1*> \brief \b DDRVSY_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 DDRVSY_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*       DOUBLE PRECISION   THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NVAL( * )
23*       DOUBLE PRECISION   A( * ), AFAC( * ), AINV( * ), B( * ),
24*      $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
25*       ..
26*
27*
28*> \par Purpose:
29*  =============
30*>
31*> \verbatim
32*>
33*> DDRVSY_ROOK tests the driver routines DSYSV_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 DOUBLE PRECISION array, dimension (NMAX*NMAX)
90*> \endverbatim
91*>
92*> \param[out] AFAC
93*> \verbatim
94*>          AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
95*> \endverbatim
96*>
97*> \param[out] AINV
98*> \verbatim
99*>          AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
100*> \endverbatim
101*>
102*> \param[out] B
103*> \verbatim
104*>          B is DOUBLE PRECISION array, dimension (NMAX*NRHS)
105*> \endverbatim
106*>
107*> \param[out] X
108*> \verbatim
109*>          X is DOUBLE PRECISION array, dimension (NMAX*NRHS)
110*> \endverbatim
111*>
112*> \param[out] XACT
113*> \verbatim
114*>          XACT is DOUBLE PRECISION array, dimension (NMAX*NRHS)
115*> \endverbatim
116*>
117*> \param[out] WORK
118*> \verbatim
119*>          WORK is DOUBLE PRECISION array, dimension (NMAX*max(2,NRHS))
120*> \endverbatim
121*>
122*> \param[out] RWORK
123*> \verbatim
124*>          RWORK is DOUBLE PRECISION 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 double_lin
147*
148*  =====================================================================
149      SUBROUTINE DDRVSY_ROOK( 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      DOUBLE PRECISION   THRESH
161*     ..
162*     .. Array Arguments ..
163      LOGICAL            DOTYPE( * )
164      INTEGER            IWORK( * ), NVAL( * )
165      DOUBLE PRECISION   A( * ), AFAC( * ), AINV( * ), B( * ),
166     $                   RWORK( * ), WORK( * ), X( * ), XACT( * )
167*     ..
168*
169*  =====================================================================
170*
171*     .. Parameters ..
172      DOUBLE PRECISION   ONE, ZERO
173      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+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        PATH, MATPATH
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      DOUBLE PRECISION   AINVNM, ANORM, CNDNUM, RCONDC
187*     ..
188*     .. Local Arrays ..
189      CHARACTER          FACTS( NFACT ), UPLOS( 2 )
190      INTEGER            ISEED( 4 ), ISEEDY( 4 )
191      DOUBLE PRECISION   RESULT( NTESTS )
192*     ..
193*     .. External Functions ..
194      DOUBLE PRECISION   DLANSY
195      EXTERNAL           DLANSY
196*     ..
197*     .. External Subroutines ..
198      EXTERNAL           ALADHD, ALAERH, ALASVM, DERRVX, DGET04, DLACPY,
199     $                   DLARHS, DLASET, DLATB4, DLATMS, DPOT02, DPOT05,
200     $                   DSYSV_ROOK, DSYT01_ROOK, DSYTRF_ROOK,
201     $                   DSYTRI_ROOK,
202     $                   XLAENV
203*     ..
204*     .. Scalars in Common ..
205      LOGICAL            LERR, OK
206      CHARACTER*32       SRNAMT
207      INTEGER            INFOT, NUNIT
208*     ..
209*     .. Common blocks ..
210      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
211      COMMON             / SRNAMC / SRNAMT
212*     ..
213*     .. Intrinsic Functions ..
214      INTRINSIC          MAX, MIN
215*     ..
216*     .. Data statements ..
217      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
218      DATA               UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
219*     ..
220*     .. Executable Statements ..
221*
222*     Initialize constants and the random number seed.
223*
224*     Test path
225*
226      PATH( 1: 1 ) = 'Double precision'
227      PATH( 2: 3 ) = 'SR'
228*
229*     Path to generate matrices
230*
231      MATPATH( 1: 1 ) = 'Double precision'
232      MATPATH( 2: 3 ) = 'SY'
233*
234      NRUN = 0
235      NFAIL = 0
236      NERRS = 0
237      DO 10 I = 1, 4
238         ISEED( I ) = ISEEDY( I )
239   10 CONTINUE
240      LWORK = MAX( 2*NMAX, NMAX*NRHS )
241*
242*     Test the error exits
243*
244      IF( TSTERR )
245     $   CALL DERRVX( PATH, NOUT )
246      INFOT = 0
247*
248*     Set the block size and minimum block size for which the block
249*     routine should be used, which will be later returned by ILAENV.
