LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
sdrvls.f
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1 *> \brief \b SDRVLS
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 SDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
12 * NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
13 * COPYB, C, S, COPYS, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NM, NN, NNB, NNS, NOUT
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER MVAL( * ), NBVAL( * ), NSVAL( * ),
23 * $ NVAL( * ), NXVAL( * )
24 * REAL A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
25 * $ COPYS( * ), S( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> SDRVLS tests the least squares driver routines SGELS, SGETSLS, SGELSS, SGELSY,
35 *> and SGELSD.
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 *> The matrix of type j is generated as follows:
48 *> j=1: A = U*D*V where U and V are random orthogonal matrices
49 *> and D has random entries (> 0.1) taken from a uniform
50 *> distribution (0,1). A is full rank.
51 *> j=2: The same of 1, but A is scaled up.
52 *> j=3: The same of 1, but A is scaled down.
53 *> j=4: A = U*D*V where U and V are random orthogonal matrices
54 *> and D has 3*min(M,N)/4 random entries (> 0.1) taken
55 *> from a uniform distribution (0,1) and the remaining
56 *> entries set to 0. A is rank-deficient.
57 *> j=5: The same of 4, but A is scaled up.
58 *> j=6: The same of 5, but A is scaled down.
59 *> \endverbatim
60 *>
61 *> \param[in] NM
62 *> \verbatim
63 *> NM is INTEGER
64 *> The number of values of M contained in the vector MVAL.
65 *> \endverbatim
66 *>
67 *> \param[in] MVAL
68 *> \verbatim
69 *> MVAL is INTEGER array, dimension (NM)
70 *> The values of the matrix row dimension M.
71 *> \endverbatim
72 *>
73 *> \param[in] NN
74 *> \verbatim
75 *> NN is INTEGER
76 *> The number of values of N contained in the vector NVAL.
77 *> \endverbatim
78 *>
79 *> \param[in] NVAL
80 *> \verbatim
81 *> NVAL is INTEGER array, dimension (NN)
82 *> The values of the matrix column dimension N.
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] NNB
98 *> \verbatim
99 *> NNB is INTEGER
100 *> The number of values of NB and NX contained in the
101 *> vectors NBVAL and NXVAL. The blocking parameters are used
102 *> in pairs (NB,NX).
103 *> \endverbatim
104 *>
105 *> \param[in] NBVAL
106 *> \verbatim
107 *> NBVAL is INTEGER array, dimension (NNB)
108 *> The values of the blocksize NB.
109 *> \endverbatim
110 *>
111 *> \param[in] NXVAL
112 *> \verbatim
113 *> NXVAL is INTEGER array, dimension (NNB)
114 *> The values of the crossover point NX.
115 *> \endverbatim
116 *>
117 *> \param[in] THRESH
118 *> \verbatim
119 *> THRESH is REAL
120 *> The threshold value for the test ratios. A result is
121 *> included in the output file if RESULT >= THRESH. To have
122 *> every test ratio printed, use THRESH = 0.
123 *> \endverbatim
124 *>
125 *> \param[in] TSTERR
126 *> \verbatim
127 *> TSTERR is LOGICAL
128 *> Flag that indicates whether error exits are to be tested.
129 *> \endverbatim
130 *>
131 *> \param[out] A
132 *> \verbatim
133 *> A is REAL array, dimension (MMAX*NMAX)
134 *> where MMAX is the maximum value of M in MVAL and NMAX is the
135 *> maximum value of N in NVAL.
136 *> \endverbatim
137 *>
138 *> \param[out] COPYA
139 *> \verbatim
140 *> COPYA is REAL array, dimension (MMAX*NMAX)
141 *> \endverbatim
142 *>
143 *> \param[out] B
144 *> \verbatim
145 *> B is REAL array, dimension (MMAX*NSMAX)
146 *> where MMAX is the maximum value of M in MVAL and NSMAX is the
147 *> maximum value of NRHS in NSVAL.
148 *> \endverbatim
149 *>
150 *> \param[out] COPYB
151 *> \verbatim
152 *> COPYB is REAL array, dimension (MMAX*NSMAX)
153 *> \endverbatim
154 *>
155 *> \param[out] C
156 *> \verbatim
157 *> C is REAL array, dimension (MMAX*NSMAX)
158 *> \endverbatim
159 *>
160 *> \param[out] S
161 *> \verbatim
162 *> S is REAL array, dimension
163 *> (min(MMAX,NMAX))
164 *> \endverbatim
165 *>
166 *> \param[out] COPYS
167 *> \verbatim
168 *> COPYS is REAL array, dimension
169 *> (min(MMAX,NMAX))
170 *> \endverbatim
171 *>
172 *> \param[in] NOUT
173 *> \verbatim
174 *> NOUT is INTEGER
175 *> The unit number for output.
