1*> \brief \b SDRVPP
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 SDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12*                          A, AFAC, ASAV, B, BSAV, X, XACT, S, 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               A( * ), AFAC( * ), ASAV( * ), B( * ),
24*      $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
25*      $                   X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> SDRVPP tests the driver routines SPPSV 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 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 REAL array, dimension
91*>                      (NMAX*(NMAX+1)/2)
92*> \endverbatim
93*>
94*> \param[out] AFAC
95*> \verbatim
96*>          AFAC is REAL array, dimension
97*>                      (NMAX*(NMAX+1)/2)
98*> \endverbatim
99*>
100*> \param[out] ASAV
101*> \verbatim
102*>          ASAV is REAL array, dimension
103*>                      (NMAX*(NMAX+1)/2)
104*> \endverbatim
105*>
106*> \param[out] B
107*> \verbatim
108*>          B is REAL array, dimension (NMAX*NRHS)
109*> \endverbatim
110*>
111*> \param[out] BSAV
112*> \verbatim
113*>          BSAV is REAL array, dimension (NMAX*NRHS)
114*> \endverbatim
115*>
116*> \param[out] X
117*> \verbatim
118*>          X is REAL array, dimension (NMAX*NRHS)
119*> \endverbatim
120*>
121*> \param[out] XACT
122*> \verbatim
123*>          XACT is REAL array, dimension (NMAX*NRHS)
124*> \endverbatim
125*>
126*> \param[out] S
127*> \verbatim
128*>          S is REAL array, dimension (NMAX)
129*> \endverbatim
130*>
131*> \param[out] WORK
132*> \verbatim
133*>          WORK is REAL array, dimension
134*>                      (NMAX*max(3,NRHS))
135*> \endverbatim
136*>
137*> \param[out] RWORK
138*> \verbatim
139*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
140*> \endverbatim
141*>
142*> \param[out] IWORK
143*> \verbatim
144*>          IWORK is INTEGER array, dimension (NMAX)
145*> \endverbatim
146*>
147*> \param[in] NOUT
148*> \verbatim
149*>          NOUT is INTEGER
150*>          The unit number for output.
151*> \endverbatim
152*
153*  Authors:
154*  ========
155*
156*> \author Univ. of Tennessee
157*> \author Univ. of California Berkeley
158*> \author Univ. of Colorado Denver
159*> \author NAG Ltd.
160*
161*> \ingroup single_lin
162*
163*  =====================================================================
164      SUBROUTINE SDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
165     $                   A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
166     $                   RWORK, IWORK, NOUT )
167*
168*  -- LAPACK test routine --
169*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
170*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172*     .. Scalar Arguments ..
173      LOGICAL            TSTERR
174      INTEGER            NMAX, NN, NOUT, NRHS
175      REAL               THRESH
176*     ..
177*     .. Array Arguments ..
178      LOGICAL            DOTYPE( * )
179      INTEGER            IWORK( * ), NVAL( * )
180      REAL               A( * ), AFAC( * ), ASAV( * ), B( * ),
181     $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
182     $                   X( * ), XACT( * )
183*     ..
184*
185*  =====================================================================
186*
187*     .. Parameters ..
188      REAL               ONE, ZERO
189      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
190      INTEGER            NTYPES
191      PARAMETER          ( NTYPES = 9 )
192      INTEGER            NTESTS
193      PARAMETER          ( NTESTS = 6 )
194*     ..
195*     .. Local Scalars ..
196      LOGICAL            EQUIL, NOFACT, PREFAC, ZEROT
197      CHARACTER          DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE
198      CHARACTER*3        PATH
199      INTEGER            I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
200     $                   IZERO, K, K1, KL, KU, LDA, MODE, N, NERRS,
201     $                   NFACT, NFAIL, NIMAT, NPP, NRUN, NT
202      REAL               AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
203     $                   ROLDC, SCOND
204*     ..
205*     .. Local Arrays ..
206      CHARACTER          EQUEDS( 2 ), FACTS( 3 ), PACKS( 2 ), UPLOS( 2 )
207      INTEGER            ISEED( 4 ), ISEEDY( 4 )
208      REAL               RESULT( NTESTS )
209*     ..
210*     .. External Functions ..
211      LOGICAL            LSAME
212      REAL               SGET06, SLANSP
213      EXTERNAL           LSAME, SGET06, SLANSP
214*     ..
215*     .. External Subroutines ..