250*
251      NB = 1
252      NBMIN = 2
253      CALL XLAENV( 1, NB )
254      CALL XLAENV( 2, NBMIN )
255*
256*     Do for each value of N in NVAL
257*
258      DO 180 IN = 1, NN
259         N = NVAL( IN )
260         LDA = MAX( N, 1 )
261         XTYPE = 'N'
262         NIMAT = NTYPES
263         IF( N.LE.0 )
264     $      NIMAT = 1
265*
266         DO 170 IMAT = 1, NIMAT
267*
268*           Do the tests only if DOTYPE( IMAT ) is true.
269*
270            IF( .NOT.DOTYPE( IMAT ) )
271     $         GO TO 170
272*
273*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
274*
275            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
276            IF( ZEROT .AND. N.LT.IMAT-2 )
277     $         GO TO 170
278*
279*           Do first for UPLO = 'U', then for UPLO = 'L'
280*
281            DO 160 IUPLO = 1, 2
282               UPLO = UPLOS( IUPLO )
283*
284*              Begin generate the test matrix A.
285*
286*              Set up parameters with DLATB4 for the matrix generator
287*              based on the type of matrix to be generated.
288*
289               CALL DLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
290     $                      MODE, CNDNUM, DIST )
291*
292*              Generate a matrix with DLATMS.
293*
294               SRNAMT = 'DLATMS'
295               CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
296     $                      CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
297     $                      INFO )
298*
299*              Check error code from DLATMS and handle error.
300*
301               IF( INFO.NE.0 ) THEN
302                  CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
303     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
304*
305*                 Skip all tests for this generated matrix
306*
307                  GO TO 160
308               END IF
309*
310*              For types 3-6, zero one or more rows and columns of the
311*              matrix to test that INFO is returned correctly.
312*
313               IF( ZEROT ) THEN
314                  IF( IMAT.EQ.3 ) THEN
315                     IZERO = 1
316                  ELSE IF( IMAT.EQ.4 ) THEN
317                     IZERO = N
318                  ELSE
319                     IZERO = N / 2 + 1
320                  END IF
321*
322                  IF( IMAT.LT.6 ) THEN
323*
324*                    Set row and column IZERO to zero.
325*
326                     IF( IUPLO.EQ.1 ) THEN
327                        IOFF = ( IZERO-1 )*LDA
328                        DO 20 I = 1, IZERO - 1
329                           A( IOFF+I ) = ZERO
330   20                   CONTINUE
331                        IOFF = IOFF + IZERO
332                        DO 30 I = IZERO, N
333                           A( IOFF ) = ZERO
334                           IOFF = IOFF + LDA
335   30                   CONTINUE
336                     ELSE
337                        IOFF = IZERO
338                        DO 40 I = 1, IZERO - 1
339                           A( IOFF ) = ZERO
340                           IOFF = IOFF + LDA
341   40                   CONTINUE
342                        IOFF = IOFF - IZERO
343                        DO 50 I = IZERO, N
344                           A( IOFF+I ) = ZERO
345   50                   CONTINUE
346                     END IF
347                  ELSE
348                     IOFF = 0
349                     IF( IUPLO.EQ.1 ) THEN
350*
351*                       Set the first IZERO rows and columns to zero.
352*
353                        DO 70 J = 1, N
354                           I2 = MIN( J, IZERO )
355                           DO 60 I = 1, I2
356                              A( IOFF+I ) = ZERO
357   60                      CONTINUE
358                           IOFF = IOFF + LDA
359   70                   CONTINUE
360                     ELSE
361*
362*                       Set the last IZERO rows and columns to zero.
363*
364                        DO 90 J = 1, N
365                           I1 = MAX( J, IZERO )
366                           DO 80 I = I1, N
367                              A( IOFF+I ) = ZERO
368   80                      CONTINUE
369                           IOFF = IOFF + LDA
370   90                   CONTINUE
371                     END IF
372                  END IF
373               ELSE
374                  IZERO = 0
375               END IF
376*
377*              End generate the test matrix A.
378*
379               DO 150 IFACT = 1, NFACT
380*
381*                 Do first for FACT = 'F', then for other values.
