1*> \brief \b CDRVHE
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 CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12*                          A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13*                          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               RWORK( * )
24*       COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> CDRVHE tests the driver routines CHESV 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 COMPLEX array, dimension (NMAX*NMAX)
91*> \endverbatim
92*>
93*> \param[out] AFAC
94*> \verbatim
95*>          AFAC is COMPLEX array, dimension (NMAX*NMAX)
96*> \endverbatim
97*>
98*> \param[out] AINV
99*> \verbatim
100*>          AINV is COMPLEX array, dimension (NMAX*NMAX)
101*> \endverbatim
102*>
103*> \param[out] B
104*> \verbatim
105*>          B is COMPLEX array, dimension (NMAX*NRHS)
106*> \endverbatim
107*>
108*> \param[out] X
109*> \verbatim
110*>          X is COMPLEX array, dimension (NMAX*NRHS)
111*> \endverbatim
112*>
113*> \param[out] XACT
114*> \verbatim
115*>          XACT is COMPLEX array, dimension (NMAX*NRHS)
116*> \endverbatim
117*>
118*> \param[out] WORK
119*> \verbatim
120*>          WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))
121*> \endverbatim
122*>
123*> \param[out] RWORK
124*> \verbatim
125*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
126*> \endverbatim
127*>
128*> \param[out] IWORK
129*> \verbatim
130*>          IWORK is INTEGER array, dimension (NMAX)
131*> \endverbatim
132*>
133*> \param[in] NOUT
134*> \verbatim
135*>          NOUT is INTEGER
136*>          The unit number for output.
137*> \endverbatim
138*
139*  Authors:
140*  ========
141*
142*> \author Univ. of Tennessee
143*> \author Univ. of California Berkeley
144*> \author Univ. of Colorado Denver
145*> \author NAG Ltd.
146*
147*> \date November 2013
148*
149*> \ingroup complex_lin
150*
151*  =====================================================================
152      SUBROUTINE CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
153     $                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
154     $                   NOUT )
155*
156*  -- LAPACK test routine (version 3.5.0) --
157*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
158*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159*     November 2013
160*
161*     .. Scalar Arguments ..
162      LOGICAL            TSTERR
163      INTEGER            NMAX, NN, NOUT, NRHS
164      REAL               THRESH
165*     ..
166*     .. Array Arguments ..
167      LOGICAL            DOTYPE( * )
168      INTEGER            IWORK( * ), NVAL( * )
169      REAL               RWORK( * )
170      COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
171     $                   WORK( * ), X( * ), XACT( * )
172*     ..
173*
174*  =====================================================================
175*
176*     .. Parameters ..
177      REAL               ONE, ZERO
178      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
179      INTEGER            NTYPES, NTESTS
180      PARAMETER          ( NTYPES = 10, NTESTS = 6 )
181      INTEGER            NFACT
182      PARAMETER          ( NFACT = 2 )
183*     ..
184*     .. Local Scalars ..
185      LOGICAL            ZEROT
186      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
187      CHARACTER*3        PATH
188      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
189     $                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
190     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
191      REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC
192*     ..
193*     .. Local Arrays ..
194      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
195      INTEGER            ISEED( 4 ), ISEEDY( 4 )
196      REAL               RESULT( NTESTS )
197*     ..
198*     .. External Functions ..
199      REAL               CLANHE, SGET06
200      EXTERNAL           CLANHE, SGET06
201*     ..
202*     .. External Subroutines ..
203      EXTERNAL           ALADHD, ALAERH, ALASVM, CERRVX, CGET04, CHESV,
204     $                   CHESVX, CHET01, CHETRF, CHETRI2, CLACPY,
205     $                   CLAIPD, CLARHS, CLASET, CLATB4, CLATMS, CPOT02,
206     $                   CPOT05, XLAENV
207*     ..
208*     .. Scalars in Common ..
209      LOGICAL            LERR, OK
210      CHARACTER*32       SRNAMT
211      INTEGER            INFOT, NUNIT
212*     ..
213*     .. Common blocks ..
214      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
215      COMMON             / SRNAMC / SRNAMT
216*     ..