216      EXTERNAL           ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04,
217     $                   SLACPY, SLAQSP, SLARHS, SLASET, SLATB4, SLATMS,
218     $                   SPPEQU, SPPSV, SPPSVX, SPPT01, SPPT02, SPPT05,
219     $                   SPPTRF, SPPTRI
220*     ..
221*     .. Scalars in Common ..
222      LOGICAL            LERR, OK
223      CHARACTER*32       SRNAMT
224      INTEGER            INFOT, NUNIT
225*     ..
226*     .. Common blocks ..
227      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
228      COMMON             / SRNAMC / SRNAMT
229*     ..
230*     .. Intrinsic Functions ..
231      INTRINSIC          MAX
232*     ..
233*     .. Data statements ..
234      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
235      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N', 'E' / ,
236     $                   PACKS / 'C', 'R' / , EQUEDS / 'N', 'Y' /
237*     ..
238*     .. Executable Statements ..
239*
240*     Initialize constants and the random number seed.
241*
242      PATH( 1: 1 ) = 'Single precision'
243      PATH( 2: 3 ) = 'PP'
244      NRUN = 0
245      NFAIL = 0
246      NERRS = 0
247      DO 10 I = 1, 4
248         ISEED( I ) = ISEEDY( I )
249   10 CONTINUE
250*
251*     Test the error exits
252*
253      IF( TSTERR )
254     $   CALL SERRVX( PATH, NOUT )
255      INFOT = 0
256*
257*     Do for each value of N in NVAL
258*
259      DO 140 IN = 1, NN
260         N = NVAL( IN )
261         LDA = MAX( N, 1 )
262         NPP = N*( N+1 ) / 2
263         XTYPE = 'N'
264         NIMAT = NTYPES
265         IF( N.LE.0 )
266     $      NIMAT = 1
267*
268         DO 130 IMAT = 1, NIMAT
269*
270*           Do the tests only if DOTYPE( IMAT ) is true.
271*
272            IF( .NOT.DOTYPE( IMAT ) )
273     $         GO TO 130
274*
275*           Skip types 3, 4, or 5 if the matrix size is too small.
276*
277            ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
278            IF( ZEROT .AND. N.LT.IMAT-2 )
279     $         GO TO 130
280*
281*           Do first for UPLO = 'U', then for UPLO = 'L'
282*
283            DO 120 IUPLO = 1, 2
284               UPLO = UPLOS( IUPLO )
285               PACKIT = PACKS( IUPLO )
286*
287*              Set up parameters with SLATB4 and generate a test matrix
288*              with SLATMS.
289*
290               CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
291     $                      CNDNUM, DIST )
292               RCONDC = ONE / CNDNUM
293*
294               SRNAMT = 'SLATMS'
295               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
296     $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
297     $                      INFO )
298*
299*              Check error code from SLATMS.
300*
301               IF( INFO.NE.0 ) THEN
302                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
303     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
304                  GO TO 120
305               END IF
306*
307*              For types 3-5, zero one row and column of the matrix to
308*              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*                 Set row and column IZERO of A to 0.
320*
321                  IF( IUPLO.EQ.1 ) THEN
322                     IOFF = ( IZERO-1 )*IZERO / 2
323                     DO 20 I = 1, IZERO - 1
324                        A( IOFF+I ) = ZERO
325   20                CONTINUE
326                     IOFF = IOFF + IZERO
327                     DO 30 I = IZERO, N
328                        A( IOFF ) = ZERO
329                        IOFF = IOFF + I
330   30                CONTINUE
331                  ELSE
332                     IOFF = IZERO
333                     DO 40 I = 1, IZERO - 1
334                        A( IOFF ) = ZERO
335                        IOFF = IOFF + N - I
336   40                CONTINUE
337                     IOFF = IOFF - IZERO
338                     DO 50 I = IZERO, N
339                        A( IOFF+I ) = ZERO
340   50                CONTINUE
341                  END IF
342               ELSE
343                  IZERO = 0
344               END IF
345*
346*              Save a copy of the matrix A in ASAV.
347*
348               CALL SCOPY( NPP, A, 1, ASAV, 1 )
349*
350               DO 110 IEQUED = 1, 2
351                  EQUED = EQUEDS( IEQUED )
352                  IF( IEQUED.EQ.1 ) THEN
353                     NFACT = 3
354                  ELSE
355                     NFACT = 1
356                  END IF
357*
358                  DO 100 IFACT = 1, NFACT
359                     FACT = FACTS( IFACT )
360                     PREFAC = LSAME( FACT, 'F' )
361                     NOFACT = LSAME( FACT, 'N' )
362                     EQUIL = LSAME( FACT, 'E' )
363*
364                     IF( ZEROT ) THEN
365                        IF( PREFAC )
366     $                     GO TO 100
367                        RCONDC = ZERO
368*
369                     ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN
370*
371*                       Compute the condition number for comparison with
372*                       the value returned by SPPSVX (FACT = 'N' reuses
373*                       the condition number from the previous iteration
374*                       with FACT = 'F').
