1*> \brief \b SCHKLQ
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 SCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
12*                          NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
13*                          B, X, XACT, TAU, WORK, RWORK, 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            MVAL( * ), NBVAL( * ), NVAL( * ),
23*      $                   NXVAL( * )
24*       REAL               A( * ), AC( * ), AF( * ), AL( * ), AQ( * ),
25*      $                   B( * ), RWORK( * ), TAU( * ), WORK( * ),
26*      $                   X( * ), XACT( * )
27*       ..
28*
29*
30*> \par Purpose:
31*  =============
32*>
33*> \verbatim
34*>
35*> SCHKLQ tests SGELQF, SORGLQ and SORMLQ.
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] AL
137*> \verbatim
138*>          AL 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[in] NOUT
177*> \verbatim
178*>          NOUT is INTEGER
179*>          The unit number for output.
180*> \endverbatim
181*
182*  Authors:
183*  ========
184*
185*> \author Univ. of Tennessee
186*> \author Univ. of California Berkeley
187*> \author Univ. of Colorado Denver
188*> \author NAG Ltd.
189*
190*> \date November 2011
191*
192*> \ingroup single_lin
193*
194*  =====================================================================
195      SUBROUTINE SCHKLQ( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
196     $                   NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC,
197     $                   B, X, XACT, TAU, WORK, RWORK, NOUT )
198*
199*  -- LAPACK test routine (version 3.4.0) --
200*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
201*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
202*     November 2011
203*
204*     .. Scalar Arguments ..
205      LOGICAL            TSTERR
206      INTEGER            NM, NMAX, NN, NNB, NOUT, NRHS
207      REAL               THRESH
208*     ..
209*     .. Array Arguments ..
210      LOGICAL            DOTYPE( * )
211      INTEGER            MVAL( * ), NBVAL( * ), NVAL( * ),
212     $                   NXVAL( * )
213      REAL               A( * ), AC( * ), AF( * ), AL( * ), AQ( * ),
214     $                   B( * ), RWORK( * ), TAU( * ), WORK( * ),
215     $                   X( * ), XACT( * )
216*     ..
217*
218*  =====================================================================
219*
220*     .. Parameters ..
221      INTEGER            NTESTS
222      PARAMETER          ( NTESTS = 7 )
223      INTEGER            NTYPES
224      PARAMETER          ( NTYPES = 8 )
225      REAL               ZERO
226      PARAMETER          ( ZERO = 0.0E0 )
227*     ..
228*     .. Local Scalars ..
229      CHARACTER          DIST, TYPE
230      CHARACTER*3        PATH
231      INTEGER            I, IK, IM, IMAT, IN, INB, INFO, K, KL, KU, LDA,
232     $                   LWORK, M, MINMN, MODE, N, NB, NERRS, NFAIL, NK,
233     $                   NRUN, NT, NX
234      REAL               ANORM, CNDNUM
235*     ..
236*     .. Local Arrays ..
237      INTEGER            ISEED( 4 ), ISEEDY( 4 ), KVAL( 4 )
238      REAL               RESULT( NTESTS )
239*     ..
240*     .. External Subroutines ..
241      EXTERNAL           ALAERH, ALAHD, ALASUM, SERRLQ, SGELQS, SGET02,
242     $                   SLACPY, SLARHS, SLATB4, SLATMS, SLQT01, SLQT02,
243     $                   SLQT03, XLAENV
244*     ..
245*     .. Intrinsic Functions ..
246      INTRINSIC          MAX, MIN
247*     ..
248*     .. Scalars in Common ..
249      LOGICAL            LERR, OK
250      CHARACTER*32       SRNAMT
251      INTEGER            INFOT, NUNIT
252*     ..
253*     .. Common blocks ..
254      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
255      COMMON             / SRNAMC / SRNAMT
256*     ..
257*     .. Data statements ..
258      DATA               ISEEDY / 1988, 1989, 1990, 1991 /
259*     ..
260*     .. Executable Statements ..
261*
262*     Initialize constants and the random number seed.
263*
264      PATH( 1: 1 ) = 'Single precision'
265      PATH( 2: 3 ) = 'LQ'
266      NRUN = 0
267      NFAIL = 0
268      NERRS = 0
269      DO 10 I = 1, 4
270         ISEED( I ) = ISEEDY( I )
271   10 CONTINUE
272*
273*     Test the error exits
274*
275      IF( TSTERR )
276     $   CALL SERRLQ( PATH, NOUT )
277      INFOT = 0
278      CALL XLAENV( 2, 2 )
279*
280      LDA = NMAX
281      LWORK = NMAX*MAX( NMAX, NRHS )
282*
283*     Do for each value of M in MVAL.
284*
285      DO 70 IM = 1, NM
286         M = MVAL( IM )
287*
288*        Do for each value of N in NVAL.
289*
290         DO 60 IN = 1, NN
291            N = NVAL( IN )
292            MINMN = MIN( M, N )
293            DO 50 IMAT = 1, NTYPES
294*
295*              Do the tests only if DOTYPE( IMAT ) is true.
296*
297               IF( .NOT.DOTYPE( IMAT ) )
298     $            GO TO 50
299*
300*              Set up parameters with SLATB4 and generate a test matrix
301*              with SLATMS.
