LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
sdrvpb.f
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1 *> \brief \b SDRVPB
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SDRVPB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
13 * RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NOUT, NRHS
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), ASAV( * ), B( * ),
24 * \$ BSAV( * ), RWORK( * ), S( * ), WORK( * ),
25 * \$ X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> SDRVPB tests the driver routines SPBSV and -SVX.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] DOTYPE
41 *> \verbatim
42 *> DOTYPE is LOGICAL array, dimension (NTYPES)
43 *> The matrix types to be used for testing. Matrices of type j
44 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46 *> \endverbatim
47 *>
48 *> \param[in] NN
49 *> \verbatim
50 *> NN is INTEGER
51 *> The number of values of N contained in the vector NVAL.
52 *> \endverbatim
53 *>
54 *> \param[in] NVAL
55 *> \verbatim
56 *> NVAL is INTEGER array, dimension (NN)
57 *> The values of the matrix dimension N.
58 *> \endverbatim
59 *>
60 *> \param[in] NRHS
61 *> \verbatim
62 *> NRHS is INTEGER
63 *> The number of right hand side vectors to be generated for
64 *> each linear system.
65 *> \endverbatim
66 *>
67 *> \param[in] THRESH
68 *> \verbatim
69 *> THRESH is REAL
70 *> The threshold value for the test ratios. A result is
71 *> included in the output file if RESULT >= THRESH. To have
72 *> every test ratio printed, use THRESH = 0.
73 *> \endverbatim
74 *>
75 *> \param[in] TSTERR
76 *> \verbatim
77 *> TSTERR is LOGICAL
78 *> Flag that indicates whether error exits are to be tested.
79 *> \endverbatim
80 *>
81 *> \param[in] NMAX
82 *> \verbatim
83 *> NMAX is INTEGER
84 *> The maximum value permitted for N, used in dimensioning the
85 *> work arrays.
86 *> \endverbatim
87 *>
88 *> \param[out] A
89 *> \verbatim
90 *> A is REAL array, dimension (NMAX*NMAX)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is REAL array, dimension (NMAX*NMAX)
96 *> \endverbatim
97 *>
98 *> \param[out] ASAV
99 *> \verbatim
100 *> ASAV is REAL array, dimension (NMAX*NMAX)
101 *> \endverbatim
102 *>
103 *> \param[out] B
104 *> \verbatim
105 *> B is REAL array, dimension (NMAX*NRHS)
106 *> \endverbatim
107 *>
108 *> \param[out] BSAV
109 *> \verbatim
110 *> BSAV is REAL array, dimension (NMAX*NRHS)
111 *> \endverbatim
112 *>
113 *> \param[out] X
114 *> \verbatim
115 *> X is REAL array, dimension (NMAX*NRHS)
116 *> \endverbatim
117 *>
118 *> \param[out] XACT
119 *> \verbatim
120 *> XACT is REAL array, dimension (NMAX*NRHS)
121 *> \endverbatim
122 *>
123 *> \param[out] S
124 *> \verbatim
125 *> S is REAL array, dimension (NMAX)
126 *> \endverbatim
127 *>
128 *> \param[out] WORK
129 *> \verbatim
130 *> WORK is REAL array, dimension
131 *> (NMAX*max(3,NRHS))
132 *> \endverbatim
133 *>
134 *> \param[out] RWORK
135 *> \verbatim
136 *> RWORK is REAL array, dimension (NMAX+2*NRHS)
137 *> \endverbatim
138 *>
139 *> \param[out] IWORK
140 *> \verbatim
141 *> IWORK is INTEGER array, dimension (NMAX)
142 *> \endverbatim
143 *>
144 *> \param[in] NOUT
145 *> \verbatim
146 *> NOUT is INTEGER
147 *> The unit number for output.
