1       SUBROUTINE ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
  2      $                   THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
  3      $                   XACT, WORK, RWORK, NOUT )
  4 *
  5 *  -- LAPACK test routine (version 3.1) --
  6 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
  7 *     November 2006
  8 *
  9 *     .. Scalar Arguments ..
 10       LOGICAL            TSTERR
 11       INTEGER            NMAX, NN, NNB, NNS, NOUT
 12       DOUBLE PRECISION   THRESH
 13 *     ..
 14 *     .. Array Arguments ..
 15       LOGICAL            DOTYPE( * )
 16       INTEGER            NBVAL( * ), NSVAL( * ), NVAL( * )
 17       DOUBLE PRECISION   RWORK( * )
 18       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
 19      $                   WORK( * ), X( * ), XACT( * )
 20 *     ..
 21 *
 22 *  Purpose
 23 *  =======
 24 *
 25 *  ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
 26 *
 27 *  Arguments
 28 *  =========
 29 *
 30 *  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
 31 *          The matrix types to be used for testing.  Matrices of type j
 32 *          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
 33 *          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
 34 *
 35 *  NN      (input) INTEGER
 36 *          The number of values of N contained in the vector NVAL.
 37 *
 38 *  NVAL    (input) INTEGER array, dimension (NN)
 39 *          The values of the matrix dimension N.
 40 *
 41 *  NNB     (input) INTEGER
 42 *          The number of values of NB contained in the vector NBVAL.
 43 *
 44 *  NBVAL   (input) INTEGER array, dimension (NBVAL)
 45 *          The values of the blocksize NB.
 46 *
 47 *  NNS     (input) INTEGER
 48 *          The number of values of NRHS contained in the vector NSVAL.
 49 *
 50 *  NSVAL   (input) INTEGER array, dimension (NNS)
 51 *          The values of the number of right hand sides NRHS.
 52 *
 53 *  THRESH  (input) DOUBLE PRECISION
 54 *          The threshold value for the test ratios.  A result is
 55 *          included in the output file if RESULT >= THRESH.  To have
 56 *          every test ratio printed, use THRESH = 0.
 57 *
 58 *  TSTERR  (input) LOGICAL
 59 *          Flag that indicates whether error exits are to be tested.
 60 *
 61 *  NMAX    (input) INTEGER
 62 *          The maximum value permitted for N, used in dimensioning the
 63 *          work arrays.
 64 *
 65 *  A       (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
 66 *
 67 *  AFAC    (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
 68 *
 69 *  AINV    (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX)
 70 *
 71 *  B       (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
 72 *          where NSMAX is the largest entry in NSVAL.
 73 *
 74 *  X       (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
 75 *
 76 *  XACT    (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
 77 *
 78 *  WORK    (workspace) DOUBLE PRECISION array, dimension
 79 *                      (NMAX*max(3,NSMAX))
 80 *
 81 *  RWORK   (workspace) DOUBLE PRECISION array, dimension
 82 *                      (max(NMAX,2*NSMAX))
 83 *
 84 *  NOUT    (input) INTEGER
 85 *          The unit number for output.
 86 *
 87 *  =====================================================================
 88 *
 89 *     .. Parameters ..
 90       DOUBLE PRECISION   ONE, ZERO
 91       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
 92       INTEGER            NTYPES, NTESTS
 93       PARAMETER          ( NTYPES = 8, NTESTS = 7 )
 94       INTEGER            NBW
 95       PARAMETER          ( NBW = 4 )
 96 *     ..
 97 *     .. Local Scalars ..
 98       LOGICAL            ZEROT
 99       CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
100       CHARACTER*3        PATH
101       INTEGER            I, I1, I2, IKD, IMAT, IN, INB, INFO, IOFF,
102      $                   IRHS, IUPLO, IW, IZERO, K, KD, KL, KOFF, KU,
103      $                   LDA, LDAB, MODE, N, NB, NERRS, NFAIL, NIMAT,
104      $                   NKD, NRHS, NRUN
105       DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCOND, RCONDC
106 *     ..
