1*> \brief \b DDRVPP
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 DDRVPP( 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*       DOUBLE PRECISION   THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NVAL( * )
23*       DOUBLE PRECISION   A( * ), AFAC( * ), ASAV( * ), B( * ),
24*      $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
25*      $                   X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> DDRVPP tests the driver routines DPPSV 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 DOUBLE PRECISION array, dimension
91*>                      (NMAX*(NMAX+1)/2)
92*> \endverbatim
93*>
94*> \param[out] AFAC
95*> \verbatim
96*>          AFAC is DOUBLE PRECISION array, dimension
97*>                      (NMAX*(NMAX+1)/2)
98*> \endverbatim
99*>
100*> \param[out] ASAV
101*> \verbatim
102*>          ASAV is DOUBLE PRECISION array, dimension
103*>                      (NMAX*(NMAX+1)/2)
104*> \endverbatim
105*>
106*> \param[out] B
107*> \verbatim
108*>          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
109*> \endverbatim
110*>
111*> \param[out] BSAV
112*> \verbatim
113*>          BSAV is DOUBLE PRECISION array, dimension (NMAX*NRHS)
114*> \endverbatim
115*>
116*> \param[out] X
117*> \verbatim
118*>          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
119*> \endverbatim
120*>
121*> \param[out] XACT
122*> \verbatim
123*>          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
124*> \endverbatim
125*>
126*> \param[out] S
127*> \verbatim
128*>          S is DOUBLE PRECISION array, dimension (NMAX)
129*> \endverbatim
130*>
131*> \param[out] WORK
132*> \verbatim
133*>          WORK is DOUBLE PRECISION array, dimension
134*>                      (NMAX*max(3,NRHS))
135*> \endverbatim
136*>
137*> \param[out] RWORK
138*> \verbatim
139*>          RWORK is DOUBLE PRECISION 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*> \date November 2011
162*
163*> \ingroup double_lin
164*
165*  =====================================================================
166      SUBROUTINE DDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
167     $                   A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
168     $                   RWORK, IWORK, NOUT )
169*
170*  -- LAPACK test routine (version 3.4.0) --
171*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
172*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173*     November 2011
174*
175*     .. Scalar Arguments ..
176      LOGICAL            TSTERR
177      INTEGER            NMAX, NN, NOUT, NRHS
178      DOUBLE PRECISION   THRESH
179*     ..
180*     .. Array Arguments ..
181      LOGICAL            DOTYPE( * )
182      INTEGER            IWORK( * ), NVAL( * )
183      DOUBLE PRECISION   A( * ), AFAC( * ), ASAV( * ), B( * ),
184     $                   BSAV( * ), RWORK( * ), S( * ), WORK( * ),
185     $                   X( * ), XACT( * )
186*     ..
187*
188*  =====================================================================
189*
190*     .. Parameters ..
191      DOUBLE PRECISION   ONE, ZERO
192      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
193      INTEGER            NTYPES
194      PARAMETER          ( NTYPES = 9 )
195      INTEGER            NTESTS
196      PARAMETER          ( NTESTS = 6 )
197*     ..
198*     .. Local Scalars ..
199      LOGICAL            EQUIL, NOFACT, PREFAC, ZEROT
200      CHARACTER          DIST, EQUED, FACT, PACKIT, TYPE, UPLO, XTYPE
201      CHARACTER*3        PATH
202      INTEGER            I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
203     $                   IZERO, K, K1, KL, KU, LDA, MODE, N, NERRS,
204     $                   NFACT, NFAIL, NIMAT, NPP, NRUN, NT
205      DOUBLE PRECISION   AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
206     $                   ROLDC, SCOND
207*     ..
208*     .. Local Arrays ..
209      CHARACTER          EQUEDS( 2 ), FACTS( 3 ), PACKS( 2 ), UPLOS( 2 )
210      INTEGER            ISEED( 4 ), ISEEDY( 4 )
211      DOUBLE PRECISION   RESULT( NTESTS )
212*     ..
213*     .. External Functions ..
214      LOGICAL            LSAME
215      DOUBLE PRECISION   DGET06, DLANSP
216      EXTERNAL           LSAME, DGET06, DLANSP
217*     ..
218*     .. External Subroutines ..
219      EXTERNAL           ALADHD, ALAERH, ALASVM, DCOPY, DERRVX, DGET04,
220     $                   DLACPY, DLAQSP, DLARHS, DLASET, DLATB4, DLATMS,
221     $                   DPPEQU, DPPSV, DPPSVX, DPPT01, DPPT02, DPPT05,
222     $                   DPPTRF, DPPTRI
223*     ..
