1*> \brief \b SDRVSY
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 SDRVSY( 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*> SDRVSY tests the driver routines SSYSV 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 (NMAX*NMAX)
90*> \endverbatim
91*>
92*> \param[out] AFAC
93*> \verbatim
94*>          AFAC is REAL array, dimension (NMAX*NMAX)
95*> \endverbatim
96*>
97*> \param[out] AINV
98*> \verbatim
99*>          AINV is REAL array, dimension (NMAX*NMAX)
100*> \endverbatim
101*>
102*> \param[out] B
103*> \verbatim
104*>          B is REAL array, dimension (NMAX*NRHS)
105*> \endverbatim
106*>
107*> \param[out] X
108*> \verbatim
109*>          X is REAL array, dimension (NMAX*NRHS)
110*> \endverbatim
111*>
112*> \param[out] XACT
113*> \verbatim
114*>          XACT is REAL array, dimension (NMAX*NRHS)
115*> \endverbatim
116*>
117*> \param[out] WORK
118*> \verbatim
119*>          WORK is REAL array, dimension
120*>                      (NMAX*max(2,NRHS))
121*> \endverbatim
122*>
123*> \param[out] RWORK
124*> \verbatim
125*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
126*> \endverbatim
127*>
128*> \param[out] IWORK
129*> \verbatim
130*>          IWORK is INTEGER array, dimension (2*NMAX)
131*> \endverbatim
132*>
133*> \param[in] NOUT
134*> \verbatim
135*>          NOUT is INTEGER
136*>          The unit number for output.
137*> \endverbatim
138*
139*  Authors:
140*  ========
141*
142*> \author Univ. of Tennessee
143*> \author Univ. of California Berkeley
144*> \author Univ. of Colorado Denver
145*> \author NAG Ltd.
146*
147*> \date November 2011
148*
149*> \ingroup single_lin
150*
151*  =====================================================================
152      SUBROUTINE SDRVSY( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
153     $                   A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
154     $                   NOUT )
155*
156*  -- LAPACK test routine (version 3.4.0) --
157*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
158*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159*     November 2011
160*
161*     .. Scalar Arguments ..
162      LOGICAL            TSTERR
163      INTEGER            NMAX, NN, NOUT, NRHS
164      REAL               THRESH
165*     ..
166*     .. Array Arguments ..
167      LOGICAL            DOTYPE( * )
168      INTEGER            IWORK( * ), NVAL( * )
169      REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
170     $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
171*     ..
172*
173*  =====================================================================
174*
175*     .. Parameters ..
176      REAL               ONE, ZERO
177      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
178      INTEGER            NTYPES, NTESTS
179      PARAMETER          ( NTYPES = 10, NTESTS = 6 )
180      INTEGER            NFACT
181      PARAMETER          ( NFACT = 2 )
182*     ..
183*     .. Local Scalars ..
184      LOGICAL            ZEROT
185      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
186      CHARACTER*3        PATH
187      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
188     $                   IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
189     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
190      REAL               AINVNM, ANORM, CNDNUM, RCOND, RCONDC
191*     ..
192*     .. Local Arrays ..
193      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
194      INTEGER            ISEED( 4 ), ISEEDY( 4 )
195      REAL               RESULT( NTESTS )
196*     ..
197*     .. External Functions ..
198      REAL               SGET06, SLANSY
199      EXTERNAL           SGET06, SLANSY
200*     ..
201*     .. External Subroutines ..
202      EXTERNAL           ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
203     $                   SLARHS, SLASET, SLATB4, SLATMS, SPOT02, SPOT05,
204     $                   SSYSV, SSYSVX, SSYT01, SSYTRF, SSYTRI2, XLAENV
205*     ..
206*     .. Scalars in Common ..
207      LOGICAL            LERR, OK
208      CHARACTER*32       SRNAMT
209      INTEGER            INFOT, NUNIT
210*     ..
211*     .. Common blocks ..
212      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
213      COMMON             / SRNAMC / SRNAMT
214*     ..
215*     .. Intrinsic Functions ..
216      INTRINSIC          MAX, MIN
217*     ..
218*     .. Data statements ..
