1*> \brief \b ZDRVSY_ROOK
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_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12*                          NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
13*                          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( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> ZDRVSY_ROOK tests the driver routines ZSYSV_ROOK.
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 ZDRVSY_ROOK( 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 = 11, 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   AINVNM, ANORM, CNDNUM, RCONDC
189*     ..
190*     .. Local Arrays ..
191      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
192      INTEGER            ISEED( 4 ), ISEEDY( 4 )
193      DOUBLE PRECISION   RESULT( NTESTS )
194
195*     ..
196*     .. External Functions ..
197      DOUBLE PRECISION   ZLANSY
198      EXTERNAL           ZLANSY
199*     ..
200*     .. External Subroutines ..
201      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
202     $                   ZLACPY, ZLARHS, ZLASET, ZLATB4, ZLATMS, ZLATSY,
203     $                   ZPOT05, ZSYSV_ROOK, ZSYT01_ROOK, ZSYT02,
204     $                   ZSYTRF_ROOK, ZSYTRI_ROOK
205*     ..
206*     .. Scalars in Common ..
207      LOGICAL            LERR, OK
208      CHARACTER*32       SRNAMT
209      INTEGER            INFOT, NUNIT
210*     ..
211*     .. Common blocks ..
212      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
213      COMMON             / SRNAMC / SRNAMT
214*     ..
215*     .. Intrinsic Functions ..
216      INTRINSIC          MAX, MIN
217*     ..
218*     .. Data statements ..
219      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
220      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
221*     ..
222*     .. Executable Statements ..
223*
224*     Initialize constants and the random number seed.
225*
226*     Test path
227*
228      PATH( 1: 1 ) = 'Zomplex precision'
229      PATH( 2: 3 ) = 'SR'
230*
231*     Path to generate matrices
232*
233      MATPATH( 1: 1 ) = 'Zomplex precision'
234      MATPATH( 2: 3 ) = 'SY'
235*
236      NRUN = 0
237      NFAIL = 0
238      NERRS = 0
239      DO 10 I = 1, 4
240         ISEED( I ) = ISEEDY( I )
241   10 CONTINUE
242      LWORK = MAX( 2*NMAX, NMAX*NRHS )
243*
244*     Test the error exits
245*
246      IF( TSTERR )
247     $   CALL ZERRVX( PATH, NOUT )
248      INFOT = 0
249*
250*     Set the block size and minimum block size for which the block
251*     routine should be used, which will be later returned by ILAENV.
252*
253      NB = 1
254      NBMIN = 2
255      CALL XLAENV( 1, NB )
256      CALL XLAENV( 2, NBMIN )
257*
258*     Do for each value of N in NVAL
259*
260      DO 180 IN = 1, NN
261         N = NVAL( IN )
262         LDA = MAX( N, 1 )
263         XTYPE = 'N'
264         NIMAT = NTYPES
265         IF( N.LE.0 )
266     $      NIMAT = 1
267*
268         DO 170 IMAT = 1, NIMAT
269*
270*           Do the tests only if DOTYPE( IMAT ) is true.
271*
272            IF( .NOT.DOTYPE( IMAT ) )
273     $         GO TO 170
274*
275*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
276*
277            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
278            IF( ZEROT .AND. N.LT.IMAT-2 )
279     $         GO TO 170
280*
281*           Do first for UPLO = 'U', then for UPLO = 'L'
282*
283            DO 160 IUPLO = 1, 2
284               UPLO = UPLOS( IUPLO )
285*
286               IF( IMAT.NE.NTYPES ) THEN
287*
288*              Begin generate the test matrix A.
289*
290*              Set up parameters with ZLATB4 for the matrix generator
291*              based on the type of matrix to be generated.
292*
293                  CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
294     $                         MODE, CNDNUM, DIST )
295*
296*              Generate a matrix with ZLATMS.
297*
298                  SRNAMT = 'ZLATMS'
299                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
300     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
301     $                         WORK, INFO )
302*
303*              Check error code from DLATMS and handle error.
304*
305                  IF( INFO.NE.0 ) THEN
306                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
307     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
308                     GO TO 160
309                  END IF
310*
311*                 For types 3-6, zero one or more rows and columns of
312*                 the matrix to test that INFO is returned correctly.
313*
314                  IF( ZEROT ) THEN
315                     IF( IMAT.EQ.3 ) THEN
316                        IZERO = 1
317                     ELSE IF( IMAT.EQ.4 ) THEN
318                        IZERO = N
319                     ELSE
320                        IZERO = N / 2 + 1
321                     END IF
322*
323                     IF( IMAT.LT.6 ) THEN
324*
325*                       Set row and column IZERO to zero.
326*
327                        IF( IUPLO.EQ.1 ) THEN
328                           IOFF = ( IZERO-1 )*LDA
329                           DO 20 I = 1, IZERO - 1
330                              A( IOFF+I ) = ZERO
331   20                      CONTINUE
332                           IOFF = IOFF + IZERO
333                           DO 30 I = IZERO, N
334                              A( IOFF ) = ZERO
335                              IOFF = IOFF + LDA
336   30                      CONTINUE
337                        ELSE
338                           IOFF = IZERO
339                           DO 40 I = 1, IZERO - 1
340                              A( IOFF ) = ZERO
341                              IOFF = IOFF + LDA
342   40                      CONTINUE
343                           IOFF = IOFF - IZERO
344                           DO 50 I = IZERO, N
345                              A( IOFF+I ) = ZERO
346   50                      CONTINUE
347                        END IF
348                     ELSE
349                        IF( IUPLO.EQ.1 ) THEN
350*
351*                       Set the first IZERO rows and columns to zero.
