1*> \brief \b ZCHKHP
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 ZCHKHP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
12*                          NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
13*                          IWORK, NOUT )
14*
15*       .. Scalar Arguments ..
16*       LOGICAL            TSTERR
17*       INTEGER            NMAX, NN, NNS, NOUT
18*       DOUBLE PRECISION   THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), 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*> ZCHKHP tests ZHPTRF, -TRI, -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] NNS
61*> \verbatim
62*>          NNS is INTEGER
63*>          The number of values of NRHS contained in the vector NSVAL.
64*> \endverbatim
65*>
66*> \param[in] NSVAL
67*> \verbatim
68*>          NSVAL is INTEGER array, dimension (NNS)
69*>          The values of the number of right hand sides NRHS.
70*> \endverbatim
71*>
72*> \param[in] THRESH
73*> \verbatim
74*>          THRESH is DOUBLE PRECISION
75*>          The threshold value for the test ratios.  A result is
76*>          included in the output file if RESULT >= THRESH.  To have
77*>          every test ratio printed, use THRESH = 0.
78*> \endverbatim
79*>
80*> \param[in] TSTERR
81*> \verbatim
82*>          TSTERR is LOGICAL
83*>          Flag that indicates whether error exits are to be tested.
84*> \endverbatim
85*>
86*> \param[in] NMAX
87*> \verbatim
88*>          NMAX is INTEGER
89*>          The maximum value permitted for N, used in dimensioning the
90*>          work arrays.
91*> \endverbatim
92*>
93*> \param[out] A
94*> \verbatim
95*>          A is COMPLEX*16 array, dimension
96*>                      (NMAX*(NMAX+1)/2)
97*> \endverbatim
98*>
99*> \param[out] AFAC
100*> \verbatim
101*>          AFAC is COMPLEX*16 array, dimension
102*>                      (NMAX*(NMAX+1)/2)
103*> \endverbatim
104*>
105*> \param[out] AINV
106*> \verbatim
107*>          AINV is COMPLEX*16 array, dimension
108*>                      (NMAX*(NMAX+1)/2)
109*> \endverbatim
110*>
111*> \param[out] B
112*> \verbatim
113*>          B is COMPLEX*16 array, dimension (NMAX*NSMAX)
114*>          where NSMAX is the largest entry in NSVAL.
115*> \endverbatim
116*>
117*> \param[out] X
118*> \verbatim
119*>          X is COMPLEX*16 array, dimension (NMAX*NSMAX)
120*> \endverbatim
121*>
122*> \param[out] XACT
123*> \verbatim
124*>          XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*>          WORK is COMPLEX*16 array, dimension
130*>                      (NMAX*max(2,NSMAX))
131*> \endverbatim
132*>
133*> \param[out] RWORK
134*> \verbatim
135*>          RWORK is DOUBLE PRECISION array,
136*>                                 dimension (NMAX+2*NSMAX)
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*> \ingroup complex16_lin
159*
160*  =====================================================================
161      SUBROUTINE ZCHKHP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
162     $                   NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
163     $                   IWORK, NOUT )
164*
165*  -- LAPACK test routine --
166*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
167*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168*
169*     .. Scalar Arguments ..
170      LOGICAL            TSTERR
171      INTEGER            NMAX, NN, NNS, NOUT
172      DOUBLE PRECISION   THRESH
173*     ..
174*     .. Array Arguments ..
175      LOGICAL            DOTYPE( * )
176      INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
177      DOUBLE PRECISION   RWORK( * )
178      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
179     $                   WORK( * ), X( * ), XACT( * )
180*     ..
181*
182*  =====================================================================
183*
184*     .. Parameters ..
185      DOUBLE PRECISION   ZERO
186      PARAMETER          ( ZERO = 0.0D+0 )
187      INTEGER            NTYPES
188      PARAMETER          ( NTYPES = 10 )
189      INTEGER            NTESTS
190      PARAMETER          ( NTESTS = 8 )
191*     ..
192*     .. Local Scalars ..
193      LOGICAL            TRFCON, ZEROT
194      CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
195      CHARACTER*3        PATH
196      INTEGER            I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
197     $                   IZERO, J, K, KL, KU, LDA, MODE, N, NERRS,
198     $                   NFAIL, NIMAT, NPP, NRHS, NRUN, NT
199      DOUBLE PRECISION   ANORM, CNDNUM, RCOND, RCONDC
200*     ..
