This file is indexed.

/usr/include/linbox/algorithms/wiedemann.inl is in liblinbox-dev 1.3.2-1.1build2.

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
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
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
/* linbox/algorithms/wiedemann.inl
 * Copyright (C) 2002 Zhendong Wan
 * Copyright (C) 2002 Bradford Hovinen
 *
 * Written by Zhendong Wan <wan@mail.eecis.udel.edu>,
 *            Bradford Hovinen <hovinen@cis.udel.edu>
 *
 * ------------------------------------
 * 2002-10-02  Bradford Hovinen  <bghovinen@math.uwaterloo.ca>
 *
 * Refactoring:
 * Put everything inside a WiedemannSolver class, with the following
 * interface:
 *    solve - Solve a general linear system
 *    solveNonsingular - Solve a nonsingular system
 *    solveSingular - Solve a general singular system
 *    findRandomSolution - Find a random solution to a singular preconditioned
 *                         problem
 *    findNullspaceElement - Find an element of the right nullspace
 *    certifyInconsistency - Find a certificate of inconsistency for a
 *                           linear system
 *    precondition - Form a preconditioner and return it
 * ------------------------------------
 * 2002-08-09  Bradford Hovinen  <hovinen@cis.udel.edu>
 *
 * Move the Wiedemann stuff over to this file
 *
 * Create a singular and nonsingular version that is a bit intelligent about
 * which one to use in different circumstances
 * ------------------------------------
 *
 * 
 * ========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_wiedemann_INL
#define __LINBOX_wiedemann_INL

#include <vector>
#include <algorithm>

#include "linbox/solutions/minpoly.h"
#include "linbox/algorithms/wiedemann.h"
#include "linbox/blackbox/submatrix.h"
#include "linbox/blackbox/butterfly.h"
#include "linbox/blackbox/transpose.h"
#include "linbox/algorithms/blackbox-container.h"
#include "linbox/algorithms/blackbox-container-symmetric.h"
//#include "linbox/algorithms/blackbox-container-generic.h"
#include "linbox/algorithms/massey-domain.h"
#include "linbox/switch/cekstv.h"
#include "linbox/solutions/rank.h"
#include "linbox/vector/stream.h"

namespace LinBox
{

	template <class Field>
	template<class Blackbox, class Vector>
	typename WiedemannSolver<Field>::ReturnStatus
	WiedemannSolver<Field>::solve (const Blackbox   &A,
				       Vector           &x,
				       const Vector     &b,
				       Vector           &u)
	{
		linbox_check ((x.size () == A.coldim ()) &&
			      (b.size () == A.rowdim ()));
		linbox_check (_traits.singular () != WiedemannTraits::NONSINGULAR || A.coldim () == A.rowdim ());

		commentator().start ("Solving linear system (Wiedemann)", "WiedemannSolver::solve");

		WiedemannTraits::SingularState singular = _traits.singular ();
		if (A.rowdim() != A.coldim() ) _traits.singular (singular = WiedemannTraits::SINGULAR);
		ReturnStatus status = FAILED;

		unsigned int tries = (int)_traits.maxTries ();

		unsigned long r = (unsigned long) -1;

		// Dan Roche 6-21-04 Changed this from UNKNOWN which I think was incorrect
		if (_traits.rank () != WiedemannTraits::RANK_UNKNOWN)
			r = _traits.rank ();

		while (status == FAILED && tries-- > 0) {
			switch (singular) {
			case WiedemannTraits::SINGULARITY_UNKNOWN:
				{
					switch (solveNonsingular (A, x, b, true)) {
					case OK:
						status = OK;
						break;

					case FAILED:
						break;

					case SINGULAR:
						commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
						<< "System found to be singular. Reverting to nonsingular solver." << std::endl;
						tries = (int)_traits.maxTries ();
						singular = WiedemannTraits::SINGULAR;
						break;
					default:
						throw LinboxError ("Bad return value from solveNonsingular");
					}
					break;
				}

			case WiedemannTraits::NONSINGULAR:
				{
					switch (solveNonsingular (A, x, b, false)) {
					case OK:
						status = OK;
						break;

					case FAILED:
						break;

					case SINGULAR:
						status = SINGULAR;
						break;

					default:
						throw LinboxError ("Bad return value from solveNonsingular");
					}

					break;
				}

			case WiedemannTraits::SINGULAR:
				{
					if (r == (unsigned long) -1) {
						rank (r, A);
						commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
						<< "Rank of A = " << r << std::endl;
					}

					switch (solveSingular (A, x, b, u, r)) {
					case OK:
						status = OK;
						break;

