/usr/include/fflas-ffpack/checkers/checker_charpoly.inl is in fflas-ffpack-common 2.2.2-5.
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// vim:sts=4:sw=4:ts=4:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/* checkers/Checker_charpoly.inl
* Copyright (C) 2016 Ashley Lesdalons
*
* Written by Ashley Lesdalons <Ashley.Lesdalons@e.ujf-grenoble.fr>
*
*
* ========LICENCE========
* This file is part of the library FFLAS-FFPACK.
*
* FFLAS-FFPACK 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 __FFLASFFPACK_checker_charpoly_INL
#define __FFLASFFPACK_checker_charpoly_INL
#include "fflas-ffpack/ffpack/ffpack.h"
#ifdef TIME_CHECKER_CHARPOLY
#include <givaro/givtimer.h>
#endif
namespace FFPACK {
template <class Field, class Polynomial>
class CheckerImplem_charpoly {
const Field& F;
const size_t n, lda;
typename Field::Element lambda, det;
bool pass;
#ifdef TIME_CHECKER_CHARPOLY
Givaro::Timer _time;
#endif
public:
CheckerImplem_charpoly(const Field& F_, const size_t n_, typename Field::ConstElement_ptr A, size_t lda_)
: F(F_), n(n_), lda(lda_)
{
typename Field::RandIter G(F);
init(G,A);
}
CheckerImplem_charpoly(typename Field::RandIter &G, const size_t n_, typename Field::ConstElement_ptr A, size_t lda_)
: F(G.ring()), n(n_), lda(lda_)
{
init(G,A);
}
~CheckerImplem_charpoly() {
}
inline bool check(Polynomial &g) {
#ifdef TIME_CHECKER_CHARPOLY
Givaro::Timer checktime; checktime.start();
#endif
typename Field::Element h = F.zero,
t = F.one,
u;
for (size_t i=0; i < g.size(); ++i) {
F.mul(u,g[i],t);
F.add(h,h,u);
F.mul(t,t,lambda);
}
// is h == det ?
pass = pass && F.areEqual(h,det);
if (!pass) throw FailureCharpolyCheck();
#ifdef TIME_CHECKER_CHARPOLY
checktime.stop(); _time += checktime;
std::cerr << "CHARPol CHECK: " << _time << std::endl;
#endif
return pass;
}
private:
inline void init(typename Field::RandIter &G, typename Field::ConstElement_ptr A) {
#ifdef TIME_CHECKER_CHARPOLY
Givaro::Timer inittime; inittime.start();
#endif
// random lambda
G.random(lambda);
typename Field::Element_ptr v = FFLAS::fflas_new(F,n,1),
w = FFLAS::fflas_new(F,n,1),
Ac = FFLAS::fflas_new(F,n,n);
FFLAS::frand(F,G,n,v,1);
// w <- -A.v
FFLAS::fgemv(F, FFLAS::FflasNoTrans, n, n, F.mOne, A, lda, v, 1, F.zero, w, 1);
if (!F.isZero(lambda)) {
// w <- lambda.v + w
FFLAS::faxpy(F, n, lambda, v, 1, w, 1);
}
// Ac <- A - lambda.I
FFLAS::fassign(F,n,n,A,lda,Ac,n);
for (size_t i=0; i<n; ++i)
F.subin(*(Ac+i*n+i),lambda);
// w <- Ac.v + w
FFLAS::fgemv(F, FFLAS::FflasNoTrans, n, n, F.one, Ac, n, v, 1, F.one, w, 1);
// is w == 0 ?
pass = FFLAS::fiszero(F,n,1,w,1);
FFLAS::fflas_delete(v,w);
if (!pass) throw FailureCharpolyCheck();
// P,Ac,Q <- PLUQ(Ac)
size_t *P = FFLAS::fflas_new<size_t>(n);
size_t *Q = FFLAS::fflas_new<size_t>(n);
#ifdef TIME_CHECKER_CHARPOLY
Givaro::Timer pluqtime; pluqtime.start();
#endif
FFPACK::PLUQ(F, FFLAS::FflasNonUnit, n, n, Ac, n, P, Q);
#ifdef TIME_CHECKER_CHARPOLY
pluqtime.stop(); _time -= pluqtime;
inittime.stop(); _time += inittime;
std::cerr << "CHARPol server PLUQ:" << pluqtime << std::endl;
inittime.start();
#endif
// compute the determinant of A
F.init(det,*Ac);
for (size_t i=1; i<n; ++i)
F.mul(det,det,*(Ac+i*n+i));
if (n%2 == 1) F.neg(det,det);
// count the number of permutations
int t = 0;
for (size_t i=0; i<n; ++i) {
if (P[i] != i) t++;
if (Q[i] != i) t++;
}
if (t%2 == 1) F.neg(det,det);
FFLAS::fflas_delete(Ac);
#ifdef TIME_CHECKER_CHARPOLY
inittime.stop(); _time += inittime;
#endif
}
};
}
#endif // __FFLASFFPACK_checker_charpoly_INL
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