176 *> \endverbatim
177 *
178 * Authors:
179 * ========
180 *
181 *> \author Univ. of Tennessee
182 *> \author Univ. of California Berkeley
183 *> \author Univ. of Colorado Denver
184 *> \author NAG Ltd.
185 *
186 *> \date November 2017
187 *
188 *> \ingroup single_lin
189 *
190 * =====================================================================
191  SUBROUTINE sdrvls( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
192  $ NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
193  $ COPYB, C, S, COPYS, NOUT )
194 *
195 * -- LAPACK test routine (version 3.8.0) --
196 * -- LAPACK is a software package provided by Univ. of Tennessee, --
197 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
198 * November 2017
199 *
200 * .. Scalar Arguments ..
201  LOGICAL tsterr
202  INTEGER nm, nn, nnb, nns, nout
203  REAL thresh
204 * ..
205 * .. Array Arguments ..
206  LOGICAL dotype( * )
207  INTEGER MVAL( * ), NBVAL( * ), NSVAL( * ),
208  $ nval( * ), nxval( * )
209  REAL A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
210  $ COPYS( * ), S( * )
211 * ..
212 *
213 * =====================================================================
214 *
215 * .. Parameters ..
216  INTEGER NTESTS
217  PARAMETER ( NTESTS = 16 )
218  INTEGER SMLSIZ
219  parameter( smlsiz = 25 )
220  REAL ONE, TWO, ZERO
221  parameter( one = 1.0e0, two = 2.0e0, zero = 0.0e0 )
222 * ..
223 * .. Local Scalars ..
224  CHARACTER TRANS
225  CHARACTER*3 PATH
226  INTEGER CRANK, I, IM, IMB, IN, INB, INFO, INS, IRANK,
227  $ iscale, itran, itype, j, k, lda, ldb, ldwork,
228  $ lwlsy, lwork, m, mnmin, n, nb, ncols, nerrs,
229  $ nfail, nrhs, nrows, nrun, rank, mb,
230  $ mmax, nmax, nsmax, liwork,
231  $ lwork_sgels, lwork_sgetsls, lwork_sgelss,
232  $ lwork_sgelsy, lwork_sgelsd
233  REAL EPS, NORMA, NORMB, RCOND
234 * ..
235 * .. Local Arrays ..
236  INTEGER ISEED( 4 ), ISEEDY( 4 ), IWQ( 1 )
237  REAL RESULT( NTESTS ), WQ( 1 )
238 * ..
239 * .. Allocatable Arrays ..
240  REAL, ALLOCATABLE :: WORK (:)
241  INTEGER, ALLOCATABLE :: IWORK (:)
242 * ..
243 * .. External Functions ..
244  REAL SASUM, SLAMCH, SQRT12, SQRT14, SQRT17
245  EXTERNAL SASUM, SLAMCH, SQRT12, SQRT14, SQRT17
246 * ..
247 * .. External Subroutines ..
248  EXTERNAL alaerh, alahd, alasvm, saxpy, serrls, sgels,
249  $ sgelsd, sgelss, sgelsy, sgemm, slacpy,
250  $ slarnv, sqrt13, sqrt15, sqrt16, sscal,
251  $ xlaenv, sgetsls
252 * ..
253 * .. Intrinsic Functions ..
254  INTRINSIC int, log, max, min, real, sqrt
255 * ..
256 * .. Scalars in Common ..
257  LOGICAL LERR, OK
258  CHARACTER*32 SRNAMT
259  INTEGER INFOT, IOUNIT
260 * ..
261 * .. Common blocks ..
262  COMMON / infoc / infot, iounit, ok, lerr
263  COMMON / srnamc / srnamt
264 * ..
265 * .. Data statements ..
266  DATA iseedy / 1988, 1989, 1990, 1991 /
267 * ..
268 * .. Executable Statements ..
269 *
270 * Initialize constants and the random number seed.
