1*> \brief \b ZDRVHE_AA
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 ZDRVHE_AA( 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*       DOUBLE PRECISION   THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), 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*> ZDRVHE_AA tests the driver routine ZHESV_AA.
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 DOUBLE PRECISION
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*16 array, dimension (NMAX*NMAX)
91*> \endverbatim
92*>
93*> \param[out] AFAC
94*> \verbatim
95*>          AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
96*> \endverbatim
97*>
98*> \param[out] AINV
99*> \verbatim
100*>          AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
101*> \endverbatim
102*>
103*> \param[out] B
104*> \verbatim
105*>          B is COMPLEX*16 array, dimension (NMAX*NRHS)
106*> \endverbatim
107*>
108*> \param[out] X
109*> \verbatim
110*>          X is COMPLEX*16 array, dimension (NMAX*NRHS)
111*> \endverbatim
112*>
113*> \param[out] XACT
114*> \verbatim
115*>          XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
116*> \endverbatim
117*>
118*> \param[out] WORK
119*> \verbatim
120*>          WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))
121*> \endverbatim
122*>
123*> \param[out] RWORK
124*> \verbatim
125*>          RWORK is DOUBLE PRECISION 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*> \ingroup complex16_lin
148*
149*  =====================================================================
150      SUBROUTINE ZDRVHE_AA( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
151     $                         NMAX, A, AFAC, AINV, B, X, XACT, WORK,
152     $                         RWORK, IWORK, NOUT )
153*
154*  -- LAPACK test routine --
155*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
156*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157*
158*     .. Scalar Arguments ..
159      LOGICAL            TSTERR
160      INTEGER            NMAX, NN, NOUT, NRHS
161      DOUBLE PRECISION   THRESH
162*     ..
163*     .. Array Arguments ..
164      LOGICAL            DOTYPE( * )
165      INTEGER            IWORK( * ), NVAL( * )
166      DOUBLE PRECISION   RWORK( * )
167      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
168     $                   WORK( * ), X( * ), XACT( * )
169*     ..
170*
171*  =====================================================================
172*
173*     .. Parameters ..
174      DOUBLE PRECISION   ONE, ZERO
175      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
176      INTEGER            NTYPES, NTESTS
177      PARAMETER          ( NTYPES = 10, NTESTS = 3 )
178      INTEGER            NFACT
179      PARAMETER          ( NFACT = 2 )
180*     ..
181*     .. Local Scalars ..
182      LOGICAL            ZEROT
183      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
184      CHARACTER*3        MATPATH, PATH
185      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
186     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
187     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
188      DOUBLE PRECISION   ANORM, CNDNUM
189*     ..
190*     .. Local Arrays ..
191      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
192      INTEGER            ISEED( 4 ), ISEEDY( 4 )
193      DOUBLE PRECISION   RESULT( NTESTS )
194*     ..
195*     .. External Functions ..
196      DOUBLE PRECISION   DGET06, ZLANHE
197      EXTERNAL           DGET06, ZLANHE
198*     ..
199*     .. External Subroutines ..
200      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
201     $                   ZHESV_AA, ZHET01_AA, ZHETRF_AA,
202     $                   ZHETRI2, ZLACPY, ZLAIPD, ZLARHS, ZLATB4,
203     $                   ZLATMS, ZPOT02
204*     ..
205*     .. Scalars in Common ..
206      LOGICAL            LERR, OK
207      CHARACTER*32       SRNAMT
208      INTEGER            INFOT, NUNIT
209*     ..
210*     .. Common blocks ..
211      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
212      COMMON             / SRNAMC / SRNAMT
213*     ..
214*     .. Intrinsic Functions ..
215      INTRINSIC          DCMPLX, MAX, MIN
216*     ..
217*     .. Data statements ..
218      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
219      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
220*     ..
221*     .. Executable Statements ..
222*
223*     Initialize constants and the random number seed.
224*
225*     Test path
226*
227      PATH( 1: 1 ) = 'Zomplex precision'
228      PATH( 2: 3 ) = 'HA'
229*
230*     Path to generate matrices
231*
232      MATPATH( 1: 1 ) = 'Zomplex precision'
233      MATPATH( 2: 3 ) = 'HE'
234*
235      NRUN = 0
236      NFAIL = 0
237      NERRS = 0
238      DO 10 I = 1, 4
239         ISEED( I ) = ISEEDY( I )
240   10 CONTINUE
241*
242*     Test the error exits
243*
244      IF( TSTERR )
245     $   CALL ZERRVX( PATH, NOUT )
246      INFOT = 0
247*
248*     Set the block size and minimum block size for testing.
249*
250      NB = 1
251      NBMIN = 2
252      CALL XLAENV( 1, NB )
253      CALL XLAENV( 2, NBMIN )
254*
255*     Do for each value of N in NVAL
256*
257      DO 180 IN = 1, NN
258         N = NVAL( IN )
259         LWORK = MAX( 3*N-2, N*(1+NB) )
260         LWORK = MAX( LWORK, 1 )
261         LDA = MAX( N, 1 )
262         XTYPE = 'N'
263         NIMAT = NTYPES
264         IF( N.LE.0 )
265     $      NIMAT = 1
266*
267         DO 170 IMAT = 1, NIMAT
268*
269*           Do the tests only if DOTYPE( IMAT ) is true.
270*
271            IF( .NOT.DOTYPE( IMAT ) )
272     $         GO TO 170
273*
274*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
275*
276            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
277            IF( ZEROT .AND. N.LT.IMAT-2 )
278     $         GO TO 170
279*
280*           Do first for UPLO = 'U', then for UPLO = 'L'
281*
282            DO 160 IUPLO = 1, 2
283               UPLO = UPLOS( IUPLO )
284*
285*              Begin generate the test matrix A.
286*
287*              Set up parameters with ZLATB4 and generate a test matrix
288*              with ZLATMS.
289*
290               CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
291     $                       MODE, CNDNUM, DIST )
292*
293               SRNAMT = 'ZLATMS'
294               CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
295     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
296     $                      INFO )
297*
298*              Check error code from ZLATMS.
299*
300               IF( INFO.NE.0 ) THEN
301                  CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N, -1,
302     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
303                  GO TO 160
304               END IF
305*
306*              For types 3-6, zero one or more rows and columns of the
307*              matrix to test that INFO is returned correctly.
308*
309               IF( ZEROT ) THEN
310                  IF( IMAT.EQ.3 ) THEN
311                     IZERO = 1
312                  ELSE IF( IMAT.EQ.4 ) THEN
313                     IZERO = N
314                  ELSE
315                     IZERO = N / 2 + 1
316                  END IF
317*
318                  IF( IMAT.LT.6 ) THEN
319*
320*                    Set row and column IZERO to zero.
321*
322                     IF( IUPLO.EQ.1 ) THEN
323                        IOFF = ( IZERO-1 )*LDA
324                        DO 20 I = 1, IZERO - 1
325                           A( IOFF+I ) = ZERO
326   20                   CONTINUE
327                        IOFF = IOFF + IZERO
328                        DO 30 I = IZERO, N
329                           A( IOFF ) = ZERO
330                           IOFF = IOFF + LDA
331   30                   CONTINUE
332                     ELSE
333                        IOFF = IZERO
334                        DO 40 I = 1, IZERO - 1
335                           A( IOFF ) = ZERO
336                           IOFF = IOFF + LDA
337   40                   CONTINUE
338                        IOFF = IOFF - IZERO
339                        DO 50 I = IZERO, N
340                           A( IOFF+I ) = ZERO
341   50                   CONTINUE
342                     END IF
343                  ELSE
344                     IOFF = 0
345                     IF( IUPLO.EQ.1 ) THEN
346*
347*                       Set the first IZERO rows and columns to zero.