375*
376                        CALL SCOPY( NPP, ASAV, 1, AFAC, 1 )
377                        IF( EQUIL .OR. IEQUED.GT.1 ) THEN
378*
379*                          Compute row and column scale factors to
380*                          equilibrate the matrix A.
381*
382                           CALL SPPEQU( UPLO, N, AFAC, S, SCOND, AMAX,
383     $                                  INFO )
384                           IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
385                              IF( IEQUED.GT.1 )
386     $                           SCOND = ZERO
387*
388*                             Equilibrate the matrix.
389*
390                              CALL SLAQSP( UPLO, N, AFAC, S, SCOND,
391     $                                     AMAX, EQUED )
392                           END IF
393                        END IF
394*
395*                       Save the condition number of the
396*                       non-equilibrated system for use in SGET04.
397*
398                        IF( EQUIL )
399     $                     ROLDC = RCONDC
400*
401*                       Compute the 1-norm of A.
402*
403                        ANORM = SLANSP( '1', UPLO, N, AFAC, RWORK )
404*
405*                       Factor the matrix A.
406*
407                        CALL SPPTRF( UPLO, N, AFAC, INFO )
408*
409*                       Form the inverse of A.
410*
411                        CALL SCOPY( NPP, AFAC, 1, A, 1 )
412                        CALL SPPTRI( UPLO, N, A, INFO )
413*
414*                       Compute the 1-norm condition number of A.
415*
416                        AINVNM = SLANSP( '1', UPLO, N, A, RWORK )
417                        IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
418                           RCONDC = ONE
419                        ELSE
420                           RCONDC = ( ONE / ANORM ) / AINVNM
421                        END IF
422                     END IF
423*
424*                    Restore the matrix A.
425*
426                     CALL SCOPY( NPP, ASAV, 1, A, 1 )
427*
428*                    Form an exact solution and set the right hand side.
429*
430                     SRNAMT = 'SLARHS'
431                     CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
432     $                            NRHS, A, LDA, XACT, LDA, B, LDA,
433     $                            ISEED, INFO )
434                     XTYPE = 'C'
435                     CALL SLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
436*
437                     IF( NOFACT ) THEN
438*
439*                       --- Test SPPSV  ---
440*
441*                       Compute the L*L' or U'*U factorization of the
442*                       matrix and solve the system.
443*
444                        CALL SCOPY( NPP, A, 1, AFAC, 1 )
445                        CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
446*
447                        SRNAMT = 'SPPSV '
448                        CALL SPPSV( UPLO, N, NRHS, AFAC, X, LDA, INFO )
449*
450*                       Check error code from SPPSV .
451*
452                        IF( INFO.NE.IZERO ) THEN
453                           CALL ALAERH( PATH, 'SPPSV ', INFO, IZERO,
454     $                                  UPLO, N, N, -1, -1, NRHS, IMAT,
455     $                                  NFAIL, NERRS, NOUT )
456                           GO TO 70
457                        ELSE IF( INFO.NE.0 ) THEN
458                           GO TO 70
459                        END IF
460*
461*                       Reconstruct matrix from factors and compute
462*                       residual.
463*
464                        CALL SPPT01( UPLO, N, A, AFAC, RWORK,
465     $                               RESULT( 1 ) )
466*
467*                       Compute residual of the computed solution.
468*
469                        CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK,
470     $                               LDA )
471                        CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK,
472     $                               LDA, RWORK, RESULT( 2 ) )
473*
474*                       Check solution from generated exact solution.
475*
476                        CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
477     $                               RESULT( 3 ) )
478                        NT = 3
479*
480*                       Print information about the tests that did not
481*                       pass the threshold.
