1*> \brief \b SDRVSP
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 SDRVSP( 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*       REAL               THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NVAL( * )
23*       REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
24*      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
25*       ..
26*
27*
28*> \par Purpose:
29*  =============
30*>
31*> \verbatim
32*>
33*> SDRVSP tests the driver routines SSPSV and -SVX.
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] DOTYPE
40*> \verbatim
41*>          DOTYPE is LOGICAL array, dimension (NTYPES)
42*>          The matrix types to be used for testing.  Matrices of type j
43*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45*> \endverbatim
46*>
47*> \param[in] NN
48*> \verbatim
49*>          NN is INTEGER
50*>          The number of values of N contained in the vector NVAL.
51*> \endverbatim
52*>
53*> \param[in] NVAL
54*> \verbatim
55*>          NVAL is INTEGER array, dimension (NN)
56*>          The values of the matrix dimension N.
57*> \endverbatim
58*>
59*> \param[in] NRHS
60*> \verbatim
61*>          NRHS is INTEGER
62*>          The number of right hand side vectors to be generated for
63*>          each linear system.
64*> \endverbatim
65*>
66*> \param[in] THRESH
67*> \verbatim
68*>          THRESH is REAL
69*>          The threshold value for the test ratios.  A result is
70*>          included in the output file if RESULT >= THRESH.  To have
71*>          every test ratio printed, use THRESH = 0.
72*> \endverbatim
73*>
74*> \param[in] TSTERR
75*> \verbatim
76*>          TSTERR is LOGICAL
77*>          Flag that indicates whether error exits are to be tested.
78*> \endverbatim
79*>
80*> \param[in] NMAX
81*> \verbatim
82*>          NMAX is INTEGER
83*>          The maximum value permitted for N, used in dimensioning the
84*>          work arrays.
85*> \endverbatim
86*>
87*> \param[out] A
88*> \verbatim
89*>          A is REAL array, dimension
90*>                      (NMAX*(NMAX+1)/2)
91*> \endverbatim
92*>
93*> \param[out] AFAC
94*> \verbatim
95*>          AFAC is REAL array, dimension
96*>                      (NMAX*(NMAX+1)/2)
97*> \endverbatim
98*>
99*> \param[out] AINV
100*> \verbatim
101*>          AINV is REAL array, dimension
102*>                      (NMAX*(NMAX+1)/2)
103*> \endverbatim
104*>
105*> \param[out] B
106*> \verbatim
107*>          B is REAL array, dimension (NMAX*NRHS)
108*> \endverbatim
109*>
110*> \param[out] X
111*> \verbatim
112*>          X is REAL array, dimension (NMAX*NRHS)
113*> \endverbatim
114*>
115*> \param[out] XACT
116*> \verbatim
117*>          XACT is REAL array, dimension (NMAX*NRHS)
118*> \endverbatim
119*>
120*> \param[out] WORK
121*> \verbatim
122*>          WORK is REAL array, dimension
123*>                      (NMAX*max(2,NRHS))
124*> \endverbatim
125*>
126*> \param[out] RWORK
127*> \verbatim
128*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
129*> \endverbatim
130*>
131*> \param[out] IWORK
132*> \verbatim
133*>          IWORK is INTEGER array, dimension (2*NMAX)
134*> \endverbatim
135*>
136*> \param[in] NOUT
137*> \verbatim
138*>          NOUT is INTEGER
139*>          The unit number for output.
140*> \endverbatim
141*
142*  Authors:
143*  ========
144*
145*> \author Univ. of Tennessee
146*> \author Univ. of California Berkeley
147*> \author Univ. of Colorado Denver
148*> \author NAG Ltd.
149*
150*> \date December 2016
151*
152*> \ingroup single_lin
153*
154*  =====================================================================
155      SUBROUTINE SDRVSP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
156     $                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
157     $                   NOUT )
158*
159*  -- LAPACK test routine (version 3.7.0) --
160*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
161*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162*     December 2016
163*
164*     .. Scalar Arguments ..
165      LOGICAL            TSTERR
166      INTEGER            NMAX, NN, NOUT, NRHS
167      REAL               THRESH
168*     ..
169*     .. Array Arguments ..
170      LOGICAL            DOTYPE( * )
171      INTEGER            IWORK( * ), NVAL( * )
172      REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
173     $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
174*     ..
