/usr/include/linbox/algorithms/signature.h is in liblinbox-dev 1.3.2-1.1build2.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 | /* Copyright (C) LinBox
* Written by Zhendong Wan
*
*
*
* ========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_signature_H
#define __LINBOX_signature_H
/* Function related to the signature computation of symmetric matrices */
#include "linbox/field/modular.h"
#include "linbox/algorithms/cra-early-multip.h"
#include <fflas-ffpack/ffpack/ffpack.h>
#include "linbox/randiter/random-prime.h"
#include "linbox/matrix/blas-matrix.h"
#include "linbox/algorithms/blas-domain.h"
#include "linbox/solutions/minpoly.h"
namespace LinBox
{
class Signature {
public:
class BLAS_LPM_Method {};
class Minpoly_Method {};
template <class Matrix>
bool isPosDef (const Matrix& M);
template <class Matrix>
static bool isPosDef (const Matrix& M, const BLAS_LPM_Method& meth)
{
RandomPrimeIterator::setSeed(time(0));
size_t n = M. rowdim();
std::vector<int> P;
symmetricLU (P, M);
if (P. size () < n)
return false;
typedef typename Matrix::Field::Element Int;
std::vector<Int> D(n);
semiD(D, M);
//std::cout << "All principal minors are: [";
//for (int i = 0; i < n; ++ i)
// std::cout << D[i] << ", ";
//std::cout << "]\n";
if (allPos(D)) return true;
else return false;
}
template <class Matrix>
static bool isPosDef (const Matrix& M, const Minpoly_Method& meth)
{
typedef typename Matrix::Field::Element Int;
typedef std::vector<Int> Poly;
Poly p;
minpoly (p, M);
typename Poly::reverse_iterator p_p;
typename Matrix::Field R = M. field();
bool flip = false;
for (p_p = p .rbegin(); p_p != p. rend(); ++ p_p) {
if (flip)
R. negin(*p_p);
flip = 1 - flip;
}
if(allPos(p)) return true;
else return false;
}
template <class Matrix>
static bool isPosSemiDef (const Matrix& M, const BLAS_LPM_Method& meth)
{
RandomPrimeIterator::setSeed(time(0));
size_t n = M. rowdim();
std::vector<int> P;
size_t r = rank_random (M);
//std::clog << "Rank:= " << r << std::endl;
if (r == 0)
return true;
symmetricLU (P, M);
if (P. size () < r)
return false;
typedef typename Matrix::Field::Element Int;
std::vector<Int> D(P.size());
typename Matrix::Field R = M. field();
//std::cout << "Begin semiD:\n";
if(P. size() == n)
semiD(D, M);
else {
Matrix PM (R, P.size(), P.size());
typename Matrix::RowIterator cur_r; int j = 0;
for (cur_r = PM. rowBegin(); cur_r != PM. rowEnd(); ++ cur_r, ++j) {
typename Matrix::ConstRowIterator m_r = M. rowBegin() + P[j];
for (size_t k = 0; k < P.size(); ++ k)
R. assign (cur_r -> operator[] (k),
m_r -> operator[] (P[k]));
}
semiD (D, PM);
}
//std::cout << "End semiD:\n";
if (allPos(D)) return true;
else return false;
}
template <class Matrix>
static bool isPosSemiDef (const Matrix& M, const Minpoly_Method& meth)
{
typedef typename Matrix::Field::Element Int;
typedef std::vector<Int> Poly;
Poly p;
minpoly (p, M);
typename Poly::reverse_iterator p_p;
typename Matrix::Field R = M. field();
bool flip = false;
for (p_p = p .rbegin(); p_p != p. rend(); ++ p_p) {
if (flip)
R. negin(*p_p);
flip = 1 - flip;
}
if(allNonNeg(p)) return true;
else return false;
}
private:
template <class Vector>
static bool allPos (const Vector& v)
{
typename Vector::const_iterator p;
for (p = v. begin(); p != v. end(); ++ p)
if (*p <= 0)
return false;
return true;
}
template <class Vector>