482*
483                        DO 60 K = 1, NT
484                           IF( RESULT( K ).GE.THRESH ) THEN
485                              IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
486     $                           CALL ALADHD( NOUT, PATH )
487                              WRITE( NOUT, FMT = 9999 )'SPPSV ', UPLO,
488     $                           N, IMAT, K, RESULT( K )
489                              NFAIL = NFAIL + 1
490                           END IF
491   60                   CONTINUE
492                        NRUN = NRUN + NT
493   70                   CONTINUE
494                     END IF
495*
496*                    --- Test SPPSVX ---
497*
498                     IF( .NOT.PREFAC .AND. NPP.GT.0 )
499     $                  CALL SLASET( 'Full', NPP, 1, ZERO, ZERO, AFAC,
500     $                               NPP )
501                     CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
502                     IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
503*
504*                       Equilibrate the matrix if FACT='F' and
505*                       EQUED='Y'.
506*
507                        CALL SLAQSP( UPLO, N, A, S, SCOND, AMAX, EQUED )
508                     END IF
509*
510*                    Solve the system and compute the condition number
511*                    and error bounds using SPPSVX.
512*
513                     SRNAMT = 'SPPSVX'
514                     CALL SPPSVX( FACT, UPLO, N, NRHS, A, AFAC, EQUED,
515     $                            S, B, LDA, X, LDA, RCOND, RWORK,
516     $                            RWORK( NRHS+1 ), WORK, IWORK, INFO )
517*
518*                    Check the error code from SPPSVX.
519*
520                     IF( INFO.NE.IZERO ) THEN
521                        CALL ALAERH( PATH, 'SPPSVX', INFO, IZERO,
522     $                               FACT // UPLO, N, N, -1, -1, NRHS,
523     $                               IMAT, NFAIL, NERRS, NOUT )
524                        GO TO 90
525                     END IF
526*
527                     IF( INFO.EQ.0 ) THEN
528                        IF( .NOT.PREFAC ) THEN
529*
530*                          Reconstruct matrix from factors and compute
531*                          residual.
532*
533                           CALL SPPT01( UPLO, N, A, AFAC,
534     $                                  RWORK( 2*NRHS+1 ), RESULT( 1 ) )
535                           K1 = 1
536                        ELSE
537                           K1 = 2
538                        END IF
539*
540*                       Compute residual of the computed solution.
541*
542                        CALL SLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
543     $                               LDA )
544                        CALL SPPT02( UPLO, N, NRHS, ASAV, X, LDA, WORK,
545     $                               LDA, RWORK( 2*NRHS+1 ),
546     $                               RESULT( 2 ) )
547*
548*                       Check solution from generated exact solution.
549*
550                        IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
551     $                      'N' ) ) ) THEN
552                           CALL SGET04( N, NRHS, X, LDA, XACT, LDA,
553     $                                  RCONDC, RESULT( 3 ) )
554                        ELSE
555                           CALL SGET04( N, NRHS, X, LDA, XACT, LDA,
556     $                                  ROLDC, RESULT( 3 ) )
557                        END IF
558*
559*                       Check the error bounds from iterative
560*                       refinement.
561*
562                        CALL SPPT05( UPLO, N, NRHS, ASAV, B, LDA, X,
563     $                               LDA, XACT, LDA, RWORK,
564     $                               RWORK( NRHS+1 ), RESULT( 4 ) )
565                     ELSE
566                        K1 = 6
567                     END IF
568*
569*                    Compare RCOND from SPPSVX with the computed value
570*                    in RCONDC.
571*
572                     RESULT( 6 ) = SGET06( RCOND, RCONDC )
573*
574*                    Print information about the tests that did not pass
575*                    the threshold.
576*
577                     DO 80 K = K1, 6
578                        IF( RESULT( K ).GE.THRESH ) THEN
579                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
580     $                        CALL ALADHD( NOUT, PATH )
581                           IF( PREFAC ) THEN
582                              WRITE( NOUT, FMT = 9997 )'SPPSVX', FACT,
583     $                           UPLO, N, EQUED, IMAT, K, RESULT( K )
584                           ELSE
585                              WRITE( NOUT, FMT = 9998 )'SPPSVX', FACT,
586     $                           UPLO, N, IMAT, K, RESULT( K )
587                           END IF
588                           NFAIL = NFAIL + 1
589                        END IF
590   80                CONTINUE
591                     NRUN = NRUN + 7 - K1
592   90                CONTINUE
593  100             CONTINUE
594  110          CONTINUE
595  120       CONTINUE
596  130    CONTINUE
597  140 CONTINUE
598*
599*     Print a summary of the results.
600*
601      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
602*
603 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
604     $      ', test(', I1, ')=', G12.5 )
605 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
606     $      ', type ', I1, ', test(', I1, ')=', G12.5 )
607 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
608     $      ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ')=',
609     $      G12.5 )
610      RETURN
611*
612*     End of SDRVPP
613*
614      END
615