1*> \brief \b SCHKSY_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 SCHKSY_AA( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12*                             THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13*                             XACT, WORK, RWORK, IWORK, NOUT )
14*
15*       .. Scalar Arguments ..
16*       LOGICAL    TSTERR
17*       INTEGER    NMAX, NN, NNB, NNS, NOUT
18*       REAL       THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL    DOTYPE( * )
22*       INTEGER    IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23*       REAL       A( * ), AFAC( * ), AINV( * ), B( * ),
24*      $           RWORK( * ), WORK( * ), X( * ), XACT( * )
25*       ..
26*
27*
28*> \par Purpose:
29*  =============
30*>
31*> \verbatim
32*>
33*> SCHKSY_AA tests SSYTRF_AA, -TRS_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] NNB
60*> \verbatim
61*>          NNB is INTEGER
62*>          The number of values of NB contained in the vector NBVAL.
63*> \endverbatim
64*>
65*> \param[in] NBVAL
66*> \verbatim
67*>          NBVAL is INTEGER array, dimension (NNB)
68*>          The values of the blocksize NB.
69*> \endverbatim
70*>
71*> \param[in] NNS
72*> \verbatim
73*>          NNS is INTEGER
74*>          The number of values of NRHS contained in the vector NSVAL.
75*> \endverbatim
76*>
77*> \param[in] NSVAL
78*> \verbatim
79*>          NSVAL is INTEGER array, dimension (NNS)
80*>          The values of the number of right hand sides NRHS.
81*> \endverbatim
82*>
83*> \param[in] THRESH
84*> \verbatim
85*>          THRESH is REAL
86*>          The threshold value for the test ratios.  A result is
87*>          included in the output file if RESULT >= THRESH.  To have
88*>          every test ratio printed, use THRESH = 0.
89*> \endverbatim
90*>
91*> \param[in] TSTERR
92*> \verbatim
93*>          TSTERR is LOGICAL
94*>          Flag that indicates whether error exits are to be tested.
95*> \endverbatim
96*>
97*> \param[in] NMAX
98*> \verbatim
99*>          NMAX is INTEGER
100*>          The maximum value permitted for N, used in dimensioning the
101*>          work arrays.
102*> \endverbatim
103*>
104*> \param[out] A
105*> \verbatim
106*>          A is REAL array, dimension (NMAX*NMAX)
107*> \endverbatim
108*>
109*> \param[out] AFAC
110*> \verbatim
111*>          AFAC is REAL array, dimension (NMAX*NMAX)
112*> \endverbatim
113*>
114*> \param[out] AINV
115*> \verbatim
116*>          AINV is REAL array, dimension (NMAX*NMAX)
117*> \endverbatim
118*>
119*> \param[out] B
120*> \verbatim
121*>          B is REAL array, dimension (NMAX*NSMAX)
122*>          where NSMAX is the largest entry in NSVAL.
123*> \endverbatim
124*>
125*> \param[out] X
126*> \verbatim
127*>          X is REAL array, dimension (NMAX*NSMAX)
128*> \endverbatim
129*>
130*> \param[out] XACT
131*> \verbatim
132*>          XACT is REAL array, dimension (NMAX*NSMAX)
133*> \endverbatim
134*>
135*> \param[out] WORK
136*> \verbatim
137*>          WORK is REAL array, dimension (NMAX*max(3,NSMAX))
138*> \endverbatim
139*>
140*> \param[out] RWORK
141*> \verbatim
142*>          RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
143*> \endverbatim
144*>
145*> \param[out] IWORK
146*> \verbatim
147*>          IWORK is INTEGER array, dimension (2*NMAX)
148*> \endverbatim
149*>
150*> \param[in] NOUT
151*> \verbatim
152*>          NOUT is INTEGER
153*>          The unit number for output.
154*> \endverbatim
155*
156*  Authors:
157*  ========
158*
159*> \author Univ. of Tennessee
160*> \author Univ. of California Berkeley
161*> \author Univ. of Colorado Denver
162*> \author NAG Ltd.
163*
164*> \ingroup real_lin
165*
166*  =====================================================================
167      SUBROUTINE SCHKSY_AA( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
168     $                      THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
169     $                      X, XACT, WORK, RWORK, IWORK, NOUT )
170*
171*  -- LAPACK test routine --
172*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
173*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174*
175      IMPLICIT NONE
176*
177*     .. Scalar Arguments ..
