1*> \brief \b CDRVRF3
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 CDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
12*      +                    S_WORK_CLANGE, C_WORK_CGEQRF, TAU )
13*
14*       .. Scalar Arguments ..
15*       INTEGER            LDA, NN, NOUT
16*       REAL               THRESH
17*       ..
18*       .. Array Arguments ..
19*       INTEGER            NVAL( NN )
20*       REAL               S_WORK_CLANGE( * )
21*       COMPLEX            A( LDA, * ), ARF( * ), B1( LDA, * ),
22*      +                   B2( LDA, * )
23*       COMPLEX            C_WORK_CGEQRF( * ), TAU( * )
24*       ..
25*
26*
27*> \par Purpose:
28*  =============
29*>
30*> \verbatim
31*>
32*> CDRVRF3 tests the LAPACK RFP routines:
33*>     CTFSM
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] NOUT
40*> \verbatim
41*>          NOUT is INTEGER
42*>                The unit number for output.
43*> \endverbatim
44*>
45*> \param[in] NN
46*> \verbatim
47*>          NN is INTEGER
48*>                The number of values of N contained in the vector NVAL.
49*> \endverbatim
50*>
51*> \param[in] NVAL
52*> \verbatim
53*>          NVAL is INTEGER array, dimension (NN)
54*>                The values of the matrix dimension N.
55*> \endverbatim
56*>
57*> \param[in] THRESH
58*> \verbatim
59*>          THRESH is DOUBLE PRECISION
60*>                The threshold value for the test ratios.  A result is
61*>                included in the output file if RESULT >= THRESH.  To have
62*>                every test ratio printed, use THRESH = 0.
63*> \endverbatim
64*>
65*> \param[out] A
66*> \verbatim
67*>          A is COMPLEX*16 array, dimension (LDA,NMAX)
68*> \endverbatim
69*>
70*> \param[in] LDA
71*> \verbatim
72*>          LDA is INTEGER
73*>                The leading dimension of the array A.  LDA >= max(1,NMAX).
74*> \endverbatim
75*>
76*> \param[out] ARF
77*> \verbatim
78*>          ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).
79*> \endverbatim
80*>
81*> \param[out] B1
82*> \verbatim
83*>          B1 is COMPLEX array, dimension (LDA,NMAX)
84*> \endverbatim
85*>
86*> \param[out] B2
87*> \verbatim
88*>          B2 is COMPLEX array, dimension (LDA,NMAX)
89*> \endverbatim
90*>
91*> \param[out] S_WORK_CLANGE
92*> \verbatim
93*>          S_WORK_CLANGE is REAL array, dimension (NMAX)
94*> \endverbatim
95*>
96*> \param[out] C_WORK_CGEQRF
97*> \verbatim
98*>          C_WORK_CGEQRF is COMPLEX array, dimension (NMAX)
99*> \endverbatim
100*>
101*> \param[out] TAU
102*> \verbatim
103*>          TAU is COMPLEX array, dimension (NMAX)
104*> \endverbatim
105*
106*  Authors:
107*  ========
108*
109*> \author Univ. of Tennessee
110*> \author Univ. of California Berkeley
111*> \author Univ. of Colorado Denver
112*> \author NAG Ltd.
113*
114*> \ingroup complex_lin
115*
116*  =====================================================================
117      SUBROUTINE CDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
118     +                    S_WORK_CLANGE, C_WORK_CGEQRF, TAU )
119*
120*  -- LAPACK test routine --
121*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
122*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123*
124*     .. Scalar Arguments ..
125      INTEGER            LDA, NN, NOUT
126      REAL               THRESH
127*     ..
128*     .. Array Arguments ..
129      INTEGER            NVAL( NN )
130      REAL               S_WORK_CLANGE( * )
131      COMPLEX            A( LDA, * ), ARF( * ), B1( LDA, * ),
132     +                   B2( LDA, * )
133      COMPLEX            C_WORK_CGEQRF( * ), TAU( * )
134*     ..
135*
136*  =====================================================================
137*     ..
138*     .. Parameters ..
139      COMPLEX            ZERO, ONE
140      PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) ,
141     +                     ONE  = ( 1.0E+0, 0.0E+0 ) )
142      INTEGER            NTESTS
143      PARAMETER          ( NTESTS = 1 )
144*     ..
145*     .. Local Scalars ..
