1*> \brief \b CDRVSY_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 CDRVSY_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*       REAL               THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NVAL( * )
23*       REAL               RWORK( * )
24*       COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> CDRVSY_ROOK tests the driver routines CSYSV_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 REAL
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 array, dimension (NMAX*NMAX)
91*> \endverbatim
92*>
93*> \param[out] AFAC
94*> \verbatim
95*>          AFAC is COMPLEX array, dimension (NMAX*NMAX)
96*> \endverbatim
97*>
98*> \param[out] AINV
99*> \verbatim
100*>          AINV is COMPLEX array, dimension (NMAX*NMAX)
101*> \endverbatim
102*>
103*> \param[out] B
104*> \verbatim
105*>          B is COMPLEX array, dimension (NMAX*NRHS)
106*> \endverbatim
107*>
108*> \param[out] X
109*> \verbatim
110*>          X is COMPLEX array, dimension (NMAX*NRHS)
111*> \endverbatim
112*>
113*> \param[out] XACT
114*> \verbatim
115*>          XACT is COMPLEX array, dimension (NMAX*NRHS)
116*> \endverbatim
117*>
118*> \param[out] WORK
119*> \verbatim
120*> \endverbatim
121*>
122*> \param[out] RWORK
123*> \verbatim
124*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
125*> \endverbatim
126*>
127*> \param[out] IWORK
128*> \verbatim
129*>          IWORK is INTEGER array, dimension (NMAX)
130*> \endverbatim
131*>
132*> \param[in] NOUT
133*> \verbatim
134*>          NOUT is INTEGER
135*>          The unit number for output.
136*> \endverbatim
137*
138*  Authors:
139*  ========
140*
141*> \author Univ. of Tennessee
142*> \author Univ. of California Berkeley
143*> \author Univ. of Colorado Denver
144*> \author NAG Ltd.
145*
146*> \ingroup complex_lin
147*
148*  =====================================================================
149      SUBROUTINE CDRVSY_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
150     $                        NMAX, A, AFAC, AINV, B, X, XACT, WORK,
151     $                        RWORK, IWORK, NOUT )
152*
153*  -- LAPACK test routine --
154*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
155*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157*     .. Scalar Arguments ..
158      LOGICAL            TSTERR
159      INTEGER            NMAX, NN, NOUT, NRHS
160      REAL               THRESH
161*     ..
162*     .. Array Arguments ..
163      LOGICAL            DOTYPE( * )
164      INTEGER            IWORK( * ), NVAL( * )
165      REAL               RWORK( * )
166      COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
167     $                   WORK( * ), X( * ), XACT( * )
168*     ..
169*
170*  =====================================================================
171*
172*     .. Parameters ..
173      REAL               ONE, ZERO
174      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
175      INTEGER            NTYPES, NTESTS
176      PARAMETER          ( NTYPES = 11, NTESTS = 3 )
177      INTEGER            NFACT
178      PARAMETER          ( NFACT = 2 )
179*     ..
180*     .. Local Scalars ..
181      LOGICAL            ZEROT
182      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
183      CHARACTER*3        MATPATH, PATH
184      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
185     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
186     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
187      REAL               AINVNM, ANORM, CNDNUM, RCONDC
188*     ..
189*     .. Local Arrays ..
190      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
191      INTEGER            ISEED( 4 ), ISEEDY( 4 )
192      REAL               RESULT( NTESTS )
193
194*     ..
195*     .. External Functions ..
196      REAL               CLANSY
197      EXTERNAL           CLANSY
198*     ..
199*     .. External Subroutines ..
200      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, CERRVX, CGET04,
201     $                   CLACPY, CLARHS, CLASET, CLATB4, CLATMS, CLATSY,
202     $                   CPOT05, CSYSV_ROOK, CSYT01_ROOK, CSYT02,
203     $                   CSYTRF_ROOK, CSYTRI_ROOK
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          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 ) = 'Complex precision'
228      PATH( 2: 3 ) = 'SR'
229*
230*     Path to generate matrices
231*
232      MATPATH( 1: 1 ) = 'Complex precision'
233      MATPATH( 2: 3 ) = 'SY'
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      LWORK = MAX( 2*NMAX, NMAX*NRHS )
242*
243*     Test the error exits
244*
245      IF( TSTERR )
246     $   CALL CERRVX( PATH, NOUT )
247      INFOT = 0
248*
249*     Set the block size and minimum block size for which the block
250*     routine should be used, which will be later returned by ILAENV.
