/usr/include/fflas-ffpack/ffpack/ffpack_charpoly_kgfast.inl is in fflas-ffpack-common 1.6.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 | /* -*- mode: C++; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/* ffpack/ffpack_charpoly_kgfast.inl
* Copyright (C) 2004 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_charpoly_kgfast_INL
#define __FFLASFFPACK_ffpack_charpoly_kgfast_INL
#ifndef MIN
#define MIN(a,b) (a<b)?a:b
#endif
namespace FFPACK {
namespace Protected {
//---------------------------------------------------------------------
// CharPoly: Compute the characteristic polynomial of A using
// Keller-Gehrig's fast algorithm. A must be generic.
//---------------------------------------------------------------------
template <class Field, class Polynomial>
int
KGFast ( const Field& F, std::list<Polynomial>& charp,
const size_t N,
typename Field::Element * A, const size_t lda,
size_t * kg_mc, size_t* kg_mb, size_t* kg_j )
{
//std::cerr<<"Dans KGFast"<<std::endl;
size_t mc=N>>1; // Matrix A is transformed into a mc_Frobenius form
size_t mb=N-mc;
size_t r;
typename Field::Element * C, *B;
while ( mc > 0 ) {
#if 0
std::cerr<<"Boucle1: mc,mb,N="<<mc<<" "<<mb<<" "<<N<<std::endl;
write_field( F, std::cerr, A, N, N, lda );
#endif
size_t j=0;
C = A + (N-mc);
//std::cerr<<std::endl<<"mc="<<mc<<":";
while ( (j+1)*mc < N ) {
mb = MIN ( mb, N-(j+1)*mc );
#if 0
std::cerr<<"Boucle2: j,mb="<<j<<" "<<mb<<std::endl;
write_field( F, std::cerr, A, N, N, lda );
#endif
B = A + (N-mc-mb);
// B1 <- C1^-1.B1
typename Field::Element * LUP = new typename Field::Element[mc*mc];
for (size_t i=0; i<mc; ++i)
FFLAS::fcopy( F, mc, LUP+i*mc, 1, C+i*lda, 1);
size_t * P = new size_t[mc];
size_t * Q = new size_t[mc];
if ( (r = LUdivine( F, FFLAS::FflasNonUnit, FFLAS::FflasNoTrans, mc, mc,
LUP, mc, P, Q, FfpackLQUP)) < mc ){
* kg_mc = mc;
* kg_mb = mb;
* kg_j = j;
delete[] P;
delete[] Q;
delete[] LUP;
return -1;
}
#if 0
std::cerr<<"LUP="<<std::endl;
write_field( F, std::cerr, LUP, mc, mc, mc );
#endif
//std::cerr<<" "<<r;
ftrsm(F, FFLAS::FflasLeft, FFLAS::FflasLower, FFLAS::FflasNoTrans, FFLAS::FflasUnit,
mc, mb, F.one, LUP, mc , B, lda);
ftrsm(F, FFLAS::FflasLeft, FFLAS::FflasUpper, FFLAS::FflasNoTrans, FFLAS::FflasNonUnit,
mc, mb, F.one, LUP, mc , B, lda);
delete[] LUP;
applyP( F, FFLAS::FflasLeft, FFLAS::FflasTrans, mb, 0, (int)mc, B, lda, P );
delete[] P;
delete[] Q;
#if 0
std::cerr<<"Apres B1<-C1^-1"<<std::endl;
write_field( F, std::cerr, A, N, N, lda );
#endif
// B2 <- B2 - C2.B1
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, N-mc, mb, mc,
F.mOne, C+mc*lda, lda, B, lda,
F.one, B+mc*lda, lda);
#if 0
std::cerr<<"Apres B2<-B2-C2.B1"<<std::endl;
write_field( F, std::cerr, A, N, N, lda );
#endif
// Shifting B: B1;B2 -> B2;B1
typename Field::Element * tmp = new typename Field::Element[mc*mb];
for (size_t i=0; i<mc; ++i)
FFLAS::fcopy( F, mb, tmp+i*mb, 1, B+i*lda, 1);
for (size_t i=mc; i<N; ++i)
FFLAS::fcopy( F, mb, B+(i-mc)*lda, 1, B+i*lda, 1);
for (size_t i=0; i<mc; ++i)
FFLAS::fcopy( F, mb, B+(i+N-mc)*lda, 1, tmp+i*mb, 1);
delete[] tmp;
#if 0
std::cerr<<"Apres shift de B"<<std::endl;
write_field( F, std::cerr, A, N, N, lda );
#endif
// C3 <- B3.C1 + C3
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, (j+1)*mc, mc, mb,