					case FAILED:
						r = (unsigned long) -1;
						break;

					case SINGULAR:
						throw LinboxError ("solveSingular returned SINGULAR");

					default:
						break;

					case INCONSISTENT:
						status = INCONSISTENT;
					}

					break;
				}
			}
		}

		if (status == FAILED)
			commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
			<< "Maximum tries exceeded with no resolution. Giving up." << std::endl;

		commentator().stop ("done", NULL, "WiedemannSolver::solve");

		return status;
	}

	template <class Field>
	template<class Blackbox, class Vector>
	typename WiedemannSolver<Field>::ReturnStatus
	WiedemannSolver<Field>::solveNonsingular (const Blackbox      &A,
						  Vector              &x,
						  const Vector        &b,
						  bool       useRandIter)
	{
		typedef std::vector<typename Field::Element> Polynomial;
		typedef typename Polynomial::iterator        PolyIterator;

		commentator().start ("Solving nonsingular system (Wiedemann)", "WiedemannSolver::solveNonsingular");

		Polynomial m_A;
		Vector     z;
		bool       ret = true;

		{
			// Make it just Blackbox trait and not wiedemann:
			// Might need extension field for minpoly
			// Might also also use better method than Wiedemann ...
			minpoly(m_A, A,RingCategories::ModularTag(),  Method::Blackbox(_traits) );
		}

		std::ostream &report = commentator().report (Commentator::LEVEL_UNIMPORTANT, INTERNAL_DESCRIPTION);
		report << "Minimal polynomial of degree " << (m_A.size()-1) << std::endl;
		if (m_A.size() < 50) {
			report << "Minimal polynomial coefficients: ";
			_VD.write (report, m_A) << std::endl;
		}

		if (_field.isZero (m_A.front ())) {
			commentator().stop ("singular", "System found to be singular",
					  "WiedemannSolver::solveNonsingular");
			return SINGULAR;
		}

		{
			commentator().start ("Preparing polynomial for application");

			PolyIterator iter = m_A.begin ();

			while (++iter != m_A.end ()) {
				_field.divin (*iter, m_A.front ());
				_field.negin (*iter);
			}

			commentator().stop ("done");
		}

		{
			commentator().start ("Applying polynomial via Horner's rule", NULL, m_A.size () - 1);

			_VD.mul (x, b, m_A.back ());

			VectorWrapper::ensureDim (z, A.rowdim ());

			for (int i = (int) m_A.size () - 1; --i > 0;) {
				if ((m_A.size () - i) & (0xff == 0))
					commentator().progress (m_A.size () - i);

				A.apply (z, x);
				_VD.axpy (x, m_A[i], b, z);
			}

			commentator().stop ("done");
		}

		if (_traits.checkResult ()) {
			commentator().start ("Checking whether Ax=b");
			A.apply (z, x);

			if (_VD.areEqual (z, b))
				ret = true;
			else {
				std::ostream& Report = commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION);
				_VD.write(Report << "x is ", x) << std::endl;
				_VD.write(Report << "b is ", b) << std::endl;
				_VD.write(Report << "Ax is " , z) << std::endl;

				ret = false;

			}

			commentator().stop (MSG_STATUS (ret));
		}

		commentator().stop (MSG_STATUS (ret), NULL, "WiedemannSolver::solveNonsingular");

		if (!ret)
			return FAILED;

		return OK;
	}

	template <class Field>
	template<class Blackbox, class Vector>
	typename WiedemannSolver<Field>::ReturnStatus
	WiedemannSolver<Field>::solveSingular (const Blackbox       &A,
					       Vector               &x,
					       const Vector         &b,
					       Vector               &u,
					       unsigned long         r)
	{
		commentator().start ("Solving singular system (Wiedemann)", "WiedemannSolver::solveSingular");

		Vector Ax;
		ReturnStatus status = OK, sfrs = OK;


		switch (_traits.preconditioner ()) {
		case WiedemannTraits::BUTTERFLY:
			{
				commentator().start ("Constructing butterfly preconditioner");

				CekstvSwitchFactory<Field> factory (_randiter);
				typedef Butterfly<Field, CekstvSwitch<Field> > ButterflyP;
				ButterflyP P(_field, A.rowdim (), factory);
				ButterflyP Q(_field, A.coldim (), factory);
				Compose< Blackbox, ButterflyP > AQ(&A, &Q);
				Compose< ButterflyP, Compose< Blackbox, ButterflyP > > PAQ(&P, &AQ);

				commentator().stop ("done");

				sfrs = findRandomSolution (PAQ, x, b, r, &P, &Q);
				break;
			}

		case WiedemannTraits::SPARSE:
			{
				commentator().start ("Constructing sparse preconditioner");