146      CHARACTER          UPLO, CFORM, DIAG, TRANS, SIDE
147      INTEGER            I, IFORM, IIM, IIN, INFO, IUPLO, J, M, N, NA,
148     +                   NFAIL, NRUN, ISIDE, IDIAG, IALPHA, ITRANS
149      COMPLEX            ALPHA
150      REAL               EPS
151*     ..
152*     .. Local Arrays ..
153      CHARACTER          UPLOS( 2 ), FORMS( 2 ), TRANSS( 2 ),
154     +                   DIAGS( 2 ), SIDES( 2 )
155      INTEGER            ISEED( 4 ), ISEEDY( 4 )
156      REAL               RESULT( NTESTS )
157*     ..
158*     .. External Functions ..
159      REAL               SLAMCH, CLANGE
160      COMPLEX            CLARND
161      EXTERNAL           SLAMCH, CLARND, CLANGE
162*     ..
163*     .. External Subroutines ..
164      EXTERNAL           CTRTTF, CGEQRF, CGEQLF, CTFSM, CTRSM
165*     ..
166*     .. Intrinsic Functions ..
167      INTRINSIC          MAX, SQRT
168*     ..
169*     .. Scalars in Common ..
170      CHARACTER*32       SRNAMT
171*     ..
172*     .. Common blocks ..
173      COMMON             / SRNAMC / SRNAMT
174*     ..
175*     .. Data statements ..
176      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
177      DATA               UPLOS  / 'U', 'L' /
178      DATA               FORMS  / 'N', 'C' /
179      DATA               SIDES  / 'L', 'R' /
180      DATA               TRANSS / 'N', 'C' /
181      DATA               DIAGS  / 'N', 'U' /
182*     ..
183*     .. Executable Statements ..
184*
185*     Initialize constants and the random number seed.
186*
187      NRUN = 0
188      NFAIL = 0
189      INFO = 0
190      DO 10 I = 1, 4
191         ISEED( I ) = ISEEDY( I )
192   10 CONTINUE
193      EPS = SLAMCH( 'Precision' )
194*
195      DO 170 IIM = 1, NN
196*
197         M = NVAL( IIM )
198*
199         DO 160 IIN = 1, NN
200*
201            N = NVAL( IIN )
202*
203            DO 150 IFORM = 1, 2
204*
205               CFORM = FORMS( IFORM )
206*
207               DO 140 IUPLO = 1, 2
208*
209                  UPLO = UPLOS( IUPLO )
210*
211                  DO 130 ISIDE = 1, 2
212*
213                     SIDE = SIDES( ISIDE )
214*
215                     DO 120 ITRANS = 1, 2
216*
217                        TRANS = TRANSS( ITRANS )
218*
219                        DO 110 IDIAG = 1, 2
220*
221                           DIAG = DIAGS( IDIAG )
222*
223                           DO 100 IALPHA = 1, 3
224*
225                              IF ( IALPHA.EQ. 1) THEN
226                                 ALPHA = ZERO
227                              ELSE IF ( IALPHA.EQ. 2) THEN
228                                 ALPHA = ONE
229                              ELSE
230                                 ALPHA = CLARND( 4, ISEED )
231                              END IF
232*
233*                             All the parameters are set:
234*                                CFORM, SIDE, UPLO, TRANS, DIAG, M, N,
235*                                and ALPHA
236*                             READY TO TEST!
237*
238                              NRUN = NRUN + 1
239*
240                              IF ( ISIDE.EQ.1 ) THEN
241*
242*                                The case ISIDE.EQ.1 is when SIDE.EQ.'L'
243*                                -> A is M-by-M ( B is M-by-N )
244*
245                                 NA = M
246*
247                              ELSE
248*
249*                                The case ISIDE.EQ.2 is when SIDE.EQ.'R'
250*                                -> A is N-by-N ( B is M-by-N )
251*
252                                 NA = N
253*
254                              END IF
255*
256*                             Generate A our NA--by--NA triangular
257*                             matrix.
258*                             Our test is based on forward error so we
259*                             do want A to be well conditioned! To get
260*                             a well-conditioned triangular matrix, we
261*                             take the R factor of the QR/LQ factorization
262*                             of a random matrix.
263*
264                              DO J = 1, NA
265                                 DO I = 1, NA
266                                    A( I, J) = CLARND( 4, ISEED )
267                                 END DO
268                              END DO
269*
270                              IF ( IUPLO.EQ.1 ) THEN
271*
272*                                The case IUPLO.EQ.1 is when SIDE.EQ.'U'
273*                                -> QR factorization.
