LAPACK  3.4.2
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zchkpb.f
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1 *> \brief \b ZCHKPB
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 ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER NBVAL( * ), NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION RWORK( * )
24 * COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
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] NNB
61 *> \verbatim
62 *> NNB is INTEGER
63 *> The number of values of NB contained in the vector NBVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NBVAL
67 *> \verbatim
68 *> NBVAL is INTEGER array, dimension (NBVAL)
69 *> The values of the blocksize NB.
70 *> \endverbatim
71 *>
72 *> \param[in] NNS
73 *> \verbatim
74 *> NNS is INTEGER
75 *> The number of values of NRHS contained in the vector NSVAL.
76 *> \endverbatim
77 *>
78 *> \param[in] NSVAL
79 *> \verbatim
80 *> NSVAL is INTEGER array, dimension (NNS)
81 *> The values of the number of right hand sides NRHS.
82 *> \endverbatim
83 *>
84 *> \param[in] THRESH
85 *> \verbatim
86 *> THRESH is DOUBLE PRECISION
87 *> The threshold value for the test ratios. A result is
88 *> included in the output file if RESULT >= THRESH. To have
89 *> every test ratio printed, use THRESH = 0.
90 *> \endverbatim
91 *>
92 *> \param[in] TSTERR
93 *> \verbatim
94 *> TSTERR is LOGICAL
95 *> Flag that indicates whether error exits are to be tested.
96 *> \endverbatim
97 *>
98 *> \param[in] NMAX
99 *> \verbatim
100 *> NMAX is INTEGER
101 *> The maximum value permitted for N, used in dimensioning the
102 *> work arrays.
103 *> \endverbatim
104 *>
105 *> \param[out] A
106 *> \verbatim
107 *> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
108 *> \endverbatim
109 *>
110 *> \param[out] AFAC
111 *> \verbatim
112 *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
113 *> \endverbatim
114 *>
115 *> \param[out] AINV
116 *> \verbatim
117 *> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
118 *> \endverbatim
119 *>
120 *> \param[out] B
121 *> \verbatim
122 *> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
123 *> where NSMAX is the largest entry in NSVAL.
124 *> \endverbatim
125 *>
126 *> \param[out] X
127 *> \verbatim
128 *> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
129 *> \endverbatim
130 *>
131 *> \param[out] XACT
132 *> \verbatim
133 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
134 *> \endverbatim
135 *>
136 *> \param[out] WORK
137 *> \verbatim
138 *> WORK is DOUBLE PRECISION array, dimension
139 *> (NMAX*max(3,NSMAX))
140 *> \endverbatim
141 *>
142 *> \param[out] RWORK
143 *> \verbatim
144 *> RWORK is DOUBLE PRECISION array, dimension
145 *> (max(NMAX,2*NSMAX))
146 *> \endverbatim
147 *>
148 *> \param[in] NOUT
149 *> \verbatim
150 *> NOUT is INTEGER
151 *> The unit number for output.
152 *> \endverbatim
153 *
154 * Authors:
155 * ========
156 *
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
160 *> \author NAG Ltd.
161 *
162 *> \date November 2011
163 *
164 *> \ingroup complex16_lin
165 *
166 * =====================================================================
167  SUBROUTINE zchkpb( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
168  $ thresh, tsterr, nmax, a, afac, ainv, b, x,
169  $ xact, work, rwork, nout )
170 *
171 * -- LAPACK test routine (version 3.4.0) --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 * November 2011
175 *
176 * .. Scalar Arguments ..
177  LOGICAL tsterr
178  INTEGER nmax, nn, nnb, nns, nout
179  DOUBLE PRECISION thresh
180 * ..
181 * .. Array Arguments ..
182  LOGICAL dotype( * )
183  INTEGER nbval( * ), nsval( * ), nval( * )
184  DOUBLE PRECISION rwork( * )
185  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
186  $ work( * ), x( * ), xact( * )
187 * ..
188 *
189 * =====================================================================
190 *
191 * .. Parameters ..
192  DOUBLE PRECISION one, zero
193  parameter( one = 1.0d+0, zero = 0.0d+0 )
194  INTEGER ntypes, ntests
195  parameter( ntypes = 8, ntests = 7 )
196  INTEGER nbw
197  parameter( nbw = 4 )
198 * ..
199 * .. Local Scalars ..
200  LOGICAL zerot
201  CHARACTER dist, packit, type, uplo, xtype
202  CHARACTER*3 path
203  INTEGER i, i1, i2, ikd, imat, in, inb, info, ioff,
204  $ irhs, iuplo, iw, izero, k, kd, kl, koff, ku,
205  $ lda, ldab, mode, n, nb, nerrs, nfail, nimat,
206  $ nkd, nrhs, nrun
207  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
208 * ..