175*
176*  =====================================================================
177*
178*     .. Parameters ..
179      REAL               ONE, ZERO
180      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
181      INTEGER            NTYPES, NTESTS
182      PARAMETER          ( NTYPES = 10, NTESTS = 6 )
183      INTEGER            NFACT
184      PARAMETER          ( NFACT = 2 )
185*     ..
186*     .. Local Scalars ..
187      LOGICAL            ZEROT
188      CHARACTER          DIST, FACT, PACKIT, TYPE, UPLO, XTYPE
189      CHARACTER*3        PATH
190      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
191     $                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
192     $                   NERRS, NFAIL, NIMAT, NPP, NRUN, NT
193      REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC
194*     ..
195*     .. Local Arrays ..
196      CHARACTER          FACTS( NFACT )
197      INTEGER            ISEED( 4 ), ISEEDY( 4 )
198      REAL               RESULT( NTESTS )
199*     ..
200*     .. External Functions ..
201      REAL               SGET06, SLANSP
202      EXTERNAL           SGET06, SLANSP
203*     ..
204*     .. External Subroutines ..
205      EXTERNAL           ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04,
206     $                   SLACPY, SLARHS, SLASET, SLATB4, SLATMS, SPPT02,
207     $                   SPPT05, SSPSV, SSPSVX, SSPT01, SSPTRF, SSPTRI
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          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 ) = 'Single 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      LWORK = MAX( 2*NMAX, NMAX*NRHS )
238*
239*     Test the error exits
240*
241      IF( TSTERR )
242     $   CALL SERRVX( PATH, NOUT )
243      INFOT = 0
244*
245*     Do for each value of N in NVAL
246*
247      DO 180 IN = 1, NN
248         N = NVAL( IN )
249         LDA = MAX( N, 1 )
250         NPP = N*( N+1 ) / 2
251         XTYPE = 'N'
252         NIMAT = NTYPES
253         IF( N.LE.0 )
254     $      NIMAT = 1
255*
256         DO 170 IMAT = 1, NIMAT
257*
258*           Do the tests only if DOTYPE( IMAT ) is true.
259*
260            IF( .NOT.DOTYPE( IMAT ) )
261     $         GO TO 170
262*
263*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
264*
265            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
266            IF( ZEROT .AND. N.LT.IMAT-2 )
267     $         GO TO 170
268*
269*           Do first for UPLO = 'U', then for UPLO = 'L'
270*
271            DO 160 IUPLO = 1, 2
272               IF( IUPLO.EQ.1 ) THEN
273                  UPLO = 'U'
274                  PACKIT = 'C'
275               ELSE
276                  UPLO = 'L'
277                  PACKIT = 'R'
278               END IF
279*
280*              Set up parameters with SLATB4 and generate a test matrix
281*              with SLATMS.
282*
283               CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
284     $                      CNDNUM, DIST )
285*
286               SRNAMT = 'SLATMS'
287               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
288     $                      CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
289     $                      INFO )
290*
291*              Check error code from SLATMS.
292*
293               IF( INFO.NE.0 ) THEN
294                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
295     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
296                  GO TO 160
297               END IF
298*
299*              For types 3-6, zero one or more rows and columns of the
300*              matrix to test that INFO is returned correctly.
301*
302               IF( ZEROT ) THEN
303                  IF( IMAT.EQ.3 ) THEN
304                     IZERO = 1
305                  ELSE IF( IMAT.EQ.4 ) THEN
306                     IZERO = N
307                  ELSE
308                     IZERO = N / 2 + 1
309                  END IF
310*
311                  IF( IMAT.LT.6 ) THEN
312*
313*                    Set row and column IZERO to zero.
314*
315                     IF( IUPLO.EQ.1 ) THEN
316                        IOFF = ( IZERO-1 )*IZERO / 2
317                        DO 20 I = 1, IZERO - 1
318                           A( IOFF+I ) = ZERO
319   20                   CONTINUE
320                        IOFF = IOFF + IZERO
321                        DO 30 I = IZERO, N
322                           A( IOFF ) = ZERO
323                           IOFF = IOFF + I
324   30                   CONTINUE
325                     ELSE
326                        IOFF = IZERO
327                        DO 40 I = 1, IZERO - 1
328                           A( IOFF ) = ZERO
329                           IOFF = IOFF + N - I
330   40                   CONTINUE
331                        IOFF = IOFF - IZERO
332                        DO 50 I = IZERO, N
333                           A( IOFF+I ) = ZERO
334   50                   CONTINUE
335                     END IF
336                  ELSE
337                     IOFF = 0
338                     IF( IUPLO.EQ.1 ) THEN
339*
340*                       Set the first IZERO rows and columns to zero.