148 *> \endverbatim
149 *
150 * Authors:
151 * ========
152 *
153 *> \author Univ. of Tennessee
154 *> \author Univ. of California Berkeley
155 *> \author Univ. of Colorado Denver
156 *> \author NAG Ltd.
157 *
158 *> \date November 2011
159 *
160 *> \ingroup single_lin
161 *
162 * =====================================================================
163  SUBROUTINE sdrvpb( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
164  \$ a, afac, asav, b, bsav, x, xact, s, work,
165  \$ rwork, iwork, nout )
166 *
167 * -- LAPACK test routine (version 3.4.0) --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 * November 2011
171 *
172 * .. Scalar Arguments ..
173  LOGICAL tsterr
174  INTEGER nmax, nn, nout, nrhs
175  REAL thresh
176 * ..
177 * .. Array Arguments ..
178  LOGICAL dotype( * )
179  INTEGER iwork( * ), nval( * )
180  REAL a( * ), afac( * ), asav( * ), b( * ),
181  \$ bsav( * ), rwork( * ), s( * ), work( * ),
182  \$ x( * ), xact( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  REAL one, zero
189  parameter( one = 1.0e+0, zero = 0.0e+0 )
190  INTEGER ntypes, ntests
191  parameter( ntypes = 8, ntests = 6 )
192  INTEGER nbw
193  parameter( nbw = 4 )
194 * ..
195 * .. Local Scalars ..
196  LOGICAL equil, nofact, prefac, zerot
197  CHARACTER dist, equed, fact, packit, type, uplo, xtype
198  CHARACTER*3 path
199  INTEGER i, i1, i2, iequed, ifact, ikd, imat, in, info,
200  \$ ioff, iuplo, iw, izero, k, k1, kd, kl, koff,
201  \$ ku, lda, ldab, mode, n, nb, nbmin, nerrs,
202  \$ nfact, nfail, nimat, nkd, nrun, nt
203  REAL ainvnm, amax, anorm, cndnum, rcond, rcondc,
204  \$ roldc, scond
205 * ..
206 * .. Local Arrays ..
207  CHARACTER equeds( 2 ), facts( 3 )
208  INTEGER iseed( 4 ), iseedy( 4 ), kdval( nbw )
209  REAL result( ntests )
210 * ..
211 * .. External Functions ..
212  LOGICAL lsame
213  REAL sget06, slange, slansb
214  EXTERNAL lsame, sget06, slange, slansb
215 * ..
216 * .. External Subroutines ..
217  EXTERNAL aladhd, alaerh, alasvm, scopy, serrvx, sget04,
221 * ..
222 * .. Intrinsic Functions ..
223  INTRINSIC max, min
224 * ..
225 * .. Scalars in Common ..
226  LOGICAL lerr, ok
227  CHARACTER*32 srnamt
228  INTEGER infot, nunit
229 * ..
230 * .. Common blocks ..
231  common / infoc / infot, nunit, ok, lerr
232  common / srnamc / srnamt
233 * ..
234 * .. Data statements ..
235  DATA iseedy / 1988, 1989, 1990, 1991 /
236  DATA facts / 'F', 'N', 'E' /
237  DATA equeds / 'N', 'Y' /
238 * ..
239 * .. Executable Statements ..
240 *
241 * Initialize constants and the random number seed.
242 *
243  path( 1: 1 ) = 'Single precision'
244  path( 2: 3 ) = 'PB'
245  nrun = 0
246  nfail = 0
247  nerrs = 0
248  DO 10 i = 1, 4
249  iseed( i ) = iseedy( i )
250  10 continue
251 *
252 * Test the error exits
253 *
254  IF( tsterr )
255  \$ CALL serrvx( path, nout )
256  infot = 0
257  kdval( 1 ) = 0
258 *
259 * Set the block size and minimum block size for testing.