209 * .. Local Arrays ..
210  INTEGER iseed( 4 ), iseedy( 4 ), kdval( nbw )
211  DOUBLE PRECISION result( ntests )
212 * ..
213 * .. External Functions ..
214  DOUBLE PRECISION dget06, zlange, zlanhb
215  EXTERNAL dget06, zlange, zlanhb
216 * ..
217 * .. External Subroutines ..
218  EXTERNAL alaerh, alahd, alasum, xlaenv, zcopy, zerrpo,
219  $ zget04, zlacpy, zlaipd, zlarhs, zlaset, zlatb4,
220  $ zlatms, zpbcon, zpbrfs, zpbt01, zpbt02, zpbt05,
221  $ zpbtrf, zpbtrs, zswap
222 * ..
223 * .. Intrinsic Functions ..
224  INTRINSIC dcmplx, max, min
225 * ..
226 * .. Scalars in Common ..
227  LOGICAL lerr, ok
228  CHARACTER*32 srnamt
229  INTEGER infot, nunit
230 * ..
231 * .. Common blocks ..
232  common / infoc / infot, nunit, ok, lerr
233  common / srnamc / srnamt
234 * ..
235 * .. Data statements ..
236  DATA iseedy / 1988, 1989, 1990, 1991 /
237 * ..
238 * .. Executable Statements ..
239 *
240 * Initialize constants and the random number seed.
241 *
242  path( 1: 1 ) = 'Zomplex precision'
243  path( 2: 3 ) = 'PB'
244  nrun = 0
245  nfail = 0
246  nerrs = 0
247  DO 10 i = 1, 4
248  iseed( i ) = iseedy( i )
249  10 continue
250 *
251 * Test the error exits
252 *
253  IF( tsterr )
254  $ CALL zerrpo( path, nout )
255  infot = 0
256  kdval( 1 ) = 0
257 *
258 * Do for each value of N in NVAL
259 *
260  DO 90 in = 1, nn
261  n = nval( in )
262  lda = max( n, 1 )
263  xtype = 'N'
264 *
265 * Set limits on the number of loop iterations.
266 *
267  nkd = max( 1, min( n, 4 ) )
268  nimat = ntypes
269  IF( n.EQ.0 )
270  $ nimat = 1
271 *
272  kdval( 2 ) = n + ( n+1 ) / 4
273  kdval( 3 ) = ( 3*n-1 ) / 4
274  kdval( 4 ) = ( n+1 ) / 4
275 *
276  DO 80 ikd = 1, nkd
277 *
278 * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
279 * makes it easier to skip redundant values for small values
280 * of N.
281 *
282  kd = kdval( ikd )
283  ldab = kd + 1
284 *
285 * Do first for UPLO = 'U', then for UPLO = 'L'
286 *
287  DO 70 iuplo = 1, 2
288  koff = 1
289  IF( iuplo.EQ.1 ) THEN
290  uplo = 'U'
291  koff = max( 1, kd+2-n )
292  packit = 'Q'
293  ELSE
294  uplo = 'L'
295  packit = 'B'
296  END IF
297 *
298  DO 60 imat = 1, nimat
299 *
300 * Do the tests only if DOTYPE( IMAT ) is true.
301 *
302  IF( .NOT.dotype( imat ) )
303  $ go to 60
304 *
305 * Skip types 2, 3, or 4 if the matrix size is too small.
306 *
307  zerot = imat.GE.2 .AND. imat.LE.4
308  IF( zerot .AND. n.LT.imat-1 )
309  $ go to 60
310 *
311  IF( .NOT.zerot .OR. .NOT.dotype( 1 ) ) THEN
312 *
313 * Set up parameters with ZLATB4 and generate a test
314 * matrix with ZLATMS.
315 *
316  CALL zlatb4( path, imat, n, n, type, kl, ku, anorm,
317  $ mode, cndnum, dist )
318 *
319  srnamt = 'ZLATMS'
320  CALL zlatms( n, n, dist, iseed, type, rwork, mode,
321  $ cndnum, anorm, kd, kd, packit,
322  $ a( koff ), ldab, work, info )
323 *
324 * Check error code from ZLATMS.