				SparseMatrix<Field> *P, *QT;
				P = makeLambdaSparseMatrix (A.rowdim ());
				QT = makeLambdaSparseMatrix (A.coldim ());

				Transpose< SparseMatrix<Field> > Q(QT);

				Compose< Blackbox, Transpose< SparseMatrix<Field> > > AQ(&A, &Q);
				Compose< SparseMatrix<Field>, Compose< Blackbox, Transpose< SparseMatrix<Field> > > > PAQ(P, &AQ);
				commentator().stop ("done");

				sfrs = findRandomSolution (PAQ, x, b, r, P, &Q);

				break;
			}

		case WiedemannTraits::TOEPLITZ:
			commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR)
			<< "ERROR: Toeplitz preconditioner not implemented yet. Sorry." << std::endl;
			break;

		case WiedemannTraits::NO_PRECONDITIONER:
			{
				SparseMatrix<Field> *P = NULL;
				sfrs = findRandomSolution (A, x, b, r, P, P);
				delete P;
				break;
			}
		default:
			throw PreconditionFailed (__func__, __LINE__, "preconditioner is BUTTERFLY, SPARSE, or TOEPLITZ");
		}





		switch (sfrs) {
		case BAD_PRECONDITIONER:
			commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
			<< "Preconditioned matrix did not have generic rank profile" << std::endl;

			status = BAD_PRECONDITIONER;
			break;

		case FAILED:
			if (_traits.certificate ()) {
				VectorWrapper::ensureDim (u, A.rowdim ());

				if (certifyInconsistency (u, A, b))
					status = INCONSISTENT;
				else
					status = FAILED;
			}
			else
				status = FAILED;

			break;

		case SINGULAR:
			throw LinboxError ("findRandomSolution returned SINGULAR");

		case INCONSISTENT:
			throw LinboxError ("findRandomSolution returned INCONSISTENT");

		case OK:
			break;
		}

		if (status == OK && _traits.checkResult ()) {
			commentator().start ("Checking system solution");

			VectorWrapper::ensureDim (Ax, A.rowdim ());

			A.apply (Ax, x);

			if (_VD.areEqual (Ax, b))
				commentator().stop ("passed");
			else {
				commentator().stop ("FAILED");

				if (_traits.certificate ()) {
					commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
					<< "Computed system solution is not correct. "
					<< "Attempting to find certificate of inconsistency." << std::endl;

					VectorWrapper::ensureDim (u, A.rowdim ());

					if (certifyInconsistency (u, A, b))
						status = INCONSISTENT;
					else
						status = FAILED;
				}
				else
					status = FAILED;
			}
		}

		commentator().stop ("done", NULL, "WiedemannSolver::solveSingular");

		return status;
	}

	template <class Field>
	template <class Blackbox, class Vector, class Prec1, class Prec2>
	typename WiedemannSolver<Field>::ReturnStatus
	WiedemannSolver<Field>::findRandomSolution (const Blackbox        &A,
						    Vector                &x,
						    const Vector          &b,
						    size_t                 r,
						    const Prec1           *P,
						    const Prec2           *Q)
	{
		commentator().start ("Solving singular system with generic rank profile (Wiedemann)",
				   "WiedemannSolver::findRandomSolution");

		Vector v, Avpb, PAvpb, bp, xp, Qinvx;

		RandomDenseStream<Field, Vector> stream (_field, _randiter, A.coldim ());

		VectorWrapper::ensureDim (v, A.coldim ());
		VectorWrapper::ensureDim (Avpb, A.rowdim ());
		VectorWrapper::ensureDim (xp, r);
		VectorWrapper::ensureDim (bp, r);

		{
			commentator().start ("Preparing right hand side");

			stream >> v;
			A.apply (Avpb, v);
			_VD.addin (Avpb, b);
			if (P != NULL) {
				VectorWrapper::ensureDim (PAvpb, A.rowdim ());
				P->apply (PAvpb, Avpb);
				_VD.copy (bp, PAvpb, 0, r);
			}
			else {
				_VD.copy (bp, Avpb, 0, r);
			}

			commentator().stop ("done");
		}

		Submatrix<Blackbox> Ap (&A, 0, 0, r, r);

		switch (solveNonsingular (Ap, xp, bp, false)) {
		case SINGULAR:
			commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
			<< "Leading principal minor was found to be singular." << std::endl;
			commentator().stop ("bad preconditioner", "System was not well-conditioned",
					  "WiedemannSolver::findRandomSolution");
			return BAD_PRECONDITIONER;

		case OK:
			break;

		default:
			throw LinboxError ("solveNonsingular returned bad value");
		}

		if (Q != NULL) {
			VectorWrapper::ensureDim (Qinvx, A.coldim ());
			_VD.copy (Qinvx, xp);
			Q->apply (x, Qinvx);
		}
		else {
			_VD.copy (x, xp);
		}