260 *
261  nb = 1
262  nbmin = 2
263  CALL xlaenv( 1, nb )
264  CALL xlaenv( 2, nbmin )
265 *
266 * Do for each value of N in NVAL
267 *
268  DO 110 in = 1, nn
269  n = nval( in )
270  lda = max( n, 1 )
271  xtype = 'N'
272 *
273 * Set limits on the number of loop iterations.
274 *
275  nkd = max( 1, min( n, 4 ) )
276  nimat = ntypes
277  IF( n.EQ.0 )
278  \$ nimat = 1
279 *
280  kdval( 2 ) = n + ( n+1 ) / 4
281  kdval( 3 ) = ( 3*n-1 ) / 4
282  kdval( 4 ) = ( n+1 ) / 4
283 *
284  DO 100 ikd = 1, nkd
285 *
286 * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
287 * makes it easier to skip redundant values for small values
288 * of N.
289 *
290  kd = kdval( ikd )
291  ldab = kd + 1
292 *
293 * Do first for UPLO = 'U', then for UPLO = 'L'
294 *
295  DO 90 iuplo = 1, 2
296  koff = 1
297  IF( iuplo.EQ.1 ) THEN
298  uplo = 'U'
299  packit = 'Q'
300  koff = max( 1, kd+2-n )
301  ELSE
302  uplo = 'L'
303  packit = 'B'
304  END IF
305 *
306  DO 80 imat = 1, nimat
307 *
308 * Do the tests only if DOTYPE( IMAT ) is true.
309 *
310  IF( .NOT.dotype( imat ) )
311  \$ go to 80
312 *
313 * Skip types 2, 3, or 4 if the matrix size is too small.
314 *
315  zerot = imat.GE.2 .AND. imat.LE.4
316  IF( zerot .AND. n.LT.imat-1 )
317  \$ go to 80
318 *
319  IF( .NOT.zerot .OR. .NOT.dotype( 1 ) ) THEN
320 *
321 * Set up parameters with SLATB4 and generate a test
322 * matrix with SLATMS.
323 *
324  CALL slatb4( path, imat, n, n, type, kl, ku, anorm,
325  \$ mode, cndnum, dist )
326 *
327  srnamt = 'SLATMS'
328  CALL slatms( n, n, dist, iseed, type, rwork, mode,
329  \$ cndnum, anorm, kd, kd, packit,
330  \$ a( koff ), ldab, work, info )
331 *
332 * Check error code from SLATMS.
333 *
334  IF( info.NE.0 ) THEN
335  CALL alaerh( path, 'SLATMS', info, 0, uplo, n,
336  \$ n, -1, -1, -1, imat, nfail, nerrs,
337  \$ nout )
338  go to 80
339  END IF
340  ELSE IF( izero.GT.0 ) THEN
341 *
342 * Use the same matrix for types 3 and 4 as for type
343 * 2 by copying back the zeroed out column,
344 *
345  iw = 2*lda + 1
346  IF( iuplo.EQ.1 ) THEN
347  ioff = ( izero-1 )*ldab + kd + 1
348  CALL scopy( izero-i1, work( iw ), 1,
349  \$ a( ioff-izero+i1 ), 1 )
350  iw = iw + izero - i1
351  CALL scopy( i2-izero+1, work( iw ), 1,
352  \$ a( ioff ), max( ldab-1, 1 ) )
353  ELSE
354  ioff = ( i1-1 )*ldab + 1
355  CALL scopy( izero-i1, work( iw ), 1,
356  \$ a( ioff+izero-i1 ),
357  \$ max( ldab-1, 1 ) )
358  ioff = ( izero-1 )*ldab + 1
359  iw = iw + izero - i1
360  CALL scopy( i2-izero+1, work( iw ), 1,
361  \$ a( ioff ), 1 )
362  END IF
363  END IF
364 *
365 * For types 2-4, zero one row and column of the matrix
366 * to test that INFO is returned correctly.
