1*> \brief \b CDRVSY_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 CDRVSY_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*       REAL               THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NVAL( * )
23*       REAL               RWORK( * )
24*       COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> CDRVSY_RK tests the driver routines CSYSV_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 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] E
99*> \verbatim
100*>          E is COMPLEX array, dimension (NMAX)
101*> \endverbatim
102*>
103*> \param[out] AINV
104*> \verbatim
105*>          AINV is COMPLEX array, dimension (NMAX*NMAX)
106*> \endverbatim
107*>
108*> \param[out] B
109*> \verbatim
110*>          B is COMPLEX array, dimension (NMAX*NRHS)
111*> \endverbatim
112*>
113*> \param[out] X
114*> \verbatim
115*>          X is COMPLEX array, dimension (NMAX*NRHS)
116*> \endverbatim
117*>
118*> \param[out] XACT
119*> \verbatim
120*>          XACT is COMPLEX array, dimension (NMAX*NRHS)
121*> \endverbatim
122*>
123*> \param[out] WORK
124*> \verbatim
125*> \endverbatim
126*>
127*> \param[out] RWORK
128*> \verbatim
129*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
130*> \endverbatim
131*>
132*> \param[out] IWORK
133*> \verbatim
134*>          IWORK is INTEGER array, dimension (NMAX)
135*> \endverbatim
136*>
137*> \param[in] NOUT
138*> \verbatim
139*>          NOUT is INTEGER
140*>          The unit number for output.
141*> \endverbatim
142*
143*  Authors:
144*  ========
145*
146*> \author Univ. of Tennessee
147*> \author Univ. of California Berkeley
148*> \author Univ. of Colorado Denver
149*> \author NAG Ltd.
150*
151*> \date December 2016
152*
153*> \ingroup complex_lin
154*
155*  =====================================================================
156      SUBROUTINE CDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
157     $                      NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
158     $                      RWORK, IWORK, NOUT )
159*
160*  -- LAPACK test routine (version 3.7.0) --
161*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
162*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*     December 2016
164*
165*     .. Scalar Arguments ..
166      LOGICAL            TSTERR
167      INTEGER            NMAX, NN, NOUT, NRHS
168      REAL               THRESH
169*     ..
170*     .. Array Arguments ..
171      LOGICAL            DOTYPE( * )
172      INTEGER            IWORK( * ), NVAL( * )
173      REAL               RWORK( * )
174      COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
175     $                   WORK( * ), X( * ), XACT( * )
176*     ..
177*
178*  =====================================================================
179*
180*     .. Parameters ..
181      REAL               ONE, ZERO
182      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
183      INTEGER            NTYPES, NTESTS
184      PARAMETER          ( NTYPES = 11, NTESTS = 3 )
185      INTEGER            NFACT
186      PARAMETER          ( NFACT = 2 )
187*     ..
188*     .. Local Scalars ..
189      LOGICAL            ZEROT
190      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
191      CHARACTER*3        MATPATH, PATH
192      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
193     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
194     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
195      REAL               AINVNM, ANORM, CNDNUM, RCONDC
196*     ..
197*     .. Local Arrays ..
198      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
199      INTEGER            ISEED( 4 ), ISEEDY( 4 )
200      REAL               RESULT( NTESTS )
201
202*     ..
203*     .. External Functions ..
204      REAL               CLANSY
205      EXTERNAL           CLANSY
206*     ..
207*     .. External Subroutines ..
208      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, CERRVX, CGET04,
209     $                   CLACPY, CLARHS, CLATB4, CLATMS, CLATSY,
210     $                   CSYSV_RK, CSYT01_3, CSYT02, CSYTRF_RK, CSYTRI_3
211*     ..
212*     .. Scalars in Common ..
213      LOGICAL            LERR, OK
214      CHARACTER*32       SRNAMT
215      INTEGER            INFOT, NUNIT
216*     ..
217*     .. Common blocks ..
218      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
219      COMMON             / SRNAMC / SRNAMT
220*     ..
221*     .. Intrinsic Functions ..
222      INTRINSIC          MAX, MIN
223*     ..
224*     .. Data statements ..
225      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
226      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
227*     ..
228*     .. Executable Statements ..
229*
230*     Initialize constants and the random number seed.
231*
232*     Test path
233*
234      PATH( 1: 1 ) = 'Complex precision'
235      PATH( 2: 3 ) = 'SK'
236*
237*     Path to generate matrices
238*
239      MATPATH( 1: 1 ) = 'Complex precision'
240      MATPATH( 2: 3 ) = 'SY'
241*
242      NRUN = 0
243      NFAIL = 0
244      NERRS = 0
245      DO 10 I = 1, 4
246         ISEED( I ) = ISEEDY( I )
247   10 CONTINUE
248      LWORK = MAX( 2*NMAX, NMAX*NRHS )
249*
250*     Test the error exits
251*
252      IF( TSTERR )
253     $   CALL CERRVX( PATH, NOUT )
254      INFOT = 0
255*
256*     Set the block size and minimum block size for which the block
257*     routine should be used, which will be later returned by ILAENV.