217*     .. Intrinsic Functions ..
218      INTRINSIC          CMPLX, MAX, MIN
219*     ..
220*     .. Data statements ..
221      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
222      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
223*     ..
224*     .. Executable Statements ..
225*
226*     Initialize constants and the random number seed.
227*
228      PATH( 1: 1 ) = 'Complex precision'
229      PATH( 2: 3 ) = 'HE'
230      NRUN = 0
231      NFAIL = 0
232      NERRS = 0
233      DO 10 I = 1, 4
234         ISEED( I ) = ISEEDY( I )
235   10 CONTINUE
236      LWORK = MAX( 2*NMAX, NMAX*NRHS )
237*
238*     Test the error exits
239*
240      IF( TSTERR )
241     $   CALL CERRVX( PATH, NOUT )
242      INFOT = 0
243*
244*     Set the block size and minimum block size for testing.
245*
246      NB = 1
247      NBMIN = 2
248      CALL XLAENV( 1, NB )
249      CALL XLAENV( 2, NBMIN )
250*
251*     Do for each value of N in NVAL
252*
253      DO 180 IN = 1, NN
254         N = NVAL( IN )
255         LDA = MAX( N, 1 )
256         XTYPE = 'N'
257         NIMAT = NTYPES
258         IF( N.LE.0 )
259     $      NIMAT = 1
260*
261         DO 170 IMAT = 1, NIMAT
262*
263*           Do the tests only if DOTYPE( IMAT ) is true.
264*
265            IF( .NOT.DOTYPE( IMAT ) )
266     $         GO TO 170
267*
268*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
269*
270            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
271            IF( ZEROT .AND. N.LT.IMAT-2 )
272     $         GO TO 170
273*
274*           Do first for UPLO = 'U', then for UPLO = 'L'
275*
276            DO 160 IUPLO = 1, 2
277               UPLO = UPLOS( IUPLO )
278*
279*              Set up parameters with CLATB4 and generate a test matrix
280*              with CLATMS.
281*
282               CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
283     $                      CNDNUM, DIST )
284*
285               SRNAMT = 'CLATMS'
286               CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
287     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
288     $                      INFO )
289*
290*              Check error code from CLATMS.
291*
292               IF( INFO.NE.0 ) THEN
293                  CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N, -1,
294     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
295                  GO TO 160
296               END IF
297*
298*              For types 3-6, zero one or more rows and columns of the
299*              matrix to test that INFO is returned correctly.
300*
301               IF( ZEROT ) THEN
302                  IF( IMAT.EQ.3 ) THEN
303                     IZERO = 1
304                  ELSE IF( IMAT.EQ.4 ) THEN
305                     IZERO = N
306                  ELSE
307                     IZERO = N / 2 + 1
308                  END IF
309*
310                  IF( IMAT.LT.6 ) THEN
311*
312*                    Set row and column IZERO to zero.
313*
314                     IF( IUPLO.EQ.1 ) THEN
315                        IOFF = ( IZERO-1 )*LDA
316                        DO 20 I = 1, IZERO - 1
317                           A( IOFF+I ) = ZERO
318   20                   CONTINUE
319                        IOFF = IOFF + IZERO
320                        DO 30 I = IZERO, N
321                           A( IOFF ) = ZERO
322                           IOFF = IOFF + LDA
323   30                   CONTINUE
324                     ELSE
325                        IOFF = IZERO
326                        DO 40 I = 1, IZERO - 1
327                           A( IOFF ) = ZERO
328                           IOFF = IOFF + LDA
329   40                   CONTINUE
330                        IOFF = IOFF - IZERO
331                        DO 50 I = IZERO, N
332                           A( IOFF+I ) = ZERO
333   50                   CONTINUE
334                     END IF
335                  ELSE
336                     IOFF = 0
337                     IF( IUPLO.EQ.1 ) THEN
338*
339*                       Set the first IZERO rows and columns to zero.
340*
341                        DO 70 J = 1, N
342                           I2 = MIN( J, IZERO )
343                           DO 60 I = 1, I2
344                              A( IOFF+I ) = ZERO
345   60                      CONTINUE
346                           IOFF = IOFF + LDA
347   70                   CONTINUE
348                     ELSE
349*
350*                       Set the last IZERO rows and columns to zero.
351*
352                        DO 90 J = 1, N
353                           I1 = MAX( J, IZERO )
354                           DO 80 I = I1, N
355                              A( IOFF+I ) = ZERO
356   80                      CONTINUE
357                           IOFF = IOFF + LDA
358   90                   CONTINUE
359                     END IF
360                  END IF
361               ELSE
362                  IZERO = 0
363               END IF
364*
365*              Set the imaginary part of the diagonals.
366*
367               CALL CLAIPD( N, A, LDA+1, 0 )
368*
369               DO 150 IFACT = 1, NFACT
370*
371*                 Do first for FACT = 'F', then for other values.
372*
373                  FACT = FACTS( IFACT )
374*
375*                 Compute the condition number for comparison with
376*                 the value returned by CHESVX.
377*
378                  IF( ZEROT ) THEN
379                     IF( IFACT.EQ.1 )
380     $                  GO TO 150
381                     RCONDC = ZERO
382*
383                  ELSE IF( IFACT.EQ.1 ) THEN
384*
385*                    Compute the 1-norm of A.
386*
387                     ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
388*
389*                    Factor the matrix A.
390*
391                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
392                     CALL CHETRF( UPLO, N, AFAC, LDA, IWORK, WORK,
393     $                            LWORK, INFO )
394*
395*                    Compute inv(A) and take its norm.
396*
397                     CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
398                     LWORK = (N+NB+1)*(NB+3)
399                     CALL CHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
400     $                            LWORK, INFO )
401                     AINVNM = CLANHE( '1', UPLO, N, AINV, LDA, RWORK )
402*
403*                    Compute the 1-norm condition number of A.
404*
405                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
406                        RCONDC = ONE
407                     ELSE
408                        RCONDC = ( ONE / ANORM ) / AINVNM
409                     END IF
410                  END IF
411*
412*                 Form an exact solution and set the right hand side.
413*
414                  SRNAMT = 'CLARHS'
415                  CALL CLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
416     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
417     $                         INFO )
418                  XTYPE = 'C'
419*
420*                 --- Test CHESV  ---
421*
422                  IF( IFACT.EQ.2 ) THEN
423                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
424                     CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
425*
426*                    Factor the matrix and solve the system using CHESV.
427*
428                     SRNAMT = 'CHESV '
429                     CALL CHESV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
430     $                           LDA, WORK, LWORK, INFO )
431*
432*                    Adjust the expected value of INFO to account for
433*                    pivoting.
434*
435                     K = IZERO
436                     IF( K.GT.0 ) THEN
437  100                   CONTINUE
438                        IF( IWORK( K ).LT.0 ) THEN
439                           IF( IWORK( K ).NE.-K ) THEN
440                              K = -IWORK( K )
441                              GO TO 100
442                           END IF
443                        ELSE IF( IWORK( K ).NE.K ) THEN
444                           K = IWORK( K )
445                           GO TO 100
446                        END IF
447                     END IF
448*
449*                    Check error code from CHESV .
450*
451                     IF( INFO.NE.K ) THEN
452                        CALL ALAERH( PATH, 'CHESV ', INFO, K, UPLO, N,
453     $                               N, -1, -1, NRHS, IMAT, NFAIL,
454     $                               NERRS, NOUT )
455                        GO TO 120
456                     ELSE IF( INFO.NE.0 ) THEN
457                        GO TO 120
458                     END IF
459*
460*                    Reconstruct matrix from factors and compute
461*                    residual.
462*
463                     CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
464     $                            AINV, LDA, RWORK, RESULT( 1 ) )
465*
466*                    Compute residual of the computed solution.
467*
468                     CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
469                     CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
470     $                            LDA, RWORK, RESULT( 2 ) )
471*
472*                    Check solution from generated exact solution.
473*
474                     CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
475     $                            RESULT( 3 ) )
476                     NT = 3
477*
478*                    Print information about the tests that did not pass
479*                    the threshold.