178      LOGICAL      TSTERR
179      INTEGER      NN, NNB, NNS, NMAX, NOUT
180      REAL         THRESH
181*     ..
182*     .. Array Arguments ..
183      LOGICAL      DOTYPE( * )
184      INTEGER      IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
185      REAL         A( * ), AFAC( * ), AINV( * ), B( * ),
186     $             RWORK( * ), WORK( * ), X( * ), XACT( * )
187*     ..
188*
189*  =====================================================================
190*
191*     .. Parameters ..
192      REAL         ZERO
193      PARAMETER    ( ZERO = 0.0E+0 )
194      INTEGER      NTYPES
195      PARAMETER    ( NTYPES = 10 )
196      INTEGER      NTESTS
197      PARAMETER    ( NTESTS = 9 )
198*     ..
199*     .. Local Scalars ..
200      LOGICAL      ZEROT
201      CHARACTER    DIST, TYPE, UPLO, XTYPE
202      CHARACTER*3  PATH, MATPATH
203      INTEGER      I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
204     $             IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
205     $             N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
206      REAL         ANORM, CNDNUM
207*     ..
208*     .. Local Arrays ..
209      CHARACTER    UPLOS( 2 )
210      INTEGER      ISEED( 4 ), ISEEDY( 4 )
211      REAL         RESULT( NTESTS )
212*     ..
213*     .. External Subroutines ..
214      EXTERNAL           ALAERH, ALAHD, ALASUM, SERRSY, SLACPY, SLARHS,
215     $                   SLATB4, SLATMS, SPOT02, SSYT01_AA, SSYTRF_AA,
216     $                   SSYTRS_AA, XLAENV
217*     ..
218*     .. Intrinsic Functions ..
219      INTRINSIC    MAX, MIN
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*     .. Data statements ..
231      DATA         ISEEDY / 1988, 1989, 1990, 1991 /
232      DATA         UPLOS / 'U', 'L' /
233*     ..
234*     .. Executable Statements ..
235*
236*     Initialize constants and the random number seed.
237*
238*
239*     Test path
240*
241      PATH( 1: 1 ) = 'Single precision'
242      PATH( 2: 3 ) = 'SA'
243*
244*     Path to generate matrices
245*
246      MATPATH( 1: 1 ) = 'Single precision'
247      MATPATH( 2: 3 ) = 'SY'
248      NRUN = 0
249      NFAIL = 0
250      NERRS = 0
251      DO 10 I = 1, 4
252         ISEED( I ) = ISEEDY( I )
253   10 CONTINUE
254*
255*     Test the error exits
256*
257      IF( TSTERR )
258     $   CALL SERRSY( PATH, NOUT )
259      INFOT = 0
260*
261*     Set the minimum block size for which the block routine should
262*     be used, which will be later returned by ILAENV
263*
264      CALL XLAENV( 2, 2 )
265*
266*     Do for each value of N in NVAL
267*
268      DO 180 IN = 1, NN
269         N = NVAL( IN )
270         IF( N .GT. NMAX ) THEN
271            NFAIL = NFAIL + 1
272            WRITE(NOUT, 9995) 'M ', N, NMAX
273            GO TO 180
274         END IF
275         LDA = MAX( N, 1 )
276         XTYPE = 'N'
277         NIMAT = NTYPES
278         IF( N.LE.0 )
279     $      NIMAT = 1
280*
281         IZERO = 0
282*
283*        Do for each value of matrix type IMAT
284*
285         DO 170 IMAT = 1, NIMAT
286*
287*           Do the tests only if DOTYPE( IMAT ) is true.
288*
289            IF( .NOT.DOTYPE( IMAT ) )
290     $         GO TO 170
291*
292*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
293*
294            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
295            IF( ZEROT .AND. N.LT.IMAT-2 )
296     $         GO TO 170
297*
298*           Do first for UPLO = 'U', then for UPLO = 'L'
299*
300            DO 160 IUPLO = 1, 2
301               UPLO = UPLOS( IUPLO )
302*
303*              Begin generate the test matrix A.