302*
303               CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
304     $                      CNDNUM, DIST )
305*
306               SRNAMT = 'SLATMS'
307               CALL SLATMS( M, N, DIST, ISEED, TYPE, RWORK, MODE,
308     $                      CNDNUM, ANORM, KL, KU, 'No packing', A, LDA,
309     $                      WORK, INFO )
310*
311*              Check error code from SLATMS.
312*
313               IF( INFO.NE.0 ) THEN
314                  CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, N, -1,
315     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
316                  GO TO 50
317               END IF
318*
319*              Set some values for K: the first value must be MINMN,
320*              corresponding to the call of SLQT01; other values are
321*              used in the calls of SLQT02, and must not exceed MINMN.
322*
323               KVAL( 1 ) = MINMN
324               KVAL( 2 ) = 0
325               KVAL( 3 ) = 1
326               KVAL( 4 ) = MINMN / 2
327               IF( MINMN.EQ.0 ) THEN
328                  NK = 1
329               ELSE IF( MINMN.EQ.1 ) THEN
330                  NK = 2
331               ELSE IF( MINMN.LE.3 ) THEN
332                  NK = 3
333               ELSE
334                  NK = 4
335               END IF
336*
337*              Do for each value of K in KVAL
338*
339               DO 40 IK = 1, NK
340                  K = KVAL( IK )
341*
342*                 Do for each pair of values (NB,NX) in NBVAL and NXVAL.
343*
344                  DO 30 INB = 1, NNB
345                     NB = NBVAL( INB )
346                     CALL XLAENV( 1, NB )
347                     NX = NXVAL( INB )
348                     CALL XLAENV( 3, NX )
349                     DO I = 1, NTESTS
350                        RESULT( I ) = ZERO
351                     END DO
352                     NT = 2
353                     IF( IK.EQ.1 ) THEN
354*
355*                       Test SGELQF
356*
357                        CALL SLQT01( M, N, A, AF, AQ, AL, LDA, TAU,
358     $                               WORK, LWORK, RWORK, RESULT( 1 ) )
359                     ELSE IF( M.LE.N ) THEN
360*
361*                       Test SORGLQ, using factorization
362*                       returned by SLQT01
363*
364                        CALL SLQT02( M, N, K, A, AF, AQ, AL, LDA, TAU,
365     $                               WORK, LWORK, RWORK, RESULT( 1 ) )
366                     END IF
367                     IF( M.GE.K ) THEN
368*
369*                       Test SORMLQ, using factorization returned
370*                       by SLQT01
371*
372                        CALL SLQT03( M, N, K, AF, AC, AL, AQ, LDA, TAU,
373     $                               WORK, LWORK, RWORK, RESULT( 3 ) )
374                        NT = NT + 4
375*
376*                       If M>=N and K=N, call SGELQS to solve a system
377*                       with NRHS right hand sides and compute the
378*                       residual.
379*
380                        IF( K.EQ.M .AND. INB.EQ.1 ) THEN
381*
382*                          Generate a solution and set the right
383*                          hand side.
384*
385                           SRNAMT = 'SLARHS'
386                           CALL SLARHS( PATH, 'New', 'Full',
387     $                                  'No transpose', M, N, 0, 0,
388     $                                  NRHS, A, LDA, XACT, LDA, B, LDA,
389     $                                  ISEED, INFO )
390*
391                           CALL SLACPY( 'Full', M, NRHS, B, LDA, X,
392     $                                  LDA )
393                           SRNAMT = 'SGELQS'
394                           CALL SGELQS( M, N, NRHS, AF, LDA, TAU, X,
395     $                                  LDA, WORK, LWORK, INFO )
396*
397*                          Check error code from SGELQS.
398*
399                           IF( INFO.NE.0 )
400     $                        CALL ALAERH( PATH, 'SGELQS', INFO, 0, ' ',
401     $                                     M, N, NRHS, -1, NB, IMAT,
402     $                                     NFAIL, NERRS, NOUT )
403*
404                           CALL SGET02( 'No transpose', M, N, NRHS, A,
405     $                                  LDA, X, LDA, B, LDA, RWORK,
406     $                                  RESULT( 7 ) )
407                           NT = NT + 1
408                        END IF
409                     END IF
410*
411*                    Print information about the tests that did not
412*                    pass the threshold.
413*
414                     DO 20 I = 1, NTESTS
415                        IF( RESULT( I ).GE.THRESH ) THEN
416                           IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
417     $                        CALL ALAHD( NOUT, PATH )
418                           WRITE( NOUT, FMT = 9999 )M, N, K, NB, NX,
419     $                        IMAT, I, RESULT( I )
420                           NFAIL = NFAIL + 1
421                        END IF
422   20                CONTINUE
423                     NRUN = NRUN + NT
424   30             CONTINUE
425   40          CONTINUE
426   50       CONTINUE
427   60    CONTINUE
428   70 CONTINUE
429*
430*     Print a summary of the results.
431*
432      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
433*
434 9999 FORMAT( ' M=', I5, ', N=', I5, ', K=', I5, ', NB=', I4, ', NX=',
435     $      I5, ', type ', I2, ', test(', I2, ')=', G12.5 )
436      RETURN
437*
438*     End of SCHKLQ
439*
440      END
441