224*     .. Scalars in Common ..
225      LOGICAL            LERR, OK
226      CHARACTER*32       SRNAMT
227      INTEGER            INFOT, NUNIT
228*     ..
229*     .. Common blocks ..
230      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
231      COMMON             / SRNAMC / SRNAMT
232*     ..
233*     .. Intrinsic Functions ..
234      INTRINSIC          MAX
235*     ..
236*     .. Data statements ..
237      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
238      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N', 'E' / ,
239     $                   PACKS / 'C', 'R' / , EQUEDS / 'N', 'Y' /
240*     ..
241*     .. Executable Statements ..
242*
243*     Initialize constants and the random number seed.
244*
245      PATH( 1: 1 ) = 'Double precision'
246      PATH( 2: 3 ) = 'PP'
247      NRUN = 0
248      NFAIL = 0
249      NERRS = 0
250      DO 10 I = 1, 4
251         ISEED( I ) = ISEEDY( I )
252   10 CONTINUE
253*
254*     Test the error exits
255*
256      IF( TSTERR )
257     $   CALL DERRVX( PATH, NOUT )
258      INFOT = 0
259*
260*     Do for each value of N in NVAL
261*
262      DO 140 IN = 1, NN
263         N = NVAL( IN )
264         LDA = MAX( N, 1 )
265         NPP = N*( N+1 ) / 2
266         XTYPE = 'N'
267         NIMAT = NTYPES
268         IF( N.LE.0 )
269     $      NIMAT = 1
270*
271         DO 130 IMAT = 1, NIMAT
272*
273*           Do the tests only if DOTYPE( IMAT ) is true.
274*
275            IF( .NOT.DOTYPE( IMAT ) )
276     $         GO TO 130
277*
278*           Skip types 3, 4, or 5 if the matrix size is too small.
279*
280            ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
281            IF( ZEROT .AND. N.LT.IMAT-2 )
282     $         GO TO 130
283*
284*           Do first for UPLO = 'U', then for UPLO = 'L'
285*
286            DO 120 IUPLO = 1, 2
287               UPLO = UPLOS( IUPLO )
288               PACKIT = PACKS( IUPLO )
289*
290*              Set up parameters with DLATB4 and generate a test matrix
291*              with DLATMS.
292*
293               CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
294     $                      CNDNUM, DIST )
295               RCONDC = ONE / CNDNUM
296*
297               SRNAMT = 'DLATMS'
298               CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
299     $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
300     $                      INFO )
301*
302*              Check error code from DLATMS.
303*
304               IF( INFO.NE.0 ) THEN
305                  CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
306     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
307                  GO TO 120
308               END IF
309*
310*              For types 3-5, zero one row and column of the matrix to
311*              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*                 Set row and column IZERO of A to 0.
323*
324                  IF( IUPLO.EQ.1 ) THEN
325                     IOFF = ( IZERO-1 )*IZERO / 2
326                     DO 20 I = 1, IZERO - 1
327                        A( IOFF+I ) = ZERO
328   20                CONTINUE
329                     IOFF = IOFF + IZERO
330                     DO 30 I = IZERO, N
331                        A( IOFF ) = ZERO
332                        IOFF = IOFF + I
333   30                CONTINUE
334                  ELSE
335                     IOFF = IZERO
336                     DO 40 I = 1, IZERO - 1
337                        A( IOFF ) = ZERO
338                        IOFF = IOFF + N - I
339   40                CONTINUE
340                     IOFF = IOFF - IZERO
341                     DO 50 I = IZERO, N
342                        A( IOFF+I ) = ZERO
343   50                CONTINUE
344                  END IF
345               ELSE
346                  IZERO = 0
347               END IF
348*
349*              Save a copy of the matrix A in ASAV.
350*
351               CALL DCOPY( NPP, A, 1, ASAV, 1 )
352*
353               DO 110 IEQUED = 1, 2
354                  EQUED = EQUEDS( IEQUED )
355                  IF( IEQUED.EQ.1 ) THEN
356                     NFACT = 3
357                  ELSE
358                     NFACT = 1
359                  END IF
360*
361                  DO 100 IFACT = 1, NFACT
362                     FACT = FACTS( IFACT )
363                     PREFAC = LSAME( FACT, 'F' )
364                     NOFACT = LSAME( FACT, 'N' )
365                     EQUIL = LSAME( FACT, 'E' )
366*
367                     IF( ZEROT ) THEN
368                        IF( PREFAC )
369     $                     GO TO 100
370                        RCONDC = ZERO
371*
372                     ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN
373*
374*                       Compute the condition number for comparison with
375*                       the value returned by DPPSVX (FACT = 'N' reuses
376*                       the condition number from the previous iteration
377*                       with FACT = 'F').
