1*> \brief \b SDRVSY_AA
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_AA( 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_AA tests the driver routine SSYSV_AA.
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 (NMAX*max(2,NRHS))
120*> \endverbatim
121*>
122*> \param[out] RWORK
123*> \verbatim
124*>          RWORK is REAL array, dimension (NMAX+2*NRHS)
125*> \endverbatim
126*>
127*> \param[out] IWORK
128*> \verbatim
129*>          IWORK is INTEGER array, dimension (2*NMAX)
130*> \endverbatim
131*>
132*> \param[in] NOUT
133*> \verbatim
134*>          NOUT is INTEGER
135*>          The unit number for output.
136*> \endverbatim
137*
138*  Authors:
139*  ========
140*
141*> \author Univ. of Tennessee
142*> \author Univ. of California Berkeley
143*> \author Univ. of Colorado Denver
144*> \author NAG Ltd.
145*
146*> \ingroup real_lin
147*
148*  =====================================================================
149      SUBROUTINE SDRVSY_AA( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
150     $                      NMAX, A, AFAC, AINV, B, X, XACT, WORK,
151     $                      RWORK, IWORK, NOUT )
152*
153*  -- LAPACK test routine --
154*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
155*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157*     .. Scalar Arguments ..
158      LOGICAL            TSTERR
159      INTEGER            NMAX, NN, NOUT, NRHS
160      REAL               THRESH
161*     ..
162*     .. Array Arguments ..
163      LOGICAL            DOTYPE( * )
164      INTEGER            IWORK( * ), NVAL( * )
165      REAL               A( * ), AFAC( * ), AINV( * ), B( * ),
166     $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
167*     ..
168*
169*  =====================================================================
170*
171*     .. Parameters ..
172      REAL               ONE, ZERO
173      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
174      INTEGER            NTYPES, NTESTS
175      PARAMETER          ( NTYPES = 10, NTESTS = 3 )
176      INTEGER            NFACT
177      PARAMETER          ( NFACT = 2 )
178*     ..
179*     .. Local Scalars ..
180      LOGICAL            ZEROT
181      CHARACTER          DIST, FACT, TYPE, UPLO, XTYPE
182      CHARACTER*3        MATPATH, PATH
183      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
184     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
185     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
186      REAL               ANORM, CNDNUM
187*     ..
188*     .. Local Arrays ..
189      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
190      INTEGER            ISEED( 4 ), ISEEDY( 4 )
191      REAL               RESULT( NTESTS )
192*     ..
193*     .. External Functions ..
194      REAL               DGET06, SLANSY
195      EXTERNAL           DGET06, SLANSY
196*     ..
197*     .. External Subroutines ..
198      EXTERNAL           ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
199     $                   SLARHS, SLASET, SLATB4, SLATMS, SPOT02,
200     $                   SSYSV_AA, SSYT01_AA, SSYTRF_AA, XLAENV
201*     ..
202*     .. Scalars in Common ..
203      LOGICAL            LERR, OK
204      CHARACTER*32       SRNAMT
205      INTEGER            INFOT, NUNIT
206*     ..
207*     .. Common blocks ..
208      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
209      COMMON             / SRNAMC / SRNAMT
210*     ..
211*     .. Intrinsic Functions ..
212      INTRINSIC          MAX, MIN
213*     ..
214*     .. Data statements ..
215      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
216      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
217*     ..
218*     .. Executable Statements ..
219*
220*     Initialize constants and the random number seed.
221*
222*     Test path
223*
224      PATH( 1: 1 ) = 'Single precision'
225      PATH( 2: 3 ) = 'SA'
226*
227*     Path to generate matrices
228*
229      MATPATH( 1: 1 ) = 'Single precision'
230      MATPATH( 2: 3 ) = 'SY'
231*
232      NRUN = 0
233      NFAIL = 0
234      NERRS = 0
235      DO 10 I = 1, 4
236         ISEED( I ) = ISEEDY( I )
237   10 CONTINUE
238*
239*     Test the error exits
240*
241      IF( TSTERR )
242     $   CALL SERRVX( PATH, NOUT )
243      INFOT = 0
244*
245*     Set the block size and minimum block size for testing.
246*
247      NB = 1
248      NBMIN = 2
249      CALL XLAENV( 1, NB )
250      CALL XLAENV( 2, NBMIN )
251*
252*     Do for each value of N in NVAL
253*
254      DO 180 IN = 1, NN
255         N = NVAL( IN )
256         LWORK = MAX( 3*N-2, N*(1+NB) )
257         LWORK = MAX( LWORK, 1 )
258         LDA = MAX( N, 1 )
259         XTYPE = 'N'
260         NIMAT = NTYPES
261         IF( N.LE.0 )
262     $      NIMAT = 1
263*
264         DO 170 IMAT = 1, NIMAT
265*
266*           Do the tests only if DOTYPE( IMAT ) is true.
267*
268            IF( .NOT.DOTYPE( IMAT ) )
269     $         GO TO 170
270*
271*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
272*
273            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
274            IF( ZEROT .AND. N.LT.IMAT-2 )
275     $         GO TO 170
276*
277*           Do first for UPLO = 'U', then for UPLO = 'L'
278*
279            DO 160 IUPLO = 1, 2
280               UPLO = UPLOS( IUPLO )
281*
282*              Set up parameters with SLATB4 and generate a test matrix
283*              with SLATMS.
284*
285               CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
286     $                      MODE, CNDNUM, DIST )
287*
288               SRNAMT = 'SLATMS'
289               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
290     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
291     $                      INFO )
292*
293*              Check error code from SLATMS.
