/usr/include/fflas-ffpack/ffpack/ffpack_minpoly_construct.inl is in fflas-ffpack-common 2.2.2-5.
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// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/* fflas-ffpack/ffpack/ffpack_minpoly_construct.inl
* Copyright (C) 2003 Clement Pernet
*
* Written by Clement Pernet <Clement.Pernet@imag.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_ffpack_minpoly_construct_INL
#define __FFLASFFPACK_ffpack_minpoly_construct_INL
#error "not included anywhere"
namespace FFPACK {
//#define LB_DEBUG
//---------------------------------------------------------------------
// MinPoly: Compute the minimal polynomial of (A,v) using an LUP
// factorization of the Krylov Base (v, Av, .., A^kv)
// U must be (n+1)*n
//---------------------------------------------------------------------
template <class Field, class Polynomial>
Polynomial&
MinPoly( const Field& F, Polynomial& minP, const size_t N,
typename Field::ConstElement_ptr A, const size_t lda,
typename Field::Element_ptr U, size_t ldu, typename Field::Element_ptr X, size_t ldx,
size_t* P)
{
// nRow is the number of row in the krylov base already computed
size_t j, k, nRow = 2;
typename Field::Element_ptr B = FFLAS::fflas_new (F, N, N);
typename Polynomial::iterator it;
typename Field::Element_ptr Xi, *Ui;
typename Field::RandIter g (F);
bool KeepOn=true;
// Creating the Krylov Base copy matrix X where to factorize
//typename Field::Element_ptr X = FFLAS::fflas_new<elt>((N+1)*N);
#ifdef LB_DEBUG
for (j=0;j<(N+1)*N;j++)
X[j] = zero;
#endif
// Creating the copy of A, where to compute A^2^i
// Try memcopy here
for (size_t i=0; i<N; ++i)
for ( size_t j=0; j<N; ++j)
*(B+i*N+j) = *(A+i*N+j);
// Picking a non zero vector
do{
for (Ui=U, Xi = X; Ui<U+N; ++Ui, ++Xi){
g.random (*Ui);
*Xi = *Ui;
if (!F.isZero(*Ui))
KeepOn = false;
}
}while(KeepOn);
nRow = 1;
size_t nUsedRow = 0;
// LUP factorization of the Krylov Base Matrix
k = Protected::LUdivine_construct(F, FflasUnit, N+1, N, B, N, U, ldu, X, N, P,
&nRow, N+1, &nUsedRow );
FFLAS::fflas_delete (B);
minP.resize(k+1);
minP[k] = one;
if (k==1 && F.isZero(*(X+N))){ // minpoly is X
return minP;
}
// m contains the k first coefs of the minpoly
typename Field::Element_ptr m= FFLAS::fflas_new (F,k,1);
fassign( F, k, X+k*N, 1, m, 1);
ftrsv( F, FflasLower, FflasTrans, FflasNonUnit, k, X, N, m, 1);
//FFLAS::fflas_delete( X);
it = minP.begin();
for (j=0; j<k; ++j, it++){
F.neg(*it, m[j]);
}
FFLAS::fflas_delete (m);
return minP;
}
} // FFPACK
#undef LB_DEBUG
#endif //__FFLASFFPACK_ffpack_minpoly_construct_INL
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