107 *     .. Local Arrays ..
108       INTEGER            ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW )
109       DOUBLE PRECISION   RESULT( NTESTS )
110 *     ..
111 *     .. External Functions ..
112       DOUBLE PRECISION   DGET06, ZLANGE, ZLANHB
113       EXTERNAL           DGET06, ZLANGE, ZLANHB
114 *     ..
115 *     .. External Subroutines ..
116       EXTERNAL           ALAERH, ALAHD, ALASUM, XLAENV, ZCOPY, ZERRPO,
117      $                   ZGET04, ZLACPY, ZLAIPD, ZLARHS, ZLASET, ZLATB4,
118      $                   ZLATMS, ZPBCON, ZPBRFS, ZPBT01, ZPBT02, ZPBT05,
119      $                   ZPBTRF, ZPBTRS, ZSWAP
120 *     ..
121 *     .. Intrinsic Functions ..
122       INTRINSIC          DCMPLXMAXMIN
123 *     ..
124 *     .. Scalars in Common ..
125       LOGICAL            LERR, OK
126       CHARACTER*32       SRNAMT
127       INTEGER            INFOT, NUNIT
128 *     ..
129 *     .. Common blocks ..
130       COMMON             / INFOC / INFOT, NUNIT, OK, LERR
131       COMMON             / SRNAMC / SRNAMT
132 *     ..
133 *     .. Data statements ..
134       DATA               ISEEDY / 1988198919901991 /
135 *     ..
136 *     .. Executable Statements ..
137 *
138 *     Initialize constants and the random number seed.
139 *
140       PATH( 11 ) = 'Zomplex precision'
141       PATH( 23 ) = 'PB'
142       NRUN = 0
143       NFAIL = 0
144       NERRS = 0
145       DO 10 I = 14
146          ISEED( I ) = ISEEDY( I )
147    10 CONTINUE
148 *
149 *     Test the error exits
150 *
151       IF( TSTERR )
152      $   CALL ZERRPO( PATH, NOUT )
153       INFOT = 0
154       KDVAL( 1 ) = 0
155 *
156 *     Do for each value of N in NVAL
157 *
158       DO 90 IN = 1, NN
159          N = NVAL( IN )
160          LDA = MAX( N, 1 )
161          XTYPE = 'N'
162 *
163 *        Set limits on the number of loop iterations.
164 *
165          NKD = MAX1MIN( N, 4 ) )
166          NIMAT = NTYPES
167          IF( N.EQ.0 )
168      $      NIMAT = 1
169 *
170          KDVAL( 2 ) = N + ( N+1 ) / 4
171          KDVAL( 3 ) = ( 3*N-1 ) / 4
172          KDVAL( 4 ) = ( N+1 ) / 4
173 *
174          DO 80 IKD = 1, NKD
175 *
176 *           Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
177 *           makes it easier to skip redundant values for small values
178 *           of N.
179 *
180             KD = KDVAL( IKD )
181             LDAB = KD + 1
182 *
183 *           Do first for UPLO = 'U', then for UPLO = 'L'
184 *
185             DO 70 IUPLO = 12
186                KOFF = 1
187                IF( IUPLO.EQ.1 ) THEN
188                   UPLO = 'U'
189                   KOFF = MAX1, KD+2-N )
190                   PACKIT = 'Q'
191                ELSE
192                   UPLO = 'L'
193                   PACKIT = 'B'
194                END IF
195 *
196                DO 60 IMAT = 1, NIMAT
197 *
198 *                 Do the tests only if DOTYPE( IMAT ) is true.
199 *
200                   IF.NOT.DOTYPE( IMAT ) )
201      $               GO TO 60
202 *
203 *                 Skip types 2, 3, or 4 if the matrix size is too small.
