1*> \brief \b ZCHKSP
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 ZCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
12*                          NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
13*                          IWORK, NOUT )
14*
15*       .. Scalar Arguments ..
16*       LOGICAL            TSTERR
17*       INTEGER            NMAX, NN, NNS, NOUT
18*       DOUBLE PRECISION   THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
23*       DOUBLE PRECISION   RWORK( * )
24*       COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
25*      $                   WORK( * ), X( * ), XACT( * )
26*       ..
27*
28*
29*> \par Purpose:
30*  =============
31*>
32*> \verbatim
33*>
34*> ZCHKSP tests ZSPTRF, -TRI, -TRS, -RFS, and -CON
35*> \endverbatim
36*
37*  Arguments:
38*  ==========
39*
40*> \param[in] DOTYPE
41*> \verbatim
42*>          DOTYPE is LOGICAL array, dimension (NTYPES)
43*>          The matrix types to be used for testing.  Matrices of type j
44*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46*> \endverbatim
47*>
48*> \param[in] NN
49*> \verbatim
50*>          NN is INTEGER
51*>          The number of values of N contained in the vector NVAL.
52*> \endverbatim
53*>
54*> \param[in] NVAL
55*> \verbatim
56*>          NVAL is INTEGER array, dimension (NN)
57*>          The values of the matrix dimension N.
58*> \endverbatim
59*>
60*> \param[in] NNS
61*> \verbatim
62*>          NNS is INTEGER
63*>          The number of values of NRHS contained in the vector NSVAL.
64*> \endverbatim
65*>
66*> \param[in] NSVAL
67*> \verbatim
68*>          NSVAL is INTEGER array, dimension (NNS)
69*>          The values of the number of right hand sides NRHS.
70*> \endverbatim
71*>
72*> \param[in] THRESH
73*> \verbatim
74*>          THRESH is DOUBLE PRECISION
75*>          The threshold value for the test ratios.  A result is
76*>          included in the output file if RESULT >= THRESH.  To have
77*>          every test ratio printed, use THRESH = 0.
78*> \endverbatim
79*>
80*> \param[in] TSTERR
81*> \verbatim
82*>          TSTERR is LOGICAL
83*>          Flag that indicates whether error exits are to be tested.
84*> \endverbatim
85*>
86*> \param[in] NMAX
87*> \verbatim
88*>          NMAX is INTEGER
89*>          The maximum value permitted for N, used in dimensioning the
90*>          work arrays.
91*> \endverbatim
92*>
93*> \param[out] A
94*> \verbatim
95*>          A is COMPLEX*16 array, dimension
96*>                      (NMAX*(NMAX+1)/2)
97*> \endverbatim
98*>
99*> \param[out] AFAC
100*> \verbatim
101*>          AFAC is COMPLEX*16 array, dimension
102*>                      (NMAX*(NMAX+1)/2)
103*> \endverbatim
104*>
105*> \param[out] AINV
106*> \verbatim
107*>          AINV is COMPLEX*16 array, dimension
108*>                      (NMAX*(NMAX+1)/2)
109*> \endverbatim
110*>
111*> \param[out] B
112*> \verbatim
113*>          B is COMPLEX*16 array, dimension (NMAX*NSMAX)
114*>          where NSMAX is the largest entry in NSVAL.
115*> \endverbatim
116*>
117*> \param[out] X
118*> \verbatim
119*>          X is COMPLEX*16 array, dimension (NMAX*NSMAX)
120*> \endverbatim
121*>
122*> \param[out] XACT
123*> \verbatim
124*>          XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*>          WORK is COMPLEX*16 array, dimension
130*>                      (NMAX*max(2,NSMAX))
131*> \endverbatim
132*>
133*> \param[out] RWORK
134*> \verbatim
135*>          RWORK is DOUBLE PRECISION array,
136*>                                 dimension (NMAX+2*NSMAX)
137*> \endverbatim
138*>
139*> \param[out] IWORK
140*> \verbatim
141*>          IWORK is INTEGER array, dimension (NMAX)
142*> \endverbatim
143*>
144*> \param[in] NOUT
145*> \verbatim
146*>          NOUT is INTEGER
147*>          The unit number for output.
148*> \endverbatim
149*
150*  Authors:
151*  ========
152*
153*> \author Univ. of Tennessee
154*> \author Univ. of California Berkeley
155*> \author Univ. of Colorado Denver
156*> \author NAG Ltd.
157*
158*> \ingroup complex16_lin
159*
160*  =====================================================================
161      SUBROUTINE ZCHKSP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
162     $                   NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
163     $                   IWORK, NOUT )
164*
165*  -- LAPACK test routine --
166*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
167*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168*
169*     .. Scalar Arguments ..
170      LOGICAL            TSTERR
171      INTEGER            NMAX, NN, NNS, NOUT
172      DOUBLE PRECISION   THRESH
173*     ..
