LAPACK  3.4.2
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schkpb.f
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1 *> \brief \b SCHKPB
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 SCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> SCHKPB tests SPBTRF, -TRS, -RFS, and -CON.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NN
48 *> \verbatim
49 *> NN is INTEGER
50 *> The number of values of N contained in the vector NVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] NVAL
54 *> \verbatim
55 *> NVAL is INTEGER array, dimension (NN)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NNB
60 *> \verbatim
61 *> NNB is INTEGER
62 *> The number of values of NB contained in the vector NBVAL.
63 *> \endverbatim
64 *>
65 *> \param[in] NBVAL
66 *> \verbatim
67 *> NBVAL is INTEGER array, dimension (NBVAL)
68 *> The values of the blocksize NB.
69 *> \endverbatim
70 *>
71 *> \param[in] NNS
72 *> \verbatim
73 *> NNS is INTEGER
74 *> The number of values of NRHS contained in the vector NSVAL.
75 *> \endverbatim
76 *>
77 *> \param[in] NSVAL
78 *> \verbatim
79 *> NSVAL is INTEGER array, dimension (NNS)
80 *> The values of the number of right hand sides NRHS.
81 *> \endverbatim
82 *>
83 *> \param[in] THRESH
84 *> \verbatim
85 *> THRESH is REAL
86 *> The threshold value for the test ratios. A result is
87 *> included in the output file if RESULT >= THRESH. To have
88 *> every test ratio printed, use THRESH = 0.
89 *> \endverbatim
90 *>
91 *> \param[in] TSTERR
92 *> \verbatim
93 *> TSTERR is LOGICAL
94 *> Flag that indicates whether error exits are to be tested.
95 *> \endverbatim
96 *>
97 *> \param[in] NMAX
98 *> \verbatim
99 *> NMAX is INTEGER
100 *> The maximum value permitted for N, used in dimensioning the
101 *> work arrays.
102 *> \endverbatim
103 *>
104 *> \param[out] A
105 *> \verbatim
106 *> A is REAL array, dimension (NMAX*NMAX)
107 *> \endverbatim
108 *>
109 *> \param[out] AFAC
110 *> \verbatim
111 *> AFAC is REAL array, dimension (NMAX*NMAX)
112 *> \endverbatim
113 *>
114 *> \param[out] AINV
115 *> \verbatim
116 *> AINV is REAL array, dimension (NMAX*NMAX)
117 *> \endverbatim
118 *>
119 *> \param[out] B
120 *> \verbatim
121 *> B is REAL array, dimension (NMAX*NSMAX)
122 *> where NSMAX is the largest entry in NSVAL.
123 *> \endverbatim
124 *>
125 *> \param[out] X
126 *> \verbatim
127 *> X is REAL array, dimension (NMAX*NSMAX)
128 *> \endverbatim
129 *>
130 *> \param[out] XACT
131 *> \verbatim
132 *> XACT is REAL array, dimension (NMAX*NSMAX)
133 *> \endverbatim
134 *>
135 *> \param[out] WORK
136 *> \verbatim
137 *> WORK is REAL array, dimension
138 *> (NMAX*max(3,NSMAX))
139 *> \endverbatim
140 *>
141 *> \param[out] RWORK
142 *> \verbatim
143 *> RWORK is REAL array, dimension
144 *> (max(NMAX,2*NSMAX))
145 *> \endverbatim
146 *>
147 *> \param[out] IWORK
148 *> \verbatim
149 *> IWORK is INTEGER array, dimension (NMAX)
150 *> \endverbatim
151 *>
152 *> \param[in] NOUT
153 *> \verbatim
154 *> NOUT is INTEGER
155 *> The unit number for output.
156 *> \endverbatim
157 *
158 * Authors:
159 * ========
160 *
161 *> \author Univ. of Tennessee
162 *> \author Univ. of California Berkeley
163 *> \author Univ. of Colorado Denver
164 *> \author NAG Ltd.