		_VD.subin (x, v);

		commentator().stop ("done", NULL, "WiedemannSolver::findRandomSolution");

		return OK;
	}

	template <class Field>
	template<class Blackbox, class Vector>
	typename WiedemannSolver<Field>::ReturnStatus
	WiedemannSolver<Field>::findNullspaceElement (Vector             &x,
						      const Blackbox     &A)
	{
		commentator().start ("Finding a nullspace element (Wiedemann)", "WiedemannSolver::findNullspaceElement");

		Vector v, Av, PAv, vp, xp, Qinvx;

		RandomDenseStream<Field, Vector> stream (_field, _randiter, A.coldim ());

		unsigned long r = (A.coldim () < A.rowdim ()) ? A.coldim () : A.rowdim ();

		VectorWrapper::ensureDim (v, A.coldim ());
		VectorWrapper::ensureDim (Av, A.rowdim ());

		ReturnStatus status;

		{
			commentator().start ("Constructing right hand side");

			stream >> v;
			A.apply (Av, v);

			if (A.coldim () < A.rowdim ()) {
				VectorWrapper::ensureDim (vp, r);
				_VD.copy (vp, Av, 0, r);
			}

			commentator().stop ("done");
		}

		if (A.coldim () < A.rowdim ()) {
			Submatrix<Blackbox> Ap (&A, 0, 0, r, r);
			status = solveNonsingular (Ap, x, vp, false);
		}
		else if (A.rowdim () < A.coldim ()) {
			Submatrix<Blackbox> Ap (&A, 0, 0, r, r);
			VectorWrapper::ensureDim (xp, r);
			status = solveNonsingular (Ap, xp, Av, false);
			_VD.copy (x, xp);
		}
		else
			status = solveNonsingular (A, x, Av, false);

		if (status == SINGULAR) {
			commentator().report (Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION)
			<< "Leading principal minor was found to be singular." << std::endl;
			commentator().stop ("bad preconditioner", "System not well-conditioned",
					  "WiedemannSolver::findNullspaceElement");
			return BAD_PRECONDITIONER;
		}

		_VD.subin (x, v);

		commentator().stop ("done", NULL, "WiedemannSolver::findNullspaceElement");

		return OK;
	}

	template <class Field>
	template <class Blackbox, class Vector>
	bool WiedemannSolver<Field>::certifyInconsistency (Vector                          &u,
							   const Blackbox                  &A,
							   const Vector                    &b)
	{
		commentator().start ("Obtaining certificate of inconsistency (Wiedemann)",
				   "WiedemannSolver::certifyInconsistency");

		Vector PTinvu;
		typename Field::Element uTb;

		WiedemannTraits cert_traits;

		bool ret = false;

		cert_traits.preconditioner (WiedemannTraits::NO_PRECONDITIONER);
		cert_traits.certificate (false);
		cert_traits.singular (WiedemannTraits::SINGULAR);
		cert_traits.maxTries (1);

		WiedemannSolver solver (_field, cert_traits, _randiter);

		Transpose<Blackbox> AT (&A);

		solver.findNullspaceElement (u, AT);
		_VD.dot (uTb, u, b);

		if (!_field.isZero (uTb))
			ret = true;

		commentator().stop (MSG_STATUS (ret), NULL, "WiedemannSolver::certifyInconsistency");

		return ret;
	}


	template <class Field>
	SparseMatrix<Field> *WiedemannSolver<Field>::makeLambdaSparseMatrix (size_t m)
	{
		const double             LAMBDA = 3;
		integer                  card;

		_field.cardinality (card);

		double                   init_p = 1.0 - 1.0 / (double) card;
		double                   log_m = LAMBDA * log ((double) m) / M_LN2;
		double                   new_p;

		SparseMatrix<Field>    *P = new SparseMatrix<Field> (_field, m, m);

		RandomSparseStream<Field> stream (_field, _randiter, init_p, m, m);

		for (unsigned int i = 0; i < m; ++i) {
			new_p = log_m / double(m - i + 1);

			if (init_p < new_p)
				stream.setP (init_p);
			else
				stream.setP (new_p);

			stream >> P->getRow (i);
		}

		return P;
	}

}

#endif // __LINBOX_wiedemann_INL


// 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: