1*> \brief \b SDRVSY_ROOK
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_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12*    $                        NMAX, A, AFAC, AINV, B, X, XACT, WORK,
13*    $                        RWORK, IWORK, 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_ROOK tests the driver routines SSYSV_ROOK.
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 DOUBLE PRECISION
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 2013
148*
149*> \ingroup double_lin
150*
151*  =====================================================================
152      SUBROUTINE SDRVSY_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
153     $                        NMAX, A, AFAC, AINV, B, X, XACT, WORK,
154     $                        RWORK, IWORK, NOUT )
155*
156*  -- LAPACK test routine (version 3.5.0) --
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 2013
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 = 3 )
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, MATPATH
187      INTEGER            I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
188     $                   IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
189     $                   NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
190      REAL               AINVNM, ANORM, CNDNUM, 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               SLANSY
199      EXTERNAL           SLANSY
200*     ..
201*     .. External Subroutines ..
202      EXTERNAL           ALADHD, ALAERH, ALASVM, SERRVX, SGET04, SLACPY,
203     $                   SLARHS, SLASET, SLATB4, SLATMS, SPOT02, SPOT05,
204     $                   SSYSV_ROOK, SSYT01_ROOK, SSYTRF_ROOK,
205     $                   SSYTRI_ROOK,
206     $                   XLAENV
207*     ..
208*     .. Scalars in Common ..
209      LOGICAL            LERR, OK
210      CHARACTER*32       SRNAMT
211      INTEGER            INFOT, NUNIT
212*     ..
213*     .. Common blocks ..
214      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
215      COMMON             / SRNAMC / SRNAMT
216*     ..
217*     .. Intrinsic Functions ..
218      INTRINSIC          MAX, MIN
219*     ..
220*     .. Data statements ..
221      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
222      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
223*     ..
224*     .. Executable Statements ..
225*
226*     Initialize constants and the random number seed.
227*
228*     Test path
229*
230      PATH( 1: 1 ) = 'Single precision'
231      PATH( 2: 3 ) = 'SR'
232*
233*     Path to generate matrices
234*
235      MATPATH( 1: 1 ) = 'Single precision'
236      MATPATH( 2: 3 ) = 'SY'
237*
238      NRUN = 0
239      NFAIL = 0
240      NERRS = 0
241      DO 10 I = 1, 4
242         ISEED( I ) = ISEEDY( I )
243   10 CONTINUE
244      LWORK = MAX( 2*NMAX, NMAX*NRHS )
245*
246*     Test the error exits
247*
248      IF( TSTERR )
249     $   CALL SERRVX( PATH, NOUT )
250      INFOT = 0
251*
252*     Set the block size and minimum block size for which the block
253*     routine should be used, which will be later returned by ILAENV.
254*
255      NB = 1
256      NBMIN = 2
257      CALL XLAENV( 1, NB )
258      CALL XLAENV( 2, NBMIN )
259*
260*     Do for each value of N in NVAL
261*
262      DO 180 IN = 1, NN
263         N = NVAL( IN )
264         LDA = MAX( N, 1 )
265         XTYPE = 'N'
266         NIMAT = NTYPES
267         IF( N.LE.0 )
268     $      NIMAT = 1
269*
270         DO 170 IMAT = 1, NIMAT
271*
272*           Do the tests only if DOTYPE( IMAT ) is true.
273*
274            IF( .NOT.DOTYPE( IMAT ) )
275     $         GO TO 170
276*
277*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
278*
279            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
280            IF( ZEROT .AND. N.LT.IMAT-2 )
281     $         GO TO 170
282*
283*           Do first for UPLO = 'U', then for UPLO = 'L'
284*
285            DO 160 IUPLO = 1, 2
286               UPLO = UPLOS( IUPLO )
287*
288*              Begin generate the test matrix A.
289*
290*              Set up parameters with SLATB4 for the matrix generator
291*              based on the type of matrix to be generated.
292*
293               CALL SLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
294     $                      MODE, CNDNUM, DIST )
295*
296*              Generate a matrix with SLATMS.
297*
298               SRNAMT = 'SLATMS'
299               CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
300     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
301     $                      INFO )
302*
303*              Check error code from SLATMS and handle error.
304*
305               IF( INFO.NE.0 ) THEN
306                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
307     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
308*
309*                 Skip all tests for this generated matrix
310*
311                  GO TO 160
312               END IF
313*
314*              For types 3-6, zero one or more rows and columns of the
315*              matrix to test that INFO is returned correctly.
316*
317               IF( ZEROT ) THEN
318                  IF( IMAT.EQ.3 ) THEN
319                     IZERO = 1
320                  ELSE IF( IMAT.EQ.4 ) THEN
321                     IZERO = N
322                  ELSE
323                     IZERO = N / 2 + 1
324                  END IF
325*
326                  IF( IMAT.LT.6 ) THEN
327*
328*                    Set row and column IZERO to zero.
329*
330                     IF( IUPLO.EQ.1 ) THEN
331                        IOFF = ( IZERO-1 )*LDA
332                        DO 20 I = 1, IZERO - 1
333                           A( IOFF+I ) = ZERO
334   20                   CONTINUE
335                        IOFF = IOFF + IZERO
336                        DO 30 I = IZERO, N
337                           A( IOFF ) = ZERO
338                           IOFF = IOFF + LDA
339   30                   CONTINUE
340                     ELSE
341                        IOFF = IZERO
342                        DO 40 I = 1, IZERO - 1
343                           A( IOFF ) = ZERO
344                           IOFF = IOFF + LDA
345   40                   CONTINUE
346                        IOFF = IOFF - IZERO
347                        DO 50 I = IZERO, N
348                           A( IOFF+I ) = ZERO
349   50                   CONTINUE
350                     END IF
351                  ELSE
352                     IOFF = 0
353                     IF( IUPLO.EQ.1 ) THEN
354*
355*                       Set the first IZERO rows and columns to zero.