204 *
205                   ZEROT = IMAT.GE.2 .AND. IMAT.LE.4
206                   IF( ZEROT .AND. N.LT.IMAT-1 )
207      $               GO TO 60
208 *
209                   IF.NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN
210 *
211 *                    Set up parameters with ZLATB4 and generate a test
212 *                    matrix with ZLATMS.
213 *
214                      CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
215      $                            MODE, CNDNUM, DIST )
216 *
217                      SRNAMT = 'ZLATMS'
218                      CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
219      $                            CNDNUM, ANORM, KD, KD, PACKIT,
220      $                            A( KOFF ), LDAB, WORK, INFO )
221 *
222 *                    Check error code from ZLATMS.
223 *
224                      IF( INFO.NE.0 ) THEN
225                         CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N,
226      $                               N, KD, KD, -1, IMAT, NFAIL, NERRS,
227      $                               NOUT )
228                         GO TO 60
229                      END IF
230                   ELSE IF( IZERO.GT.0 ) THEN
231 *
232 *                    Use the same matrix for types 3 and 4 as for type
233 *                    2 by copying back the zeroed out column,
234 *
235                      IW = 2*LDA + 1
236                      IF( IUPLO.EQ.1 ) THEN
237                         IOFF = ( IZERO-1 )*LDAB + KD + 1
238                         CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
239      $                              A( IOFF-IZERO+I1 ), 1 )
240                         IW = IW + IZERO - I1
241                         CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
242      $                              A( IOFF ), MAX( LDAB-11 ) )
243                      ELSE
244                         IOFF = ( I1-1 )*LDAB + 1
245                         CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
246      $                              A( IOFF+IZERO-I1 ),
247      $                              MAX( LDAB-11 ) )
248                         IOFF = ( IZERO-1 )*LDAB + 1
249                         IW = IW + IZERO - I1
250                         CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
251      $                              A( IOFF ), 1 )
252                      END IF
253                   END IF
254 *
255 *                 For types 2-4, zero one row and column of the matrix
256 *                 to test that INFO is returned correctly.
257 *
258                   IZERO = 0
259                   IF( ZEROT ) THEN
260                      IF( IMAT.EQ.2 ) THEN
261                         IZERO = 1
262                      ELSE IF( IMAT.EQ.3 ) THEN
263                         IZERO = N
264                      ELSE
265                         IZERO = N / 2 + 1
266                      END IF
267 *
268 *                    Save the zeroed out row and column in WORK(*,3)
269 *
270                      IW = 2*LDA
271                      DO 20 I = 1MIN2*KD+1, N )
272                         WORK( IW+I ) = ZERO
273    20                CONTINUE
274                      IW = IW + 1
275                      I1 = MAX( IZERO-KD, 1 )
276                      I2 = MIN( IZERO+KD, N )
277 *
278                      IF( IUPLO.EQ.1 ) THEN
279                         IOFF = ( IZERO-1 )*LDAB + KD + 1
280                         CALL ZSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1,
281      $                              WORK( IW ), 1 )
282                         IW = IW + IZERO - I1
283                         CALL ZSWAP( I2-IZERO+1, A( IOFF ),
284      $                              MAX( LDAB-11 ), WORK( IW ), 1 )
285                      ELSE
286                         IOFF = ( I1-1 )*LDAB + 1
287                         CALL ZSWAP( IZERO-I1, A( IOFF+IZERO-I1 ),
288      $                              MAX( LDAB-11 ), WORK( IW ), 1 )
289                         IOFF = ( IZERO-1 )*LDAB + 1
290                         IW = IW + IZERO - I1
291                         CALL ZSWAP( I2-IZERO+1, A( IOFF ), 1,
292      $                              WORK( IW ), 1 )
293                      END IF
294                   END IF
295 *
296 *                 Set the imaginary part of the diagonals.