F.one, B+(N-(j+1)*mc)*lda, lda, C+(N-(j+1)*mc-mb)*lda, lda,
F.one, C+(N-(j+1)*mc)*lda, lda);
#if 0
std::cerr<<"C3 <- B3.C1 + C3: B3="<<std::endl;
write_field( F, std::cerr, B+(N-(j+1)*mc)*lda, (j+1)*mc, mb, lda );
std::cerr<<"C3 <- B3.C1 + C3: C1"<<std::endl;
write_field( F, std::cerr, C+(N-(j+1)*mc-mb)*lda, mb, mc, lda );
std::cerr<<"C3 <- B3.C1 + C3: C3="<<std::endl;
write_field( F, std::cerr, C+(N-(j+1)*mc)*lda, (j+1)*mc, mc, lda );
#endif
int lambda = (int)(N - mb - (j+1)*mc );
if ( int(mb) < lambda ){
#if 0
std::cerr<<"mb<lambda"<<std::endl;
#endif
typename Field::Element * tmp2 = new typename Field::Element[lambda*mc];
// tmp2 <- C1
for (int i=0; i<lambda; ++i)
FFLAS::fcopy( F, mc, tmp2+i*mc, 1, C+i*lda, 1);
// C1' <- B1.C2
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, mb, mc, mb,
F.one, B, lda, C+lambda*lda, lda,
F.zero, C, lda);
// tmp2 <- B2.C2 + tmp2
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, lambda, mc, mb,
F.one, B+mb*lda, lda, C+lambda*lda, lda,
F.one, tmp2, mc);
// C2' <- tmp2
for (int i=0; i<lambda; ++i)
FFLAS::fcopy( F, mc, C+mb*lda+i*lda, 1, tmp2+i*mc, 1);
delete[] tmp2;
}
else if ( lambda > 0 ){
#if 0
std::cerr<<"lambda>0"<<std::endl;
#endif
typename Field::Element * tmp2 = new typename Field::Element[mb*mc];
// C1 <- B2.C2 + C1
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, lambda, mc, mb,
F.one, B+mb*lda, lda, C+lambda*lda, lda,
F.one, C, lda);
// tmp2 <-B1.C2
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, mb, mc, mb,
F.one, B, lda, C+lambda*lda, lda,
F.zero, tmp2, mc);
// C2' <- C1
for (int i=0; i<lambda; ++i)
FFLAS::fcopy( F, mc, C+mb*lda+i*lda, 1, C+i*lda, 1);
// C1' <- tmp2
for (size_t i=0; i<mb; ++i)
FFLAS::fcopy( F, mc, C+i*lda, 1, tmp2+i*mc, 1);
delete[] tmp2;
}
else{
#if 0
std::cerr<<"lambda<0"<<std::endl;
#endif
mb = N - (j+1)*mc;
typename Field::Element * tmp2 = new typename Field::Element[mb*mc];
// tmp2 <-B1.C1
fgemm(F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, mb, mc, mb,
F.one, B, lda, C, lda,
F.zero, tmp2, mc);
// C1' <- tmp2
for (size_t i=0; i<mb; ++i)
FFLAS::fcopy( F, mc, C+i*lda, 1, tmp2+i*mc, 1);
delete[] tmp2;
}
j++;
}
mb = mc;
mc>>=1;
mb -= mc;
}
Polynomial *minP = new Polynomial();
minP->resize(N+1);
minP->operator[](N) = F.one;
typename Polynomial::iterator it = minP->begin();
for (size_t j=0; j<N; ++j, it++){
F.neg(*it, *(A+N-1+j*lda));
}
charp.clear();
charp.push_front(*minP);
return 0;
}
template<class Field>
void
fgemv_kgf( const Field& F, const size_t N,
const typename Field::Element * A, const size_t lda,
const typename Field::Element * X, const size_t incX,
typename Field::Element * Y, const size_t incY,
const size_t kg_mc, const size_t kg_mb, const size_t kg_j )
{
size_t big_truc =kg_mb-kg_mc*(kg_j+1) ;
size_t lambda = (N<big_truc)?(0):(N-big_truc);
// Y1 <- X2
FFLAS::fcopy ( F, lambda, Y, incY, X+(kg_mb+kg_mc)*incX, incX );
// Y2 <- X.B
fgemv( F, FFLAS::FflasTrans, N, kg_mb, F.one, A+N-kg_mc-kg_mb, lda, X, incX, F.zero, Y+lambda*incY, incY );
// Y3 <- X3
FFLAS::fcopy ( F, kg_j*kg_mc, Y+(lambda+kg_mb)*incY, incY, X+(lambda+kg_mb+kg_mc)*incX, incX );
// Y4 <- X.C
fgemv( F, FFLAS::FflasTrans, N, kg_mc, F.one, A+N-kg_mc, lda, X, incX, F.zero, Y+(N-kg_mc)*incY, incY );
}
} // Protected
} // FFPACK
#endif // __FFLASFFPACK_ffpack_charpoly_kgfast_INL
|