352*
353                           IOFF = 0
354                           DO 70 J = 1, N
355                              I2 = MIN( J, IZERO )
356                              DO 60 I = 1, I2
357                                 A( IOFF+I ) = ZERO
358   60                         CONTINUE
359                              IOFF = IOFF + LDA
360   70                      CONTINUE
361                        ELSE
362*
363*                       Set the first IZERO rows and columns to zero.
364*
365                           IOFF = 0
366                           DO 90 J = 1, N
367                              I1 = MAX( J, IZERO )
368                              DO 80 I = I1, N
369                                 A( IOFF+I ) = ZERO
370   80                         CONTINUE
371                              IOFF = IOFF + LDA
372   90                      CONTINUE
373                        END IF
374                     END IF
375                  ELSE
376                     IZERO = 0
377                  END IF
378               ELSE
379*
380*                 IMAT = NTYPES:  Use a special block diagonal matrix to
381*                 test alternate code for the 2-by-2 blocks.
382*
383                  CALL ZLATSY( UPLO, N, A, LDA, ISEED )
384               END IF
385*
386               DO 150 IFACT = 1, NFACT
387*
388*                 Do first for FACT = 'F', then for other values.
389*
390                  FACT = FACTS( IFACT )
391*
392*                 Compute the condition number for comparison with
393*                 the value returned by ZSYSVX_ROOK.
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 = ZLANSY( '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 ZSYTRF_ROOK( UPLO, N, AFAC, LDA, 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                     CALL ZSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK,
418     $                                 WORK, INFO )
419                     AINVNM = ZLANSY( '1', UPLO, N, AINV, LDA, RWORK )
420*
421*                    Compute the 1-norm condition number of A.
422*
423                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
424                        RCONDC = ONE
425                     ELSE
426                        RCONDC = ( ONE / ANORM ) / AINVNM
427                     END IF
428                  END IF
429*
430*                 Form an exact solution and set the right hand side.
431*
432                  SRNAMT = 'ZLARHS'
433                  CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
434     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
435     $                         INFO )
436                  XTYPE = 'C'
437*
438*                 --- Test ZSYSV_ROOK  ---
439*
440                  IF( IFACT.EQ.2 ) THEN
441                     CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
442                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
443*
444*                    Factor the matrix and solve the system using
445*                    ZSYSV_ROOK.
446*
447                     SRNAMT = 'ZSYSV_ROOK'
448                     CALL ZSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
449     $                                X, LDA, WORK, LWORK, INFO )
450*
451*                    Adjust the expected value of INFO to account for
452*                    pivoting.
453*
454                     K = IZERO
455                     IF( K.GT.0 ) THEN
456  100                   CONTINUE
457                        IF( IWORK( K ).LT.0 ) THEN
458                           IF( IWORK( K ).NE.-K ) THEN
459                              K = -IWORK( K )
460                              GO TO 100
461                           END IF
462                        ELSE IF( IWORK( K ).NE.K ) THEN
463                           K = IWORK( K )
464                           GO TO 100
465                        END IF
466                     END IF
467*
468*                    Check error code from ZSYSV_ROOK and handle error.
469*
470                     IF( INFO.NE.K ) THEN
471                        CALL ALAERH( PATH, 'ZSYSV_ROOK', INFO, K, UPLO,
472     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
473     $                               NERRS, NOUT )
474                        GO TO 120
475                     ELSE IF( INFO.NE.0 ) THEN
476                        GO TO 120
477                     END IF
478*
479*+    TEST 1      Reconstruct matrix from factors and compute
480*                 residual.
481*
482                     CALL ZSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA,
483     $                                 IWORK, AINV, LDA, RWORK,
484     $                                 RESULT( 1 ) )
485*
486*+    TEST 2      Compute residual of the computed solution.
487*
488                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
489                     CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
490     $                            LDA, RWORK, RESULT( 2 ) )
491*
492*+    TEST 3
493*                 Check solution from generated exact solution.
494*
495                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
496     $                            RESULT( 3 ) )
497                     NT = 3
498*
499*                    Print information about the tests that did not pass
500*                    the threshold.
501*
502                     DO 110 K = 1, NT
503                        IF( RESULT( K ).GE.THRESH ) THEN
504                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
505     $                        CALL ALADHD( NOUT, PATH )
506                           WRITE( NOUT, FMT = 9999 )'ZSYSV_ROOK', UPLO,
507     $                            N, IMAT, K, RESULT( K )
508                           NFAIL = NFAIL + 1
509                        END IF
510  110                CONTINUE
511                     NRUN = NRUN + NT
512  120                CONTINUE
513                  END IF
514*
515  150          CONTINUE
516*
517  160       CONTINUE
518  170    CONTINUE
519  180 CONTINUE
520*
521*     Print a summary of the results.
522*
523      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
524*
525 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
526     $      ', test ', I2, ', ratio =', G12.5 )
527      RETURN
528*
529*     End of ZDRVSY_ROOK
530*
531      END
532