165 *
166 *> \date November 2011
167 *
168 *> \ingroup single_lin
169 *
170 * =====================================================================
171  SUBROUTINE schkpb( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
172  $ thresh, tsterr, nmax, a, afac, ainv, b, x,
173  $ xact, work, rwork, iwork, nout )
174 *
175 * -- LAPACK test routine (version 3.4.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * November 2011
179 *
180 * .. Scalar Arguments ..
181  LOGICAL tsterr
182  INTEGER nmax, nn, nnb, nns, nout
183  REAL thresh
184 * ..
185 * .. Array Arguments ..
186  LOGICAL dotype( * )
187  INTEGER iwork( * ), nbval( * ), nsval( * ), nval( * )
188  REAL a( * ), afac( * ), ainv( * ), b( * ),
189  $ rwork( * ), work( * ), x( * ), xact( * )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  REAL one, zero
196  parameter( one = 1.0e+0, zero = 0.0e+0 )
197  INTEGER ntypes, ntests
198  parameter( ntypes = 8, ntests = 7 )
199  INTEGER nbw
200  parameter( nbw = 4 )
201 * ..
202 * .. Local Scalars ..
203  LOGICAL zerot
204  CHARACTER dist, packit, type, uplo, xtype
205  CHARACTER*3 path
206  INTEGER i, i1, i2, ikd, imat, in, inb, info, ioff,
207  $ irhs, iuplo, iw, izero, k, kd, kl, koff, ku,
208  $ lda, ldab, mode, n, nb, nerrs, nfail, nimat,
209  $ nkd, nrhs, nrun
210  REAL ainvnm, anorm, cndnum, rcond, rcondc
211 * ..
212 * .. Local Arrays ..
213  INTEGER iseed( 4 ), iseedy( 4 ), kdval( nbw )
214  REAL result( ntests )
215 * ..
216 * .. External Functions ..
217  REAL sget06, slange, slansb
218  EXTERNAL sget06, slange, slansb
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL alaerh, alahd, alasum, scopy, serrpo, sget04,
222  $ slacpy, slarhs, slaset, slatb4, slatms, spbcon,
223  $ spbrfs, spbt01, spbt02, spbt05, spbtrf, spbtrs,
224  $ sswap, xlaenv
225 * ..
226 * .. Intrinsic Functions ..
227  INTRINSIC max, min
228 * ..
229 * .. Scalars in Common ..
230  LOGICAL lerr, ok
231  CHARACTER*32 srnamt
232  INTEGER infot, nunit
233 * ..
234 * .. Common blocks ..
235  common / infoc / infot, nunit, ok, lerr
236  common / srnamc / srnamt
237 * ..
238 * .. Data statements ..
239  DATA iseedy / 1988, 1989, 1990, 1991 /
240 * ..
241 * .. Executable Statements ..
242 *
243 * Initialize constants and the random number seed.
244 *
245  path( 1: 1 ) = 'Single precision'
246  path( 2: 3 ) = 'PB'
247  nrun = 0
248  nfail = 0
249  nerrs = 0
250  DO 10 i = 1, 4
251  iseed( i ) = iseedy( i )
252  10 continue
253 *
254 * Test the error exits
255 *
256  IF( tsterr )
257  $ CALL serrpo( path, nout )
258  infot = 0
259  CALL xlaenv( 2, 2 )
260  kdval( 1 ) = 0
261 *
262 * Do for each value of N in NVAL
263 *
264  DO 90 in = 1, nn
265  n = nval( in )
266  lda = max( n, 1 )
267  xtype = 'N'
268 *
269 * Set limits on the number of loop iterations.