356*
357                        DO 70 J = 1, N
358                           I2 = MIN( J, IZERO )
359                           DO 60 I = 1, I2
360                              A( IOFF+I ) = ZERO
361   60                      CONTINUE
362                           IOFF = IOFF + LDA
363   70                   CONTINUE
364                     ELSE
365*
366*                       Set the last IZERO rows and columns to zero.
367*
368                        DO 90 J = 1, N
369                           I1 = MAX( J, IZERO )
370                           DO 80 I = I1, N
371                              A( IOFF+I ) = ZERO
372   80                      CONTINUE
373                           IOFF = IOFF + LDA
374   90                   CONTINUE
375                     END IF
376                  END IF
377               ELSE
378                  IZERO = 0
379               END IF
380*
381*              End generate the test matrix A.
382*
383               DO 150 IFACT = 1, NFACT
384*
385*                 Do first for FACT = 'F', then for other values.
386*
387                  FACT = FACTS( IFACT )
388*
389*                 Compute the condition number for comparison with
390*                 the value returned by DSYSVX_ROOK.
391*
392                  IF( ZEROT ) THEN
393                     IF( IFACT.EQ.1 )
394     $                  GO TO 150
395                     RCONDC = ZERO
396*
397                  ELSE IF( IFACT.EQ.1 ) THEN
398*
399*                    Compute the 1-norm of A.
400*
401                     ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
402*
403*                    Factor the matrix A.
404*
405                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
406                     CALL SSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, WORK,
407     $                            LWORK, INFO )
408*
409*                    Compute inv(A) and take its norm.
410*
411                     CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
412                     LWORK = (N+NB+1)*(NB+3)
413                     CALL SSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK,
414     $                                 WORK, INFO )
415                     AINVNM = SLANSY( '1', UPLO, N, AINV, LDA, RWORK )
416*
417*                    Compute the 1-norm condition number of A.
418*
419                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
420                        RCONDC = ONE
421                     ELSE
422                        RCONDC = ( ONE / ANORM ) / AINVNM
423                     END IF
424                  END IF
425*
426*                 Form an exact solution and set the right hand side.
427*
428                  SRNAMT = 'SLARHS'
429                  CALL SLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
430     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
431     $                         INFO )
432                  XTYPE = 'C'
433*
434*                 --- Test SSYSV_ROOK  ---
435*
436                  IF( IFACT.EQ.2 ) THEN
437                     CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
438                     CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
439*
440*                    Factor the matrix and solve the system using
441*                    SSYSV_ROOK.
442*
443                     SRNAMT = 'SSYSV_ROOK'
444                     CALL SSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
445     $                                X, LDA, WORK, LWORK, INFO )
446*
447*                    Adjust the expected value of INFO to account for
448*                    pivoting.
449*
450                     K = IZERO
451                     IF( K.GT.0 ) THEN
452  100                   CONTINUE
453                        IF( IWORK( K ).LT.0 ) THEN
454                           IF( IWORK( K ).NE.-K ) THEN
455                              K = -IWORK( K )
456                              GO TO 100
457                           END IF
458                        ELSE IF( IWORK( K ).NE.K ) THEN
459                           K = IWORK( K )
460                           GO TO 100
461                        END IF
462                     END IF
463*
464*                    Check error code from SSYSV_ROOK and handle error.
465*
466                     IF( INFO.NE.K ) THEN
467                        CALL ALAERH( PATH, 'SSYSV_ROOK', INFO, K, UPLO,
468     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
469     $                               NERRS, NOUT )
470                        GO TO 120
471                     ELSE IF( INFO.NE.0 ) THEN
472                        GO TO 120
473                     END IF
474*
475*+    TEST 1      Reconstruct matrix from factors and compute
476*                 residual.
477*
478                     CALL SSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA,
479     $                                 IWORK, AINV, LDA, RWORK,
480     $                                 RESULT( 1 ) )
481*
482*+    TEST 2      Compute residual of the computed solution.
483*
484                     CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
485                     CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
486     $                            LDA, RWORK, RESULT( 2 ) )
487*
488*+    TEST 3
489*                 Check solution from generated exact solution.
490*
491                     CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
492     $                            RESULT( 3 ) )
493                     NT = 3
494*
495*                    Print information about the tests that did not pass
496*                    the threshold.
497*
498                     DO 110 K = 1, NT
499                        IF( RESULT( K ).GE.THRESH ) THEN
500                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
501     $                        CALL ALADHD( NOUT, PATH )
502                           WRITE( NOUT, FMT = 9999 )'SSYSV_ROOK', UPLO,
503     $                           N, IMAT, K, RESULT( K )
504                           NFAIL = NFAIL + 1
505                        END IF
506  110                CONTINUE
507                     NRUN = NRUN + NT
508  120                CONTINUE
509                  END IF
510*
511  150          CONTINUE
512*
513  160       CONTINUE
514  170    CONTINUE
515  180 CONTINUE
516*
517*     Print a summary of the results.
518*
519      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
520*
521 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
522     $      ', test ', I2, ', ratio =', G12.5 )
523      RETURN
524*
525*     End of SDRVSY_ROOK
526*
527      END
528