325 *
326  IF( info.NE.0 ) THEN
327  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n,
328  $ n, kd, kd, -1, imat, nfail, nerrs,
329  $ nout )
330  go to 60
331  END IF
332  ELSE IF( izero.GT.0 ) THEN
333 *
334 * Use the same matrix for types 3 and 4 as for type
335 * 2 by copying back the zeroed out column,
336 *
337  iw = 2*lda + 1
338  IF( iuplo.EQ.1 ) THEN
339  ioff = ( izero-1 )*ldab + kd + 1
340  CALL zcopy( izero-i1, work( iw ), 1,
341  $ a( ioff-izero+i1 ), 1 )
342  iw = iw + izero - i1
343  CALL zcopy( i2-izero+1, work( iw ), 1,
344  $ a( ioff ), max( ldab-1, 1 ) )
345  ELSE
346  ioff = ( i1-1 )*ldab + 1
347  CALL zcopy( izero-i1, work( iw ), 1,
348  $ a( ioff+izero-i1 ),
349  $ max( ldab-1, 1 ) )
350  ioff = ( izero-1 )*ldab + 1
351  iw = iw + izero - i1
352  CALL zcopy( i2-izero+1, work( iw ), 1,
353  $ a( ioff ), 1 )
354  END IF
355  END IF
356 *
357 * For types 2-4, zero one row and column of the matrix
358 * to test that INFO is returned correctly.
359 *
360  izero = 0
361  IF( zerot ) THEN
362  IF( imat.EQ.2 ) THEN
363  izero = 1
364  ELSE IF( imat.EQ.3 ) THEN
365  izero = n
366  ELSE
367  izero = n / 2 + 1
368  END IF
369 *
370 * Save the zeroed out row and column in WORK(*,3)
371 *
372  iw = 2*lda
373  DO 20 i = 1, min( 2*kd+1, n )
374  work( iw+i ) = zero
375  20 continue
376  iw = iw + 1
377  i1 = max( izero-kd, 1 )
378  i2 = min( izero+kd, n )
379 *
380  IF( iuplo.EQ.1 ) THEN
381  ioff = ( izero-1 )*ldab + kd + 1
382  CALL zswap( izero-i1, a( ioff-izero+i1 ), 1,
383  $ work( iw ), 1 )
384  iw = iw + izero - i1
385  CALL zswap( i2-izero+1, a( ioff ),
386  $ max( ldab-1, 1 ), work( iw ), 1 )
387  ELSE
388  ioff = ( i1-1 )*ldab + 1
389  CALL zswap( izero-i1, a( ioff+izero-i1 ),
390  $ max( ldab-1, 1 ), work( iw ), 1 )
391  ioff = ( izero-1 )*ldab + 1
392  iw = iw + izero - i1
393  CALL zswap( i2-izero+1, a( ioff ), 1,
394  $ work( iw ), 1 )
395  END IF
396  END IF
397 *
398 * Set the imaginary part of the diagonals.
399 *
400  IF( iuplo.EQ.1 ) THEN
401  CALL zlaipd( n, a( kd+1 ), ldab, 0 )
402  ELSE
403  CALL zlaipd( n, a( 1 ), ldab, 0 )
404  END IF
405 *
406 * Do for each value of NB in NBVAL
407 *
408  DO 50 inb = 1, nnb
409  nb = nbval( inb )
410  CALL xlaenv( 1, nb )
411 *
412 * Compute the L*L' or U'*U factorization of the band
413 * matrix.
414 *
415  CALL zlacpy( 'Full', kd+1, n, a, ldab, afac, ldab )
416  srnamt = 'ZPBTRF'
417  CALL zpbtrf( uplo, n, kd, afac, ldab, info )
418 *
419 * Check error code from ZPBTRF.
420 *
421  IF( info.NE.izero ) THEN
422  CALL alaerh( path, 'ZPBTRF', info, izero, uplo,
423  $ n, n, kd, kd, nb, imat, nfail,
424  $ nerrs, nout )
425  go to 50
426  END IF
427 *
428 * Skip the tests if INFO is not 0.
429 *
430  IF( info.NE.0 )
431  $ go to 50
432 *
433 *+ TEST 1
434 * Reconstruct matrix from factors and compute
435 * residual.
436 *
437  CALL zlacpy( 'Full', kd+1, n, afac, ldab, ainv,
438  $ ldab )
439  CALL zpbt01( uplo, n, kd, a, ldab, ainv, ldab,
440  $ rwork, result( 1 ) )
441 *
442 * Print the test ratio if it is .GE. THRESH.
443 *
444  IF( result( 1 ).GE.thresh ) THEN
445  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
446  $ CALL alahd( nout, path )
447  WRITE( nout, fmt = 9999 )uplo, n, kd, nb, imat,
448  $ 1, result( 1 )
449  nfail = nfail + 1
450  END IF
451  nrun = nrun + 1
452 *
453 * Only do other tests if this is the first blocksize.
454 *
455  IF( inb.GT.1 )
456  $ go to 50
457 *
458 * Form the inverse of A so we can get a good estimate
459 * of RCONDC = 1/(norm(A) * norm(inv(A))).
460 *
461  CALL zlaset( 'Full', n, n, dcmplx( zero ),
462  $ dcmplx( one ), ainv, lda )
463  srnamt = 'ZPBTRS'
464  CALL zpbtrs( uplo, n, kd, n, afac, ldab, ainv, lda,
465  $ info )
466 *
467 * Compute RCONDC = 1/(norm(A) * norm(inv(A))).