251*
252      NB = 1
253      NBMIN = 2
254      CALL XLAENV( 1, NB )
255      CALL XLAENV( 2, NBMIN )
256*
257*     Do for each value of N in NVAL
258*
259      DO 180 IN = 1, NN
260         N = NVAL( IN )
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               IF( IMAT.NE.NTYPES ) THEN
286*
287*                 Begin generate the test matrix A.
288*
289*                 Set up parameters with CLATB4 for the matrix generator
290*                 based on the type of matrix to be generated.
291*
292                  CALL CLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
293     $                         MODE, CNDNUM, DIST )
294*
295*                 Generate a matrix with CLATMS.
296*
297                  SRNAMT = 'CLATMS'
298                  CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
299     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
300     $                         WORK, INFO )
301*
302*                 Check error code from CLATMS and handle error.
303*
304                  IF( INFO.NE.0 ) THEN
305                     CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N,
306     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
307                     GO TO 160
308                  END IF
309*
310*                 For types 3-6, zero one or more rows and columns of
311*                 the matrix to test that INFO is returned correctly.
312*
313                  IF( ZEROT ) THEN
314                     IF( IMAT.EQ.3 ) THEN
315                        IZERO = 1
316                     ELSE IF( IMAT.EQ.4 ) THEN
317                        IZERO = N
318                     ELSE
319                        IZERO = N / 2 + 1
320                     END IF
321*
322                     IF( IMAT.LT.6 ) THEN
323*
324*                       Set row and column IZERO to zero.
325*
326                        IF( IUPLO.EQ.1 ) THEN
327                           IOFF = ( IZERO-1 )*LDA
328                           DO 20 I = 1, IZERO - 1
329                              A( IOFF+I ) = ZERO
330   20                      CONTINUE
331                           IOFF = IOFF + IZERO
332                           DO 30 I = IZERO, N
333                              A( IOFF ) = ZERO
334                              IOFF = IOFF + LDA
335   30                      CONTINUE
336                        ELSE
337                           IOFF = IZERO
338                           DO 40 I = 1, IZERO - 1
339                              A( IOFF ) = ZERO
340                              IOFF = IOFF + LDA
341   40                      CONTINUE
342                           IOFF = IOFF - IZERO
343                           DO 50 I = IZERO, N
344                              A( IOFF+I ) = ZERO
345   50                      CONTINUE
346                        END IF
347                     ELSE
348                        IF( IUPLO.EQ.1 ) THEN
349*
350*                       Set the first IZERO rows and columns to zero.
351*
352                           IOFF = 0
353                           DO 70 J = 1, N
354                              I2 = MIN( J, IZERO )
355                              DO 60 I = 1, I2
356                                 A( IOFF+I ) = ZERO
357   60                         CONTINUE
358                              IOFF = IOFF + LDA
359   70                      CONTINUE
360                        ELSE
361*
362*                       Set the first IZERO rows and columns to zero.
363*
364                           IOFF = 0
365                           DO 90 J = 1, N
366                              I1 = MAX( J, IZERO )
367                              DO 80 I = I1, N
368                                 A( IOFF+I ) = ZERO
369   80                         CONTINUE
370                              IOFF = IOFF + LDA
371   90                      CONTINUE
372                        END IF
373                     END IF
374                  ELSE
375                     IZERO = 0
376                  END IF
377*
378*                 End generate the test matrix A.
379*
380               ELSE
381*
382*                 IMAT = NTYPES:  Use a special block diagonal matrix to
383*                 test alternate code for the 2-by-2 blocks.
384*
385                  CALL CLATSY( UPLO, N, A, LDA, ISEED )
386               END IF
387*
388               DO 150 IFACT = 1, NFACT
389*
390*                 Do first for FACT = 'F', then for other values.
391*
392                  FACT = FACTS( IFACT )
393*
394*                 Compute the condition number for comparison with
395*                 the value returned by CSYSVX_ROOK.