270 *
271  nkd = max( 1, min( n, 4 ) )
272  nimat = ntypes
273  IF( n.EQ.0 )
274  $ nimat = 1
275 *
276  kdval( 2 ) = n + ( n+1 ) / 4
277  kdval( 3 ) = ( 3*n-1 ) / 4
278  kdval( 4 ) = ( n+1 ) / 4
279 *
280  DO 80 ikd = 1, nkd
281 *
282 * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
283 * makes it easier to skip redundant values for small values
284 * of N.
285 *
286  kd = kdval( ikd )
287  ldab = kd + 1
288 *
289 * Do first for UPLO = 'U', then for UPLO = 'L'
290 *
291  DO 70 iuplo = 1, 2
292  koff = 1
293  IF( iuplo.EQ.1 ) THEN
294  uplo = 'U'
295  koff = max( 1, kd+2-n )
296  packit = 'Q'
297  ELSE
298  uplo = 'L'
299  packit = 'B'
300  END IF
301 *
302  DO 60 imat = 1, nimat
303 *
304 * Do the tests only if DOTYPE( IMAT ) is true.
305 *
306  IF( .NOT.dotype( imat ) )
307  $ go to 60
308 *
309 * Skip types 2, 3, or 4 if the matrix size is too small.
310 *
311  zerot = imat.GE.2 .AND. imat.LE.4
312  IF( zerot .AND. n.LT.imat-1 )
313  $ go to 60
314 *
315  IF( .NOT.zerot .OR. .NOT.dotype( 1 ) ) THEN
316 *
317 * Set up parameters with SLATB4 and generate a test
318 * matrix with SLATMS.
319 *
320  CALL slatb4( path, imat, n, n, type, kl, ku, anorm,
321  $ mode, cndnum, dist )
322 *
323  srnamt = 'SLATMS'
324  CALL slatms( n, n, dist, iseed, type, rwork, mode,
325  $ cndnum, anorm, kd, kd, packit,
326  $ a( koff ), ldab, work, info )
327 *
328 * Check error code from SLATMS.
329 *
330  IF( info.NE.0 ) THEN
331  CALL alaerh( path, 'SLATMS', info, 0, uplo, n,
332  $ n, kd, kd, -1, imat, nfail, nerrs,
333  $ nout )
334  go to 60
335  END IF
336  ELSE IF( izero.GT.0 ) THEN
337 *
338 * Use the same matrix for types 3 and 4 as for type
339 * 2 by copying back the zeroed out column,
340 *
341  iw = 2*lda + 1
342  IF( iuplo.EQ.1 ) THEN
343  ioff = ( izero-1 )*ldab + kd + 1
344  CALL scopy( izero-i1, work( iw ), 1,
345  $ a( ioff-izero+i1 ), 1 )
346  iw = iw + izero - i1
347  CALL scopy( i2-izero+1, work( iw ), 1,
348  $ a( ioff ), max( ldab-1, 1 ) )
349  ELSE
350  ioff = ( i1-1 )*ldab + 1
351  CALL scopy( izero-i1, work( iw ), 1,
352  $ a( ioff+izero-i1 ),
353  $ max( ldab-1, 1 ) )
354  ioff = ( izero-1 )*ldab + 1
355  iw = iw + izero - i1
356  CALL scopy( i2-izero+1, work( iw ), 1,
357  $ a( ioff ), 1 )
358  END IF
359  END IF
360 *
361 * For types 2-4, zero one row and column of the matrix
362 * to test that INFO is returned correctly.
