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*> \date December 2016
153*
154*> \ingroup complex16_lin
155*
156*  =====================================================================
157      SUBROUTINE ZDRVHE_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
158     $                      NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
159     $                      RWORK, IWORK, NOUT )
160*
161*  -- LAPACK test routine (version 3.7.0) --
162*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
163*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164*     December 2016
165*
166*     .. Scalar Arguments ..
167      LOGICAL            TSTERR
168      INTEGER            NMAX, NN, NOUT, NRHS
169      DOUBLE PRECISION   THRESH
170*     ..
171*     .. Array Arguments ..
172      LOGICAL            DOTYPE( * )
173      INTEGER            IWORK( * ), NVAL( * )
174      DOUBLE PRECISION   RWORK( * )
175      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
176     $                   WORK( * ), X( * ), XACT( * )
177*     ..
178*
179*  =====================================================================
180*
181*     .. Parameters ..
182      DOUBLE PRECISION   ONE, ZERO
183      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
184      INTEGER            NTYPES, NTESTS
185      PARAMETER          ( NTYPES = 10, NTESTS = 3 )
186      INTEGER            NFACT
187      PARAMETER          ( NFACT = 2 )
188*     ..
189*     .. Local Scalars ..
190      LOGICAL            ZEROT
191      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
192      CHARACTER*3        MATPATH, PATH
193      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
194     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
195     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
196      DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCONDC
197*     ..
198*     .. Local Arrays ..
199      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
200      INTEGER            ISEED( 4 ), ISEEDY( 4 )
201      DOUBLE PRECISION   RESULT( NTESTS )
202
203*     ..
204*     .. External Functions ..
205      DOUBLE PRECISION   ZLANHE
206      EXTERNAL           ZLANHE
207*     ..
208*     .. External Subroutines ..
209      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX,
210     $                   ZGET04, ZLACPY, ZLARHS, ZLATB4, ZLATMS,
211     $                   ZHESV_RK, ZHET01_3, ZPOT02, ZHETRF_RK, ZHETRI_3
212*     ..
213*     .. Scalars in Common ..
214      LOGICAL            LERR, OK
215      CHARACTER*32       SRNAMT
216      INTEGER            INFOT, NUNIT
217*     ..
218*     .. Common blocks ..
219      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
220      COMMON             / SRNAMC / SRNAMT
221*     ..
222*     .. Intrinsic Functions ..
223      INTRINSIC          MAX, MIN
224*     ..
225*     .. Data statements ..
226      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
227      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
228*     ..
229*     .. Executable Statements ..
230*
231*     Initialize constants and the random number seed.
232*
233*     Test path
234*
235      PATH( 1: 1 ) = 'Zomplex precision'
236      PATH( 2: 3 ) = 'HK'
237*
238*     Path to generate matrices
239*
240      MATPATH( 1: 1 ) = 'Zomplex precision'
241      MATPATH( 2: 3 ) = 'HE'
242*
243      NRUN = 0
244      NFAIL = 0
245      NERRS = 0
246      DO 10 I = 1, 4
247         ISEED( I ) = ISEEDY( I )
248   10 CONTINUE
249      LWORK = MAX( 2*NMAX, NMAX*NRHS )
250*
251*     Test the error exits
252*
253      IF( TSTERR )
254     $   CALL ZERRVX( PATH, NOUT )
255      INFOT = 0
256*
257*     Set the block size and minimum block size for which the block
258*     routine should be used, which will be later returned by ILAENV.
259*
260      NB = 1
261      NBMIN = 2
262      CALL XLAENV( 1, NB )
263      CALL XLAENV( 2, NBMIN )
264*
265*     Do for each value of N in NVAL
266*
267      DO 180 IN = 1, NN
268         N = NVAL( IN )
269         LDA = MAX( N, 1 )
270         XTYPE = 'N'
271         NIMAT = NTYPES
272         IF( N.LE.0 )
273     $      NIMAT = 1
274*
275         DO 170 IMAT = 1, NIMAT
276*
277*           Do the tests only if DOTYPE( IMAT ) is true.