258*
259      NB = 1
260      NBMIN = 2
261      CALL XLAENV( 1, NB )
262      CALL XLAENV( 2, NBMIN )
263*
264*     Do for each value of N in NVAL
265*
266      DO 180 IN = 1, NN
267         N = NVAL( IN )
268         LDA = MAX( N, 1 )
269         XTYPE = 'N'
270         NIMAT = NTYPES
271         IF( N.LE.0 )
272     $      NIMAT = 1
273*
274         DO 170 IMAT = 1, NIMAT
275*
276*           Do the tests only if DOTYPE( IMAT ) is true.
277*
278            IF( .NOT.DOTYPE( IMAT ) )
279     $         GO TO 170
280*
281*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
282*
283            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
284            IF( ZEROT .AND. N.LT.IMAT-2 )
285     $         GO TO 170
286*
287*           Do first for UPLO = 'U', then for UPLO = 'L'
288*
289            DO 160 IUPLO = 1, 2
290               UPLO = UPLOS( IUPLO )
291*
292               IF( IMAT.NE.NTYPES ) THEN
293*
294*                 Begin generate the test matrix A.
295*
296*                 Set up parameters with CLATB4 for the matrix generator
297*                 based on the type of matrix to be generated.
298*
299                  CALL CLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
300     $                         MODE, CNDNUM, DIST )
301*
302*                 Generate a matrix with CLATMS.
303*
304                  SRNAMT = 'CLATMS'
305                  CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
306     $                         CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
307     $                         WORK, INFO )
308*
309*                 Check error code from CLATMS and handle error.
310*
311                  IF( INFO.NE.0 ) THEN
312                     CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N,
313     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
314                     GO TO 160
315                  END IF
316*
317*                 For types 3-6, zero one or more rows and columns of
318*                 the matrix to test that INFO is returned correctly.
319*
320                  IF( ZEROT ) THEN
321                     IF( IMAT.EQ.3 ) THEN
322                        IZERO = 1
323                     ELSE IF( IMAT.EQ.4 ) THEN
324                        IZERO = N
325                     ELSE
326                        IZERO = N / 2 + 1
327                     END IF
328*
329                     IF( IMAT.LT.6 ) THEN
330*
331*                       Set row and column IZERO to zero.
332*
333                        IF( IUPLO.EQ.1 ) THEN
334                           IOFF = ( IZERO-1 )*LDA
335                           DO 20 I = 1, IZERO - 1
336                              A( IOFF+I ) = ZERO
337   20                      CONTINUE
338                           IOFF = IOFF + IZERO
339                           DO 30 I = IZERO, N
340                              A( IOFF ) = ZERO
341                              IOFF = IOFF + LDA
342   30                      CONTINUE
343                        ELSE
344                           IOFF = IZERO
345                           DO 40 I = 1, IZERO - 1
346                              A( IOFF ) = ZERO
347                              IOFF = IOFF + LDA
348   40                      CONTINUE
349                           IOFF = IOFF - IZERO
350                           DO 50 I = IZERO, N
351                              A( IOFF+I ) = ZERO
352   50                      CONTINUE
353                        END IF
354                     ELSE
355                        IF( IUPLO.EQ.1 ) THEN
356*
357*                       Set the first IZERO rows and columns to zero.
358*
359                           IOFF = 0
360                           DO 70 J = 1, N
361                              I2 = MIN( J, IZERO )
362                              DO 60 I = 1, I2
363                                 A( IOFF+I ) = ZERO
364   60                         CONTINUE
365                              IOFF = IOFF + LDA
366   70                      CONTINUE
367                        ELSE
368*
369*                       Set the first IZERO rows and columns to zero.
370*
371                           IOFF = 0
372                           DO 90 J = 1, N
373                              I1 = MAX( J, IZERO )
374                              DO 80 I = I1, N
375                                 A( IOFF+I ) = ZERO
376   80                         CONTINUE
377                              IOFF = IOFF + LDA
378   90                      CONTINUE
379                        END IF
380                     END IF
381                  ELSE
382                     IZERO = 0
383                  END IF
384*
385*                 End generate the test matrix A.
386*
387               ELSE
388*
389*                 IMAT = NTYPES:  Use a special block diagonal matrix to
390*                 test alternate code for the 2-by-2 blocks.