294*
295               IF( INFO.NE.0 ) THEN
296                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
297     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
298                  GO TO 160
299               END IF
300*
301*              For types 3-6, zero one or more rows and columns of the
302*              matrix to test that INFO is returned correctly.
303*
304               IF( ZEROT ) THEN
305                  IF( IMAT.EQ.3 ) THEN
306                     IZERO = 1
307                  ELSE IF( IMAT.EQ.4 ) THEN
308                     IZERO = N
309                  ELSE
310                     IZERO = N / 2 + 1
311                  END IF
312*
313                  IF( IMAT.LT.6 ) THEN
314*
315*                    Set row and column IZERO to zero.
316*
317                     IF( IUPLO.EQ.1 ) THEN
318                        IOFF = ( IZERO-1 )*LDA
319                        DO 20 I = 1, IZERO - 1
320                           A( IOFF+I ) = ZERO
321   20                   CONTINUE
322                        IOFF = IOFF + IZERO
323                        DO 30 I = IZERO, N
324                           A( IOFF ) = ZERO
325                           IOFF = IOFF + LDA
326   30                   CONTINUE
327                     ELSE
328                        IOFF = IZERO
329                        DO 40 I = 1, IZERO - 1
330                           A( IOFF ) = ZERO
331                           IOFF = IOFF + LDA
332   40                   CONTINUE
333                        IOFF = IOFF - IZERO
334                        DO 50 I = IZERO, N
335                           A( IOFF+I ) = ZERO
336   50                   CONTINUE
337                     END IF
338                  ELSE
339                     IOFF = 0
340                     IF( IUPLO.EQ.1 ) THEN
341*
342*                       Set the first IZERO rows and columns to zero.
343*
344                        DO 70 J = 1, N
345                           I2 = MIN( J, IZERO )
346                           DO 60 I = 1, I2
347                              A( IOFF+I ) = ZERO
348   60                      CONTINUE
349                           IOFF = IOFF + LDA
350   70                   CONTINUE
351                        IZERO = 1
352                     ELSE
353*
354*                       Set the last IZERO rows and columns to zero.
355*
356                        DO 90 J = 1, N
357                           I1 = MAX( J, IZERO )
358                           DO 80 I = I1, N
359                              A( IOFF+I ) = ZERO
360   80                      CONTINUE
361                           IOFF = IOFF + LDA
362   90                   CONTINUE
363                     END IF
364                  END IF
365               ELSE
366                  IZERO = 0
367               END IF
368*
369               DO 150 IFACT = 1, NFACT
370*
371*                 Do first for FACT = 'F', then for other values.
372*
373                  FACT = FACTS( IFACT )
374*
375*                 Form an exact solution and set the right hand side.
376*
377                  SRNAMT = 'SLARHS'
378                  CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
379     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
380     $                         INFO )
381                  XTYPE = 'C'
382*
383*                 --- Test SSYSV_AA  ---
384*
385                  IF( IFACT.EQ.2 ) THEN
386                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
387                     CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
388*
389*                    Factor the matrix and solve the system using SSYSV_AA.
390*
391                     SRNAMT = 'SSYSV_AA'
392                     CALL SSYSV_AA( UPLO, N, NRHS, AFAC, LDA, IWORK,
393     $                                 X, LDA, WORK, LWORK, INFO )
394*
395*                    Adjust the expected value of INFO to account for
396*                    pivoting.
397*
398                     IF( IZERO.GT.0 ) THEN
399                        J = 1
400                        K = IZERO
401  100                   CONTINUE
402                        IF( J.EQ.K ) THEN
403                           K = IWORK( J )
404                        ELSE IF( IWORK( J ).EQ.K ) THEN
405                           K = J
406                        END IF
407                        IF( J.LT.K ) THEN
408                           J = J + 1
409                           GO TO 100
410                        END IF
411                     ELSE
412                        K = 0
413                     END IF
414*
415*                    Check error code from SSYSV_AA .
416*
417                     IF( INFO.NE.K ) THEN
418                        CALL ALAERH( PATH, 'SSYSV_AA ', INFO, K,
419     $                               UPLO, N, N, -1, -1, NRHS,
420     $                               IMAT, NFAIL, NERRS, NOUT )
421                        GO TO 120
422                     ELSE IF( INFO.NE.0 ) THEN
423                        GO TO 120
424                     END IF
425*
426*                    Reconstruct matrix from factors and compute
427*                    residual.
428*
429                     CALL SSYT01_AA( UPLO, N, A, LDA, AFAC, LDA,
430     $                                  IWORK, AINV, LDA, RWORK,
431     $                                  RESULT( 1 ) )
432*
433*                    Compute residual of the computed solution.
434*
435                     CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
436                     CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
437     $                            LDA, RWORK, RESULT( 2 ) )
438                     NT = 2
439*
440*                    Print information about the tests that did not pass
441*                    the threshold.
442*
443                     DO 110 K = 1, NT
444                        IF( RESULT( K ).GE.THRESH ) THEN
445                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
446     $                        CALL ALADHD( NOUT, PATH )
447                           WRITE( NOUT, FMT = 9999 )'SSYSV_AA ',
448     $                        UPLO, N, IMAT, K, RESULT( K )
449                           NFAIL = NFAIL + 1
450                        END IF
451  110                CONTINUE
452                     NRUN = NRUN + NT
453  120                CONTINUE
454                  END IF
455*
456  150          CONTINUE
457*
458  160       CONTINUE
459  170    CONTINUE
460  180 CONTINUE
461*
462*     Print a summary of the results.
463*
464      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
465*
466 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
467     $      ', test ', I2, ', ratio =', G12.5 )
468      RETURN
469*
470*     End of SDRVSY_AA
471*
472      END
473