378*
379                        CALL DCOPY( NPP, ASAV, 1, AFAC, 1 )
380                        IF( EQUIL .OR. IEQUED.GT.1 ) THEN
381*
382*                          Compute row and column scale factors to
383*                          equilibrate the matrix A.
384*
385                           CALL DPPEQU( UPLO, N, AFAC, S, SCOND, AMAX,
386     $                                  INFO )
387                           IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
388                              IF( IEQUED.GT.1 )
389     $                           SCOND = ZERO
390*
391*                             Equilibrate the matrix.
392*
393                              CALL DLAQSP( UPLO, N, AFAC, S, SCOND,
394     $                                     AMAX, EQUED )
395                           END IF
396                        END IF
397*
398*                       Save the condition number of the
399*                       non-equilibrated system for use in DGET04.
400*
401                        IF( EQUIL )
402     $                     ROLDC = RCONDC
403*
404*                       Compute the 1-norm of A.
405*
406                        ANORM = DLANSP( '1', UPLO, N, AFAC, RWORK )
407*
408*                       Factor the matrix A.
409*
410                        CALL DPPTRF( UPLO, N, AFAC, INFO )
411*
412*                       Form the inverse of A.
413*
414                        CALL DCOPY( NPP, AFAC, 1, A, 1 )
415                        CALL DPPTRI( UPLO, N, A, INFO )
416*
417*                       Compute the 1-norm condition number of A.
418*
419                        AINVNM = DLANSP( '1', UPLO, N, A, RWORK )
420                        IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
421                           RCONDC = ONE
422                        ELSE
423                           RCONDC = ( ONE / ANORM ) / AINVNM
424                        END IF
425                     END IF
426*
427*                    Restore the matrix A.
428*
429                     CALL DCOPY( NPP, ASAV, 1, A, 1 )
430*
431*                    Form an exact solution and set the right hand side.
432*
433                     SRNAMT = 'DLARHS'
434                     CALL DLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
435     $                            NRHS, A, LDA, XACT, LDA, B, LDA,
436     $                            ISEED, INFO )
437                     XTYPE = 'C'
438                     CALL DLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
439*
440                     IF( NOFACT ) THEN
441*
442*                       --- Test DPPSV  ---
443*
444*                       Compute the L*L' or U'*U factorization of the
445*                       matrix and solve the system.
446*
447                        CALL DCOPY( NPP, A, 1, AFAC, 1 )
448                        CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
449*
450                        SRNAMT = 'DPPSV '
451                        CALL DPPSV( UPLO, N, NRHS, AFAC, X, LDA, INFO )
452*
453*                       Check error code from DPPSV .
454*
455                        IF( INFO.NE.IZERO ) THEN
456                           CALL ALAERH( PATH, 'DPPSV ', INFO, IZERO,
457     $                                  UPLO, N, N, -1, -1, NRHS, IMAT,
458     $                                  NFAIL, NERRS, NOUT )
459                           GO TO 70
460                        ELSE IF( INFO.NE.0 ) THEN
461                           GO TO 70
462                        END IF
463*
464*                       Reconstruct matrix from factors and compute
465*                       residual.
466*
467                        CALL DPPT01( UPLO, N, A, AFAC, RWORK,
468     $                               RESULT( 1 ) )
469*
470*                       Compute residual of the computed solution.
471*
472                        CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK,
473     $                               LDA )
474                        CALL DPPT02( UPLO, N, NRHS, A, X, LDA, WORK,
475     $                               LDA, RWORK, RESULT( 2 ) )
476*
477*                       Check solution from generated exact solution.
478*
479                        CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
480     $                               RESULT( 3 ) )
481                        NT = 3
482*
483*                       Print information about the tests that did not
484*                       pass the threshold.
485*
486                        DO 60 K = 1, NT
487                           IF( RESULT( K ).GE.THRESH ) THEN
488                              IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
489     $                           CALL ALADHD( NOUT, PATH )
490                              WRITE( NOUT, FMT = 9999 )'DPPSV ', UPLO,
491     $                           N, IMAT, K, RESULT( K )
492                              NFAIL = NFAIL + 1
493                           END IF
494   60                   CONTINUE
495                        NRUN = NRUN + NT
496   70                   CONTINUE
497                     END IF
498*
499*                    --- Test DPPSVX ---
500*
501                     IF( .NOT.PREFAC .AND. NPP.GT.0 )
502     $                  CALL DLASET( 'Full', NPP, 1, ZERO, ZERO, AFAC,
503     $                               NPP )
504                     CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
505                     IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
506*
507*                       Equilibrate the matrix if FACT='F' and
508*                       EQUED='Y'.