297 *
298                   IF( IUPLO.EQ.1 ) THEN
299                      CALL ZLAIPD( N, A( KD+1 ), LDAB, 0 )
300                   ELSE
301                      CALL ZLAIPD( N, A( 1 ), LDAB, 0 )
302                   END IF
303 *
304 *                 Do for each value of NB in NBVAL
305 *
306                   DO 50 INB = 1, NNB
307                      NB = NBVAL( INB )
308                      CALL XLAENV( 1, NB )
309 *
310 *                    Compute the L*L' or U'*U factorization of the band
311 *                    matrix.
312 *
313                      CALL ZLACPY( 'Full', KD+1, N, A, LDAB, AFAC, LDAB )
314                      SRNAMT = 'ZPBTRF'
315                      CALL ZPBTRF( UPLO, N, KD, AFAC, LDAB, INFO )
316 *
317 *                    Check error code from ZPBTRF.
318 *
319                      IF( INFO.NE.IZERO ) THEN
320                         CALL ALAERH( PATH, 'ZPBTRF', INFO, IZERO, UPLO,
321      $                               N, N, KD, KD, NB, IMAT, NFAIL,
322      $                               NERRS, NOUT )
323                         GO TO 50
324                      END IF
325 *
326 *                    Skip the tests if INFO is not 0.
327 *
328                      IF( INFO.NE.0 )
329      $                  GO TO 50
330 *
331 *+    TEST 1
332 *                    Reconstruct matrix from factors and compute
333 *                    residual.
334 *
335                      CALL ZLACPY( 'Full', KD+1, N, AFAC, LDAB, AINV,
336      $                            LDAB )
337                      CALL ZPBT01( UPLO, N, KD, A, LDAB, AINV, LDAB,
338      $                            RWORK, RESULT1 ) )
339 *
340 *                    Print the test ratio if it is .GE. THRESH.
341 *
342                      IFRESULT1 ).GE.THRESH ) THEN
343                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
344      $                     CALL ALAHD( NOUT, PATH )
345                         WRITE( NOUT, FMT = 9999 )UPLO, N, KD, NB, IMAT,
346      $                     1RESULT1 )
347                         NFAIL = NFAIL + 1
348                      END IF
349                      NRUN = NRUN + 1
350 *
351 *                    Only do other tests if this is the first blocksize.
352 *
353                      IF( INB.GT.1 )
354      $                  GO TO 50
355 *
356 *                    Form the inverse of A so we can get a good estimate
357 *                    of RCONDC = 1/(norm(A) * norm(inv(A))).
358 *
359                      CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ),
360      $                            DCMPLX( ONE ), AINV, LDA )
361                      SRNAMT = 'ZPBTRS'
362                      CALL ZPBTRS( UPLO, N, KD, N, AFAC, LDAB, AINV, LDA,
363      $                            INFO )
364 *
365 *                    Compute RCONDC = 1/(norm(A) * norm(inv(A))).
366 *
367                      ANORM = ZLANHB( '1', UPLO, N, KD, A, LDAB, RWORK )
368                      AINVNM = ZLANGE( '1', N, N, AINV, LDA, RWORK )
369                      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
370                         RCONDC = ONE
371                      ELSE
372                         RCONDC = ( ONE / ANORM ) / AINVNM
373                      END IF
374 *
375                      DO 40 IRHS = 1, NNS
376                         NRHS = NSVAL( IRHS )
377 *
378 *+    TEST 2
379 *                    Solve and compute residual for A * X = B.
380 *
381                         SRNAMT = 'ZLARHS'
382                         CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD,
383      $                               KD, NRHS, A, LDAB, XACT, LDA, B,
384      $                               LDA, ISEED, INFO )
385                         CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
386 *
387                         SRNAMT = 'ZPBTRS'
388                         CALL ZPBTRS( UPLO, N, KD, NRHS, AFAC, LDAB, X,
389      $                               LDA, INFO )
390 *
391 *                    Check error code from ZPBTRS.