367 *
368  izero = 0
369  IF( zerot ) THEN
370  IF( imat.EQ.2 ) THEN
371  izero = 1
372  ELSE IF( imat.EQ.3 ) THEN
373  izero = n
374  ELSE
375  izero = n / 2 + 1
376  END IF
377 *
378 * Save the zeroed out row and column in WORK(*,3)
379 *
380  iw = 2*lda
381  DO 20 i = 1, min( 2*kd+1, n )
382  work( iw+i ) = zero
383  20 continue
384  iw = iw + 1
385  i1 = max( izero-kd, 1 )
386  i2 = min( izero+kd, n )
387 *
388  IF( iuplo.EQ.1 ) THEN
389  ioff = ( izero-1 )*ldab + kd + 1
390  CALL sswap( izero-i1, a( ioff-izero+i1 ), 1,
391  \$ work( iw ), 1 )
392  iw = iw + izero - i1
393  CALL sswap( i2-izero+1, a( ioff ),
394  \$ max( ldab-1, 1 ), work( iw ), 1 )
395  ELSE
396  ioff = ( i1-1 )*ldab + 1
397  CALL sswap( izero-i1, a( ioff+izero-i1 ),
398  \$ max( ldab-1, 1 ), work( iw ), 1 )
399  ioff = ( izero-1 )*ldab + 1
400  iw = iw + izero - i1
401  CALL sswap( i2-izero+1, a( ioff ), 1,
402  \$ work( iw ), 1 )
403  END IF
404  END IF
405 *
406 * Save a copy of the matrix A in ASAV.
407 *
408  CALL slacpy( 'Full', kd+1, n, a, ldab, asav, ldab )
409 *
410  DO 70 iequed = 1, 2
411  equed = equeds( iequed )
412  IF( iequed.EQ.1 ) THEN
413  nfact = 3
414  ELSE
415  nfact = 1
416  END IF
417 *
418  DO 60 ifact = 1, nfact
419  fact = facts( ifact )
420  prefac = lsame( fact, 'F' )
421  nofact = lsame( fact, 'N' )
422  equil = lsame( fact, 'E' )
423 *
424  IF( zerot ) THEN
425  IF( prefac )
426  \$ go to 60
427  rcondc = zero
428 *
429  ELSE IF( .NOT.lsame( fact, 'N' ) ) THEN
430 *
431 * Compute the condition number for comparison
432 * with the value returned by SPBSVX (FACT =
433 * 'N' reuses the condition number from the
434 * previous iteration with FACT = 'F').
435 *
436  CALL slacpy( 'Full', kd+1, n, asav, ldab,
437  \$ afac, ldab )
438  IF( equil .OR. iequed.GT.1 ) THEN
439 *
440 * Compute row and column scale factors to
441 * equilibrate the matrix A.
442 *
443  CALL spbequ( uplo, n, kd, afac, ldab, s,
444  \$ scond, amax, info )
445  IF( info.EQ.0 .AND. n.GT.0 ) THEN
446  IF( iequed.GT.1 )
447  \$ scond = zero
448 *
449 * Equilibrate the matrix.
450 *
451  CALL slaqsb( uplo, n, kd, afac, ldab,
452  \$ s, scond, amax, equed )
453  END IF
454  END IF
455 *
456 * Save the condition number of the
457 * non-equilibrated system for use in SGET04.
458 *
459  IF( equil )
460  \$ roldc = rcondc
461 *
462 * Compute the 1-norm of A.
463 *
464  anorm = slansb( '1', uplo, n, kd, afac, ldab,
465  \$ rwork )
466 *
467 * Factor the matrix A.
468 *
469  CALL spbtrf( uplo, n, kd, afac, ldab, info )
470 *
471 * Form the inverse of A.
472 *
473  CALL slaset( 'Full', n, n, zero, one, a,
474  \$ lda )
475  srnamt = 'SPBTRS'
476  CALL spbtrs( uplo, n, kd, n, afac, ldab, a,
477  \$ lda, info )
478 *
479 * Compute the 1-norm condition number of A.