509*
510                        CALL DLAQSP( UPLO, N, A, S, SCOND, AMAX, EQUED )
511                     END IF
512*
513*                    Solve the system and compute the condition number
514*                    and error bounds using DPPSVX.
515*
516                     SRNAMT = 'DPPSVX'
517                     CALL DPPSVX( FACT, UPLO, N, NRHS, A, AFAC, EQUED,
518     $                            S, B, LDA, X, LDA, RCOND, RWORK,
519     $                            RWORK( NRHS+1 ), WORK, IWORK, INFO )
520*
521*                    Check the error code from DPPSVX.
522*
523                     IF( INFO.NE.IZERO ) THEN
524                        CALL ALAERH( PATH, 'DPPSVX', INFO, IZERO,
525     $                               FACT // UPLO, N, N, -1, -1, NRHS,
526     $                               IMAT, NFAIL, NERRS, NOUT )
527                        GO TO 90
528                     END IF
529*
530                     IF( INFO.EQ.0 ) THEN
531                        IF( .NOT.PREFAC ) THEN
532*
533*                          Reconstruct matrix from factors and compute
534*                          residual.
535*
536                           CALL DPPT01( UPLO, N, A, AFAC,
537     $                                  RWORK( 2*NRHS+1 ), RESULT( 1 ) )
538                           K1 = 1
539                        ELSE
540                           K1 = 2
541                        END IF
542*
543*                       Compute residual of the computed solution.
544*
545                        CALL DLACPY( 'Full', N, NRHS, BSAV, LDA, WORK,
546     $                               LDA )
547                        CALL DPPT02( UPLO, N, NRHS, ASAV, X, LDA, WORK,
548     $                               LDA, RWORK( 2*NRHS+1 ),
549     $                               RESULT( 2 ) )
550*
551*                       Check solution from generated exact solution.
552*
553                        IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
554     $                      'N' ) ) ) THEN
555                           CALL DGET04( N, NRHS, X, LDA, XACT, LDA,
556     $                                  RCONDC, RESULT( 3 ) )
557                        ELSE
558                           CALL DGET04( N, NRHS, X, LDA, XACT, LDA,
559     $                                  ROLDC, RESULT( 3 ) )
560                        END IF
561*
562*                       Check the error bounds from iterative
563*                       refinement.
564*
565                        CALL DPPT05( UPLO, N, NRHS, ASAV, B, LDA, X,
566     $                               LDA, XACT, LDA, RWORK,
567     $                               RWORK( NRHS+1 ), RESULT( 4 ) )
568                     ELSE
569                        K1 = 6
570                     END IF
571*
572*                    Compare RCOND from DPPSVX with the computed value
573*                    in RCONDC.
574*
575                     RESULT( 6 ) = DGET06( RCOND, RCONDC )
576*
577*                    Print information about the tests that did not pass
578*                    the threshold.
579*
580                     DO 80 K = K1, 6
581                        IF( RESULT( K ).GE.THRESH ) THEN
582                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
583     $                        CALL ALADHD( NOUT, PATH )
584                           IF( PREFAC ) THEN
585                              WRITE( NOUT, FMT = 9997 )'DPPSVX', FACT,
586     $                           UPLO, N, EQUED, IMAT, K, RESULT( K )
587                           ELSE
588                              WRITE( NOUT, FMT = 9998 )'DPPSVX', FACT,
589     $                           UPLO, N, IMAT, K, RESULT( K )
590                           END IF
591                           NFAIL = NFAIL + 1
592                        END IF
593   80                CONTINUE
594                     NRUN = NRUN + 7 - K1
595   90                CONTINUE
596  100             CONTINUE
597  110          CONTINUE
598  120       CONTINUE
599  130    CONTINUE
600  140 CONTINUE
601*
602*     Print a summary of the results.
603*
604      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
605*
606 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
607     $      ', test(', I1, ')=', G12.5 )
608 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
609     $      ', type ', I1, ', test(', I1, ')=', G12.5 )
610 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
611     $      ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ')=',
612     $      G12.5 )
613      RETURN
614*
615*     End of DDRVPP
616*
617      END
618