382*
383                  FACT = FACTS( IFACT )
384*
385*                 Compute the condition number for comparison with
386*                 the value returned by DSYSVX_ROOK.
387*
388                  IF( ZEROT ) THEN
389                     IF( IFACT.EQ.1 )
390     $                  GO TO 150
391                     RCONDC = ZERO
392*
393                  ELSE IF( IFACT.EQ.1 ) THEN
394*
395*                    Compute the 1-norm of A.
396*
397                     ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
398*
399*                    Factor the matrix A.
400*
401                     CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
402                     CALL DSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, WORK,
403     $                            LWORK, INFO )
404*
405*                    Compute inv(A) and take its norm.
406*
407                     CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
408                     LWORK = (N+NB+1)*(NB+3)
409                     CALL DSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK,
410     $                                 WORK, INFO )
411                     AINVNM = DLANSY( '1', UPLO, N, AINV, LDA, RWORK )
412*
413*                    Compute the 1-norm condition number of A.
414*
415                     IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
416                        RCONDC = ONE
417                     ELSE
418                        RCONDC = ( ONE / ANORM ) / AINVNM
419                     END IF
420                  END IF
421*
422*                 Form an exact solution and set the right hand side.
423*
424                  SRNAMT = 'DLARHS'
425                  CALL DLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
426     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
427     $                         INFO )
428                  XTYPE = 'C'
429*
430*                 --- Test DSYSV_ROOK  ---
431*
432                  IF( IFACT.EQ.2 ) THEN
433                     CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
434                     CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
435*
436*                    Factor the matrix and solve the system using
437*                    DSYSV_ROOK.
438*
439                     SRNAMT = 'DSYSV_ROOK'
440                     CALL DSYSV_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
441     $                                X, LDA, WORK, LWORK, INFO )
442*
443*                    Adjust the expected value of INFO to account for
444*                    pivoting.
445*
446                     K = IZERO
447                     IF( K.GT.0 ) THEN
448  100                   CONTINUE
449                        IF( IWORK( K ).LT.0 ) THEN
450                           IF( IWORK( K ).NE.-K ) THEN
451                              K = -IWORK( K )
452                              GO TO 100
453                           END IF
454                        ELSE IF( IWORK( K ).NE.K ) THEN
455                           K = IWORK( K )
456                           GO TO 100
457                        END IF
458                     END IF
459*
460*                    Check error code from DSYSV_ROOK and handle error.
461*
462                     IF( INFO.NE.K ) THEN
463                        CALL ALAERH( PATH, 'DSYSV_ROOK', INFO, K, UPLO,
464     $                               N, N, -1, -1, NRHS, IMAT, NFAIL,
465     $                               NERRS, NOUT )
466                        GO TO 120
467                     ELSE IF( INFO.NE.0 ) THEN
468                        GO TO 120
469                     END IF
470*
471*+    TEST 1      Reconstruct matrix from factors and compute
472*                 residual.
473*
474                     CALL DSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA,
475     $                                 IWORK, AINV, LDA, RWORK,
476     $                                 RESULT( 1 ) )
477*
478*+    TEST 2      Compute residual of the computed solution.
479*
480                     CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
481                     CALL DPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
482     $                            LDA, RWORK, RESULT( 2 ) )
483*
484*+    TEST 3
485*                 Check solution from generated exact solution.
486*
487                     CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
488     $                            RESULT( 3 ) )
489                     NT = 3
490*
491*                    Print information about the tests that did not pass
492*                    the threshold.
493*
494                     DO 110 K = 1, NT
495                        IF( RESULT( K ).GE.THRESH ) THEN
496                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
497     $                        CALL ALADHD( NOUT, PATH )
498                           WRITE( NOUT, FMT = 9999 )'DSYSV_ROOK', UPLO,
499     $                           N, IMAT, K, RESULT( K )
500                           NFAIL = NFAIL + 1
501                        END IF
502  110                CONTINUE
503                     NRUN = NRUN + NT
504  120                CONTINUE
505                  END IF
506*
507  150          CONTINUE
508*
509  160       CONTINUE
510  170    CONTINUE
511  180 CONTINUE
512*
513*     Print a summary of the results.
514*
515      CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
516*
517 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
518     $      ', test ', I2, ', ratio =', G12.5 )
519      RETURN
520*
521*     End of DDRVSY_ROOK
522*
523      END
524