1*> \brief \b CCHKGE
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 CCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
12*                          NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
13*                          X, XACT, WORK, RWORK, IWORK, NOUT )
14*
15*       .. Scalar Arguments ..
16*       LOGICAL            TSTERR
17*       INTEGER            NM, NMAX, NN, NNB, NNS, NOUT
18*       REAL               THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
23*      $                   NVAL( * )
24*       REAL               RWORK( * )
25*       COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
26*      $                   WORK( * ), X( * ), XACT( * )
27*       ..
28*
29*
30*> \par Purpose:
31*  =============
32*>
33*> \verbatim
34*>
35*> CCHKGE tests CGETRF, -TRI, -TRS, -RFS, and -CON.
36*> \endverbatim
37*
38*  Arguments:
39*  ==========
40*
41*> \param[in] DOTYPE
42*> \verbatim
43*>          DOTYPE is LOGICAL array, dimension (NTYPES)
44*>          The matrix types to be used for testing.  Matrices of type j
45*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
46*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
47*> \endverbatim
48*>
49*> \param[in] NM
50*> \verbatim
51*>          NM is INTEGER
52*>          The number of values of M contained in the vector MVAL.
53*> \endverbatim
54*>
55*> \param[in] MVAL
56*> \verbatim
57*>          MVAL is INTEGER array, dimension (NM)
58*>          The values of the matrix row dimension M.
59*> \endverbatim
60*>
61*> \param[in] NN
62*> \verbatim
63*>          NN is INTEGER
64*>          The number of values of N contained in the vector NVAL.
65*> \endverbatim
66*>
67*> \param[in] NVAL
68*> \verbatim
69*>          NVAL is INTEGER array, dimension (NN)
70*>          The values of the matrix column dimension N.
71*> \endverbatim
72*>
73*> \param[in] NNB
74*> \verbatim
75*>          NNB is INTEGER
76*>          The number of values of NB contained in the vector NBVAL.
77*> \endverbatim
78*>
79*> \param[in] NBVAL
80*> \verbatim
81*>          NBVAL is INTEGER array, dimension (NNB)
82*>          The values of the blocksize NB.
83*> \endverbatim
84*>
85*> \param[in] NNS
86*> \verbatim
87*>          NNS is INTEGER
88*>          The number of values of NRHS contained in the vector NSVAL.
89*> \endverbatim
90*>
91*> \param[in] NSVAL
92*> \verbatim
93*>          NSVAL is INTEGER array, dimension (NNS)
94*>          The values of the number of right hand sides NRHS.
95*> \endverbatim
96*>
97*> \param[in] THRESH
98*> \verbatim
99*>          THRESH is REAL
100*>          The threshold value for the test ratios.  A result is
101*>          included in the output file if RESULT >= THRESH.  To have
102*>          every test ratio printed, use THRESH = 0.
103*> \endverbatim
104*>
105*> \param[in] TSTERR
106*> \verbatim
107*>          TSTERR is LOGICAL
108*>          Flag that indicates whether error exits are to be tested.
109*> \endverbatim
110*>
111*> \param[in] NMAX
112*> \verbatim
113*>          NMAX is INTEGER
114*>          The maximum value permitted for M or N, used in dimensioning
115*>          the work arrays.
116*> \endverbatim
117*>
118*> \param[out] A
119*> \verbatim
120*>          A is COMPLEX array, dimension (NMAX*NMAX)
121*> \endverbatim
122*>
123*> \param[out] AFAC
124*> \verbatim
125*>          AFAC is COMPLEX array, dimension (NMAX*NMAX)
126*> \endverbatim
127*>
128*> \param[out] AINV
129*> \verbatim
130*>          AINV is COMPLEX array, dimension (NMAX*NMAX)
131*> \endverbatim
132*>
133*> \param[out] B
134*> \verbatim
135*>          B is COMPLEX array, dimension (NMAX*NSMAX)
136*>          where NSMAX is the largest entry in NSVAL.