static bool allNonNeg (const Vector& v)
{
typename Vector::const_iterator p;
for (p = v. begin(); p != v. end(); ++ p)
if (*p < 0)
return false;
return true;
}
/* Compute the equivalent diagonal matrix
* ie. with the same signature
* Assume M is non-singular and symmetric with generic rank profile
*/
template <class Matrix, class Vector>
static Vector& semiD (Vector& out, const Matrix& M)
{
//std::cout << "Debug begin with input matrix:\n";
//M. write (std::cout);
typedef typename Matrix::Field Ring;
typedef typename Ring::Element Integer_t;
typedef Modular<double> Field;
typedef Field::Element Element;
size_t n = M. rowdim();
integer mmodulus;
FieldTraits<Field>::maxModulus(mmodulus);
long bit1 = (long) floor (log((double)mmodulus)/M_LN2);
long bit2 = (long) floor (log(sqrt(double(4503599627370496LL/n)))/M_LN2);
RandomPrimeIterator primeg(unsigned(bit1 < bit2 ? bit1 : bit2));
Field::Element* FA = new Field::Element[n*n];
size_t* P= new size_t[n], *PQ = new size_t[n];
size_t* P_p, * PQ_p;
Field::Element* p; Field::Element tmp;
EarlyMultipCRA< Field > cra(3UL);
Integer_t m = 1;
std::vector<Field::Element> v(n);
size_t j = 0;
Field K2;
bool faithful = true;
typename Matrix::ConstIterator raw_p;
do {
// get a prime.
// Compute mod that prime. Accumulate into v with CRA.
++primeg ; while(cra.noncoprime(*primeg)) ++primeg;
Field K1(*primeg);
K2 = K1;
//clog << "Computing blackbox matrix mod " << prime;
for (p = FA, raw_p = M. Begin(); p != FA + (n*n); ++ p, ++ raw_p)
K1. init (*p, *raw_p);
//clog << "\rComputing lup mod " << prime << ". ";
FFPACK::LUdivine((typename Field::Father_t)K1, FFLAS::FflasNonUnit, FFLAS::FflasNoTrans, n, n, FA, n, P, PQ, FFPACK::FfpackLQUP);
faithful = true;
for ( j = 0, P_p = P, PQ_p = PQ; j < n; ++ j, ++ P_p, ++ PQ_p)
if ((*P_p != j) || (*PQ_p != j)) {
faithful = false;
break;
}
} while(! faithful);
K2. init (tmp, 1UL);
typename std::vector<Field::Element>::iterator vp;
for (j = 0, vp = v.begin(); vp != v.end(); ++j, ++vp) {
K2.mulin(tmp, *(FA + (j * n + j)));
K2.assign(*vp, tmp);
}
cra. initialize(K2, v);
while (! cra.terminated() ){
// get a prime.
++primeg; while(cra.noncoprime(*primeg)) ++primeg;
Field K3(*primeg);
//clog << "Computing blackbox matrix mod " << prime;
for (p = FA, raw_p = M. Begin(); p != FA + (n*n); ++ p, ++ raw_p)
K3. init (*p, *raw_p);
//clog << "\rComputing lup mod " << prime << ". ";
FFPACK::LUdivine((typename Field::Father_t)K3, FFLAS::FflasNonUnit, FFLAS::FflasNoTrans, n, n, FA, n, P, PQ, FFPACK::FfpackLQUP);
faithful = true;
for ( j = 0, P_p = P, PQ_p = PQ; j < n; ++ j, ++ P_p, ++ PQ_p)
if ((*P_p != j) || (*PQ_p != j)) {
faithful = false;
break;
}
if (!faithful) {
//std::cout << "Not a faithful prime\n";
continue;
}
K3. init (tmp, 1UL);
for (j = 0, vp = v.begin(); vp != v.end(); ++j, ++vp) {
K3.mulin(tmp, *(FA + (j * n + j)));
K3.assign(*vp, tmp);
}
#if 0
std::cout << "Faithful image:[";
for (int l = 0; l < v. size(); ++ l)
std::cout << v[l] << ", ";
std::cout << "]\n";
#endif
cra. progress(K3, v);
}
delete[] FA;
delete[] P;
delete[] PQ;
//std::cout << "Compute the final answer.\n";
cra.result(out);
return out;
}
//only works with symmetric integer matrix
// return a permutation matrix which is represented as a vector, such that
// all principal of PAP^T are non-zero, up to a maximal.