348*
349                        DO 70 J = 1, N
350                           I2 = MIN( J, IZERO )
351                           DO 60 I = 1, I2
352                              A( IOFF+I ) = ZERO
353   60                      CONTINUE
354                           IOFF = IOFF + LDA
355   70                   CONTINUE
356                        IZERO = 1
357                     ELSE
358*
359*                       Set the last IZERO rows and columns to zero.
360*
361                        DO 90 J = 1, N
362                           I1 = MAX( J, IZERO )
363                           DO 80 I = I1, N
364                              A( IOFF+I ) = ZERO
365   80                      CONTINUE
366                           IOFF = IOFF + LDA
367   90                   CONTINUE
368                     END IF
369                  END IF
370               ELSE
371                  IZERO = 0
372               END IF
373*
374*              Set the imaginary part of the diagonals.
375*
376               CALL ZLAIPD( N, A, LDA+1, 0 )
377*
378               DO 150 IFACT = 1, NFACT
379*
380*                 Do first for FACT = 'F', then for other values.
381*
382                  FACT = FACTS( IFACT )
383*
384*                 Form an exact solution and set the right hand side.
385*
386                  SRNAMT = 'ZLARHS'
387                  CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
388     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
389     $                         INFO )
390                  XTYPE = 'C'
391*
392*                 --- Test ZHESV_AA  ---
393*
394                  IF( IFACT.EQ.2 ) THEN
395                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
396                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
397*
398*                    Factor the matrix and solve the system using ZHESV.
399*
400                     SRNAMT = 'ZHESV_AA '
401                     CALL ZHESV_AA( UPLO, N, NRHS, AFAC, LDA, IWORK,
402     $                                 X, LDA, WORK, LWORK, INFO )
403*
404*                    Adjust the expected value of INFO to account for
405*                    pivoting.
406*
407                     IF( IZERO.GT.0 ) THEN
408                        J = 1
409                        K = IZERO
410  100                   CONTINUE
411                        IF( J.EQ.K ) THEN
412                           K = IWORK( J )
413                        ELSE IF( IWORK( J ).EQ.K ) THEN
414                           K = J
415                        END IF
416                        IF( J.LT.K ) THEN
417                           J = J + 1
418                           GO TO 100
419                        END IF
420                     ELSE
421                        K = 0
422                     END IF
423*
424*                    Check error code from ZHESV .
425*
426                     IF( INFO.NE.K ) THEN
427                        CALL ALAERH( PATH, 'ZHESV_AA', INFO, K, UPLO, N,
428     $                               N, -1, -1, NRHS, IMAT, NFAIL,
429     $                               NERRS, NOUT )
430                        GO TO 120
431                     ELSE IF( INFO.NE.0 ) THEN
432                        GO TO 120
433                     END IF
434*
435*                    Reconstruct matrix from factors and compute
436*                    residual.
437*
438                     CALL ZHET01_AA( UPLO, N, A, LDA, AFAC, LDA,
439     $                                  IWORK, AINV, LDA, RWORK,
440     $                                  RESULT( 1 ) )
441*
442*                    Compute residual of the computed solution.
443*
444                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
445                     CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
446     $                            LDA, RWORK, RESULT( 2 ) )
447                     NT = 2
448*
449*                    Print information about the tests that did not pass
450*                    the threshold.
451*
452                     DO 110 K = 1, NT
453                        IF( RESULT( K ).GE.THRESH ) THEN
454                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
455     $                        CALL ALADHD( NOUT, PATH )
456                           WRITE( NOUT, FMT = 9999 )'ZHESV_AA', UPLO, N,
457     $                        IMAT, K, RESULT( K )
458                           NFAIL = NFAIL + 1
459                        END IF
460  110                CONTINUE
461                     NRUN = NRUN + NT
462  120                CONTINUE
463                  END IF
464*
465  150          CONTINUE
466*
467  160       CONTINUE
468  170    CONTINUE
469  180 CONTINUE
470*
471*     Print a summary of the results.
472*
473      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
474*
475 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
476     $      ', test ', I2, ', ratio =', G12.5 )
477       RETURN
478*
479*     End of ZDRVHE_AA
480*
481      END
482