137*> \endverbatim
138*>
139*> \param[out] X
140*> \verbatim
141*>          X is COMPLEX array, dimension (NMAX*NSMAX)
142*> \endverbatim
143*>
144*> \param[out] XACT
145*> \verbatim
146*>          XACT is COMPLEX array, dimension (NMAX*NSMAX)
147*> \endverbatim
148*>
149*> \param[out] WORK
150*> \verbatim
151*>          WORK is COMPLEX array, dimension
152*>                      (NMAX*max(3,NSMAX))
153*> \endverbatim
154*>
155*> \param[out] RWORK
156*> \verbatim
157*>          RWORK is REAL array, dimension
158*>                      (max(2*NMAX,2*NSMAX+NWORK))
159*> \endverbatim
160*>
161*> \param[out] IWORK
162*> \verbatim
163*>          IWORK is INTEGER array, dimension (NMAX)
164*> \endverbatim
165*>
166*> \param[in] NOUT
167*> \verbatim
168*>          NOUT is INTEGER
169*>          The unit number for output.
170*> \endverbatim
171*
172*  Authors:
173*  ========
174*
175*> \author Univ. of Tennessee
176*> \author Univ. of California Berkeley
177*> \author Univ. of Colorado Denver
178*> \author NAG Ltd.
179*
180*> \ingroup complex_lin
181*
182*  =====================================================================
183      SUBROUTINE CCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
184     $                   NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
185     $                   X, XACT, WORK, RWORK, IWORK, NOUT )
186*
187*  -- LAPACK test routine --
188*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
189*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191*     .. Scalar Arguments ..
192      LOGICAL            TSTERR
193      INTEGER            NM, NMAX, NN, NNB, NNS, NOUT
194      REAL               THRESH
195*     ..
196*     .. Array Arguments ..
197      LOGICAL            DOTYPE( * )
198      INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
199     $                   NVAL( * )
200      REAL               RWORK( * )
201      COMPLEX            A( * ), AFAC( * ), AINV( * ), B( * ),
202     $                   WORK( * ), X( * ), XACT( * )
203*     ..
204*
205*  =====================================================================
206*
207*     .. Parameters ..
208      REAL               ONE, ZERO
209      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
210      INTEGER            NTYPES
211      PARAMETER          ( NTYPES = 11 )
212      INTEGER            NTESTS
213      PARAMETER          ( NTESTS = 8 )
214      INTEGER            NTRAN
215      PARAMETER          ( NTRAN = 3 )
216*     ..
217*     .. Local Scalars ..
218      LOGICAL            TRFCON, ZEROT
219      CHARACTER          DIST, NORM, TRANS, TYPE, XTYPE
220      CHARACTER*3        PATH
221      INTEGER            I, IM, IMAT, IN, INB, INFO, IOFF, IRHS, ITRAN,
222     $                   IZERO, K, KL, KU, LDA, LWORK, M, MODE, N, NB,
223     $                   NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
224      REAL               AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, DUMMY,
225     $                   RCOND, RCONDC, RCONDI, RCONDO
226*     ..
227*     .. Local Arrays ..
228      CHARACTER          TRANSS( NTRAN )
229      INTEGER            ISEED( 4 ), ISEEDY( 4 )
230      REAL               RESULT( NTESTS )
231*     ..
232*     .. External Functions ..
233      REAL               CLANGE, SGET06
234      EXTERNAL           CLANGE, SGET06
235*     ..
236*     .. External Subroutines ..
237      EXTERNAL           ALAERH, ALAHD, ALASUM, CERRGE, CGECON, CGERFS,
238     $                   CGET01, CGET02, CGET03, CGET04, CGET07, CGETRF,
239     $                   CGETRI, CGETRS, CLACPY, CLARHS, CLASET, CLATB4,
240     $                   CLATMS, XLAENV
241*     ..
242*     .. Intrinsic Functions ..
243      INTRINSIC          CMPLX, MAX, MIN
244*     ..
245*     .. Scalars in Common ..
246      LOGICAL            LERR, OK
247      CHARACTER*32       SRNAMT
248      INTEGER            INFOT, NUNIT
249*     ..
250*     .. Common blocks ..
251      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
252      COMMON             / SRNAMC / SRNAMT
253*     ..
254*     .. Data statements ..
255      DATA               ISEEDY / 1988, 1989, 1990, 1991 / ,
256     $                   TRANSS / 'N', 'T', 'C' /
257*     ..
258*     .. Executable Statements ..
259*
260*     Initialize constants and the random number seed.