174*     .. Array Arguments ..
175      LOGICAL            DOTYPE( * )
176      INTEGER            IWORK( * ), NSVAL( * ), NVAL( * )
177      DOUBLE PRECISION   RWORK( * )
178      COMPLEX*16         A( * ), AFAC( * ), AINV( * ), B( * ),
179     $                   WORK( * ), X( * ), XACT( * )
180*     ..
181*
182*  =====================================================================
183*
184*     .. Parameters ..
185      DOUBLE PRECISION   ZERO
186      PARAMETER          ( ZERO = 0.0D+0 )
187      INTEGER            NTYPES
188      PARAMETER          ( NTYPES = 11 )
189      INTEGER            NTESTS
190      PARAMETER          ( NTESTS = 8 )
191*     ..
192*     .. Local Scalars ..
193      LOGICAL            TRFCON, ZEROT
194      CHARACTER          DIST, PACKIT, TYPE, UPLO, XTYPE
195      CHARACTER*3        PATH
196      INTEGER            I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
197     $                   IZERO, J, K, KL, KU, LDA, MODE, N, NERRS,
198     $                   NFAIL, NIMAT, NPP, NRHS, NRUN, NT
199      DOUBLE PRECISION   ANORM, CNDNUM, RCOND, RCONDC
200*     ..
201*     .. Local Arrays ..
202      CHARACTER          UPLOS( 2 )
203      INTEGER            ISEED( 4 ), ISEEDY( 4 )
204      DOUBLE PRECISION   RESULT( NTESTS )
205*     ..
206*     .. External Functions ..
207      LOGICAL            LSAME
208      DOUBLE PRECISION   DGET06, ZLANSP
209      EXTERNAL           LSAME, DGET06, ZLANSP
210*     ..
211*     .. External Subroutines ..
212      EXTERNAL           ALAERH, ALAHD, ALASUM, ZCOPY, ZERRSY, ZGET04,
213     $                   ZLACPY, ZLARHS, ZLATB4, ZLATMS, ZLATSP, ZPPT05,
214     $                   ZSPCON, ZSPRFS, ZSPT01, ZSPT02, ZSPT03, ZSPTRF,
215     $                   ZSPTRI, ZSPTRS
216*     ..
217*     .. Intrinsic Functions ..
218      INTRINSIC          MAX, MIN
219*     ..
220*     .. Scalars in Common ..
221      LOGICAL            LERR, OK
222      CHARACTER*32       SRNAMT
223      INTEGER            INFOT, NUNIT
224*     ..
225*     .. Common blocks ..
226      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
227      COMMON             / SRNAMC / SRNAMT
228*     ..
229*     .. Data statements ..
230      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
231      DATA               UPLOS / 'U', 'L' /
232*     ..
233*     .. Executable Statements ..
234*
235*     Initialize constants and the random number seed.
236*
237      PATH( 1: 1 ) = 'Zomplex precision'
238      PATH( 2: 3 ) = 'SP'
239      NRUN = 0
240      NFAIL = 0
241      NERRS = 0
242      DO 10 I = 1, 4
243         ISEED( I ) = ISEEDY( I )
244   10 CONTINUE
245*
246*     Test the error exits
247*
248      IF( TSTERR )
249     $   CALL ZERRSY( PATH, NOUT )
250      INFOT = 0
251*
252*     Do for each value of N in NVAL
253*
254      DO 170 IN = 1, NN
255         N = NVAL( IN )
256         LDA = MAX( N, 1 )
257         XTYPE = 'N'
258         NIMAT = NTYPES
259         IF( N.LE.0 )
260     $      NIMAT = 1
261*
262         DO 160 IMAT = 1, NIMAT
263*
264*           Do the tests only if DOTYPE( IMAT ) is true.
265*
266            IF( .NOT.DOTYPE( IMAT ) )
267     $         GO TO 160
268*
269*           Skip types 3, 4, 5, or 6 if the matrix size is too small.
270*
271            ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
272            IF( ZEROT .AND. N.LT.IMAT-2 )
273     $         GO TO 160
274*
275*           Do first for UPLO = 'U', then for UPLO = 'L'
276*
277            DO 150 IUPLO = 1, 2
278               UPLO = UPLOS( IUPLO )
279               IF( LSAME( UPLO, 'U' ) ) THEN
280                  PACKIT = 'C'
281               ELSE
282                  PACKIT = 'R'
283               END IF
284*
285               IF( IMAT.NE.NTYPES ) THEN
286*
287*                 Set up parameters with ZLATB4 and generate a test
288*                 matrix with ZLATMS.
289*
290                  CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
291     $                         MODE, CNDNUM, DIST )
292*
293                  SRNAMT = 'ZLATMS'
294                  CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
295     $                         CNDNUM, ANORM, KL, KU, PACKIT, A, LDA,
296     $                         WORK, INFO )
297*
298*                 Check error code from ZLATMS.