396*
397                  IF( ZEROT ) THEN
398                     IF( IFACT.EQ.1 )
399     $                  GO TO 150
400                     RCONDC = ZERO
401*
402                  ELSE IF( IFACT.EQ.1 ) THEN
403*
404*                    Compute the 1-norm of A.
405*
406                     ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK )
407*
408*                    Factor the matrix A.
409*
410
411                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
412                     CALL CSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, WORK,
413     $                                 LWORK, INFO )
414*
415*                    Compute inv(A) and take its norm.
416*
417                     CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
418                     LWORK = (N+NB+1)*(NB+3)
419                     CALL CSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK,
420     $                                 WORK, INFO )
421                     AINVNM = CLANSY( '1', UPLO, N, AINV, LDA, RWORK )
422*
423*                    Compute the 1-norm condition number of A.
424*
425                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
426                        RCONDC = ONE
427                     ELSE
428                        RCONDC = ( ONE / ANORM ) / AINVNM
429                     END IF
430                  END IF
431*
432*                 Form an exact solution and set the right hand side.
433*
434                  SRNAMT = 'CLARHS'
435                  CALL CLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
436     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
437     $                         INFO )
438                  XTYPE = 'C'
439*
440*                 --- Test CSYSV_ROOK  ---
441*
442                  IF( IFACT.EQ.2 ) THEN
443                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
444                     CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
445*
446*                    Factor the matrix and solve the system using
447*                    CSYSV_ROOK.
448*
449                     SRNAMT = 'CSYSV_ROOK'
450                     CALL CSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
451     $                                X, LDA, WORK, LWORK, INFO )
452*
453*                    Adjust the expected value of INFO to account for
454*                    pivoting.
455*
456                     K = IZERO
457                     IF( K.GT.0 ) THEN
458  100                   CONTINUE
459                        IF( IWORK( K ).LT.0 ) THEN
460                           IF( IWORK( K ).NE.-K ) THEN
461                              K = -IWORK( K )
462                              GO TO 100
463                           END IF
464                        ELSE IF( IWORK( K ).NE.K ) THEN
465                           K = IWORK( K )
466                           GO TO 100
467                        END IF
468                     END IF
469*
470*                    Check error code from CSYSV_ROOK and handle error.
471*
472                     IF( INFO.NE.K ) THEN
473                        CALL ALAERH( PATH, 'CSYSV_ROOK', INFO, K, UPLO,
474     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
475     $                               NERRS, NOUT )
476                        GO TO 120
477                     ELSE IF( INFO.NE.0 ) THEN
478                        GO TO 120
479                     END IF
480*
481*+    TEST 1      Reconstruct matrix from factors and compute
482*                 residual.
483*
484                     CALL CSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA,
485     $                                 IWORK, AINV, LDA, RWORK,
486     $                                 RESULT( 1 ) )
487*
488*+    TEST 2      Compute residual of the computed solution.
489*
490                     CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
491                     CALL CSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
492     $                            LDA, RWORK, RESULT( 2 ) )
493*
494*+    TEST 3
495*                 Check solution from generated exact solution.
496*
497                     CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
498     $                            RESULT( 3 ) )
499                     NT = 3
500*
501*                    Print information about the tests that did not pass
502*                    the threshold.
503*
504                     DO 110 K = 1, NT
505                        IF( RESULT( K ).GE.THRESH ) THEN
506                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
507     $                        CALL ALADHD( NOUT, PATH )
508                           WRITE( NOUT, FMT = 9999 )'CSYSV_ROOK', UPLO,
509     $                            N, IMAT, K, RESULT( K )
510                           NFAIL = NFAIL + 1
511                        END IF
512  110                CONTINUE
513                     NRUN = NRUN + NT
514  120                CONTINUE
515                  END IF
516*
517  150          CONTINUE
518*
519  160       CONTINUE
520  170    CONTINUE
521  180 CONTINUE
522*
523*     Print a summary of the results.
524*
525      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
526*
527 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
528     $      ', test ', I2, ', ratio =', G12.5 )
529      RETURN
530*
531*     End of CDRVSY_ROOK
532*
533      END
534