1*> \brief \b ZDRVSY_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 ZDRVSY_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*> ZDRVSY_RK tests the driver routines ZSYSV_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 ZDRVSY_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 = 11, 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   ZLANSY
203      EXTERNAL           ZLANSY
204*     ..
205*     .. External Subroutines ..
206      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
207     $                   ZLACPY, ZLARHS, ZLATB4, ZLATMS, ZLATSY,
208     $                   ZSYSV_RK, ZSYT01_3, ZSYT02, ZSYTRF_RK, ZSYTRI_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 ) = 'SK'
234*
235*     Path to generate matrices
236*
237      MATPATH( 1: 1 ) = 'Zomplex precision'
238      MATPATH( 2: 3 ) = 'SY'
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               IF( IMAT.NE.NTYPES ) THEN
291*
292*              Begin generate the test matrix A.
293*
294*              Set up parameters with ZLATB4 for the matrix generator
295*              based on the type of matrix to be generated.
296*
297                  CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
298     $                         MODE, CNDNUM, DIST )
299*
300*              Generate a matrix with ZLATMS.
301*
302                  SRNAMT = 'ZLATMS'
303                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
304     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
305     $                         WORK, INFO )
306*
307*              Check error code from DLATMS and handle error.
308*
309                  IF( INFO.NE.0 ) THEN
310                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
311     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
312                     GO TO 160
313                  END IF
314*
315*                 For types 3-6, zero one or more rows and columns of
316*                 the matrix to test that INFO is returned correctly.
317*
318                  IF( ZEROT ) THEN
319                     IF( IMAT.EQ.3 ) THEN
320                        IZERO = 1
321                     ELSE IF( IMAT.EQ.4 ) THEN
322                        IZERO = N
323                     ELSE
324                        IZERO = N / 2 + 1
325                     END IF
326*
327                     IF( IMAT.LT.6 ) THEN
328*
329*                       Set row and column IZERO to zero.
330*
331                        IF( IUPLO.EQ.1 ) THEN
332                           IOFF = ( IZERO-1 )*LDA
333                           DO 20 I = 1, IZERO - 1
334                              A( IOFF+I ) = ZERO
335   20                      CONTINUE
336                           IOFF = IOFF + IZERO
337                           DO 30 I = IZERO, N
338                              A( IOFF ) = ZERO
339                              IOFF = IOFF + LDA
340   30                      CONTINUE
341                        ELSE
342                           IOFF = IZERO
343                           DO 40 I = 1, IZERO - 1
344                              A( IOFF ) = ZERO
345                              IOFF = IOFF + LDA
346   40                      CONTINUE
347                           IOFF = IOFF - IZERO
348                           DO 50 I = IZERO, N
349                              A( IOFF+I ) = ZERO
350   50                      CONTINUE
351                        END IF
352                     ELSE
353                        IF( IUPLO.EQ.1 ) THEN
354*
355*                       Set the first IZERO rows and columns to zero.
356*
357                           IOFF = 0
358                           DO 70 J = 1, N
359                              I2 = MIN( J, IZERO )
360                              DO 60 I = 1, I2
361                                 A( IOFF+I ) = ZERO
362   60                         CONTINUE
363                              IOFF = IOFF + LDA
364   70                      CONTINUE
365                        ELSE
366*
367*                       Set the first IZERO rows and columns to zero.
368*
369                           IOFF = 0
370                           DO 90 J = 1, N
371                              I1 = MAX( J, IZERO )
372                              DO 80 I = I1, N
373                                 A( IOFF+I ) = ZERO
374   80                         CONTINUE
375                              IOFF = IOFF + LDA
376   90                      CONTINUE
377                        END IF
378                     END IF
379                  ELSE
380                     IZERO = 0
381                  END IF
382               ELSE
383*
384*                 IMAT = NTYPES:  Use a special block diagonal matrix to
385*                 test alternate code for the 2-by-2 blocks.
386*
387                  CALL ZLATSY( UPLO, N, A, LDA, ISEED )
388               END IF
389*
390               DO 150 IFACT = 1, NFACT
391*
392*                 Do first for FACT = 'F', then for other values.
393*
394                  FACT = FACTS( IFACT )
395*
396*                 Compute the condition number for comparison with
397*                 the value returned by ZSYSVX_ROOK.