261*
262      PATH( 1: 1 ) = 'Complex precision'
263      PATH( 2: 3 ) = 'GE'
264      NRUN = 0
265      NFAIL = 0
266      NERRS = 0
267      DO 10 I = 1, 4
268         ISEED( I ) = ISEEDY( I )
269   10 CONTINUE
270*
271*     Test the error exits
272*
273      CALL XLAENV( 1, 1 )
274      IF( TSTERR )
275     $   CALL CERRGE( PATH, NOUT )
276      INFOT = 0
277      CALL XLAENV( 2, 2 )
278*
279*     Do for each value of M in MVAL
280*
281      DO 120 IM = 1, NM
282         M = MVAL( IM )
283         LDA = MAX( 1, M )
284*
285*        Do for each value of N in NVAL
286*
287         DO 110 IN = 1, NN
288            N = NVAL( IN )
289            XTYPE = 'N'
290            NIMAT = NTYPES
291            IF( M.LE.0 .OR. N.LE.0 )
292     $         NIMAT = 1
293*
294            DO 100 IMAT = 1, NIMAT
295*
296*              Do the tests only if DOTYPE( IMAT ) is true.
297*
298               IF( .NOT.DOTYPE( IMAT ) )
299     $            GO TO 100
300*
301*              Skip types 5, 6, or 7 if the matrix size is too small.
302*
303               ZEROT = IMAT.GE.5 .AND. IMAT.LE.7
304               IF( ZEROT .AND. N.LT.IMAT-4 )
305     $            GO TO 100
306*
307*              Set up parameters with CLATB4 and generate a test matrix
308*              with CLATMS.
309*
310               CALL CLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
311     $                      CNDNUM, DIST )
312*
313               SRNAMT = 'CLATMS'
314               CALL CLATMS( M, N, DIST, ISEED, TYPE, RWORK, MODE,
315     $                      CNDNUM, ANORM, KL, KU, 'No packing', A, LDA,
316     $                      WORK, INFO )
317*
318*              Check error code from CLATMS.
319*
320               IF( INFO.NE.0 ) THEN
321                  CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', M, N, -1,
322     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
323                  GO TO 100
324               END IF
325*
326*              For types 5-7, zero one or more columns of the matrix to
327*              test that INFO is returned correctly.
328*
329               IF( ZEROT ) THEN
330                  IF( IMAT.EQ.5 ) THEN
331                     IZERO = 1
332                  ELSE IF( IMAT.EQ.6 ) THEN
333                     IZERO = MIN( M, N )
334                  ELSE
335                     IZERO = MIN( M, N ) / 2 + 1
336                  END IF
337                  IOFF = ( IZERO-1 )*LDA
338                  IF( IMAT.LT.7 ) THEN
339                     DO 20 I = 1, M
340                        A( IOFF+I ) = ZERO
341   20                CONTINUE
342                  ELSE
343                     CALL CLASET( 'Full', M, N-IZERO+1, CMPLX( ZERO ),
344     $                            CMPLX( ZERO ), A( IOFF+1 ), LDA )
345                  END IF
346               ELSE
347                  IZERO = 0
348               END IF
349*
350*              These lines, if used in place of the calls in the DO 60
351*              loop, cause the code to bomb on a Sun SPARCstation.
352*
353*               ANORMO = CLANGE( 'O', M, N, A, LDA, RWORK )
354*               ANORMI = CLANGE( 'I', M, N, A, LDA, RWORK )
355*
356*              Do for each blocksize in NBVAL
357*
358               DO 90 INB = 1, NNB
359                  NB = NBVAL( INB )
360                  CALL XLAENV( 1, NB )
361*
362*                 Compute the LU factorization of the matrix.
363*
364                  CALL CLACPY( 'Full', M, N, A, LDA, AFAC, LDA )
365                  SRNAMT = 'CGETRF'
366                  CALL CGETRF( M, N, AFAC, LDA, IWORK, INFO )
367*
368*                 Check error code from CGETRF.
369*
370                  IF( INFO.NE.IZERO )
371     $               CALL ALAERH( PATH, 'CGETRF', INFO, IZERO, ' ', M,
372     $                            N, -1, -1, NB, IMAT, NFAIL, NERRS,
373     $                            NOUT )
374                  TRFCON = .FALSE.
375*
376*+    TEST 1
377*                 Reconstruct matrix from factors and compute residual.
