1*> \brief \b ZDRVSP
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 ZDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12*                          A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13*                          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*> ZDRVSP tests the driver routines ZSPSV and -SVX.
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
91*>                      (NMAX*(NMAX+1)/2)
92*> \endverbatim
93*>
94*> \param[out] AFAC
95*> \verbatim
96*>          AFAC is COMPLEX*16 array, dimension
97*>                      (NMAX*(NMAX+1)/2)
98*> \endverbatim
99*>
100*> \param[out] AINV
101*> \verbatim
102*>          AINV is COMPLEX*16 array, dimension
103*>                      (NMAX*(NMAX+1)/2)
104*> \endverbatim
105*>
106*> \param[out] B
107*> \verbatim
108*>          B is COMPLEX*16 array, dimension (NMAX*NRHS)
109*> \endverbatim
110*>
111*> \param[out] X
112*> \verbatim
113*>          X is COMPLEX*16 array, dimension (NMAX*NRHS)
114*> \endverbatim
115*>
116*> \param[out] XACT
117*> \verbatim
118*>          XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
119*> \endverbatim
120*>
121*> \param[out] WORK
122*> \verbatim
123*>          WORK is COMPLEX*16 array, dimension
124*>                      (NMAX*max(2,NRHS))
125*> \endverbatim
126*>
127*> \param[out] RWORK
128*> \verbatim
129*>          RWORK is DOUBLE PRECISION 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*> \ingroup complex16_lin
152*
153*  =====================================================================
154      SUBROUTINE ZDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
155     $                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
156     $                   NOUT )
157*
158*  -- LAPACK test routine --
159*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
160*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161*
162*     .. Scalar Arguments ..
163      LOGICAL            TSTERR
164      INTEGER            NMAX, NN, NOUT, NRHS
165      DOUBLE PRECISION   THRESH
166*     ..
167*     .. Array Arguments ..
168      LOGICAL            DOTYPE( * )
169      INTEGER            IWORK( * ), NVAL( * )
170      DOUBLE PRECISION   RWORK( * )
171      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
172     $                   WORK( * ), X( * ), XACT( * )
173*     ..
174*
175*  =====================================================================
176*
177*     .. Parameters ..
178      DOUBLE PRECISION   ONE, ZERO
179      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
180      INTEGER            NTYPES, NTESTS
181      PARAMETER          ( NTYPES = 11, NTESTS = 6 )
182      INTEGER            NFACT
183      PARAMETER          ( NFACT = 2 )
184*     ..
185*     .. Local Scalars ..
186      LOGICAL            ZEROT
187      CHARACTER          DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
188      CHARACTER*3        PATH
189      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
190     $                   IZERO, J, K, K1, KL, KU, LDA, MODE, N, NB,
191     $                   NBMIN, NERRS, NFAIL, NIMAT, NPP, NRUN, NT
192      DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCOND, RCONDC
193*     ..
194*     .. Local Arrays ..
195      CHARACTER          FACTS( NFACT )
196      INTEGER            ISEED( 4 ), ISEEDY( 4 )
197      DOUBLE PRECISION   RESULT( NTESTS )
198*     ..
199*     .. External Functions ..
200      DOUBLE PRECISION   DGET06, ZLANSP
201      EXTERNAL           DGET06, ZLANSP
202*     ..
203*     .. External Subroutines ..
204      EXTERNAL           ALADHD, ALAERH, ALASVM, XLAENV, ZCOPY, ZERRVX,
205     $                   ZGET04, ZLACPY, ZLARHS, ZLASET, ZLATB4, ZLATMS,
206     $                   ZLATSP, ZPPT05, ZSPSV, ZSPSVX, ZSPT01, ZSPT02,
207     $                   ZSPTRF, ZSPTRI
208*     ..
209*     .. Scalars in Common ..
210      LOGICAL            LERR, OK
211      CHARACTER*32       SRNAMT
212      INTEGER            INFOT, NUNIT
213*     ..
214*     .. Common blocks ..
215      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
216      COMMON             / SRNAMC / SRNAMT
217*     ..
218*     .. Intrinsic Functions ..
219      INTRINSIC          DCMPLX, MAX, MIN
220*     ..
221*     .. Data statements ..
222      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
223      DATA               FACTS / 'F', 'N' /
224*     ..
