1*> \brief \b ZDRVHE_RK
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_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12*                             NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
13*                             RWORK, IWORK, 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( * ), E( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> ZDRVHE_RK tests the driver routines ZHESV_RK.
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] E
99*> \verbatim
100*>          E is COMPLEX*16 array, dimension (NMAX)
101*> \endverbatim
102*>
103*> \param[out] AINV
104*> \verbatim
105*>          AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
106*> \endverbatim
107*>
108*> \param[out] B
109*> \verbatim
110*>          B is COMPLEX*16 array, dimension (NMAX*NRHS)
111*> \endverbatim
112*>
113*> \param[out] X
114*> \verbatim
115*>          X is COMPLEX*16 array, dimension (NMAX*NRHS)
116*> \endverbatim
117*>
118*> \param[out] XACT
119*> \verbatim
120*>          XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
121*> \endverbatim
122*>
123*> \param[out] WORK
124*> \verbatim
125*>          WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))
126*> \endverbatim
127*>
128*> \param[out] RWORK
129*> \verbatim
130*>          RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
131*> \endverbatim
132*>
133*> \param[out] IWORK
134*> \verbatim
135*>          IWORK is INTEGER array, dimension (NMAX)
136*> \endverbatim
137*>
138*> \param[in] NOUT
139*> \verbatim
140*>          NOUT is INTEGER
141*>          The unit number for output.
142*> \endverbatim
143*
144*  Authors:
145*  ========
146*
147*> \author Univ. of Tennessee
148*> \author Univ. of California Berkeley
149*> \author Univ. of Colorado Denver
150*> \author NAG Ltd.
151*
152*> \ingroup complex16_lin
153*
154*  =====================================================================
155      SUBROUTINE ZDRVHE_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
156     $                      NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
157     $                      RWORK, IWORK, NOUT )
158*
159*  -- LAPACK test routine --
160*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
161*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162*
163*     .. Scalar Arguments ..
164      LOGICAL            TSTERR
165      INTEGER            NMAX, NN, NOUT, NRHS
166      DOUBLE PRECISION   THRESH
167*     ..
168*     .. Array Arguments ..
169      LOGICAL            DOTYPE( * )
170      INTEGER            IWORK( * ), NVAL( * )
171      DOUBLE PRECISION   RWORK( * )
172      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
173     $                   WORK( * ), X( * ), XACT( * )
174*     ..
175*
176*  =====================================================================
177*
178*     .. Parameters ..
179      DOUBLE PRECISION   ONE, ZERO
180      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
181      INTEGER            NTYPES, NTESTS
182      PARAMETER          ( NTYPES = 10, NTESTS = 3 )
183      INTEGER            NFACT
184      PARAMETER          ( NFACT = 2 )
185*     ..
186*     .. Local Scalars ..
187      LOGICAL            ZEROT
188      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
189      CHARACTER*3        MATPATH, PATH
190      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
191     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
192     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
193      DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCONDC
194*     ..
195*     .. Local Arrays ..
196      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
197      INTEGER            ISEED( 4 ), ISEEDY( 4 )
198      DOUBLE PRECISION   RESULT( NTESTS )
199
200*     ..
201*     .. External Functions ..
202      DOUBLE PRECISION   ZLANHE
203      EXTERNAL           ZLANHE
204*     ..
205*     .. External Subroutines ..
206      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX,
207     $                   ZGET04, ZLACPY, ZLARHS, ZLATB4, ZLATMS,
208     $                   ZHESV_RK, ZHET01_3, ZPOT02, ZHETRF_RK, ZHETRI_3
209*     ..
210*     .. Scalars in Common ..
211      LOGICAL            LERR, OK
212      CHARACTER*32       SRNAMT
213      INTEGER            INFOT, NUNIT
214*     ..
215*     .. Common blocks ..
216      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
217      COMMON             / SRNAMC / SRNAMT
218*     ..
219*     .. Intrinsic Functions ..
220      INTRINSIC          MAX, MIN
221*     ..
222*     .. Data statements ..
223      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
224      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
225*     ..
226*     .. Executable Statements ..
227*
228*     Initialize constants and the random number seed.