271 *
272  path( 1: 1 ) = 'SINGLE PRECISION'
273  path( 2: 3 ) = 'LS'
274  nrun = 0
275  nfail = 0
276  nerrs = 0
277  DO 10 i = 1, 4
278  iseed( i ) = iseedy( i )
279  10 CONTINUE
280  eps = slamch( 'Epsilon' )
281 *
282 * Threshold for rank estimation
283 *
284  rcond = sqrt( eps ) - ( sqrt( eps )-eps ) / 2
285 *
286 * Test the error exits
287 *
288  CALL xlaenv( 2, 2 )
289  CALL xlaenv( 9, smlsiz )
290  IF( tsterr )
291  $ CALL serrls( path, nout )
292 *
293 * Print the header if NM = 0 or NN = 0 and THRESH = 0.
294 *
295  IF( ( nm.EQ.0 .OR. nn.EQ.0 ) .AND. thresh.EQ.zero )
296  $ CALL alahd( nout, path )
297  infot = 0
298  CALL xlaenv( 2, 2 )
299  CALL xlaenv( 9, smlsiz )
300 *
301 * Compute maximal workspace needed for all routines
302 *
303  nmax = 0
304  mmax = 0
305  nsmax = 0
306  DO i = 1, nm
307  IF ( mval( i ).GT.mmax ) THEN
308  mmax = mval( i )
309  END IF
310  ENDDO
311  DO i = 1, nn
312  IF ( nval( i ).GT.nmax ) THEN
313  nmax = nval( i )
314  END IF
315  ENDDO
316  DO i = 1, nns
317  IF ( nsval( i ).GT.nsmax ) THEN
318  nsmax = nsval( i )
319  END IF
320  ENDDO
321  m = mmax
322  n = nmax
323  nrhs = nsmax
324  mnmin = max( min( m, n ), 1 )
325 *
326 * Compute workspace needed for routines
327 * SQRT14, SQRT17 (two side cases), SQRT15 and SQRT12
328 *
329  lwork = max( 1, ( m+n )*nrhs,
330  $ ( n+nrhs )*( m+2 ), ( m+nrhs )*( n+2 ),
331  $ max( m+mnmin, nrhs*mnmin,2*n+m ),
332  $ max( m*n+4*mnmin+max(m,n), m*n+2*mnmin+4*n ) )
333  liwork = 1
334 *
335 * Iterate through all test cases and compute necessary workspace
336 * sizes for ?GELS, ?GETSLS, ?GELSY, ?GELSS and ?GELSD routines.
337 *
338  DO im = 1, nm
339  m = mval( im )
340  lda = max( 1, m )
341  DO in = 1, nn
342  n = nval( in )
343  mnmin = max(min( m, n ),1)
344  ldb = max( 1, m, n )
345  DO ins = 1, nns
346  nrhs = nsval( ins )
347  DO irank = 1, 2
348  DO iscale = 1, 3
349  itype = ( irank-1 )*3 + iscale
350  IF( dotype( itype ) ) THEN
351  IF( irank.EQ.1 ) THEN
352  DO itran = 1, 2
353  IF( itran.EQ.1 ) THEN
354  trans = 'N'
355  ELSE
356  trans = 'T'
357  END IF
358 *
359 * Compute workspace needed for SGELS
360  CALL sgels( trans, m, n, nrhs, a, lda,
361  $ b, ldb, wq( 1 ), -1, info )
362  lwork_sgels = int( wq( 1 ) )
363 * Compute workspace needed for SGETSLS
364  CALL sgetsls( trans, m, n, nrhs, a, lda,
365  $ b, ldb, wq( 1 ), -1, info )
366  lwork_sgetsls = int( wq( 1 ) )
367  ENDDO
368  END IF
369 * Compute workspace needed for SGELSY
370  CALL sgelsy( m, n, nrhs, a, lda, b, ldb, iwq,
371  $ rcond, crank, wq, -1, info )
372  lwork_sgelsy = int( wq( 1 ) )
373 * Compute workspace needed for SGELSS
374  CALL sgelss( m, n, nrhs, a, lda, b, ldb, s,
375  $ rcond, crank, wq, -1 , info )
376  lwork_sgelss = int( wq( 1 ) )
377 * Compute workspace needed for SGELSD
378  CALL sgelsd( m, n, nrhs, a, lda, b, ldb, s,
379  $ rcond, crank, wq, -1, iwq, info )
380  lwork_sgelsd = int( wq( 1 ) )
381 * Compute LIWORK workspace needed for SGELSY and SGELSD
382  liwork = max( liwork, n, iwq( 1 ) )