363 *
364  izero = 0
365  IF( zerot ) THEN
366  IF( imat.EQ.2 ) THEN
367  izero = 1
368  ELSE IF( imat.EQ.3 ) THEN
369  izero = n
370  ELSE
371  izero = n / 2 + 1
372  END IF
373 *
374 * Save the zeroed out row and column in WORK(*,3)
375 *
376  iw = 2*lda
377  DO 20 i = 1, min( 2*kd+1, n )
378  work( iw+i ) = zero
379  20 continue
380  iw = iw + 1
381  i1 = max( izero-kd, 1 )
382  i2 = min( izero+kd, n )
383 *
384  IF( iuplo.EQ.1 ) THEN
385  ioff = ( izero-1 )*ldab + kd + 1
386  CALL sswap( izero-i1, a( ioff-izero+i1 ), 1,
387  $ work( iw ), 1 )
388  iw = iw + izero - i1
389  CALL sswap( i2-izero+1, a( ioff ),
390  $ max( ldab-1, 1 ), work( iw ), 1 )
391  ELSE
392  ioff = ( i1-1 )*ldab + 1
393  CALL sswap( izero-i1, a( ioff+izero-i1 ),
394  $ max( ldab-1, 1 ), work( iw ), 1 )
395  ioff = ( izero-1 )*ldab + 1
396  iw = iw + izero - i1
397  CALL sswap( i2-izero+1, a( ioff ), 1,
398  $ work( iw ), 1 )
399  END IF
400  END IF
401 *
402 * Do for each value of NB in NBVAL
403 *
404  DO 50 inb = 1, nnb
405  nb = nbval( inb )
406  CALL xlaenv( 1, nb )
407 *
408 * Compute the L*L' or U'*U factorization of the band
409 * matrix.
410 *
411  CALL slacpy( 'Full', kd+1, n, a, ldab, afac, ldab )
412  srnamt = 'SPBTRF'
413  CALL spbtrf( uplo, n, kd, afac, ldab, info )
414 *
415 * Check error code from SPBTRF.
416 *
417  IF( info.NE.izero ) THEN
418  CALL alaerh( path, 'SPBTRF', info, izero, uplo,
419  $ n, n, kd, kd, nb, imat, nfail,
420  $ nerrs, nout )
421  go to 50
422  END IF
423 *
424 * Skip the tests if INFO is not 0.
425 *
426  IF( info.NE.0 )
427  $ go to 50
428 *
429 *+ TEST 1
430 * Reconstruct matrix from factors and compute
431 * residual.
432 *
433  CALL slacpy( 'Full', kd+1, n, afac, ldab, ainv,
434  $ ldab )
435  CALL spbt01( uplo, n, kd, a, ldab, ainv, ldab,
436  $ rwork, result( 1 ) )
437 *
438 * Print the test ratio if it is .GE. THRESH.
439 *
440  IF( result( 1 ).GE.thresh ) THEN
441  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
442  $ CALL alahd( nout, path )
443  WRITE( nout, fmt = 9999 )uplo, n, kd, nb, imat,
444  $ 1, result( 1 )
445  nfail = nfail + 1
446  END IF
447  nrun = nrun + 1
448 *
449 * Only do other tests if this is the first blocksize.
450 *
451  IF( inb.GT.1 )
452  $ go to 50
453 *
454 * Form the inverse of A so we can get a good estimate
455 * of RCONDC = 1/(norm(A) * norm(inv(A))).
456 *
457  CALL slaset( 'Full', n, n, zero, one, ainv, lda )
458  srnamt = 'SPBTRS'
459  CALL spbtrs( uplo, n, kd, n, afac, ldab, ainv, lda,
460  $ info )
461 *
462 * Compute RCONDC = 1/(norm(A) * norm(inv(A))).
463 *
464  anorm = slansb( '1', uplo, n, kd, a, ldab, rwork )
465  ainvnm = slange( '1', n, n, ainv, lda, rwork )
466  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
467  rcondc = one
468  ELSE
469  rcondc = ( one / anorm ) / ainvnm
470  END IF
471 *
472  DO 40 irhs = 1, nns
473  nrhs = nsval( irhs )
474 *
475 *+ TEST 2
476 * Solve and compute residual for A * X = B.
477 *
478  srnamt = 'SLARHS'
479  CALL slarhs( path, xtype, uplo, ' ', n, n, kd,
480  $ kd, nrhs, a, ldab, xact, lda, b,
481  $ lda, iseed, info )
482  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
483 *
484  srnamt = 'SPBTRS'
485  CALL spbtrs( uplo, n, kd, nrhs, afac, ldab, x,
486  $ lda, info )
487 *
488 * Check error code from SPBTRS.