201*     .. Local Arrays ..
202      CHARACTER          UPLOS( 2 )
203      INTEGER            ISEED( 4 ), ISEEDY( 4 )
204      DOUBLE PRECISION   RESULT( NTESTS )
205*     ..
206*     .. External Functions ..
207      LOGICAL            LSAME
208      DOUBLE PRECISION   DGET06, ZLANHP
209      EXTERNAL           LSAME, DGET06, ZLANHP
210*     ..
211*     .. External Subroutines ..
212      EXTERNAL           ALAERH, ALAHD, ALASUM, ZCOPY, ZERRSY, ZGET04,
213     $                   ZHPCON, ZHPRFS, ZHPT01, ZHPTRF, ZHPTRI, ZHPTRS,
214     $                   ZLACPY, ZLAIPD, ZLARHS, ZLATB4, ZLATMS, ZPPT02,
215     $                   ZPPT03, ZPPT05
216*     ..
217*     .. Intrinsic Functions ..
218      INTRINSIC          MAX, MIN
219*     ..
220*     .. Scalars in Common ..
221      LOGICAL            LERR, OK
222      CHARACTER*32       SRNAMT
223      INTEGER            INFOT, NUNIT
224*     ..
225*     .. Common blocks ..
226      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
227      COMMON             / SRNAMC / SRNAMT
228*     ..
229*     .. Data statements ..
230      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
231      DATA               UPLOS / 'U', 'L' /
232*     ..
233*     .. Executable Statements ..
234*
235*     Initialize constants and the random number seed.
236*
237      PATH( 1: 1 ) = 'Zomplex precision'
238      PATH( 2: 3 ) = 'HP'
239      NRUN = 0
240      NFAIL = 0
241      NERRS = 0
242      DO 10 I = 1, 4
243         ISEED( I ) = ISEEDY( I )
244   10 CONTINUE
245*
246*     Test the error exits
247*
248      IF( TSTERR )
249     $   CALL ZERRSY( PATH, NOUT )
250      INFOT = 0
251*
252*     Do for each value of N in NVAL
253*
254      DO 170 IN = 1, NN
255         N = NVAL( IN )
256         LDA = MAX( N, 1 )
257         XTYPE = 'N'
258         NIMAT = NTYPES
259         IF( N.LE.0 )
260     $      NIMAT = 1
261*
262         IZERO = 0
263         DO 160 IMAT = 1, NIMAT
264*
265*           Do the tests only if DOTYPE( IMAT ) is true.
266*
267            IF( .NOT.DOTYPE( IMAT ) )
268     $         GO TO 160
269*
270*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
271*
272            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
273            IF( ZEROT .AND. N.LT.IMAT-2 )
274     $         GO TO 160
275*
276*           Do first for UPLO = 'U', then for UPLO = 'L'
277*
278            DO 150 IUPLO = 1, 2
279               UPLO = UPLOS( IUPLO )
280               IF( LSAME( UPLO, 'U' ) ) THEN
281                  PACKIT = 'C'
282               ELSE
283                  PACKIT = 'R'
284               END IF
285*
286*              Set up parameters with ZLATB4 and generate a test matrix
287*              with ZLATMS.
288*
289               CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
290     $                      CNDNUM, DIST )
291*
292               SRNAMT = 'ZLATMS'
293               CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
294     $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
295     $                      INFO )
296*
297*              Check error code from ZLATMS.
298*
299               IF( INFO.NE.0 ) THEN
300                  CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
301     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
302                  GO TO 150
303               END IF
304*
305*              For types 3-6, zero one or more rows and columns of
306*              the matrix to test that INFO is returned correctly.
307*
308               IF( ZEROT ) THEN
309                  IF( IMAT.EQ.3 ) THEN
310                     IZERO = 1
311                  ELSE IF( IMAT.EQ.4 ) THEN
312                     IZERO = N
313                  ELSE
314                     IZERO = N / 2 + 1
315                  END IF
316*
317                  IF( IMAT.LT.6 ) THEN
318*
319*                    Set row and column IZERO to zero.