229*
230*     Test path
231*
232      PATH( 1: 1 ) = 'Zomplex precision'
233      PATH( 2: 3 ) = 'HK'
234*
235*     Path to generate matrices
236*
237      MATPATH( 1: 1 ) = 'Zomplex precision'
238      MATPATH( 2: 3 ) = 'HE'
239*
240      NRUN = 0
241      NFAIL = 0
242      NERRS = 0
243      DO 10 I = 1, 4
244         ISEED( I ) = ISEEDY( I )
245   10 CONTINUE
246      LWORK = MAX( 2*NMAX, NMAX*NRHS )
247*
248*     Test the error exits
249*
250      IF( TSTERR )
251     $   CALL ZERRVX( PATH, NOUT )
252      INFOT = 0
253*
254*     Set the block size and minimum block size for which the block
255*     routine should be used, which will be later returned by ILAENV.
256*
257      NB = 1
258      NBMIN = 2
259      CALL XLAENV( 1, NB )
260      CALL XLAENV( 2, NBMIN )
261*
262*     Do for each value of N in NVAL
263*
264      DO 180 IN = 1, NN
265         N = NVAL( IN )
266         LDA = MAX( N, 1 )
267         XTYPE = 'N'
268         NIMAT = NTYPES
269         IF( N.LE.0 )
270     $      NIMAT = 1
271*
272         DO 170 IMAT = 1, NIMAT
273*
274*           Do the tests only if DOTYPE( IMAT ) is true.
275*
276            IF( .NOT.DOTYPE( IMAT ) )
277     $         GO TO 170
278*
279*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
280*
281            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
282            IF( ZEROT .AND. N.LT.IMAT-2 )
283     $         GO TO 170
284*
285*           Do first for UPLO = 'U', then for UPLO = 'L'
286*
287            DO 160 IUPLO = 1, 2
288               UPLO = UPLOS( IUPLO )
289*
290*                 Begin generate the test matrix A.
291*
292*                 Set up parameters with ZLATB4 for the matrix generator
293*                 based on the type of matrix to be generated.
294*
295                  CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
296     $                         MODE, CNDNUM, DIST )
297*
298*                 Generate a matrix with ZLATMS.
299*
300                  SRNAMT = 'ZLATMS'
301                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
302     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
303     $                         WORK, INFO )
304*
305*                 Check error code from ZLATMS and handle error.
306*
307                  IF( INFO.NE.0 ) THEN
308                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
309     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
310                     GO TO 160
311                  END IF
312*
313*                 For types 3-6, zero one or more rows and columns of
314*                 the matrix to test that INFO is returned correctly.
315*
316                  IF( ZEROT ) THEN
317                     IF( IMAT.EQ.3 ) THEN
318                        IZERO = 1
319                     ELSE IF( IMAT.EQ.4 ) THEN
320                        IZERO = N
321                     ELSE
322                        IZERO = N / 2 + 1
323                     END IF
324*
325                     IF( IMAT.LT.6 ) THEN
326*
327*                       Set row and column IZERO to zero.
328*
329                        IF( IUPLO.EQ.1 ) THEN
330                           IOFF = ( IZERO-1 )*LDA
331                           DO 20 I = 1, IZERO - 1
332                              A( IOFF+I ) = ZERO
333   20                      CONTINUE
334                           IOFF = IOFF + IZERO
335                           DO 30 I = IZERO, N
336                              A( IOFF ) = ZERO
337                              IOFF = IOFF + LDA
338   30                      CONTINUE
339                        ELSE
340                           IOFF = IZERO
341                           DO 40 I = 1, IZERO - 1
342                              A( IOFF ) = ZERO
343                              IOFF = IOFF + LDA
344   40                      CONTINUE
345                           IOFF = IOFF - IZERO
346                           DO 50 I = IZERO, N
347                              A( IOFF+I ) = ZERO
348   50                      CONTINUE
349                        END IF
350                     ELSE
351                        IF( IUPLO.EQ.1 ) THEN
352*
353*                       Set the first IZERO rows and columns to zero.
354*
355                           IOFF = 0
356                           DO 70 J = 1, N
357                              I2 = MIN( J, IZERO )
358                              DO 60 I = 1, I2
359                                 A( IOFF+I ) = ZERO
360   60                         CONTINUE
361                              IOFF = IOFF + LDA
362   70                      CONTINUE
363                        ELSE
364*
365*                       Set the first IZERO rows and columns to zero.
366*
367                           IOFF = 0
368                           DO 90 J = 1, N
369                              I1 = MAX( J, IZERO )
370                              DO 80 I = I1, N
371                                 A( IOFF+I ) = ZERO
372   80                         CONTINUE
373                              IOFF = IOFF + LDA
374   90                      CONTINUE
375                        END IF
376                     END IF
377                  ELSE
378                     IZERO = 0
379                  END IF
380*
381*                 End generate the test matrix A.