template <class Vector, class Matrix>
static Vector& symmetricLU (Vector& v, const Matrix& IM)
{
typedef Modular<int32_t> Field;
// typedef Modular<double> Field;
typedef Field::Element Element;
typedef BlasMatrix<Field> FMatrix;
RandomPrimeIterator primeg(20);
Field F ((unsigned long)*primeg);
FMatrix FM(F, IM.rowdim(), IM.coldim());
//std::cout << "Random prime " << p << "\n";
Element zero; F. init (zero, 0);
MatrixHom::map (FM, IM, F);
VectorDomain<Field> VD(F);
FMatrix& M = FM;
//typename FMatrix::RowIterator cur_r, tmp_r;
typedef FMatrix::Row Row;
//the index is 0-based.
int i = 0;
int n = (int) M. rowdim();
std::vector<int> P(n);
for (i = 0; i < n; ++ i)
P[i] = i;
//M. write(std::cout);
for (i = 0; i < n; ++ i) {
//std::cout << "i= " << i << "\n";
int j;
//find a pivot
for (j = i; j < n; ++ j) {
if (!F. isZero(M[j][j])) break;
}
//no piviot
if (j == n) break;
// a pivot
if (j != i) {
VD. swap (*(M. colBegin() + j), *(M. colBegin() + i));
VD. swap (*(M. rowBegin() + j), *(M. rowBegin() + i));
}
//std::cout << "Pivot= " << j << '\n';
//M. write(std::cout);
P[i] = j;
Element tmp;
F. inv (tmp, M[i][i]);
F. negin(tmp);
VD. mulin(*(M. rowBegin() + i), tmp);
//M. write(std::cout);
for (j = i + 1; j < n; ++ j) {
F. assign (tmp, M[j][i]);
VD. axpyin (*(M. rowBegin() + j), tmp,
*(M. rowBegin() + i));
}
//not necessary
//M. write(std::cout);
for (j = i + 1; j < n; ++ j)
F. assign (M[i][j], zero);
}
v. resize (n);
std::vector<int>::iterator i_p; int j;
for (i_p = v. begin(), j = 0; i_p != v. end(); ++ i_p, ++ j)
*i_p = j;
for (j = 0; j < i; ++ j) {
if (j != P[j])
std::swap (v[j], v[P[j]]);
}
v. resize (i);
//std::cout << "Pseud-rank: " << i << "\n[";
//for (i_p = v. begin(); i_p != v. end(); ++ i_p)
// std::cout << *i_p << ", ";
//std::cout << "]\n";
return v;
}
// This assumes Matrix is BlasMatrix
// (that it's rawiterator will go thru n^2 values row by row.)
template <class Matrix>
static long rank_random (const Matrix& M)
{
typedef typename Matrix::Field Ring;
// typedef typename Ring::Element Integer_t;
typedef Modular<double> Field;
typedef Field::Element Element;
int n = (int)M. rowdim();
integer mmodulus;
FieldTraits<Field>::maxModulus(mmodulus);
long bit1 = (long) floor (log((double)mmodulus)/M_LN2);
long bit2 = (long) floor (log(sqrt(double(4503599627370496LL/n)))/M_LN2);
RandomPrimeIterator primeg((unsigned)(bit1 < bit2 ? bit1 : bit2));
Field::Element* FA = new Field::Element[n*n], *p;
// get a prime.
// Compute the rank mod that prime. Accumulate into v with CRA.
Field K(*primeg);
typename Matrix::ConstIterator raw_p;
for (p = FA, raw_p = M. Begin(); p != FA + (n*n); ++ p, ++ raw_p)
K. init (*p, *raw_p);
long r = FFPACK::Rank((typename Field::Father_t) K, n, n, FA, n);
delete[] FA;
return r;
}
}; // end of class Signature
} //end of namespace LinBox
#endif //__LINBOX_signature_H
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// mode: C++
// tab-width: 8
// indent-tabs-mode: nil
// c-basic-offset: 8
// End:
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