304*
305*
306*              Set up parameters with SLATB4 for the matrix generator
307*              based on the type of matrix to be generated.
308*
309               CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU,
310     $                      ANORM, MODE, CNDNUM, DIST )
311*
312*              Generate a matrix with SLATMS.
313*
314               SRNAMT = 'SLATMS'
315               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
316     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
317     $                      INFO )
318*
319*              Check error code from SLATMS and handle error.
320*
321               IF( INFO.NE.0 ) THEN
322                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
323     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
324*
325*                    Skip all tests for this generated matrix
326*
327                  GO TO 160
328               END IF
329*
330*              For matrix types 3-6, zero one or more rows and
331*              columns of the matrix to test that INFO is returned
332*              correctly.
333*
334               IF( ZEROT ) THEN
335                  IF( IMAT.EQ.3 ) THEN
336                     IZERO = 1
337                  ELSE IF( IMAT.EQ.4 ) THEN
338                     IZERO = N
339                  ELSE
340                     IZERO = N / 2 + 1
341                  END IF
342*
343                  IF( IMAT.LT.6 ) THEN
344*
345*                    Set row and column IZERO to zero.
346*
347                     IF( IUPLO.EQ.1 ) THEN
348                        IOFF = ( IZERO-1 )*LDA
349                        DO 20 I = 1, IZERO - 1
350                           A( IOFF+I ) = ZERO
351   20                   CONTINUE
352                        IOFF = IOFF + IZERO
353                        DO 30 I = IZERO, N
354                           A( IOFF ) = ZERO
355                           IOFF = IOFF + LDA
356   30                   CONTINUE
357                     ELSE
358                        IOFF = IZERO
359                        DO 40 I = 1, IZERO - 1
360                           A( IOFF ) = ZERO
361                           IOFF = IOFF + LDA
362   40                   CONTINUE
363                        IOFF = IOFF - IZERO
364                        DO 50 I = IZERO, N
365                           A( IOFF+I ) = ZERO
366   50                   CONTINUE
367                     END IF
368                  ELSE
369                     IF( IUPLO.EQ.1 ) THEN
370*
371*                       Set the first IZERO rows and columns to zero.
372*
373                        IOFF = 0
374                        DO 70 J = 1, N
375                           I2 = MIN( J, IZERO )
376                           DO 60 I = 1, I2
377                              A( IOFF+I ) = ZERO
378   60                      CONTINUE
379                           IOFF = IOFF + LDA
380   70                   CONTINUE
381                        IZERO = 1
382                     ELSE
383*
384*                       Set the last IZERO rows and columns to zero.
385*
386                        IOFF = 0
387                        DO 90 J = 1, N
388                           I1 = MAX( J, IZERO )
389                           DO 80 I = I1, N
390                              A( IOFF+I ) = ZERO
391   80                      CONTINUE
392                           IOFF = IOFF + LDA
393   90                   CONTINUE
394                     END IF
395                  END IF
396               ELSE
397                  IZERO = 0
398               END IF
399*
400*              End generate the test matrix A.
401*
402*              Do for each value of NB in NBVAL
403*
404               DO 150 INB = 1, NNB
405*
406*                 Set the optimal blocksize, which will be later
407*                 returned by ILAENV.
408*
409                  NB = NBVAL( INB )
410                  CALL XLAENV( 1, NB )
411*
412*                 Copy the test matrix A into matrix AFAC which
413*                 will be factorized in place. This is needed to
414*                 preserve the test matrix A for subsequent tests.
415*
416                  CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
417*
418*                 Compute the L*D*L**T or U*D*U**T factorization of the
419*                 matrix. IWORK stores details of the interchanges and
420*                 the block structure of D. AINV is a work array for
421*                 block factorization, LWORK is the length of AINV.
422*
423                  SRNAMT = 'SSYTRF_AA'
424                  LWORK = MAX( 1, N*NB + N )
425                  CALL SSYTRF_AA( UPLO, N, AFAC, LDA, IWORK, AINV,
426     $                            LWORK, INFO )
427*
428*                 Adjust the expected value of INFO to account for
429*                 pivoting.