392 *
393                         IF( INFO.NE.0 )
394      $                     CALL ALAERH( PATH, 'ZPBTRS', INFO, 0, UPLO,
395      $                                  N, N, KD, KD, NRHS, IMAT, NFAIL,
396      $                                  NERRS, NOUT )
397 *
398                         CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
399      $                               LDA )
400                         CALL ZPBT02( UPLO, N, KD, NRHS, A, LDAB, X, LDA,
401      $                               WORK, LDA, RWORK, RESULT2 ) )
402 *
403 *+    TEST 3
404 *                    Check solution from generated exact solution.
405 *
406                         CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
407      $                               RESULT3 ) )
408 *
409 *+    TESTS 4, 5, and 6
410 *                    Use iterative refinement to improve the solution.
411 *
412                         SRNAMT = 'ZPBRFS'
413                         CALL ZPBRFS( UPLO, N, KD, NRHS, A, LDAB, AFAC,
414      $                               LDAB, B, LDA, X, LDA, RWORK,
415      $                               RWORK( NRHS+1 ), WORK,
416      $                               RWORK( 2*NRHS+1 ), INFO )
417 *
418 *                    Check error code from ZPBRFS.
419 *
420                         IF( INFO.NE.0 )
421      $                     CALL ALAERH( PATH, 'ZPBRFS', INFO, 0, UPLO,
422      $                                  N, N, KD, KD, NRHS, IMAT, NFAIL,
423      $                                  NERRS, NOUT )
424 *
425                         CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
426      $                               RESULT4 ) )
427                         CALL ZPBT05( UPLO, N, KD, NRHS, A, LDAB, B, LDA,
428      $                               X, LDA, XACT, LDA, RWORK,
429      $                               RWORK( NRHS+1 ), RESULT5 ) )
430 *
431 *                       Print information about the tests that did not
432 *                       pass the threshold.
433 *
434                         DO 30 K = 26
435                            IFRESULT( K ).GE.THRESH ) THEN
436                               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
437      $                           CALL ALAHD( NOUT, PATH )
438                               WRITE( NOUT, FMT = 9998 )UPLO, N, KD,
439      $                           NRHS, IMAT, K, RESULT( K )
440                               NFAIL = NFAIL + 1
441                            END IF
442    30                   CONTINUE
443                         NRUN = NRUN + 5
444    40                CONTINUE
445 *
446 *+    TEST 7
447 *                    Get an estimate of RCOND = 1/CNDNUM.
448 *
449                      SRNAMT = 'ZPBCON'
450                      CALL ZPBCON( UPLO, N, KD, AFAC, LDAB, ANORM, RCOND,
451      $                            WORK, RWORK, INFO )
452 *
453 *                    Check error code from ZPBCON.
454 *
455                      IF( INFO.NE.0 )
456      $                  CALL ALAERH( PATH, 'ZPBCON', INFO, 0, UPLO, N,
457      $                               N, KD, KD, -1, IMAT, NFAIL, NERRS,
458      $                               NOUT )
459 *
460                      RESULT7 ) = DGET06( RCOND, RCONDC )
461 *
462 *                    Print the test ratio if it is .GE. THRESH.
463 *
464                      IFRESULT7 ).GE.THRESH ) THEN
465                         IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
466      $                     CALL ALAHD( NOUT, PATH )
467                         WRITE( NOUT, FMT = 9997 )UPLO, N, KD, IMAT, 7,
468      $                     RESULT7 )
469                         NFAIL = NFAIL + 1
470                      END IF
471                      NRUN = NRUN + 1
472    50             CONTINUE
473    60          CONTINUE
474    70       CONTINUE
475    80    CONTINUE
476    90 CONTINUE
477 *
478 *     Print a summary of the results.
479 *
480       CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
481 *
482  9999 FORMAT' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NB=', I4,
483      $      ', type ', I2, ', test ', I2, ', ratio= 'G12.5 )
484  9998 FORMAT' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I3,
485      $      ', type ', I2, ', test(', I2, ') = 'G12.5 )
486  9997 FORMAT' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ','10X,
487      $      ' type ', I2, ', test(', I2, ') = 'G12.5 )
488       RETURN
489 *
490 *     End of ZCHKPB
491 *
492       END