468 *
469  anorm = zlanhb( '1', uplo, n, kd, a, ldab, rwork )
470  ainvnm = zlange( '1', n, n, ainv, lda, rwork )
471  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
472  rcondc = one
473  ELSE
474  rcondc = ( one / anorm ) / ainvnm
475  END IF
476 *
477  DO 40 irhs = 1, nns
478  nrhs = nsval( irhs )
479 *
480 *+ TEST 2
481 * Solve and compute residual for A * X = B.
482 *
483  srnamt = 'ZLARHS'
484  CALL zlarhs( path, xtype, uplo, ' ', n, n, kd,
485  $ kd, nrhs, a, ldab, xact, lda, b,
486  $ lda, iseed, info )
487  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
488 *
489  srnamt = 'ZPBTRS'
490  CALL zpbtrs( uplo, n, kd, nrhs, afac, ldab, x,
491  $ lda, info )
492 *
493 * Check error code from ZPBTRS.
494 *
495  IF( info.NE.0 )
496  $ CALL alaerh( path, 'ZPBTRS', info, 0, uplo,
497  $ n, n, kd, kd, nrhs, imat, nfail,
498  $ nerrs, nout )
499 *
500  CALL zlacpy( 'Full', n, nrhs, b, lda, work,
501  $ lda )
502  CALL zpbt02( uplo, n, kd, nrhs, a, ldab, x, lda,
503  $ work, lda, rwork, result( 2 ) )
504 *
505 *+ TEST 3
506 * Check solution from generated exact solution.
507 *
508  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
509  $ result( 3 ) )
510 *
511 *+ TESTS 4, 5, and 6
512 * Use iterative refinement to improve the solution.
513 *
514  srnamt = 'ZPBRFS'
515  CALL zpbrfs( uplo, n, kd, nrhs, a, ldab, afac,
516  $ ldab, b, lda, x, lda, rwork,
517  $ rwork( nrhs+1 ), work,
518  $ rwork( 2*nrhs+1 ), info )
519 *
520 * Check error code from ZPBRFS.
521 *
522  IF( info.NE.0 )
523  $ CALL alaerh( path, 'ZPBRFS', info, 0, uplo,
524  $ n, n, kd, kd, nrhs, imat, nfail,
525  $ nerrs, nout )
526 *
527  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
528  $ result( 4 ) )
529  CALL zpbt05( uplo, n, kd, nrhs, a, ldab, b, lda,
530  $ x, lda, xact, lda, rwork,
531  $ rwork( nrhs+1 ), result( 5 ) )
532 *
533 * Print information about the tests that did not
534 * pass the threshold.
535 *
536  DO 30 k = 2, 6
537  IF( result( k ).GE.thresh ) THEN
538  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
539  $ CALL alahd( nout, path )
540  WRITE( nout, fmt = 9998 )uplo, n, kd,
541  $ nrhs, imat, k, result( k )
542  nfail = nfail + 1
543  END IF
544  30 continue
545  nrun = nrun + 5
546  40 continue
547 *
548 *+ TEST 7
549 * Get an estimate of RCOND = 1/CNDNUM.
550 *
551  srnamt = 'ZPBCON'
552  CALL zpbcon( uplo, n, kd, afac, ldab, anorm, rcond,
553  $ work, rwork, info )
554 *
555 * Check error code from ZPBCON.
556 *
557  IF( info.NE.0 )
558  $ CALL alaerh( path, 'ZPBCON', info, 0, uplo, n,
559  $ n, kd, kd, -1, imat, nfail, nerrs,
560  $ nout )
561 *
562  result( 7 ) = dget06( rcond, rcondc )
563 *
564 * Print the test ratio if it is .GE. THRESH.
565 *
566  IF( result( 7 ).GE.thresh ) THEN
567  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
568  $ CALL alahd( nout, path )
569  WRITE( nout, fmt = 9997 )uplo, n, kd, imat, 7,
570  $ result( 7 )
571  nfail = nfail + 1
572  END IF
573  nrun = nrun + 1
574  50 continue
575  60 continue
576  70 continue
577  80 continue
578  90 continue
579 *
580 * Print a summary of the results.
581 *
582  CALL alasum( path, nout, nfail, nrun, nerrs )
583 *
584  9999 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NB=', i4,
585  $ ', type ', i2, ', test ', i2, ', ratio= ', g12.5 )
586  9998 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NRHS=', i3,
587  $ ', type ', i2, ', test(', i2, ') = ', g12.5 )
588  9997 format( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ',', 10x,
589  $ ' type ', i2, ', test(', i2, ') = ', g12.5 )
590  return
591 *
592 * End of ZCHKPB
593 *
594  END