225*     .. Executable Statements ..
226*
227*     Initialize constants and the random number seed.
228*
229      PATH( 1: 1 ) = 'Zomplex precision'
230      PATH( 2: 3 ) = 'SP'
231      NRUN = 0
232      NFAIL = 0
233      NERRS = 0
234      DO 10 I = 1, 4
235         ISEED( I ) = ISEEDY( I )
236   10 CONTINUE
237*
238*     Test the error exits
239*
240      IF( TSTERR )
241     $   CALL ZERRVX( PATH, NOUT )
242      INFOT = 0
243*
244*     Set the block size and minimum block size for testing.
245*
246      NB = 1
247      NBMIN = 2
248      CALL XLAENV( 1, NB )
249      CALL XLAENV( 2, NBMIN )
250*
251*     Do for each value of N in NVAL
252*
253      DO 180 IN = 1, NN
254         N = NVAL( IN )
255         LDA = MAX( N, 1 )
256         NPP = N*( N+1 ) / 2
257         XTYPE = 'N'
258         NIMAT = NTYPES
259         IF( N.LE.0 )
260     $      NIMAT = 1
261*
262         DO 170 IMAT = 1, NIMAT
263*
264*           Do the tests only if DOTYPE( IMAT ) is true.
265*
266            IF( .NOT.DOTYPE( IMAT ) )
267     $         GO TO 170
268*
269*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
270*
271            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
272            IF( ZEROT .AND. N.LT.IMAT-2 )
273     $         GO TO 170
274*
275*           Do first for UPLO = 'U', then for UPLO = 'L'
276*
277            DO 160 IUPLO = 1, 2
278               IF( IUPLO.EQ.1 ) THEN
279                  UPLO = 'U'
280                  PACKIT = 'C'
281               ELSE
282                  UPLO = 'L'
283                  PACKIT = 'R'
284               END IF
285*
286               IF( IMAT.NE.NTYPES ) THEN
287*
288*                 Set up parameters with ZLATB4 and generate a test
289*                 matrix with ZLATMS.
290*
291                  CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
292     $                         MODE, CNDNUM, DIST )
293*
294                  SRNAMT = 'ZLATMS'
295                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
296     $                         CNDNUM, ANORM, KL, KU, PACKIT, A, LDA,
297     $                         WORK, INFO )
298*
299*                 Check error code from ZLATMS.
300*
301                  IF( INFO.NE.0 ) THEN
302                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
303     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
304                     GO TO 160
305                  END IF
306*
307*                 For types 3-6, zero one or more rows and columns of
308*                 the matrix to test that INFO is returned correctly.
309*
310                  IF( ZEROT ) THEN
311                     IF( IMAT.EQ.3 ) THEN
312                        IZERO = 1
313                     ELSE IF( IMAT.EQ.4 ) THEN
314                        IZERO = N
315                     ELSE
316                        IZERO = N / 2 + 1
317                     END IF
318*
319                     IF( IMAT.LT.6 ) THEN
320*
321*                       Set row and column IZERO to zero.
322*
323                        IF( IUPLO.EQ.1 ) THEN
324                           IOFF = ( IZERO-1 )*IZERO / 2
325                           DO 20 I = 1, IZERO - 1
326                              A( IOFF+I ) = ZERO
327   20                      CONTINUE
328                           IOFF = IOFF + IZERO
329                           DO 30 I = IZERO, N
330                              A( IOFF ) = ZERO
331                              IOFF = IOFF + I
332   30                      CONTINUE
333                        ELSE
334                           IOFF = IZERO
335                           DO 40 I = 1, IZERO - 1
336                              A( IOFF ) = ZERO
337                              IOFF = IOFF + N - I
338   40                      CONTINUE
339                           IOFF = IOFF - IZERO
340                           DO 50 I = IZERO, N
341                              A( IOFF+I ) = ZERO
342   50                      CONTINUE
343                        END IF
344                     ELSE
345                        IF( IUPLO.EQ.1 ) THEN
346*
347*                          Set the first IZERO rows and columns to zero.
348*
349                           IOFF = 0
350                           DO 70 J = 1, N
351                              I2 = MIN( J, IZERO )
352                              DO 60 I = 1, I2
353                                 A( IOFF+I ) = ZERO
354   60                         CONTINUE
355                              IOFF = IOFF + J
356   70                      CONTINUE
357                        ELSE
358*
359*                          Set the last IZERO rows and columns to zero.
