());
commentator().stop ("done", NULL, "SEDet");
return d;
}
template <class Field, class Vector>
typename Field::Element &det (typename Field::Element &d,
const SparseMatrix<Field, Vector> &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
commentator().start ("Sparse Elimination Determinant", "SEDet");
// We make a copy as these data will be destroyed
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> A1 (A);
GaussDomain<Field> GD ( A.field() );
GD.detin (d, A1, Meth.strategy ());
commentator().stop ("done", NULL, "SEdet");
return d;
}
template <class Field>
typename Field::Element &detin (typename Field::Element &d,
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> &A,
const RingCategories::ModularTag &tag,
const Method::SparseElimination &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
commentator().start ("Sparse Elimination Determinant in place", "SEDetin");
GaussDomain<Field> GD ( A.field() );
GD.detin (d, A, Meth.strategy ());
commentator().stop ("done", NULL, "SEdetin");
return d;
}
// The det with Elimination Method
template<class Field, class Vector>
typename Field::Element &det (typename Field::Element &d,
const SparseMatrix<Field, Vector> &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
return det(d, A, tag, Method::SparseElimination(Meth));
}
template <class Field>
typename Field::Element &detin (typename Field::Element &d,
SparseMatrix<Field, typename LinBox::Vector<Field>::SparseSeq> &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
return detin(d, A, tag, Method::SparseElimination(Meth));
}
template<class Field, class Vector>
typename Field::Element &detin (typename Field::Element &d,
SparseMatrix<Field, Vector> &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
// Matrix is not of type SparseMatrix<..SparseSeq> otherwise previous specialization would occur
// will copy A into SparseMatrix<..SparseSeq> or BlasMatrix
const Field& F = A.field();
integer c; F.characteristic(c);
if ((c < LinBox::BlasBound) && ((A.rowdim() < 300) || (A.coldim() < 300) || (A.size() > (A.coldim()*A.rowdim()/100))))
return det(d, A, tag, Method::BlasElimination(Meth));
else
return det(d, A, tag, Method::SparseElimination(Meth));
}
// The det with Elimination Method
template<class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
// Matrix is not of type SparseMatrix otherwise previous specialization would occur
// will copy A into BlasMatrix
return det(d, A, tag, Method::BlasElimination(Meth));
}
template<class Blackbox>
typename Blackbox::Field::Element &detin (typename Blackbox::Field::Element &d,
Blackbox &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
// Matrix is not of type SparseMatrix not of type BlasMatrix
// otherwise previous specialization would occur
// will copy A into BlasMatrix
return det(d, A, tag, Method::BlasElimination(Meth));
}
template<class Field>
typename Field::Element &detin (typename Field::Element &d,
BlasMatrix<Field> &A,
const RingCategories::ModularTag &tag,
const Method::Elimination &Meth)
{
return detin(d, A);
}
template<class Field>
typename Field::Element &detin (typename Field::Element &d,
BlasMatrix<Field> &A,
const RingCategories::ModularTag &tag,
const Method::BlasElimination &Meth)
{
return detin(d, A);
}
// This should work for a BlasMatrix too ?
/** Rank of Blackbox \p A.
* \ingroup solutions
* A will be modified.
* \param[out] d determinant of \p A.
* \param A this BlasMatrix matrix will be modified in place in the process.