391*
392                  CALL CLATSY( UPLO, N, A, LDA, ISEED )
393               END IF
394*
395               DO 150 IFACT = 1, NFACT
396*
397*                 Do first for FACT = 'F', then for other values.
398*
399                  FACT = FACTS( IFACT )
400*
401*                 Compute the condition number
402*
403                  IF( ZEROT ) THEN
404                     IF( IFACT.EQ.1 )
405     $                  GO TO 150
406                     RCONDC = ZERO
407*
408                  ELSE IF( IFACT.EQ.1 ) THEN
409*
410*                    Compute the 1-norm of A.
411*
412                     ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK )
413*
414*                    Factor the matrix A.
415*
416
417                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
418                     CALL CSYTRF_RK( UPLO, N, AFAC, LDA, E, IWORK, WORK,
419     $                               LWORK, INFO )
420*
421*                    Compute inv(A) and take its norm.
422*
423                     CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
424                     LWORK = (N+NB+1)*(NB+3)
425*
426*                    We need to copute the invesrse to compute
427*                    RCONDC that is used later in TEST3.
428*
429                     CALL CSYTRI_3( UPLO, N, AINV, LDA, E, IWORK,
430     $                              WORK, LWORK, INFO )
431                     AINVNM = CLANSY( '1', UPLO, N, AINV, LDA, RWORK )
432*
433*                    Compute the 1-norm condition number of A.
434*
435                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
436                        RCONDC = ONE
437                     ELSE
438                        RCONDC = ( ONE / ANORM ) / AINVNM
439                     END IF
440                  END IF
441*
442*                 Form an exact solution and set the right hand side.
443*
444                  SRNAMT = 'CLARHS'
445                  CALL CLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
446     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
447     $                         INFO )
448                  XTYPE = 'C'
449*
450*                 --- Test CSYSV_RK  ---
451*
452                  IF( IFACT.EQ.2 ) THEN
453                     CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
454                     CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
455*
456*                    Factor the matrix and solve the system using
457*                    CSYSV_RK.
458*
459                     SRNAMT = 'CSYSV_RK'
460                     CALL CSYSV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK,
461     $                              X, LDA, WORK, LWORK, INFO )
462*
463*                    Adjust the expected value of INFO to account for
464*                    pivoting.
465*
466                     K = IZERO
467                     IF( K.GT.0 ) THEN
468  100                   CONTINUE
469                        IF( IWORK( K ).LT.0 ) THEN
470                           IF( IWORK( K ).NE.-K ) THEN
471                              K = -IWORK( K )
472                              GO TO 100
473                           END IF
474                        ELSE IF( IWORK( K ).NE.K ) THEN
475                           K = IWORK( K )
476                           GO TO 100
477                        END IF
478                     END IF
479*
480*                    Check error code from CSYSV_RK and handle error.
481*
482                     IF( INFO.NE.K ) THEN
483                        CALL ALAERH( PATH, 'CSYSV_RK', INFO, K, UPLO,
484     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
485     $                               NERRS, NOUT )
486                        GO TO 120
487                     ELSE IF( INFO.NE.0 ) THEN
488                        GO TO 120
489                     END IF
490*
491*+    TEST 1      Reconstruct matrix from factors and compute
492*                 residual.
493*
494                     CALL CSYT01_3( UPLO, N, A, LDA, AFAC, LDA, E,
495     $                              IWORK, AINV, LDA, RWORK,
496     $                              RESULT( 1 ) )
497*
498*+    TEST 2      Compute residual of the computed solution.
499*
500                     CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
501                     CALL CSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
502     $                            LDA, RWORK, RESULT( 2 ) )
503*
504*+    TEST 3
505*                 Check solution from generated exact solution.
506*
507                     CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
508     $                            RESULT( 3 ) )
509                     NT = 3
510*
511*                    Print information about the tests that did not pass
512*                    the threshold.
513*
514                     DO 110 K = 1, NT
515                        IF( RESULT( K ).GE.THRESH ) THEN
516                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
517     $                        CALL ALADHD( NOUT, PATH )
518                           WRITE( NOUT, FMT = 9999 )'CSYSV_RK', UPLO,
519     $                            N, IMAT, K, RESULT( K )
520                           NFAIL = NFAIL + 1
521                        END IF
522  110                CONTINUE
523                     NRUN = NRUN + NT
524  120                CONTINUE
525                  END IF
526*
527  150          CONTINUE
528*
529  160       CONTINUE
530  170    CONTINUE
531  180 CONTINUE
532*
533*     Print a summary of the results.
534*
535      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
536*
537 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
538     $      ', test ', I2, ', ratio =', G12.5 )
539      RETURN
540*
541*     End of CDRVSY_RK
542*
543      END
544