278*
279            IF( .NOT.DOTYPE( IMAT ) )
280     $         GO TO 170
281*
282*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
283*
284            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
285            IF( ZEROT .AND. N.LT.IMAT-2 )
286     $         GO TO 170
287*
288*           Do first for UPLO = 'U', then for UPLO = 'L'
289*
290            DO 160 IUPLO = 1, 2
291               UPLO = UPLOS( IUPLO )
292*
293*                 Begin generate the test matrix A.
294*
295*                 Set up parameters with ZLATB4 for the matrix generator
296*                 based on the type of matrix to be generated.
297*
298                  CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
299     $                         MODE, CNDNUM, DIST )
300*
301*                 Generate a matrix with ZLATMS.
302*
303                  SRNAMT = 'ZLATMS'
304                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
305     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
306     $                         WORK, INFO )
307*
308*                 Check error code from ZLATMS and handle error.
309*
310                  IF( INFO.NE.0 ) THEN
311                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
312     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
313                     GO TO 160
314                  END IF
315*
316*                 For types 3-6, zero one or more rows and columns of
317*                 the matrix to test that INFO is returned correctly.
318*
319                  IF( ZEROT ) THEN
320                     IF( IMAT.EQ.3 ) THEN
321                        IZERO = 1
322                     ELSE IF( IMAT.EQ.4 ) THEN
323                        IZERO = N
324                     ELSE
325                        IZERO = N / 2 + 1
326                     END IF
327*
328                     IF( IMAT.LT.6 ) THEN
329*
330*                       Set row and column IZERO to zero.
331*
332                        IF( IUPLO.EQ.1 ) THEN
333                           IOFF = ( IZERO-1 )*LDA
334                           DO 20 I = 1, IZERO - 1
335                              A( IOFF+I ) = ZERO
336   20                      CONTINUE
337                           IOFF = IOFF + IZERO
338                           DO 30 I = IZERO, N
339                              A( IOFF ) = ZERO
340                              IOFF = IOFF + LDA
341   30                      CONTINUE
342                        ELSE
343                           IOFF = IZERO
344                           DO 40 I = 1, IZERO - 1
345                              A( IOFF ) = ZERO
346                              IOFF = IOFF + LDA
347   40                      CONTINUE
348                           IOFF = IOFF - IZERO
349                           DO 50 I = IZERO, N
350                              A( IOFF+I ) = ZERO
351   50                      CONTINUE
352                        END IF
353                     ELSE
354                        IF( IUPLO.EQ.1 ) THEN
355*
356*                       Set the first IZERO rows and columns to zero.
357*
358                           IOFF = 0
359                           DO 70 J = 1, N
360                              I2 = MIN( J, IZERO )
361                              DO 60 I = 1, I2
362                                 A( IOFF+I ) = ZERO
363   60                         CONTINUE
364                              IOFF = IOFF + LDA
365   70                      CONTINUE
366                        ELSE
367*
368*                       Set the first IZERO rows and columns to zero.
369*
370                           IOFF = 0
371                           DO 90 J = 1, N
372                              I1 = MAX( J, IZERO )
373                              DO 80 I = I1, N
374                                 A( IOFF+I ) = ZERO
375   80                         CONTINUE
376                              IOFF = IOFF + LDA
377   90                      CONTINUE
378                        END IF
379                     END IF
380                  ELSE
381                     IZERO = 0
382                  END IF
383*
384*                 End generate the test matrix A.
385*
386*
387               DO 150 IFACT = 1, NFACT
388*
389*                 Do first for FACT = 'F', then for other values.
390*
391                  FACT = FACTS( IFACT )
392*
393*                 Compute the condition number
394*
395                  IF( ZEROT ) THEN
396                     IF( IFACT.EQ.1 )
397     $                  GO TO 150
398                     RCONDC = ZERO
399*
400                  ELSE IF( IFACT.EQ.1 ) THEN
401*
402*                    Compute the 1-norm of A.
403*
404                     ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
405*
406*                    Factor the matrix A.