489 *
490  IF( info.NE.0 )
491  $ CALL alaerh( path, 'SPBTRS', info, 0, uplo,
492  $ n, n, kd, kd, nrhs, imat, nfail,
493  $ nerrs, nout )
494 *
495  CALL slacpy( 'Full', n, nrhs, b, lda, work,
496  $ lda )
497  CALL spbt02( uplo, n, kd, nrhs, a, ldab, x, lda,
498  $ work, lda, rwork, result( 2 ) )
499 *
500 *+ TEST 3
501 * Check solution from generated exact solution.
502 *
503  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
504  $ result( 3 ) )
505 *
506 *+ TESTS 4, 5, and 6
507 * Use iterative refinement to improve the solution.
508 *
509  srnamt = 'SPBRFS'
510  CALL spbrfs( uplo, n, kd, nrhs, a, ldab, afac,
511  $ ldab, b, lda, x, lda, rwork,
512  $ rwork( nrhs+1 ), work, iwork,
513  $ info )
514 *
515 * Check error code from SPBRFS.
516 *
517  IF( info.NE.0 )
518  $ CALL alaerh( path, 'SPBRFS', info, 0, uplo,
519  $ n, n, kd, kd, nrhs, imat, nfail,
520  $ nerrs, nout )
521 *
522  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
523  $ result( 4 ) )
524  CALL spbt05( uplo, n, kd, nrhs, a, ldab, b, lda,
525  $ x, lda, xact, lda, rwork,
526  $ rwork( nrhs+1 ), result( 5 ) )
527 *
528 * Print information about the tests that did not
529 * pass the threshold.
530 *
531  DO 30 k = 2, 6
532  IF( result( k ).GE.thresh ) THEN
533  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
534  $ CALL alahd( nout, path )
535  WRITE( nout, fmt = 9998 )uplo, n, kd,
536  $ nrhs, imat, k, result( k )
537  nfail = nfail + 1
538  END IF
539  30 continue
540  nrun = nrun + 5
541  40 continue
542 *
543 *+ TEST 7
544 * Get an estimate of RCOND = 1/CNDNUM.
545 *
546  srnamt = 'SPBCON'
547  CALL spbcon( uplo, n, kd, afac, ldab, anorm, rcond,
548  $ work, iwork, info )
549 *
550 * Check error code from SPBCON.
551 *
552  IF( info.NE.0 )
553  $ CALL alaerh( path, 'SPBCON', info, 0, uplo, n,
554  $ n, kd, kd, -1, imat, nfail, nerrs,
555  $ nout )
556 *
557  result( 7 ) = sget06( rcond, rcondc )
558 *
559 * Print the test ratio if it is .GE. THRESH.
560 *
561  IF( result( 7 ).GE.thresh ) THEN
562  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
563  $ CALL alahd( nout, path )
564  WRITE( nout, fmt = 9997 )uplo, n, kd, imat, 7,
565  $ result( 7 )
566  nfail = nfail + 1
567  END IF
568  nrun = nrun + 1
569  50 continue
570  60 continue
571  70 continue
572  80 continue
573  90 continue
574 *
575 * Print a summary of the results.
576 *
577  CALL alasum( path, nout, nfail, nrun, nerrs )
578 *
579  9999 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NB=', i4,
580  $ ', type ', i2, ', test ', i2, ', ratio= ', g12.5 )
581  9998 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NRHS=', i3,
582  $ ', type ', i2, ', test(', i2, ') = ', g12.5 )
583  9997 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ',', 10x,
584  $ ' type ', i2, ', test(', i2, ') = ', g12.5 )
585  return
586 *
587 * End of SCHKPB
588 *
589  END