360*
361                           IOFF = 0
362                           DO 90 J = 1, N
363                              I1 = MAX( J, IZERO )
364                              DO 80 I = I1, N
365                                 A( IOFF+I ) = ZERO
366   80                         CONTINUE
367                              IOFF = IOFF + N - J
368   90                      CONTINUE
369                        END IF
370                     END IF
371                  ELSE
372                     IZERO = 0
373                  END IF
374               ELSE
375*
376*                 Use a special block diagonal matrix to test alternate
377*                 code for the 2-by-2 blocks.
378*
379                  CALL ZLATSP( UPLO, N, A, ISEED )
380               END IF
381*
382               DO 150 IFACT = 1, NFACT
383*
384*                 Do first for FACT = 'F', then for other values.
385*
386                  FACT = FACTS( IFACT )
387*
388*                 Compute the condition number for comparison with
389*                 the value returned by ZSPSVX.
390*
391                  IF( ZEROT ) THEN
392                     IF( IFACT.EQ.1 )
393     $                  GO TO 150
394                     RCONDC = ZERO
395*
396                  ELSE IF( IFACT.EQ.1 ) THEN
397*
398*                    Compute the 1-norm of A.
399*
400                     ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
401*
402*                    Factor the matrix A.
403*
404                     CALL ZCOPY( NPP, A, 1, AFAC, 1 )
405                     CALL ZSPTRF( UPLO, N, AFAC, IWORK, INFO )
406*
407*                    Compute inv(A) and take its norm.
408*
409                     CALL ZCOPY( NPP, AFAC, 1, AINV, 1 )
410                     CALL ZSPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
411                     AINVNM = ZLANSP( '1', UPLO, N, AINV, RWORK )
412*
413*                    Compute the 1-norm condition number of A.
414*
415                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
416                        RCONDC = ONE
417                     ELSE
418                        RCONDC = ( ONE / ANORM ) / AINVNM
419                     END IF
420                  END IF
421*
422*                 Form an exact solution and set the right hand side.
423*
424                  SRNAMT = 'ZLARHS'
425                  CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
426     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
427     $                         INFO )
428                  XTYPE = 'C'
429*
430*                 --- Test ZSPSV  ---
431*
432                  IF( IFACT.EQ.2 ) THEN
433                     CALL ZCOPY( NPP, A, 1, AFAC, 1 )
434                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
435*
436*                    Factor the matrix and solve the system using ZSPSV.
437*
438                     SRNAMT = 'ZSPSV '
439                     CALL ZSPSV( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
440     $                           INFO )
441*
442*                    Adjust the expected value of INFO to account for
443*                    pivoting.
444*
445                     K = IZERO
446                     IF( K.GT.0 ) THEN
447  100                   CONTINUE
448                        IF( IWORK( K ).LT.0 ) THEN
449                           IF( IWORK( K ).NE.-K ) THEN
450                              K = -IWORK( K )
451                              GO TO 100
452                           END IF
453                        ELSE IF( IWORK( K ).NE.K ) THEN
454                           K = IWORK( K )
455                           GO TO 100
456                        END IF
457                     END IF
458*
459*                    Check error code from ZSPSV .
460*
461                     IF( INFO.NE.K ) THEN
462                        CALL ALAERH( PATH, 'ZSPSV ', INFO, K, UPLO, N,
463     $                               N, -1, -1, NRHS, IMAT, NFAIL,
464     $                               NERRS, NOUT )
465                        GO TO 120
466                     ELSE IF( INFO.NE.0 ) THEN
467                        GO TO 120
468                     END IF
469*
470*                    Reconstruct matrix from factors and compute
471*                    residual.
472*
473                     CALL ZSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
474     $                            RWORK, RESULT( 1 ) )
475*
476*                    Compute residual of the computed solution.
477*
478                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
479                     CALL ZSPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
480     $                            RWORK, RESULT( 2 ) )
481*
482*                    Check solution from generated exact solution.
483*
484                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
485     $                            RESULT( 3 ) )
486                     NT = 3
487*
488*                    Print information about the tests that did not pass
489*                    the threshold.