341*
342                        DO 70 J = 1, N
343                           I2 = MIN( J, IZERO )
344                           DO 60 I = 1, I2
345                              A( IOFF+I ) = ZERO
346   60                      CONTINUE
347                           IOFF = IOFF + J
348   70                   CONTINUE
349                     ELSE
350*
351*                       Set the last IZERO rows and columns to zero.
352*
353                        DO 90 J = 1, N
354                           I1 = MAX( J, IZERO )
355                           DO 80 I = I1, N
356                              A( IOFF+I ) = ZERO
357   80                      CONTINUE
358                           IOFF = IOFF + N - J
359   90                   CONTINUE
360                     END IF
361                  END IF
362               ELSE
363                  IZERO = 0
364               END IF
365*
366               DO 150 IFACT = 1, NFACT
367*
368*                 Do first for FACT = 'F', then for other values.
369*
370                  FACT = FACTS( IFACT )
371*
372*                 Compute the condition number for comparison with
373*                 the value returned by SSPSVX.
374*
375                  IF( ZEROT ) THEN
376                     IF( IFACT.EQ.1 )
377     $                  GO TO 150
378                     RCONDC = ZERO
379*
380                  ELSE IF( IFACT.EQ.1 ) THEN
381*
382*                    Compute the 1-norm of A.
383*
384                     ANORM = SLANSP( '1', UPLO, N, A, RWORK )
385*
386*                    Factor the matrix A.
387*
388                     CALL SCOPY( NPP, A, 1, AFAC, 1 )
389                     CALL SSPTRF( UPLO, N, AFAC, IWORK, INFO )
390*
391*                    Compute inv(A) and take its norm.
392*
393                     CALL SCOPY( NPP, AFAC, 1, AINV, 1 )
394                     CALL SSPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
395                     AINVNM = SLANSP( '1', UPLO, N, AINV, RWORK )
396*
397*                    Compute the 1-norm condition number of A.
398*
399                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
400                        RCONDC = ONE
401                     ELSE
402                        RCONDC = ( ONE / ANORM ) / AINVNM
403                     END IF
404                  END IF
405*
406*                 Form an exact solution and set the right hand side.
407*
408                  SRNAMT = 'SLARHS'
409                  CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
410     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
411     $                         INFO )
412                  XTYPE = 'C'
413*
414*                 --- Test SSPSV  ---
415*
416                  IF( IFACT.EQ.2 ) THEN
417                     CALL SCOPY( NPP, A, 1, AFAC, 1 )
418                     CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
419*
420*                    Factor the matrix and solve the system using SSPSV.
421*
422                     SRNAMT = 'SSPSV '
423                     CALL SSPSV( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
424     $                           INFO )
425*
426*                    Adjust the expected value of INFO to account for
427*                    pivoting.
428*
429                     K = IZERO
430                     IF( K.GT.0 ) THEN
431  100                   CONTINUE
432                        IF( IWORK( K ).LT.0 ) THEN
433                           IF( IWORK( K ).NE.-K ) THEN
434                              K = -IWORK( K )
435                              GO TO 100
436                           END IF
437                        ELSE IF( IWORK( K ).NE.K ) THEN
438                           K = IWORK( K )
439                           GO TO 100
440                        END IF
441                     END IF
442*
443*                    Check error code from SSPSV .
444*
445                     IF( INFO.NE.K ) THEN
446                        CALL ALAERH( PATH, 'SSPSV ', INFO, K, UPLO, N,
447     $                               N, -1, -1, NRHS, IMAT, NFAIL,
448     $                               NERRS, NOUT )
449                        GO TO 120
450                     ELSE IF( INFO.NE.0 ) THEN
451                        GO TO 120
452                     END IF
453*
454*                    Reconstruct matrix from factors and compute
455*                    residual.
456*
457                     CALL SSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
458     $                            RWORK, RESULT( 1 ) )
459*
460*                    Compute residual of the computed solution.
