1*> \brief \b SCHKRQ
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 SCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
12*                          NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
13*                          B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT )
14*
15*       .. Scalar Arguments ..
16*       LOGICAL            TSTERR
17*       INTEGER            NM, NMAX, NN, NNB, NOUT, NRHS
18*       REAL               THRESH
19*       ..
20*       .. Array Arguments ..
21*       LOGICAL            DOTYPE( * )
22*       INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
23*      $                   NXVAL( * )
24*       REAL               A( * ), AC( * ), AF( * ), AQ( * ), AR( * ),
25*      $                   B( * ), RWORK( * ), TAU( * ), WORK( * ),
26*      $                   X( * ), XACT( * )
27*       ..
28*
29*
30*> \par Purpose:
31*  =============
32*>
33*> \verbatim
34*>
35*> SCHKRQ tests SGERQF, SORGRQ and SORMRQ.
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 and NX contained in the
77*>          vectors NBVAL and NXVAL.  The blocking parameters are used
78*>          in pairs (NB,NX).
79*> \endverbatim
80*>
81*> \param[in] NBVAL
82*> \verbatim
83*>          NBVAL is INTEGER array, dimension (NNB)
84*>          The values of the blocksize NB.
85*> \endverbatim
86*>
87*> \param[in] NXVAL
88*> \verbatim
89*>          NXVAL is INTEGER array, dimension (NNB)
90*>          The values of the crossover point NX.
91*> \endverbatim
92*>
93*> \param[in] NRHS
94*> \verbatim
95*>          NRHS is INTEGER
96*>          The number of right hand side vectors to be generated for
97*>          each linear system.
98*> \endverbatim
99*>
100*> \param[in] THRESH
101*> \verbatim
102*>          THRESH is REAL
103*>          The threshold value for the test ratios.  A result is
104*>          included in the output file if RESULT >= THRESH.  To have
105*>          every test ratio printed, use THRESH = 0.
106*> \endverbatim
107*>
108*> \param[in] TSTERR
109*> \verbatim
110*>          TSTERR is LOGICAL
111*>          Flag that indicates whether error exits are to be tested.
112*> \endverbatim
113*>
114*> \param[in] NMAX
115*> \verbatim
116*>          NMAX is INTEGER
117*>          The maximum value permitted for M or N, used in dimensioning
118*>          the work arrays.
119*> \endverbatim
120*>
121*> \param[out] A
122*> \verbatim
123*>          A is REAL array, dimension (NMAX*NMAX)
124*> \endverbatim
125*>
126*> \param[out] AF
127*> \verbatim
128*>          AF is REAL array, dimension (NMAX*NMAX)
129*> \endverbatim
130*>
131*> \param[out] AQ
132*> \verbatim
133*>          AQ is REAL array, dimension (NMAX*NMAX)
134*> \endverbatim
135*>
136*> \param[out] AR
137*> \verbatim
138*>          AR is REAL array, dimension (NMAX*NMAX)
139*> \endverbatim
140*>
141*> \param[out] AC
142*> \verbatim
143*>          AC is REAL array, dimension (NMAX*NMAX)
144*> \endverbatim
145*>
146*> \param[out] B
147*> \verbatim
148*>          B is REAL array, dimension (NMAX*NRHS)
149*> \endverbatim
150*>
151*> \param[out] X
152*> \verbatim
153*>          X is REAL array, dimension (NMAX*NRHS)
154*> \endverbatim
155*>
156*> \param[out] XACT
157*> \verbatim
158*>          XACT is REAL array, dimension (NMAX*NRHS)
159*> \endverbatim
160*>
161*> \param[out] TAU
162*> \verbatim
163*>          TAU is REAL array, dimension (NMAX)
164*> \endverbatim
165*>
166*> \param[out] WORK
167*> \verbatim
168*>          WORK is REAL array, dimension (NMAX*NMAX)
169*> \endverbatim
170*>
171*> \param[out] RWORK
172*> \verbatim
173*>          RWORK is REAL array, dimension (NMAX)
174*> \endverbatim
175*>
176*> \param[out] IWORK
177*> \verbatim
178*>          IWORK is INTEGER array, dimension (NMAX)
179*> \endverbatim
180*>
181*> \param[in] NOUT
182*> \verbatim
183*>          NOUT is INTEGER
184*>          The unit number for output.
185*> \endverbatim
186*
187*  Authors:
188*  ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup single_lin
196*
197*  =====================================================================
198      SUBROUTINE SCHKRQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
199     $                   NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC,
200     $                   B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT )
201*
202*  -- LAPACK test routine --
203*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
204*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205*
206*     .. Scalar Arguments ..