407*
408
409                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
410                     CALL ZHETRF_RK( UPLO, N, AFAC, LDA, E, IWORK, WORK,
411     $                               LWORK, INFO )
412*
413*                    Compute inv(A) and take its norm.
414*
415                     CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
416                     LWORK = (N+NB+1)*(NB+3)
417*
418*                    We need to copute the invesrse to compute
419*                    RCONDC that is used later in TEST3.
420*
421                     CALL ZHETRI_3( UPLO, N, AINV, LDA, E, IWORK,
422     $                              WORK, LWORK, INFO )
423                     AINVNM = ZLANHE( '1', UPLO, N, AINV, LDA, RWORK )
424*
425*                    Compute the 1-norm condition number of A.
426*
427                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
428                        RCONDC = ONE
429                     ELSE
430                        RCONDC = ( ONE / ANORM ) / AINVNM
431                     END IF
432                  END IF
433*
434*                 Form an exact solution and set the right hand side.
435*
436                  SRNAMT = 'ZLARHS'
437                  CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
438     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
439     $                         INFO )
440                  XTYPE = 'C'
441*
442*                 --- Test ZHESV_RK  ---
443*
444                  IF( IFACT.EQ.2 ) THEN
445                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
446                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
447*
448*                    Factor the matrix and solve the system using
449*                    ZHESV_RK.
450*
451                     SRNAMT = 'ZHESV_RK'
452                     CALL ZHESV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK,
453     $                              X, LDA, WORK, LWORK, INFO )
454*
455*                    Adjust the expected value of INFO to account for
456*                    pivoting.
457*
458                     K = IZERO
459                     IF( K.GT.0 ) THEN
460  100                   CONTINUE
461                        IF( IWORK( K ).LT.0 ) THEN
462                           IF( IWORK( K ).NE.-K ) THEN
463                              K = -IWORK( K )
464                              GO TO 100
465                           END IF
466                        ELSE IF( IWORK( K ).NE.K ) THEN
467                           K = IWORK( K )
468                           GO TO 100
469                        END IF
470                     END IF
471*
472*                    Check error code from ZHESV_RK and handle error.
473*
474                     IF( INFO.NE.K ) THEN
475                        CALL ALAERH( PATH, 'ZHESV_RK', INFO, K, UPLO,
476     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
477     $                               NERRS, NOUT )
478                        GO TO 120
479                     ELSE IF( INFO.NE.0 ) THEN
480                        GO TO 120
481                     END IF
482*
483*+    TEST 1      Reconstruct matrix from factors and compute
484*                 residual.
485*
486                     CALL ZHET01_3( UPLO, N, A, LDA, AFAC, LDA, E,
487     $                              IWORK, AINV, LDA, RWORK,
488     $                              RESULT( 1 ) )
489*
490*+    TEST 2      Compute residual of the computed solution.
491*
492                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
493                     CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
494     $                            LDA, RWORK, RESULT( 2 ) )
495*
496*+    TEST 3
497*                 Check solution from generated exact solution.
498*
499                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
500     $                            RESULT( 3 ) )
501                     NT = 3
502*
503*                    Print information about the tests that did not pass
504*                    the threshold.
505*
506                     DO 110 K = 1, NT
507                        IF( RESULT( K ).GE.THRESH ) THEN
508                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
509     $                        CALL ALADHD( NOUT, PATH )
510                           WRITE( NOUT, FMT = 9999 )'ZHESV_RK', UPLO,
511     $                            N, IMAT, K, RESULT( K )
512                           NFAIL = NFAIL + 1
513                        END IF
514  110                CONTINUE
515                     NRUN = NRUN + NT
516  120                CONTINUE
517                  END IF
518*
519  150          CONTINUE
520*
521  160       CONTINUE
522  170    CONTINUE
523  180 CONTINUE
524*
525*     Print a summary of the results.
526*
527      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
528*
529 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
530     $      ', test ', I2, ', ratio =', G12.5 )
531      RETURN
532*
533*     End of ZDRVHE_RK
534*
535      END
536