378*
379                  CALL CLACPY( 'Full', M, N, AFAC, LDA, AINV, LDA )
380                  CALL CGET01( M, N, A, LDA, AINV, LDA, IWORK, RWORK,
381     $                         RESULT( 1 ) )
382                  NT = 1
383*
384*+    TEST 2
385*                 Form the inverse if the factorization was successful
386*                 and compute the residual.
387*
388                  IF( M.EQ.N .AND. INFO.EQ.0 ) THEN
389                     CALL CLACPY( 'Full', N, N, AFAC, LDA, AINV, LDA )
390                     SRNAMT = 'CGETRI'
391                     NRHS = NSVAL( 1 )
392                     LWORK = NMAX*MAX( 3, NRHS )
393                     CALL CGETRI( N, AINV, LDA, IWORK, WORK, LWORK,
394     $                            INFO )
395*
396*                    Check error code from CGETRI.
397*
398                     IF( INFO.NE.0 )
399     $                  CALL ALAERH( PATH, 'CGETRI', INFO, 0, ' ', N, N,
400     $                               -1, -1, NB, IMAT, NFAIL, NERRS,
401     $                               NOUT )
402*
403*                    Compute the residual for the matrix times its
404*                    inverse.  Also compute the 1-norm condition number
405*                    of A.
406*
407                     CALL CGET03( N, A, LDA, AINV, LDA, WORK, LDA,
408     $                            RWORK, RCONDO, RESULT( 2 ) )
409                     ANORMO = CLANGE( 'O', M, N, A, LDA, RWORK )
410*
411*                    Compute the infinity-norm condition number of A.
412*
413                     ANORMI = CLANGE( 'I', M, N, A, LDA, RWORK )
414                     AINVNM = CLANGE( 'I', N, N, AINV, LDA, RWORK )
415                     IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
416                        RCONDI = ONE
417                     ELSE
418                        RCONDI = ( ONE / ANORMI ) / AINVNM
419                     END IF
420                     NT = 2
421                  ELSE
422*
423*                    Do only the condition estimate if INFO > 0.
424*
425                     TRFCON = .TRUE.
426                     ANORMO = CLANGE( 'O', M, N, A, LDA, RWORK )
427                     ANORMI = CLANGE( 'I', M, N, A, LDA, RWORK )
428                     RCONDO = ZERO
429                     RCONDI = ZERO
430                  END IF
431*
432*                 Print information about the tests so far that did not
433*                 pass the threshold.
434*
435                  DO 30 K = 1, NT
436                     IF( RESULT( K ).GE.THRESH ) THEN
437                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
438     $                     CALL ALAHD( NOUT, PATH )
439                        WRITE( NOUT, FMT = 9999 )M, N, NB, IMAT, K,
440     $                     RESULT( K )
441                        NFAIL = NFAIL + 1
442                     END IF
443   30             CONTINUE
444                  NRUN = NRUN + NT
445*
446*                 Skip the remaining tests if this is not the first
447*                 block size or if M .ne. N.  Skip the solve tests if
448*                 the matrix is singular.
449*
450                  IF( INB.GT.1 .OR. M.NE.N )
451     $               GO TO 90
452                  IF( TRFCON )
453     $               GO TO 70
454*
455                  DO 60 IRHS = 1, NNS
456                     NRHS = NSVAL( IRHS )
457                     XTYPE = 'N'
458*
459                     DO 50 ITRAN = 1, NTRAN
460                        TRANS = TRANSS( ITRAN )
461                        IF( ITRAN.EQ.1 ) THEN
462                           RCONDC = RCONDO
463                        ELSE
464                           RCONDC = RCONDI
465                        END IF
466*
467*+    TEST 3
468*                       Solve and compute residual for A * X = B.
469*
470                        SRNAMT = 'CLARHS'
471                        CALL CLARHS( PATH, XTYPE, ' ', TRANS, N, N, KL,
472     $                               KU, NRHS, A, LDA, XACT, LDA, B,
473     $                               LDA, ISEED, INFO )
474                        XTYPE = 'C'
475*
476                        CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
477                        SRNAMT = 'CGETRS'
478                        CALL CGETRS( TRANS, N, NRHS, AFAC, LDA, IWORK,
479     $                               X, LDA, INFO )
480*
481*                       Check error code from CGETRS.