430*
431c                  IF( IZERO.GT.0 ) THEN
432c                     J = 1
433c                     K = IZERO
434c  100                CONTINUE
435c                     IF( J.EQ.K ) THEN
436c                        K = IWORK( J )
437c                     ELSE IF( IWORK( J ).EQ.K ) THEN
438c                        K = J
439c                     END IF
440c                     IF( J.LT.K ) THEN
441c                        J = J + 1
442c                        GO TO 100
443c                     END IF
444c                  ELSE
445                     K = 0
446c                  END IF
447*
448*                 Check error code from SSYTRF and handle error.
449*
450                  IF( INFO.NE.K ) THEN
451                     CALL ALAERH( PATH, 'SSYTRF_AA', INFO, K, UPLO,
452     $                            N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
453     $                            NOUT )
454                  END IF
455*
456*+    TEST 1
457*                 Reconstruct matrix from factors and compute residual.
458*
459                  CALL SSYT01_AA( UPLO, N, A, LDA, AFAC, LDA, IWORK,
460     $                            AINV, LDA, RWORK, RESULT( 1 ) )
461                  NT = 1
462*
463*
464*                 Print information about the tests that did not pass
465*                 the threshold.
466*
467                  DO 110 K = 1, NT
468                     IF( RESULT( K ).GE.THRESH ) THEN
469                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
470     $                     CALL ALAHD( NOUT, PATH )
471                        WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
472     $                     RESULT( K )
473                        NFAIL = NFAIL + 1
474                     END IF
475  110             CONTINUE
476                  NRUN = NRUN + NT
477*
478*                 Skip solver test if INFO is not 0.
479*
480                  IF( INFO.NE.0 ) THEN
481                     GO TO 140
482                  END IF
483*
484*                 Do for each value of NRHS in NSVAL.
485*
486                  DO 130 IRHS = 1, NNS
487                     NRHS = NSVAL( IRHS )
488*
489*+    TEST 2 (Using TRS)
490*                 Solve and compute residual for  A * X = B.
491*
492*                    Choose a set of NRHS random solution vectors
493*                    stored in XACT and set up the right hand side B
494*
495                     SRNAMT = 'SLARHS'
496                     CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
497     $                            KL, KU, NRHS, A, LDA, XACT, LDA,
498     $                            B, LDA, ISEED, INFO )
499                     CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
500*
501                     SRNAMT = 'SSYTRS_AA'
502                     LWORK = MAX( 1, 3*N-2 )
503                     CALL SSYTRS_AA( UPLO, N, NRHS, AFAC, LDA,
504     $                               IWORK, X, LDA, WORK, LWORK,
505     $                               INFO )
506*
507*                    Check error code from SSYTRS and handle error.
508*
509                     IF( INFO.NE.0 ) THEN
510                        IF( IZERO.EQ.0 ) THEN
511                           CALL ALAERH( PATH, 'SSYTRS_AA', INFO, 0,
512     $                                  UPLO, N, N, -1, -1, NRHS, IMAT,
513     $                                  NFAIL, NERRS, NOUT )
514                        END IF
515                     ELSE
516                        CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA
517     $                              )
518*
519*                       Compute the residual for the solution
520*
521                        CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
522     $                               WORK, LDA, RWORK, RESULT( 2 ) )
523*
524*
525*                    Print information about the tests that did not pass
526*                    the threshold.
527*
528                        DO 120 K = 2, 2
529                           IF( RESULT( K ).GE.THRESH ) THEN
530                              IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
531     $                           CALL ALAHD( NOUT, PATH )
532                              WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
533     $                           IMAT, K, RESULT( K )
534                              NFAIL = NFAIL + 1
535                           END IF
536  120                   CONTINUE
537                     END IF
538                     NRUN = NRUN + 1
539*
540*                 End do for each value of NRHS in NSVAL.
541*
542  130             CONTINUE
543  140             CONTINUE
544  150          CONTINUE
545  160       CONTINUE
546  170    CONTINUE
547  180 CONTINUE
548*
549*     Print a summary of the results.
550*
551      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
552*
553 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
554     $      I2, ', test ', I2, ', ratio =', G12.5 )
555 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
556     $      I2, ', test(', I2, ') =', G12.5 )
557 9995 FORMAT( ' Invalid input value: ', A4, '=', I6, '; must be <=',
558     $      I6 )
559      RETURN
560*
561*     End of SCHKSY_AA
562*
563      END
564