382*
383*
384               DO 150 IFACT = 1, NFACT
385*
386*                 Do first for FACT = 'F', then for other values.
387*
388                  FACT = FACTS( IFACT )
389*
390*                 Compute the condition number
391*
392                  IF( ZEROT ) THEN
393                     IF( IFACT.EQ.1 )
394     $                  GO TO 150
395                     RCONDC = ZERO
396*
397                  ELSE IF( IFACT.EQ.1 ) THEN
398*
399*                    Compute the 1-norm of A.
400*
401                     ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
402*
403*                    Factor the matrix A.
404*
405
406                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
407                     CALL ZHETRF_RK( UPLO, N, AFAC, LDA, E, IWORK, WORK,
408     $                               LWORK, INFO )
409*
410*                    Compute inv(A) and take its norm.
411*
412                     CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
413                     LWORK = (N+NB+1)*(NB+3)
414*
415*                    We need to compute the inverse to compute
416*                    RCONDC that is used later in TEST3.
417*
418                     CALL ZHETRI_3( UPLO, N, AINV, LDA, E, IWORK,
419     $                              WORK, LWORK, INFO )
420                     AINVNM = ZLANHE( '1', UPLO, N, AINV, LDA, RWORK )
421*
422*                    Compute the 1-norm condition number of A.
423*
424                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
425                        RCONDC = ONE
426                     ELSE
427                        RCONDC = ( ONE / ANORM ) / AINVNM
428                     END IF
429                  END IF
430*
431*                 Form an exact solution and set the right hand side.
432*
433                  SRNAMT = 'ZLARHS'
434                  CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
435     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
436     $                         INFO )
437                  XTYPE = 'C'
438*
439*                 --- Test ZHESV_RK  ---
440*
441                  IF( IFACT.EQ.2 ) THEN
442                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
443                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
444*
445*                    Factor the matrix and solve the system using
446*                    ZHESV_RK.
447*
448                     SRNAMT = 'ZHESV_RK'
449                     CALL ZHESV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK,
450     $                              X, LDA, WORK, LWORK, INFO )
451*
452*                    Adjust the expected value of INFO to account for
453*                    pivoting.
454*
455                     K = IZERO
456                     IF( K.GT.0 ) THEN
457  100                   CONTINUE
458                        IF( IWORK( K ).LT.0 ) THEN
459                           IF( IWORK( K ).NE.-K ) THEN
460                              K = -IWORK( K )
461                              GO TO 100
462                           END IF
463                        ELSE IF( IWORK( K ).NE.K ) THEN
464                           K = IWORK( K )
465                           GO TO 100
466                        END IF
467                     END IF
468*
469*                    Check error code from ZHESV_RK and handle error.
470*
471                     IF( INFO.NE.K ) THEN
472                        CALL ALAERH( PATH, 'ZHESV_RK', INFO, K, UPLO,
473     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
474     $                               NERRS, NOUT )
475                        GO TO 120
476                     ELSE IF( INFO.NE.0 ) THEN
477                        GO TO 120
478                     END IF
479*
480*+    TEST 1      Reconstruct matrix from factors and compute
481*                 residual.
482*
483                     CALL ZHET01_3( UPLO, N, A, LDA, AFAC, LDA, E,
484     $                              IWORK, AINV, LDA, RWORK,
485     $                              RESULT( 1 ) )
486*
487*+    TEST 2      Compute residual of the computed solution.
488*
489                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
490                     CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
491     $                            LDA, RWORK, RESULT( 2 ) )
492*
493*+    TEST 3
494*                 Check solution from generated exact solution.
495*
496                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
497     $                            RESULT( 3 ) )
498                     NT = 3
499*
500*                    Print information about the tests that did not pass
501*                    the threshold.
502*
503                     DO 110 K = 1, NT
504                        IF( RESULT( K ).GE.THRESH ) THEN
505                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
506     $                        CALL ALADHD( NOUT, PATH )
507                           WRITE( NOUT, FMT = 9999 )'ZHESV_RK', UPLO,
508     $                            N, IMAT, K, RESULT( K )
509                           NFAIL = NFAIL + 1
510                        END IF
511  110                CONTINUE
512                     NRUN = NRUN + NT
513  120                CONTINUE
514                  END IF
515*
516  150          CONTINUE
517*
518  160       CONTINUE
519  170    CONTINUE
520  180 CONTINUE
521*
522*     Print a summary of the results.
523*
524      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
525*
526 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
527     $      ', test ', I2, ', ratio =', G12.5 )
528      RETURN
529*
530*     End of ZDRVHE_RK
531*
532      END
533