482*
483                        IF( INFO.NE.0 )
484     $                     CALL ALAERH( PATH, 'CGETRS', INFO, 0, TRANS,
485     $                                  N, N, -1, -1, NRHS, IMAT, NFAIL,
486     $                                  NERRS, NOUT )
487*
488                        CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK,
489     $                               LDA )
490                        CALL CGET02( TRANS, N, N, NRHS, A, LDA, X, LDA,
491     $                               WORK, LDA, RWORK, RESULT( 3 ) )
492*
493*+    TEST 4
494*                       Check solution from generated exact solution.
495*
496                        CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
497     $                               RESULT( 4 ) )
498*
499*+    TESTS 5, 6, and 7
500*                       Use iterative refinement to improve the
501*                       solution.
502*
503                        SRNAMT = 'CGERFS'
504                        CALL CGERFS( TRANS, N, NRHS, A, LDA, AFAC, LDA,
505     $                               IWORK, B, LDA, X, LDA, RWORK,
506     $                               RWORK( NRHS+1 ), WORK,
507     $                               RWORK( 2*NRHS+1 ), INFO )
508*
509*                       Check error code from CGERFS.
510*
511                        IF( INFO.NE.0 )
512     $                     CALL ALAERH( PATH, 'CGERFS', INFO, 0, TRANS,
513     $                                  N, N, -1, -1, NRHS, IMAT, NFAIL,
514     $                                  NERRS, NOUT )
515*
516                        CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
517     $                               RESULT( 5 ) )
518                        CALL CGET07( TRANS, N, NRHS, A, LDA, B, LDA, X,
519     $                               LDA, XACT, LDA, RWORK, .TRUE.,
520     $                               RWORK( NRHS+1 ), RESULT( 6 ) )
521*
522*                       Print information about the tests that did not
523*                       pass the threshold.
524*
525                        DO 40 K = 3, 7
526                           IF( RESULT( K ).GE.THRESH ) THEN
527                              IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
528     $                           CALL ALAHD( NOUT, PATH )
529                              WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS,
530     $                           IMAT, K, RESULT( K )
531                              NFAIL = NFAIL + 1
532                           END IF
533   40                   CONTINUE
534                        NRUN = NRUN + 5
535   50                CONTINUE
536   60             CONTINUE
537*
538*+    TEST 8
539*                    Get an estimate of RCOND = 1/CNDNUM.
540*
541   70             CONTINUE
542                  DO 80 ITRAN = 1, 2
543                     IF( ITRAN.EQ.1 ) THEN
544                        ANORM = ANORMO
545                        RCONDC = RCONDO
546                        NORM = 'O'
547                     ELSE
548                        ANORM = ANORMI
549                        RCONDC = RCONDI
550                        NORM = 'I'
551                     END IF
552                     SRNAMT = 'CGECON'
553                     CALL CGECON( NORM, N, AFAC, LDA, ANORM, RCOND,
554     $                            WORK, RWORK, INFO )
555*
556*                       Check error code from CGECON.
557*
558                     IF( INFO.NE.0 )
559     $                  CALL ALAERH( PATH, 'CGECON', INFO, 0, NORM, N,
560     $                               N, -1, -1, -1, IMAT, NFAIL, NERRS,
561     $                               NOUT )
562*
563*                       This line is needed on a Sun SPARCstation.
564*
565                     DUMMY = RCOND
566*
567                     RESULT( 8 ) = SGET06( RCOND, RCONDC )
568*
569*                    Print information about the tests that did not pass
570*                    the threshold.
571*
572                     IF( RESULT( 8 ).GE.THRESH ) THEN
573                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
574     $                     CALL ALAHD( NOUT, PATH )
575                        WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 8,
576     $                     RESULT( 8 )
577                        NFAIL = NFAIL + 1
578                     END IF
579                     NRUN = NRUN + 1
580   80             CONTINUE
581   90          CONTINUE
582  100       CONTINUE
583*
584  110    CONTINUE
585  120 CONTINUE
586*
587*     Print a summary of the results.
588*
589      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
590*
591 9999 FORMAT( ' M = ', I5, ', N =', I5, ', NB =', I4, ', type ', I2,
592     $      ', test(', I2, ') =', G12.5 )
593 9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
594     $      I2, ', test(', I2, ') =', G12.5 )
595 9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
596     $      ', test(', I2, ') =', G12.5 )
597      RETURN
598*
599*     End of CCHKGE
600*
601      END
602