207      LOGICAL            TSTERR
208      INTEGER            NM, NMAX, NN, NNB, NOUT, NRHS
209      REAL               THRESH
210*     ..
211*     .. Array Arguments ..
212      LOGICAL            DOTYPE( * )
213      INTEGER            IWORK( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
214     $                   NXVAL( * )
215      REAL               A( * ), AC( * ), AF( * ), AQ( * ), AR( * ),
216     $                   B( * ), RWORK( * ), TAU( * ), WORK( * ),
217     $                   X( * ), XACT( * )
218*     ..
219*
220*  =====================================================================
221*
222*     .. Parameters ..
223      INTEGER            NTESTS
224      PARAMETER          ( NTESTS = 7 )
225      INTEGER            NTYPES
226      PARAMETER          ( NTYPES = 8 )
227      REAL               ZERO
228      PARAMETER          ( ZERO = 0.0E0 )
229*     ..
230*     .. Local Scalars ..
231      CHARACTER          DIST, TYPE
232      CHARACTER*3        PATH
233      INTEGER            I, IK, IM, IMAT, IN, INB, INFO, K, KL, KU, LDA,
234     $                   LWORK, M, MINMN, MODE, N, NB, NERRS, NFAIL, NK,
235     $                   NRUN, NT, NX
236      REAL               ANORM, CNDNUM
237*     ..
238*     .. Local Arrays ..
239      INTEGER            ISEED( 4 ), ISEEDY( 4 ), KVAL( 4 )
240      REAL               RESULT( NTESTS )
241*     ..
242*     .. External Subroutines ..
243      EXTERNAL           ALAERH, ALAHD, ALASUM, SERRRQ, SGERQS, SGET02,
244     $                   SLACPY, SLARHS, SLATB4, SLATMS, SRQT01, SRQT02,
245     $                   SRQT03, XLAENV
246*     ..
247*     .. Intrinsic Functions ..
248      INTRINSIC          MAX, MIN
249*     ..
250*     .. Scalars in Common ..
251      LOGICAL            LERR, OK
252      CHARACTER*32       SRNAMT
253      INTEGER            INFOT, NUNIT
254*     ..
255*     .. Common blocks ..
256      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
257      COMMON             / SRNAMC / SRNAMT
258*     ..
259*     .. Data statements ..
260      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
261*     ..
262*     .. Executable Statements ..
263*
264*     Initialize constants and the random number seed.
265*
266      PATH( 1: 1 ) = 'Single precision'
267      PATH( 2: 3 ) = 'RQ'
268      NRUN = 0
269      NFAIL = 0
270      NERRS = 0
271      DO 10 I = 1, 4
272         ISEED( I ) = ISEEDY( I )
273   10 CONTINUE
274*
275*     Test the error exits
276*
277      IF( TSTERR )
278     $   CALL SERRRQ( PATH, NOUT )
279      INFOT = 0
280      CALL XLAENV( 2, 2 )
281*
282      LDA = NMAX
283      LWORK = NMAX*MAX( NMAX, NRHS )
284*
285*     Do for each value of M in MVAL.
286*
287      DO 70 IM = 1, NM
288         M = MVAL( IM )
289*
290*        Do for each value of N in NVAL.
291*
292         DO 60 IN = 1, NN
293            N = NVAL( IN )
294            MINMN = MIN( M, N )
295            DO 50 IMAT = 1, NTYPES
296*
297*              Do the tests only if DOTYPE( IMAT ) is true.
298*
299               IF( .NOT.DOTYPE( IMAT ) )
300     $            GO TO 50
301*
302*              Set up parameters with SLATB4 and generate a test matrix
303*              with SLATMS.
304*
305               CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
306     $                      CNDNUM, DIST )
307*
308               SRNAMT = 'SLATMS'
309               CALL SLATMS( M, N, DIST, ISEED, TYPE, RWORK, MODE,
310     $                      CNDNUM, ANORM, KL, KU, 'No packing', A, LDA,
311     $                      WORK, INFO )
312*
313*              Check error code from SLATMS.
314*
315               IF( INFO.NE.0 ) THEN
316                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, N, -1,
317     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
318                  GO TO 50
319               END IF
320*
321*              Set some values for K: the first value must be MINMN,
322*              corresponding to the call of SRQT01; other values are
323*              used in the calls of SRQT02, and must not exceed MINMN.