219      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
220      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
221*     ..
222*     .. Executable Statements ..
223*
224*     Initialize constants and the random number seed.
225*
226      PATH( 1: 1 ) = 'Single precision'
227      PATH( 2: 3 ) = 'SY'
228      NRUN = 0
229      NFAIL = 0
230      NERRS = 0
231      DO 10 I = 1, 4
232         ISEED( I ) = ISEEDY( I )
233   10 CONTINUE
234      LWORK = MAX( 2*NMAX, NMAX*NRHS )
235*
236*     Test the error exits
237*
238      IF( TSTERR )
239     $   CALL SERRVX( PATH, NOUT )
240      INFOT = 0
241*
242*     Set the block size and minimum block size for testing.
243*
244      NB = 1
245      NBMIN = 2
246      CALL XLAENV( 1, NB )
247      CALL XLAENV( 2, NBMIN )
248*
249*     Do for each value of N in NVAL
250*
251      DO 180 IN = 1, NN
252         N = NVAL( IN )
253         LDA = MAX( N, 1 )
254         XTYPE = 'N'
255         NIMAT = NTYPES
256         IF( N.LE.0 )
257     $      NIMAT = 1
258*
259         DO 170 IMAT = 1, NIMAT
260*
261*           Do the tests only if DOTYPE( IMAT ) is true.
262*
263            IF( .NOT.DOTYPE( IMAT ) )
264     $         GO TO 170
265*
266*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
267*
268            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
269            IF( ZEROT .AND. N.LT.IMAT-2 )
270     $         GO TO 170
271*
272*           Do first for UPLO = 'U', then for UPLO = 'L'
273*
274            DO 160 IUPLO = 1, 2
275               UPLO = UPLOS( IUPLO )
276*
277*              Set up parameters with SLATB4 and generate a test matrix
278*              with SLATMS.
279*
280               CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
281     $                      CNDNUM, DIST )
282*
283               SRNAMT = 'SLATMS'
284               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
285     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
286     $                      INFO )
287*
288*              Check error code from SLATMS.
289*
290               IF( INFO.NE.0 ) THEN
291                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
292     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
293                  GO TO 160
294               END IF
295*
296*              For types 3-6, zero one or more rows and columns of the
297*              matrix to test that INFO is returned correctly.
298*
299               IF( ZEROT ) THEN
300                  IF( IMAT.EQ.3 ) THEN
301                     IZERO = 1
302                  ELSE IF( IMAT.EQ.4 ) THEN
303                     IZERO = N
304                  ELSE
305                     IZERO = N / 2 + 1
306                  END IF
307*
308                  IF( IMAT.LT.6 ) THEN
309*
310*                    Set row and column IZERO to zero.
311*
312                     IF( IUPLO.EQ.1 ) THEN
313                        IOFF = ( IZERO-1 )*LDA
314                        DO 20 I = 1, IZERO - 1
315                           A( IOFF+I ) = ZERO
316   20                   CONTINUE
317                        IOFF = IOFF + IZERO
318                        DO 30 I = IZERO, N
319                           A( IOFF ) = ZERO
320                           IOFF = IOFF + LDA
321   30                   CONTINUE
322                     ELSE
323                        IOFF = IZERO
324                        DO 40 I = 1, IZERO - 1
325                           A( IOFF ) = ZERO
326                           IOFF = IOFF + LDA
327   40                   CONTINUE
328                        IOFF = IOFF - IZERO
329                        DO 50 I = IZERO, N
330                           A( IOFF+I ) = ZERO
331   50                   CONTINUE
332                     END IF
333                  ELSE
334                     IOFF = 0
335                     IF( IUPLO.EQ.1 ) THEN
336*
337*                       Set the first IZERO rows and columns to zero.
338*
339                        DO 70 J = 1, N
340                           I2 = MIN( J, IZERO )
341                           DO 60 I = 1, I2
342                              A( IOFF+I ) = ZERO
343   60                      CONTINUE
344                           IOFF = IOFF + LDA
345   70                   CONTINUE
346                     ELSE
347*
348*                       Set the last IZERO rows and columns to zero.