461*
462                     CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
463                     CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
464     $                            RWORK, RESULT( 2 ) )
465*
466*                    Check solution from generated exact solution.
467*
468                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
469     $                            RESULT( 3 ) )
470                     NT = 3
471*
472*                    Print information about the tests that did not pass
473*                    the threshold.
474*
475                     DO 110 K = 1, NT
476                        IF( RESULT( K ).GE.THRESH ) THEN
477                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
478     $                        CALL ALADHD( NOUT, PATH )
479                           WRITE( NOUT, FMT = 9999 )'SSPSV ', UPLO, N,
480     $                        IMAT, K, RESULT( K )
481                           NFAIL = NFAIL + 1
482                        END IF
483  110                CONTINUE
484                     NRUN = NRUN + NT
485  120                CONTINUE
486                  END IF
487*
488*                 --- Test SSPSVX ---
489*
490                  IF( IFACT.EQ.2 .AND. NPP.GT.0 )
491     $               CALL SLASET( 'Full', NPP, 1, ZERO, ZERO, AFAC,
492     $                            NPP )
493                  CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
494*
495*                 Solve the system and compute the condition number and
496*                 error bounds using SSPSVX.
497*
498                  SRNAMT = 'SSPSVX'
499                  CALL SSPSVX( FACT, UPLO, N, NRHS, A, AFAC, IWORK, B,
500     $                         LDA, X, LDA, RCOND, RWORK,
501     $                         RWORK( NRHS+1 ), WORK, IWORK( N+1 ),
502     $                         INFO )
503*
504*                 Adjust the expected value of INFO to account for
505*                 pivoting.
506*
507                  K = IZERO
508                  IF( K.GT.0 ) THEN
509  130                CONTINUE
510                     IF( IWORK( K ).LT.0 ) THEN
511                        IF( IWORK( K ).NE.-K ) THEN
512                           K = -IWORK( K )
513                           GO TO 130
514                        END IF
515                     ELSE IF( IWORK( K ).NE.K ) THEN
516                        K = IWORK( K )
517                        GO TO 130
518                     END IF
519                  END IF
520*
521*                 Check the error code from SSPSVX.
522*
523                  IF( INFO.NE.K ) THEN
524                     CALL ALAERH( PATH, 'SSPSVX', INFO, K, FACT // UPLO,
525     $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
526     $                            NERRS, NOUT )
527                     GO TO 150
528                  END IF
529*
530                  IF( INFO.EQ.0 ) THEN
531                     IF( IFACT.GE.2 ) THEN
532*
533*                       Reconstruct matrix from factors and compute
534*                       residual.
535*
536                        CALL SSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
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 SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
546                     CALL SPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
547     $                            RWORK( 2*NRHS+1 ), RESULT( 2 ) )
548*
549*                    Check solution from generated exact solution.
550*
551                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
552     $                            RESULT( 3 ) )
553*
554*                    Check the error bounds from iterative refinement.
555*
556                     CALL SPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA,
557     $                            XACT, LDA, RWORK, RWORK( NRHS+1 ),
558     $                            RESULT( 4 ) )
559                  ELSE
560                     K1 = 6
561                  END IF
562*
563*                 Compare RCOND from SSPSVX with the computed value
564*                 in RCONDC.
565*
566                  RESULT( 6 ) = SGET06( RCOND, RCONDC )
567*
568*                 Print information about the tests that did not pass
569*                 the threshold.
570*
571                  DO 140 K = K1, 6
572                     IF( RESULT( K ).GE.THRESH ) THEN
573                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
574     $                     CALL ALADHD( NOUT, PATH )
575                        WRITE( NOUT, FMT = 9998 )'SSPSVX', FACT, UPLO,
576     $                     N, IMAT, K, RESULT( K )
577                        NFAIL = NFAIL + 1
578                     END IF
579  140             CONTINUE
580                  NRUN = NRUN + 7 - K1
581*
582  150          CONTINUE
583*
584  160       CONTINUE
585  170    CONTINUE
586  180 CONTINUE
587*
588*     Print a summary of the results.
589*
590      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
591*
592 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
593     $      ', test ', I2, ', ratio =', G12.5 )
594 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
595     $      ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
596      RETURN
597*
598*     End of SDRVSP
599*
600      END
601