* \return \p d
*/
template <class Field>
typename Field::Element &detin (typename Field::Element &d,
BlasMatrix<Field> &A)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
Field F = A.field();
commentator().start ("Determinant", "detin");
linbox_check (A.coldim () == A.rowdim ());
BlasMatrixDomain<Field> BMD(F);
d= BMD.detin(static_cast<BlasMatrix<Field>& > (A));
commentator().stop ("done", NULL, "detin");
return d;
}
} // end of LinBox namespace
#include "linbox/field/modular.h"
//#include "linbox/field/givaro-zpz.h"
#ifdef __LINBOX_HAVE_MPI
#include "linbox/algorithms/cra-mpi.h"
#else
#ifdef __LINBOX_HAVE_KAAPI //use the kaapi version instead of the usual version if this macro is defined
#include "linbox/algorithms/cra-kaapi.h"
#else
#include "linbox/algorithms/cra-domain.h"
#endif
#endif
#include "linbox/algorithms/cra-early-single.h"
#include "linbox/randiter/random-prime.h"
#include "linbox/algorithms/matrix-hom.h"
#include <typeinfo>
namespace LinBox
{
template <class Blackbox, class MyMethod>
struct IntegerModularDet {
const Blackbox &A;
const MyMethod &M;
IntegerModularDet(const Blackbox& b, const MyMethod& n) :
A(b), M(n)
{}
template<typename Field>
typename Field::Element& operator()(typename Field::Element& d, const Field& F) const
{
typedef typename Blackbox::template rebind<Field>::other FBlackbox;
FBlackbox Ap(A, F);
detin( d, Ap, RingCategories::ModularTag(), M);
return d;
}
};
template <class Blackbox, class MyMethod>
typename Blackbox::Field::Element &cra_det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::IntegerTag &tag,
const MyMethod &Meth
#ifdef __LINBOX_HAVE_MPI
,Communicator *C = NULL
#endif
)
{
// if no parallelism or if this is the parent process
// begin the verbose output
#ifdef __LINBOX_HAVE_MPI
if(!C || C->rank() == 0)
#endif
commentator().start ("Integer Determinant", "idet");
// 0.7213475205 is an upper approximation of 1/(2log(2))
IntegerModularDet<Blackbox, MyMethod> iteration(A, Meth);
RandomPrimeIterator genprime( 26-(int)ceil(log((double)A.rowdim())*0.7213475205));
integer dd; // use of integer due to non genericity of cra. PG 2005-08-04
// will call regular cra if C=0
#ifdef __LINBOX_HAVE_MPI
MPIChineseRemainder< EarlySingleCRA< Modular<double> > > cra(4UL, C);
cra(dd, iteration, genprime);
if(!C || C->rank() == 0){
A.field().init(d, dd); // convert the result from integer to original type
commentator().stop ("done", NULL, "det");
}
#else
ChineseRemainder< EarlySingleCRA< Modular<double> > > cra(4UL);
cra(dd, iteration, genprime);
A.field().init(d, dd); // convert the result from integer to original type
commentator().stop ("done", NULL, "idet");
#endif
return d;
}
} // end of LinBox namespace
//#if 0
#ifdef __LINBOX_HAVE_NTL
# include "linbox/algorithms/hybrid-det.h"
# define SOLUTION_CRA_DET lif_cra_det
#else
# define SOLUTION_CRA_DET cra_det
#endif
#include "linbox/algorithms/rational-cra2.h"
#include "linbox/algorithms/varprec-cra-early-single.h"
#include "linbox/algorithms/det-rational.h"
namespace LinBox
{
template <class Blackbox, class MyMethod>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::IntegerTag &tag,
const MyMethod &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
return SOLUTION_CRA_DET(d, A, tag, Meth);
}
template< class Blackbox, class MyMethod>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
const RingCategories::RationalTag &tag,
const MyMethod &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
commentator().start ("Rational Determinant", "rdet");
Integer num,den;
IntegerModularDet<Blackbox, MyMethod> iteration(A, Meth);
RandomPrimeIterator genprime( 26-(int)ceil(log((double)A.rowdim())*0.7213475205));
RationalRemainder2< VarPrecEarlySingleCRA< Modular<double> > > rra(4UL);
rra(num,den, iteration, genprime);
A.field().init(d, num,den); // convert the result from integer to original type
commentator().stop ("done", NULL, "rdet");
return d;
}
template<class Field, class MyMethod>
typename Field::Element &det (typename Field::Element &d,
const BlasMatrix<Field> &A,
const RingCategories::RationalTag &tag,
const MyMethod &Meth)
{
if (A.coldim() != A.rowdim())
throw LinboxError("LinBox ERROR: matrix must be square for determinant computation\n");
commentator().start ("Dense Rational Determinant", "rdet");
rational_det(d,A,Meth);
commentator().stop ("done", NULL, "rdet");
return d;
}
} // end of LinBox namespace
#ifdef __LINBOX_HAVE_MPI
namespace LinBox
{
template <class Blackbox>
typename Blackbox::Field::Element &det (typename Blackbox::Field::Element &d,
const Blackbox &A,
/*const*/ Communicator &C)
{
return det(d, A, Method::Hybrid(C));
}
}
#endif //__LINBOX_HAVE_MPI
#endif // __LINBOX_det_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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