299*
300                  IF( INFO.NE.0 ) THEN
301                     CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
302     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
303                     GO TO 150
304                  END IF
305*
306*                 For types 3-6, zero one or more rows and columns of
307*                 the matrix to test that INFO is returned correctly.
308*
309                  IF( ZEROT ) THEN
310                     IF( IMAT.EQ.3 ) THEN
311                        IZERO = 1
312                     ELSE IF( IMAT.EQ.4 ) THEN
313                        IZERO = N
314                     ELSE
315                        IZERO = N / 2 + 1
316                     END IF
317*
318                     IF( IMAT.LT.6 ) THEN
319*
320*                       Set row and column IZERO to zero.
321*
322                        IF( IUPLO.EQ.1 ) THEN
323                           IOFF = ( IZERO-1 )*IZERO / 2
324                           DO 20 I = 1, IZERO - 1
325                              A( IOFF+I ) = ZERO
326   20                      CONTINUE
327                           IOFF = IOFF + IZERO
328                           DO 30 I = IZERO, N
329                              A( IOFF ) = ZERO
330                              IOFF = IOFF + I
331   30                      CONTINUE
332                        ELSE
333                           IOFF = IZERO
334                           DO 40 I = 1, IZERO - 1
335                              A( IOFF ) = ZERO
336                              IOFF = IOFF + N - I
337   40                      CONTINUE
338                           IOFF = IOFF - IZERO
339                           DO 50 I = IZERO, N
340                              A( IOFF+I ) = ZERO
341   50                      CONTINUE
342                        END IF
343                     ELSE
344                        IF( IUPLO.EQ.1 ) THEN
345*
346*                          Set the first IZERO rows and columns to zero.
347*
348                           IOFF = 0
349                           DO 70 J = 1, N
350                              I2 = MIN( J, IZERO )
351                              DO 60 I = 1, I2
352                                 A( IOFF+I ) = ZERO
353   60                         CONTINUE
354                              IOFF = IOFF + J
355   70                      CONTINUE
356                        ELSE
357*
358*                          Set the last IZERO rows and columns to zero.
359*
360                           IOFF = 0
361                           DO 90 J = 1, N
362                              I1 = MAX( J, IZERO )
363                              DO 80 I = I1, N
364                                 A( IOFF+I ) = ZERO
365   80                         CONTINUE
366                              IOFF = IOFF + N - J
367   90                      CONTINUE
368                        END IF
369                     END IF
370                  ELSE
371                     IZERO = 0
372                  END IF
373               ELSE
374*
375*                 Use a special block diagonal matrix to test alternate
376*                 code for the 2 x 2 blocks.
377*
378                  CALL ZLATSP( UPLO, N, A, ISEED )
379               END IF
380*
381*              Compute the L*D*L' or U*D*U' factorization of the matrix.
382*
383               NPP = N*( N+1 ) / 2
384               CALL ZCOPY( NPP, A, 1, AFAC, 1 )
385               SRNAMT = 'ZSPTRF'
386               CALL ZSPTRF( UPLO, N, AFAC, IWORK, INFO )
387*
388*              Adjust the expected value of INFO to account for
389*              pivoting.
390*
391               K = IZERO
392               IF( K.GT.0 ) THEN
393  100             CONTINUE
394                  IF( IWORK( K ).LT.0 ) THEN
395                     IF( IWORK( K ).NE.-K ) THEN
396                        K = -IWORK( K )
397                        GO TO 100
398                     END IF
399                  ELSE IF( IWORK( K ).NE.K ) THEN
400                     K = IWORK( K )
401                     GO TO 100
402                  END IF
403               END IF
404*
405*              Check error code from ZSPTRF.
406*
407               IF( INFO.NE.K )
408     $            CALL ALAERH( PATH, 'ZSPTRF', INFO, K, UPLO, N, N, -1,
409     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
410               IF( INFO.NE.0 ) THEN
411                  TRFCON = .TRUE.
412               ELSE
413                  TRFCON = .FALSE.
414               END IF
415*
416*+    TEST 1
417*              Reconstruct matrix from factors and compute residual.
418*
419               CALL ZSPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA, RWORK,
420     $                      RESULT( 1 ) )
421               NT = 1
422*
423*+    TEST 2
424*              Form the inverse and compute the residual.
425*
426               IF( .NOT.TRFCON ) THEN
427                  CALL ZCOPY( NPP, AFAC, 1, AINV, 1 )
428                  SRNAMT = 'ZSPTRI'
429                  CALL ZSPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
430*
431*              Check error code from ZSPTRI.