480*
481                     DO 110 K = 1, NT
482                        IF( RESULT( K ).GE.THRESH ) THEN
483                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
484     $                        CALL ALADHD( NOUT, PATH )
485                           WRITE( NOUT, FMT = 9999 )'CHESV ', UPLO, N,
486     $                        IMAT, K, RESULT( K )
487                           NFAIL = NFAIL + 1
488                        END IF
489  110                CONTINUE
490                     NRUN = NRUN + NT
491  120                CONTINUE
492                  END IF
493*
494*                 --- Test CHESVX ---
495*
496                  IF( IFACT.EQ.2 )
497     $               CALL CLASET( UPLO, N, N, CMPLX( ZERO ),
498     $                            CMPLX( ZERO ), AFAC, LDA )
499                  CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ),
500     $                         CMPLX( ZERO ), X, LDA )
501*
502*                 Solve the system and compute the condition number and
503*                 error bounds using CHESVX.
504*
505                  SRNAMT = 'CHESVX'
506                  CALL CHESVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
507     $                         IWORK, B, LDA, X, LDA, RCOND, RWORK,
508     $                         RWORK( NRHS+1 ), WORK, LWORK,
509     $                         RWORK( 2*NRHS+1 ), INFO )
510*
511*                 Adjust the expected value of INFO to account for
512*                 pivoting.
513*
514                  K = IZERO
515                  IF( K.GT.0 ) THEN
516  130                CONTINUE
517                     IF( IWORK( K ).LT.0 ) THEN
518                        IF( IWORK( K ).NE.-K ) THEN
519                           K = -IWORK( K )
520                           GO TO 130
521                        END IF
522                     ELSE IF( IWORK( K ).NE.K ) THEN
523                        K = IWORK( K )
524                        GO TO 130
525                     END IF
526                  END IF
527*
528*                 Check the error code from CHESVX.
529*
530                  IF( INFO.NE.K ) THEN
531                     CALL ALAERH( PATH, 'CHESVX', INFO, K, FACT // UPLO,
532     $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
533     $                            NERRS, NOUT )
534                     GO TO 150
535                  END IF
536*
537                  IF( INFO.EQ.0 ) THEN
538                     IF( IFACT.GE.2 ) THEN
539*
540*                       Reconstruct matrix from factors and compute
541*                       residual.
542*
543                        CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
544     $                               AINV, LDA, RWORK( 2*NRHS+1 ),
545     $                               RESULT( 1 ) )
546                        K1 = 1
547                     ELSE
548                        K1 = 2
549                     END IF
550*
551*                    Compute residual of the computed solution.
552*
553                     CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
554                     CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
555     $                            LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
556*
557*                    Check solution from generated exact solution.
558*
559                     CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
560     $                            RESULT( 3 ) )
561*
562*                    Check the error bounds from iterative refinement.
563*
564                     CALL CPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
565     $                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
566     $                            RESULT( 4 ) )
567                  ELSE
568                     K1 = 6
569                  END IF
570*
571*                 Compare RCOND from CHESVX with the computed value
572*                 in RCONDC.
573*
574                  RESULT( 6 ) = SGET06( RCOND, RCONDC )
575*
576*                 Print information about the tests that did not pass
577*                 the threshold.
578*
579                  DO 140 K = K1, 6
580                     IF( RESULT( K ).GE.THRESH ) THEN
581                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
582     $                     CALL ALADHD( NOUT, PATH )
583                        WRITE( NOUT, FMT = 9998 )'CHESVX', FACT, UPLO,
584     $                     N, IMAT, K, RESULT( K )
585                        NFAIL = NFAIL + 1
586                     END IF
587  140             CONTINUE
588                  NRUN = NRUN + 7 - K1
589*
590  150          CONTINUE
591*
592  160       CONTINUE
593  170    CONTINUE
594  180 CONTINUE
595*
596*     Print a summary of the results.
597*
598      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
599*
600 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
601     $      ', test ', I2, ', ratio =', G12.5 )
602 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
603     $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
604      RETURN
605*
606*     End of CDRVHE
607*
608      END
609