480 *
481  ainvnm = slange( '1', n, n, a, lda, rwork )
482  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
483  rcondc = one
484  ELSE
485  rcondc = ( one / anorm ) / ainvnm
486  END IF
487  END IF
488 *
489 * Restore the matrix A.
490 *
491  CALL slacpy( 'Full', kd+1, n, asav, ldab, a,
492  \$ ldab )
493 *
494 * Form an exact solution and set the right hand
495 * side.
496 *
497  srnamt = 'SLARHS'
498  CALL slarhs( path, xtype, uplo, ' ', n, n, kd,
499  \$ kd, nrhs, a, ldab, xact, lda, b,
500  \$ lda, iseed, info )
501  xtype = 'C'
502  CALL slacpy( 'Full', n, nrhs, b, lda, bsav,
503  \$ lda )
504 *
505  IF( nofact ) THEN
506 *
507 * --- Test SPBSV ---
508 *
509 * Compute the L*L' or U'*U factorization of the
510 * matrix and solve the system.
511 *
512  CALL slacpy( 'Full', kd+1, n, a, ldab, afac,
513  \$ ldab )
514  CALL slacpy( 'Full', n, nrhs, b, lda, x,
515  \$ lda )
516 *
517  srnamt = 'SPBSV '
518  CALL spbsv( uplo, n, kd, nrhs, afac, ldab, x,
519  \$ lda, info )
520 *
521 * Check error code from SPBSV .
522 *
523  IF( info.NE.izero ) THEN
524  CALL alaerh( path, 'SPBSV ', info, izero,
525  \$ uplo, n, n, kd, kd, nrhs,
526  \$ imat, nfail, nerrs, nout )
527  go to 40
528  ELSE IF( info.NE.0 ) THEN
529  go to 40
530  END IF
531 *
532 * Reconstruct matrix from factors and compute
533 * residual.
534 *
535  CALL spbt01( uplo, n, kd, a, ldab, afac,
536  \$ ldab, rwork, result( 1 ) )
537 *
538 * Compute residual of the computed solution.
539 *
540  CALL slacpy( 'Full', n, nrhs, b, lda, work,
541  \$ lda )
542  CALL spbt02( uplo, n, kd, nrhs, a, ldab, x,
543  \$ lda, work, lda, rwork,
544  \$ result( 2 ) )
545 *
546 * Check solution from generated exact solution.
547 *
548  CALL sget04( n, nrhs, x, lda, xact, lda,
549  \$ rcondc, result( 3 ) )
550  nt = 3
551 *
552 * Print information about the tests that did
553 * not pass the threshold.
554 *
555  DO 30 k = 1, nt
556  IF( result( k ).GE.thresh ) THEN
557  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
558  \$ CALL aladhd( nout, path )
559  WRITE( nout, fmt = 9999 )'SPBSV ',
560  \$ uplo, n, kd, imat, k, result( k )
561  nfail = nfail + 1
562  END IF
563  30 continue
564  nrun = nrun + nt
565  40 continue
566  END IF
567 *
568 * --- Test SPBSVX ---
569 *
570  IF( .NOT.prefac )
571  \$ CALL slaset( 'Full', kd+1, n, zero, zero,
572  \$ afac, ldab )
573  CALL slaset( 'Full', n, nrhs, zero, zero, x,
574  \$ lda )
575  IF( iequed.GT.1 .AND. n.GT.0 ) THEN
576 *
577 * Equilibrate the matrix if FACT='F' and
578 * EQUED='Y'
579 *
580  CALL slaqsb( uplo, n, kd, a, ldab, s, scond,
581  \$ amax, equed )
582  END IF
583 *
584 * Solve the system and compute the condition
585 * number and error bounds using SPBSVX.