320*
321                     IF( IUPLO.EQ.1 ) THEN
322                        IOFF = ( IZERO-1 )*IZERO / 2
323                        DO 20 I = 1, IZERO - 1
324                           A( IOFF+I ) = ZERO
325   20                   CONTINUE
326                        IOFF = IOFF + IZERO
327                        DO 30 I = IZERO, N
328                           A( IOFF ) = ZERO
329                           IOFF = IOFF + I
330   30                   CONTINUE
331                     ELSE
332                        IOFF = IZERO
333                        DO 40 I = 1, IZERO - 1
334                           A( IOFF ) = ZERO
335                           IOFF = IOFF + N - I
336   40                   CONTINUE
337                        IOFF = IOFF - IZERO
338                        DO 50 I = IZERO, N
339                           A( IOFF+I ) = ZERO
340   50                   CONTINUE
341                     END IF
342                  ELSE
343                     IOFF = 0
344                     IF( IUPLO.EQ.1 ) THEN
345*
346*                       Set the first IZERO rows and columns to zero.
347*
348                        DO 70 J = 1, N
349                           I2 = MIN( J, IZERO )
350                           DO 60 I = 1, I2
351                              A( IOFF+I ) = ZERO
352   60                      CONTINUE
353                           IOFF = IOFF + J
354   70                   CONTINUE
355                     ELSE
356*
357*                       Set the last IZERO rows and columns to zero.
358*
359                        DO 90 J = 1, N
360                           I1 = MAX( J, IZERO )
361                           DO 80 I = I1, N
362                              A( IOFF+I ) = ZERO
363   80                      CONTINUE
364                           IOFF = IOFF + N - J
365   90                   CONTINUE
366                     END IF
367                  END IF
368               ELSE
369                  IZERO = 0
370               END IF
371*
372*              Set the imaginary part of the diagonals.
373*
374               IF( IUPLO.EQ.1 ) THEN
375                  CALL ZLAIPD( N, A, 2, 1 )
376               ELSE
377                  CALL ZLAIPD( N, A, N, -1 )
378               END IF
379*
380*              Compute the L*D*L' or U*D*U' factorization of the matrix.
381*
382               NPP = N*( N+1 ) / 2
383               CALL ZCOPY( NPP, A, 1, AFAC, 1 )
384               SRNAMT = 'ZHPTRF'
385               CALL ZHPTRF( UPLO, N, AFAC, IWORK, INFO )
386*
387*              Adjust the expected value of INFO to account for
388*              pivoting.
389*
390               K = IZERO
391               IF( K.GT.0 ) THEN
392  100             CONTINUE
393                  IF( IWORK( K ).LT.0 ) THEN
394                     IF( IWORK( K ).NE.-K ) THEN
395                        K = -IWORK( K )
396                        GO TO 100
397                     END IF
398                  ELSE IF( IWORK( K ).NE.K ) THEN
399                     K = IWORK( K )
400                     GO TO 100
401                  END IF
402               END IF
403*
404*              Check error code from ZHPTRF.
405*
406               IF( INFO.NE.K )
407     $            CALL ALAERH( PATH, 'ZHPTRF', INFO, K, UPLO, N, N, -1,
408     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
409               IF( INFO.NE.0 ) THEN
410                  TRFCON = .TRUE.
411               ELSE
412                  TRFCON = .FALSE.
413               END IF
414*
415*+    TEST 1
416*              Reconstruct matrix from factors and compute residual.
417*
418               CALL ZHPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA, RWORK,
419     $                      RESULT( 1 ) )
420               NT = 1
421*
422*+    TEST 2
423*              Form the inverse and compute the residual.
424*
425               IF( .NOT.TRFCON ) THEN
426                  CALL ZCOPY( NPP, AFAC, 1, AINV, 1 )
427                  SRNAMT = 'ZHPTRI'
428                  CALL ZHPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
429*
430*              Check error code from ZHPTRI.
431*
432                  IF( INFO.NE.0 )
433     $               CALL ALAERH( PATH, 'ZHPTRI', INFO, 0, UPLO, N, N,
434     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
435*
436                  CALL ZPPT03( UPLO, N, A, AINV, WORK, LDA, RWORK,
437     $                         RCONDC, RESULT( 2 ) )
438                  NT = 2
439               END IF
440*
441*              Print information about the tests that did not pass
442*              the threshold.