432*
433                  IF( INFO.NE.0 )
434     $               CALL ALAERH( PATH, 'ZSPTRI', INFO, 0, UPLO, N, N,
435     $                            -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
436*
437                  CALL ZSPT03( UPLO, N, A, AINV, WORK, LDA, RWORK,
438     $                         RCONDC, RESULT( 2 ) )
439                  NT = 2
440               END IF
441*
442*              Print information about the tests that did not pass
443*              the threshold.
444*
445               DO 110 K = 1, NT
446                  IF( RESULT( K ).GE.THRESH ) THEN
447                     IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
448     $                  CALL ALAHD( NOUT, PATH )
449                     WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, K,
450     $                  RESULT( K )
451                     NFAIL = NFAIL + 1
452                  END IF
453  110          CONTINUE
454               NRUN = NRUN + NT
455*
456*              Do only the condition estimate if INFO is not 0.
457*
458               IF( TRFCON ) THEN
459                  RCONDC = ZERO
460                  GO TO 140
461               END IF
462*
463               DO 130 IRHS = 1, NNS
464                  NRHS = NSVAL( IRHS )
465*
466*+    TEST 3
467*              Solve and compute residual for  A * X = B.
468*
469                  SRNAMT = 'ZLARHS'
470                  CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
471     $                         NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
472     $                         INFO )
473                  CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
474*
475                  SRNAMT = 'ZSPTRS'
476                  CALL ZSPTRS( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
477     $                         INFO )
478*
479*              Check error code from ZSPTRS.
480*
481                  IF( INFO.NE.0 )
482     $               CALL ALAERH( PATH, 'ZSPTRS', INFO, 0, UPLO, N, N,
483     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
484     $                            NOUT )
485*
486                  CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
487                  CALL ZSPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
488     $                         RWORK, RESULT( 3 ) )
489*
490*+    TEST 4
491*              Check solution from generated exact solution.
492*
493                  CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
494     $                         RESULT( 4 ) )
495*
496*+    TESTS 5, 6, and 7
497*              Use iterative refinement to improve the solution.
498*
499                  SRNAMT = 'ZSPRFS'
500                  CALL ZSPRFS( UPLO, N, NRHS, A, AFAC, IWORK, B, LDA, X,
501     $                         LDA, RWORK, RWORK( NRHS+1 ), WORK,
502     $                         RWORK( 2*NRHS+1 ), INFO )
503*
504*              Check error code from ZSPRFS.
505*
506                  IF( INFO.NE.0 )
507     $               CALL ALAERH( PATH, 'ZSPRFS', INFO, 0, UPLO, N, N,
508     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
509     $                            NOUT )
510*
511                  CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
512     $                         RESULT( 5 ) )
513                  CALL ZPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA, XACT,
514     $                         LDA, RWORK, RWORK( NRHS+1 ),
515     $                         RESULT( 6 ) )
516*
517*                 Print information about the tests that did not pass
518*                 the threshold.
519*
520                  DO 120 K = 3, 7
521                     IF( RESULT( K ).GE.THRESH ) THEN
522                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
523     $                     CALL ALAHD( NOUT, PATH )
524                        WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS, IMAT,
525     $                     K, RESULT( K )
526                        NFAIL = NFAIL + 1
527                     END IF
528  120             CONTINUE
529                  NRUN = NRUN + 5
530  130          CONTINUE
531*
532*+    TEST 8
533*              Get an estimate of RCOND = 1/CNDNUM.
534*
535  140          CONTINUE
536               ANORM = ZLANSP( '1', UPLO, N, A, RWORK )
537               SRNAMT = 'ZSPCON'
538               CALL ZSPCON( UPLO, N, AFAC, IWORK, ANORM, RCOND, WORK,
539     $                      INFO )
540*
541*              Check error code from ZSPCON.
542*
543               IF( INFO.NE.0 )
544     $            CALL ALAERH( PATH, 'ZSPCON', INFO, 0, UPLO, N, N, -1,
545     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
546*
547               RESULT( 8 ) = DGET06( RCOND, RCONDC )
548*
549*              Print the test ratio if it is .GE. THRESH.
550*
551               IF( RESULT( 8 ).GE.THRESH ) THEN
552                  IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
553     $               CALL ALAHD( NOUT, PATH )
554                  WRITE( NOUT, FMT = 9999 )UPLO, N, IMAT, 8,
555     $               RESULT( 8 )
556                  NFAIL = NFAIL + 1
557               END IF
558               NRUN = NRUN + 1
559  150       CONTINUE
560  160    CONTINUE
561  170 CONTINUE
562*
563*     Print a summary of the results.
564*
565      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
566*
567 9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', type ', I2, ', test ',
568     $      I2, ', ratio =', G12.5 )
569 9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
570     $      I2, ', test(', I2, ') =', G12.5 )
571      RETURN
572*
573*     End of ZCHKSP
574*
575      END
576