586 *
587  srnamt = 'SPBSVX'
588  CALL spbsvx( fact, uplo, n, kd, nrhs, a, ldab,
589  \$ afac, ldab, equed, s, b, lda, x,
590  \$ lda, rcond, rwork, rwork( nrhs+1 ),
591  \$ work, iwork, info )
592 *
593 * Check the error code from SPBSVX.
594 *
595  IF( info.NE.izero ) THEN
596  CALL alaerh( path, 'SPBSVX', info, izero,
597  \$ fact // uplo, n, n, kd, kd,
598  \$ nrhs, imat, nfail, nerrs, nout )
599  go to 60
600  END IF
601 *
602  IF( info.EQ.0 ) THEN
603  IF( .NOT.prefac ) THEN
604 *
605 * Reconstruct matrix from factors and
606 * compute residual.
607 *
608  CALL spbt01( uplo, n, kd, a, ldab, afac,
609  \$ ldab, rwork( 2*nrhs+1 ),
610  \$ result( 1 ) )
611  k1 = 1
612  ELSE
613  k1 = 2
614  END IF
615 *
616 * Compute residual of the computed solution.
617 *
618  CALL slacpy( 'Full', n, nrhs, bsav, lda,
619  \$ work, lda )
620  CALL spbt02( uplo, n, kd, nrhs, asav, ldab,
621  \$ x, lda, work, lda,
622  \$ rwork( 2*nrhs+1 ), result( 2 ) )
623 *
624 * Check solution from generated exact solution.
625 *
626  IF( nofact .OR. ( prefac .AND. lsame( equed,
627  \$ 'N' ) ) ) THEN
628  CALL sget04( n, nrhs, x, lda, xact, lda,
629  \$ rcondc, result( 3 ) )
630  ELSE
631  CALL sget04( n, nrhs, x, lda, xact, lda,
632  \$ roldc, result( 3 ) )
633  END IF
634 *
635 * Check the error bounds from iterative
636 * refinement.
637 *
638  CALL spbt05( uplo, n, kd, nrhs, asav, ldab,
639  \$ b, lda, x, lda, xact, lda,
640  \$ rwork, rwork( nrhs+1 ),
641  \$ result( 4 ) )
642  ELSE
643  k1 = 6
644  END IF
645 *
646 * Compare RCOND from SPBSVX with the computed
647 * value in RCONDC.
648 *
649  result( 6 ) = sget06( rcond, rcondc )
650 *
651 * Print information about the tests that did not
652 * pass the threshold.
653 *
654  DO 50 k = k1, 6
655  IF( result( k ).GE.thresh ) THEN
656  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
657  \$ CALL aladhd( nout, path )
658  IF( prefac ) THEN
659  WRITE( nout, fmt = 9997 )'SPBSVX',
660  \$ fact, uplo, n, kd, equed, imat, k,
661  \$ result( k )
662  ELSE
663  WRITE( nout, fmt = 9998 )'SPBSVX',
664  \$ fact, uplo, n, kd, imat, k,
665  \$ result( k )
666  END IF
667  nfail = nfail + 1
668  END IF
669  50 continue
670  nrun = nrun + 7 - k1
671  60 continue
672  70 continue
673  80 continue
674  90 continue
675  100 continue
676  110 continue
677 *
678 * Print a summary of the results.
679 *
680  CALL alasvm( path, nout, nfail, nrun, nerrs )
681 *
682  9999 format( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', KD =', i5,
683  \$ ', type ', i1, ', test(', i1, ')=', g12.5 )
684  9998 format( 1x, a, '( ''', a1, ''', ''', a1, ''', ', i5, ', ', i5,
685  \$ ', ... ), type ', i1, ', test(', i1, ')=', g12.5 )
686  9997 format( 1x, a, '( ''', a1, ''', ''', a1, ''', ', i5, ', ', i5,
687  \$ ', ... ), EQUED=''', a1, ''', type ', i1, ', test(', i1,
688  \$ ')=', g12.5 )
689  return
690 *
691 * End of SDRVPB
692 *
693  END