324*
325               KVAL( 1 ) = MINMN
326               KVAL( 2 ) = 0
327               KVAL( 3 ) = 1
328               KVAL( 4 ) = MINMN / 2
329               IF( MINMN.EQ.0 ) THEN
330                  NK = 1
331               ELSE IF( MINMN.EQ.1 ) THEN
332                  NK = 2
333               ELSE IF( MINMN.LE.3 ) THEN
334                  NK = 3
335               ELSE
336                  NK = 4
337               END IF
338*
339*              Do for each value of K in KVAL
340*
341               DO 40 IK = 1, NK
342                  K = KVAL( IK )
343*
344*                 Do for each pair of values (NB,NX) in NBVAL and NXVAL.
345*
346                  DO 30 INB = 1, NNB
347                     NB = NBVAL( INB )
348                     CALL XLAENV( 1, NB )
349                     NX = NXVAL( INB )
350                     CALL XLAENV( 3, NX )
351                     DO I = 1, NTESTS
352                        RESULT( I ) = ZERO
353                     END DO
354                     NT = 2
355                     IF( IK.EQ.1 ) THEN
356*
357*                       Test SGERQF
358*
359                        CALL SRQT01( M, N, A, AF, AQ, AR, LDA, TAU,
360     $                               WORK, LWORK, RWORK, RESULT( 1 ) )
361                     ELSE IF( M.LE.N ) THEN
362*
363*                       Test SORGRQ, using factorization
364*                       returned by SRQT01
365*
366                        CALL SRQT02( M, N, K, A, AF, AQ, AR, LDA, TAU,
367     $                               WORK, LWORK, RWORK, RESULT( 1 ) )
368                     END IF
369                     IF( M.GE.K ) THEN
370*
371*                       Test SORMRQ, using factorization returned
372*                       by SRQT01
373*
374                        CALL SRQT03( M, N, K, AF, AC, AR, AQ, LDA, TAU,
375     $                               WORK, LWORK, RWORK, RESULT( 3 ) )
376                        NT = NT + 4
377*
378*                       If M>=N and K=N, call SGERQS to solve a system
379*                       with NRHS right hand sides and compute the
380*                       residual.
381*
382                        IF( K.EQ.M .AND. INB.EQ.1 ) THEN
383*
384*                          Generate a solution and set the right
385*                          hand side.
386*
387                           SRNAMT = 'SLARHS'
388                           CALL SLARHS( PATH, 'New', 'Full',
389     $                                  'No transpose', M, N, 0, 0,
390     $                                  NRHS, A, LDA, XACT, LDA, B, LDA,
391     $                                  ISEED, INFO )
392*
393                           CALL SLACPY( 'Full', M, NRHS, B, LDA,
394     $                                  X( N-M+1 ), LDA )
395                           SRNAMT = 'SGERQS'
396                           CALL SGERQS( M, N, NRHS, AF, LDA, TAU, X,
397     $                                  LDA, WORK, LWORK, INFO )
398*
399*                          Check error code from SGERQS.
400*
401                           IF( INFO.NE.0 )
402     $                        CALL ALAERH( PATH, 'SGERQS', INFO, 0, ' ',
403     $                                     M, N, NRHS, -1, NB, IMAT,
404     $                                     NFAIL, NERRS, NOUT )
405*
406                           CALL SGET02( 'No transpose', M, N, NRHS, A,
407     $                                  LDA, X, LDA, B, LDA, RWORK,
408     $                                  RESULT( 7 ) )
409                           NT = NT + 1
410                        END IF
411                     END IF
412*
413*                    Print information about the tests that did not
414*                    pass the threshold.
415*
416                     DO 20 I = 1, NT
417                        IF( RESULT( I ).GE.THRESH ) THEN
418                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
419     $                        CALL ALAHD( NOUT, PATH )
420                           WRITE( NOUT, FMT = 9999 )M, N, K, NB, NX,
421     $                        IMAT, I, RESULT( I )
422                           NFAIL = NFAIL + 1
423                        END IF
424   20                CONTINUE
425                     NRUN = NRUN + NT
426   30             CONTINUE
427   40          CONTINUE
428   50       CONTINUE
429   60    CONTINUE
430   70 CONTINUE
431*
432*     Print a summary of the results.
433*
434      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
435*
436 9999 FORMAT( ' M=', I5, ', N=', I5, ', K=', I5, ', NB=', I4, ', NX=',
437     $      I5, ', type ', I2, ', test(', I2, ')=', G12.5 )
438      RETURN
439*
440*     End of SCHKRQ
441*
442      END
443