274*
275                                 SRNAMT = 'CGEQRF'
276                                 CALL CGEQRF( NA, NA, A, LDA, TAU,
277     +                                        C_WORK_CGEQRF, LDA,
278     +                                        INFO )
279                              ELSE
280*
281*                                The case IUPLO.EQ.2 is when SIDE.EQ.'L'
282*                                -> QL factorization.
283*
284                                 SRNAMT = 'CGELQF'
285                                 CALL CGELQF( NA, NA, A, LDA, TAU,
286     +                                        C_WORK_CGEQRF, LDA,
287     +                                        INFO )
288                              END IF
289*
290*                             After the QR factorization, the diagonal
291*                             of A is made of real numbers, we multiply
292*                             by a random complex number of absolute
293*                             value 1.0E+00.
294*
295                              DO J = 1, NA
296                                 A( J, J) = A(J,J) * CLARND( 5, ISEED )
297                              END DO
298*
299*                             Store a copy of A in RFP format (in ARF).
300*
301                              SRNAMT = 'CTRTTF'
302                              CALL CTRTTF( CFORM, UPLO, NA, A, LDA, ARF,
303     +                                     INFO )
304*
305*                             Generate B1 our M--by--N right-hand side
306*                             and store a copy in B2.
307*
308                              DO J = 1, N
309                                 DO I = 1, M
310                                    B1( I, J) = CLARND( 4, ISEED )
311                                    B2( I, J) = B1( I, J)
312                                 END DO
313                              END DO
314*
315*                             Solve op( A ) X = B or X op( A ) = B
316*                             with CTRSM
317*
318                              SRNAMT = 'CTRSM'
319                              CALL CTRSM( SIDE, UPLO, TRANS, DIAG, M, N,
320     +                               ALPHA, A, LDA, B1, LDA )
321*
322*                             Solve op( A ) X = B or X op( A ) = B
323*                             with CTFSM
324*
325                              SRNAMT = 'CTFSM'
326                              CALL CTFSM( CFORM, SIDE, UPLO, TRANS,
327     +                                    DIAG, M, N, ALPHA, ARF, B2,
328     +                                    LDA )
329*
330*                             Check that the result agrees.
331*
332                              DO J = 1, N
333                                 DO I = 1, M
334                                    B1( I, J) = B2( I, J ) - B1( I, J )
335                                 END DO
336                              END DO
337*
338                              RESULT(1) = CLANGE( 'I', M, N, B1, LDA,
339     +                                            S_WORK_CLANGE )
340*
341                              RESULT(1) = RESULT(1) / SQRT( EPS )
342     +                                    / MAX ( MAX( M, N), 1 )
343*
344                              IF( RESULT(1).GE.THRESH ) THEN
345                                 IF( NFAIL.EQ.0 ) THEN
346                                    WRITE( NOUT, * )
347                                    WRITE( NOUT, FMT = 9999 )
348                                 END IF
349                                 WRITE( NOUT, FMT = 9997 ) 'CTFSM',
350     +                              CFORM, SIDE, UPLO, TRANS, DIAG, M,
351     +                              N, RESULT(1)
352                                 NFAIL = NFAIL + 1
353                              END IF
354*
355  100                      CONTINUE
356  110                   CONTINUE
357  120                CONTINUE
358  130             CONTINUE
359  140          CONTINUE
360  150       CONTINUE
361  160    CONTINUE
362  170 CONTINUE
363*
364*     Print a summary of the results.
365*
366      IF ( NFAIL.EQ.0 ) THEN
367         WRITE( NOUT, FMT = 9996 ) 'CTFSM', NRUN
368      ELSE
369         WRITE( NOUT, FMT = 9995 ) 'CTFSM', NFAIL, NRUN
370      END IF
371*
372 9999 FORMAT( 1X, ' *** Error(s) or Failure(s) while testing CTFSM
373     +         ***')
374 9997 FORMAT( 1X, '     Failure in ',A5,', CFORM=''',A1,''',',
375     + ' SIDE=''',A1,''',',' UPLO=''',A1,''',',' TRANS=''',A1,''',',
376     + ' DIAG=''',A1,''',',' M=',I3,', N =', I3,', test=',G12.5)
377 9996 FORMAT( 1X, 'All tests for ',A5,' auxiliary routine passed the ',
378     +        'threshold ( ',I5,' tests run)')
379 9995 FORMAT( 1X, A6, ' auxiliary routine: ',I5,' out of ',I5,
380     +        ' tests failed to pass the threshold')
381*
382      RETURN
383*
384*     End of CDRVRF3
385*
386      END
387