490*
491                     DO 110 K = 1, NT
492                        IF( RESULT( K ).GE.THRESH ) THEN
493                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
494     $                        CALL ALADHD( NOUT, PATH )
495                           WRITE( NOUT, FMT = 9999 )'ZSPSV ', UPLO, N,
496     $                        IMAT, K, RESULT( K )
497                           NFAIL = NFAIL + 1
498                        END IF
499  110                CONTINUE
500                     NRUN = NRUN + NT
501  120                CONTINUE
502                  END IF
503*
504*                 --- Test ZSPSVX ---
505*
506                  IF( IFACT.EQ.2 .AND. NPP.GT.0 )
507     $               CALL ZLASET( 'Full', NPP, 1, DCMPLX( ZERO ),
508     $                            DCMPLX( ZERO ), AFAC, NPP )
509                  CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
510     $                         DCMPLX( ZERO ), X, LDA )
511*
512*                 Solve the system and compute the condition number and
513*                 error bounds using ZSPSVX.
514*
515                  SRNAMT = 'ZSPSVX'
516                  CALL ZSPSVX( FACT, UPLO, N, NRHS, A, AFAC, IWORK, B,
517     $                         LDA, X, LDA, RCOND, RWORK,
518     $                         RWORK( NRHS+1 ), WORK, RWORK( 2*NRHS+1 ),
519     $                         INFO )
520*
521*                 Adjust the expected value of INFO to account for
522*                 pivoting.
523*
524                  K = IZERO
525                  IF( K.GT.0 ) THEN
526  130                CONTINUE
527                     IF( IWORK( K ).LT.0 ) THEN
528                        IF( IWORK( K ).NE.-K ) THEN
529                           K = -IWORK( K )
530                           GO TO 130
531                        END IF
532                     ELSE IF( IWORK( K ).NE.K ) THEN
533                        K = IWORK( K )
534                        GO TO 130
535                     END IF
536                  END IF
537*
538*                 Check the error code from ZSPSVX.
539*
540                  IF( INFO.NE.K ) THEN
541                     CALL ALAERH( PATH, 'ZSPSVX', INFO, K, FACT // UPLO,
542     $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
543     $                            NERRS, NOUT )
544                     GO TO 150
545                  END IF
546*
547                  IF( INFO.EQ.0 ) THEN
548                     IF( IFACT.GE.2 ) THEN
549*
550*                       Reconstruct matrix from factors and compute
551*                       residual.
552*
553                        CALL ZSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
554     $                               RWORK( 2*NRHS+1 ), RESULT( 1 ) )
555                        K1 = 1
556                     ELSE
557                        K1 = 2
558                     END IF
559*
560*                    Compute residual of the computed solution.
561*
562                     CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
563                     CALL ZSPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
564     $                            RWORK( 2*NRHS+1 ), RESULT( 2 ) )
565*
566*                    Check solution from generated exact solution.
567*
568                     CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
569     $                            RESULT( 3 ) )
570*
571*                    Check the error bounds from iterative refinement.
572*
573                     CALL ZPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA,
574     $                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
575     $                            RESULT( 4 ) )
576                  ELSE
577                     K1 = 6
578                  END IF
579*
580*                 Compare RCOND from ZSPSVX with the computed value
581*                 in RCONDC.
582*
583                  RESULT( 6 ) = DGET06( RCOND, RCONDC )
584*
585*                 Print information about the tests that did not pass
586*                 the threshold.
587*
588                  DO 140 K = K1, 6
589                     IF( RESULT( K ).GE.THRESH ) THEN
590                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
591     $                     CALL ALADHD( NOUT, PATH )
592                        WRITE( NOUT, FMT = 9998 )'ZSPSVX', FACT, UPLO,
593     $                     N, IMAT, K, RESULT( K )
594                        NFAIL = NFAIL + 1
595                     END IF
596  140             CONTINUE
597                  NRUN = NRUN + 7 - K1
598*
599  150          CONTINUE
600*
601  160       CONTINUE
602  170    CONTINUE
603  180 CONTINUE
604*
605*     Print a summary of the results.
606*
607      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
608*
609 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
610     $      ', test ', I2, ', ratio =', G12.5 )
611 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
612     $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
613      RETURN
614*
615*     End of ZDRVSP
616*
617      END
618