398*
399                  IF( ZEROT ) THEN
400                     IF( IFACT.EQ.1 )
401     $                  GO TO 150
402                     RCONDC = ZERO
403*
404                  ELSE IF( IFACT.EQ.1 ) THEN
405*
406*                    Compute the 1-norm of A.
407*
408                     ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
409*
410*                    Factor the matrix A.
411*
412
413                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
414                     CALL ZSYTRF_RK( UPLO, N, AFAC, LDA, E, IWORK, AINV,
415     $                               LWORK, INFO )
416*
417*                    Compute inv(A) and take its norm.
418*
419                     CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
420                     LWORK = (N+NB+1)*(NB+3)
421*
422*                    We need to compute the inverse to compute
423*                    RCONDC that is used later in TEST3.
424*
425                     CALL ZSYTRI_3( UPLO, N, AINV, LDA, E, IWORK,
426     $                              WORK, LWORK, INFO )
427                     AINVNM = ZLANSY( '1', UPLO, N, AINV, LDA, RWORK )
428*
429*                    Compute the 1-norm condition number of A.
430*
431                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
432                        RCONDC = ONE
433                     ELSE
434                        RCONDC = ( ONE / ANORM ) / AINVNM
435                     END IF
436                  END IF
437*
438*                 Form an exact solution and set the right hand side.
439*
440                  SRNAMT = 'ZLARHS'
441                  CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
442     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
443     $                         INFO )
444                  XTYPE = 'C'
445*
446*                 --- Test ZSYSV_RK  ---
447*
448                  IF( IFACT.EQ.2 ) THEN
449                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
450                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
451*
452*                    Factor the matrix and solve the system using
453*                    ZSYSV_RK.
454*
455                     SRNAMT = 'ZSYSV_RK'
456                     CALL ZSYSV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK,
457     $                              X, LDA, WORK, LWORK, INFO )
458*
459*                    Adjust the expected value of INFO to account for
460*                    pivoting.
461*
462                     K = IZERO
463                     IF( K.GT.0 ) THEN
464  100                   CONTINUE
465                        IF( IWORK( K ).LT.0 ) THEN
466                           IF( IWORK( K ).NE.-K ) THEN
467                              K = -IWORK( K )
468                              GO TO 100
469                           END IF
470                        ELSE IF( IWORK( K ).NE.K ) THEN
471                           K = IWORK( K )
472                           GO TO 100
473                        END IF
474                     END IF
475*
476*                    Check error code from ZSYSV_RK and handle error.
477*
478                     IF( INFO.NE.K ) THEN
479                        CALL ALAERH( PATH, 'ZSYSV_RK', INFO, K, UPLO,
480     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
481     $                               NERRS, NOUT )
482                        GO TO 120
483                     ELSE IF( INFO.NE.0 ) THEN
484                        GO TO 120
485                     END IF
486*
487*+    TEST 1      Reconstruct matrix from factors and compute
488*                 residual.
489*
490                     CALL ZSYT01_3( UPLO, N, A, LDA, AFAC, LDA, E,
491     $                              IWORK, AINV, LDA, RWORK,
492     $                              RESULT( 1 ) )
493*
494*+    TEST 2      Compute residual of the computed solution.
495*
496                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
497                     CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
498     $                            LDA, RWORK, RESULT( 2 ) )
499*
500*+    TEST 3
501*                 Check solution from generated exact solution.
502*
503                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
504     $                            RESULT( 3 ) )
505                     NT = 3
506*
507*                    Print information about the tests that did not pass
508*                    the threshold.
509*
510                     DO 110 K = 1, NT
511                        IF( RESULT( K ).GE.THRESH ) THEN
512                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
513     $                        CALL ALADHD( NOUT, PATH )
514                           WRITE( NOUT, FMT = 9999 )'ZSYSV_RK', UPLO,
515     $                            N, IMAT, K, RESULT( K )
516                           NFAIL = NFAIL + 1
517                        END IF
518  110                CONTINUE
519                     NRUN = NRUN + NT
520  120                CONTINUE
521                  END IF
522*
523  150          CONTINUE
524*
525  160       CONTINUE
526  170    CONTINUE
527  180 CONTINUE
528*
529*     Print a summary of the results.
530*
531      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
532*
533 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
534     $      ', test ', I2, ', ratio =', G12.5 )
535      RETURN
536*
537*     End of ZDRVSY_RK
538*
539      END
540