443*
444               DO 110 K = 1, NT
445                  IF( RESULT( K ).GE.THRESH ) THEN
446                     IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
447     $                  CALL ALAHD( NOUT, PATH )
448                     WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K,
449     $                  RESULT( K )
450                     NFAIL = NFAIL + 1
451                  END IF
452  110          CONTINUE
453               NRUN = NRUN + NT
454*
455*              Do only the condition estimate if INFO is not 0.
456*
457               IF( TRFCON ) THEN
458                  RCONDC = ZERO
459                  GO TO 140
460               END IF
461*
462               DO 130 IRHS = 1, NNS
463                  NRHS = NSVAL( IRHS )
464*
465*+    TEST 3
466*              Solve and compute residual for  A * X = B.
467*
468                  SRNAMT = 'ZLARHS'
469                  CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
470     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
471     $                         INFO )
472                  XTYPE = 'C'
473                  CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
474*
475                  SRNAMT = 'ZHPTRS'
476                  CALL ZHPTRS( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
477     $                         INFO )
478*
479*              Check error code from ZHPTRS.
480*
481                  IF( INFO.NE.0 )
482     $               CALL ALAERH( PATH, 'ZHPTRS', INFO, 0, UPLO, N, N,
483     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
484     $                            NOUT )
485*
486                  CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
487                  CALL ZPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
488     $                         RWORK, RESULT( 3 ) )
489*
490*+    TEST 4
491*              Check solution from generated exact solution.
492*
493                  CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
494     $                         RESULT( 4 ) )
495*
496*+    TESTS 5, 6, and 7
497*              Use iterative refinement to improve the solution.
498*
499                  SRNAMT = 'ZHPRFS'
500                  CALL ZHPRFS( UPLO, N, NRHS, A, AFAC, IWORK, B, LDA, X,
501     $                         LDA, RWORK, RWORK( NRHS+1 ), WORK,
502     $                         RWORK( 2*NRHS+1 ), INFO )
503*
504*              Check error code from ZHPRFS.
505*
506                  IF( INFO.NE.0 )
507     $               CALL ALAERH( PATH, 'ZHPRFS', INFO, 0, UPLO, N, N,
508     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
509     $                            NOUT )
510*
511                  CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
512     $                         RESULT( 5 ) )
513                  CALL ZPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA, XACT,
514     $                         LDA, RWORK, RWORK( NRHS+1 ),
515     $                         RESULT( 6 ) )
516*
517*                 Print information about the tests that did not pass
518*                 the threshold.
519*
520                  DO 120 K = 3, 7
521                     IF( RESULT( K ).GE.THRESH ) THEN
522                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
523     $                     CALL ALAHD( NOUT, PATH )
524                        WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
525     $                     K, RESULT( K )
526                        NFAIL = NFAIL + 1
527                     END IF
528  120             CONTINUE
529                  NRUN = NRUN + 5
530  130          CONTINUE
531*
532*+    TEST 8
533*              Get an estimate of RCOND = 1/CNDNUM.
534*
535  140          CONTINUE
536               ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
537               SRNAMT = 'ZHPCON'
538               CALL ZHPCON( UPLO, N, AFAC, IWORK, ANORM, RCOND, WORK,
539     $                      INFO )
540*
541*              Check error code from ZHPCON.
542*
543               IF( INFO.NE.0 )
544     $            CALL ALAERH( PATH, 'ZHPCON', INFO, 0, UPLO, N, N, -1,
545     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
546*
547               RESULT( 8 ) = DGET06( RCOND, RCONDC )
548*
549*              Print the test ratio if it is .GE. THRESH.
550*
551               IF( RESULT( 8 ).GE.THRESH ) THEN
552                  IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
553     $               CALL ALAHD( NOUT, PATH )
554                  WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, 8,
555     $               RESULT( 8 )
556                  NFAIL = NFAIL + 1
557               END IF
558               NRUN = NRUN + 1
559  150       CONTINUE
560  160    CONTINUE
561  170 CONTINUE
562*
563*     Print a summary of the results.
564*
565      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
566*
567 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', type ', I2, ', test ',
568     $      I2, ', ratio =', G12.5 )
569 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
570     $      I2, ', test(', I2, ') =', G12.5 )
571      RETURN
572*
573*     End of ZCHKHP
574*
575      END
576