349*
350                        DO 90 J = 1, N
351                           I1 = MAX( J, IZERO )
352                           DO 80 I = I1, N
353                              A( IOFF+I ) = ZERO
354   80                      CONTINUE
355                           IOFF = IOFF + LDA
356   90                   CONTINUE
357                     END IF
358                  END IF
359               ELSE
360                  IZERO = 0
361               END IF
362*
363               DO 150 IFACT = 1, NFACT
364*
365*                 Do first for FACT = 'F', then for other values.
366*
367                  FACT = FACTS( IFACT )
368*
369*                 Compute the condition number for comparison with
370*                 the value returned by SSYSVX.
371*
372                  IF( ZEROT ) THEN
373                     IF( IFACT.EQ.1 )
374     $                  GO TO 150
375                     RCONDC = ZERO
376*
377                  ELSE IF( IFACT.EQ.1 ) THEN
378*
379*                    Compute the 1-norm of A.
380*
381                     ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
382*
383*                    Factor the matrix A.
384*
385                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
386                     CALL SSYTRF( UPLO, N, AFAC, LDA, IWORK, WORK,
387     $                            LWORK, INFO )
388*
389*                    Compute inv(A) and take its norm.
390*
391                     CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
392                     LWORK = (N+NB+1)*(NB+3)
393                     CALL SSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
394     $                            LWORK, INFO )
395                     AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, 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 SSYSV  ---
415*
416                  IF( IFACT.EQ.2 ) THEN
417                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
418                     CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
419*
420*                    Factor the matrix and solve the system using SSYSV.
421*
422                     SRNAMT = 'SSYSV '
423                     CALL SSYSV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
424     $                           LDA, WORK, LWORK, 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 SSYSV .
444*
445                     IF( INFO.NE.K ) THEN
446                        CALL ALAERH( PATH, 'SSYSV ', 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 SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
458     $                            AINV, LDA, RWORK, RESULT( 1 ) )
459*
460*                    Compute residual of the computed solution.
461*
462                     CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
463                     CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
464     $                            LDA, 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 )'SSYSV ', 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 SSYSVX ---
489*
490                  IF( IFACT.EQ.2 )
491     $               CALL SLASET( UPLO, N, N, ZERO, ZERO, AFAC, LDA )
492                  CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA )
493*
494*                 Solve the system and compute the condition number and
495*                 error bounds using SSYSVX.
496*
497                  SRNAMT = 'SSYSVX'
498                  CALL SSYSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
499     $                         IWORK, B, LDA, X, LDA, RCOND, RWORK,
500     $                         RWORK( NRHS+1 ), WORK, LWORK,
501     $                         IWORK( N+1 ), INFO )
502*
503*                 Adjust the expected value of INFO to account for
504*                 pivoting.
505*
506                  K = IZERO
507                  IF( K.GT.0 ) THEN
508  130                CONTINUE
509                     IF( IWORK( K ).LT.0 ) THEN
510                        IF( IWORK( K ).NE.-K ) THEN
511                           K = -IWORK( K )
512                           GO TO 130
513                        END IF
514                     ELSE IF( IWORK( K ).NE.K ) THEN
515                        K = IWORK( K )
516                        GO TO 130
517                     END IF
518                  END IF
519*
520*                 Check the error code from SSYSVX.
521*
522                  IF( INFO.NE.K ) THEN
523                     CALL ALAERH( PATH, 'SSYSVX', INFO, K, FACT // UPLO,
524     $                            N, N, -1, -1, NRHS, IMAT, NFAIL,
525     $                            NERRS, NOUT )
526                     GO TO 150
527                  END IF
528*
529                  IF( INFO.EQ.0 ) THEN
530                     IF( IFACT.GE.2 ) THEN
531*
532*                       Reconstruct matrix from factors and compute
533*                       residual.
534*
535                        CALL SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
536     $                               AINV, LDA, RWORK( 2*NRHS+1 ),
537     $                               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 SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
547     $                            LDA, 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 SPOT05( UPLO, N, NRHS, A, LDA, 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 SSYSVX 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 )'SSYSVX', 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 SDRVSY
599*
600      END
601