383 * Compute LWORK workspace needed for all functions
384  lwork = max( lwork, lwork_sgels, lwork_sgetsls,
385  $ lwork_sgelsy, lwork_sgelss,
386  $ lwork_sgelsd )
387  END IF
388  ENDDO
389  ENDDO
390  ENDDO
391  ENDDO
392  ENDDO
393 *
394  lwlsy = lwork
395 *
396  ALLOCATE( work( lwork ) )
397  ALLOCATE( iwork( liwork ) )
398 *
399  DO 150 im = 1, nm
400  m = mval( im )
401  lda = max( 1, m )
402 *
403  DO 140 in = 1, nn
404  n = nval( in )
405  mnmin = max(min( m, n ),1)
406  ldb = max( 1, m, n )
407  mb = (mnmin+1)
408 *
409  DO 130 ins = 1, nns
410  nrhs = nsval( ins )
411 *
412  DO 120 irank = 1, 2
413  DO 110 iscale = 1, 3
414  itype = ( irank-1 )*3 + iscale
415  IF( .NOT.dotype( itype ) )
416  $ GO TO 110
417 *
418  IF( irank.EQ.1 ) THEN
419 *
420 * Test SGELS
421 *
422 * Generate a matrix of scaling type ISCALE
423 *
424  CALL sqrt13( iscale, m, n, copya, lda, norma,
425  $ iseed )
426  DO 40 inb = 1, nnb
427  nb = nbval( inb )
428  CALL xlaenv( 1, nb )
429  CALL xlaenv( 3, nxval( inb ) )
430 *
431  DO 30 itran = 1, 2
432  IF( itran.EQ.1 ) THEN
433  trans = 'N'
434  nrows = m
435  ncols = n
436  ELSE
437  trans = 'T'
438  nrows = n
439  ncols = m
440  END IF
441  ldwork = max( 1, ncols )
442 *
443 * Set up a consistent rhs
444 *
445  IF( ncols.GT.0 ) THEN
446  CALL slarnv( 2, iseed, ncols*nrhs,
447  $ work )
448  CALL sscal( ncols*nrhs,
449  $ one / real( ncols ), work,
450  $ 1 )
451  END IF
452  CALL sgemm( trans, 'No transpose', nrows,
453  $ nrhs, ncols, one, copya, lda,
454  $ work, ldwork, zero, b, ldb )
455  CALL slacpy( 'Full', nrows, nrhs, b, ldb,
456  $ copyb, ldb )
457 *
458 * Solve LS or overdetermined system
459 *
460  IF( m.GT.0 .AND. n.GT.0 ) THEN
461  CALL slacpy( 'Full', m, n, copya, lda,
462  $ a, lda )
463  CALL slacpy( 'Full', nrows, nrhs,
464  $ copyb, ldb, b, ldb )
465  END IF
466  srnamt = 'SGELS '
467  CALL sgels( trans, m, n, nrhs, a, lda, b,
468  $ ldb, work, lwork, info )
469  IF( info.NE.0 )
470  $ CALL alaerh( path, 'SGELS ', info, 0,
471  $ trans, m, n, nrhs, -1, nb,
472  $ itype, nfail, nerrs,
473  $ nout )
474 *
475 * Check correctness of results
476 *
477  ldwork = max( 1, nrows )
478  IF( nrows.GT.0 .AND. nrhs.GT.0 )
479  $ CALL slacpy( 'Full', nrows, nrhs,
480  $ copyb, ldb, c, ldb )
481  CALL sqrt16( trans, m, n, nrhs, copya,
482  $ lda, b, ldb, c, ldb, work,
483  $ result( 1 ) )
484 *
485  IF( ( itran.EQ.1 .AND. m.GE.n ) .OR.
486  $ ( itran.EQ.2 .AND. m.LT.n ) ) THEN
487 *
488 * Solving LS system
489 *
490  result( 2 ) = sqrt17( trans, 1, m, n,
491  $ nrhs, copya, lda, b, ldb,
492  $ copyb, ldb, c, work,
493  $ lwork )
494  ELSE
495 *
496 * Solving overdetermined system
497 *
498  result( 2 ) = sqrt14( trans, m, n,
499  $ nrhs, copya, lda, b, ldb,
500  $ work, lwork )
501  END IF
502 *
503 * Print information about the tests that
504 * did not pass the threshold.
505 *
506  DO 20 k = 1, 2
507  IF( result( k ).GE.thresh ) THEN
508  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
509  $ CALL alahd( nout, path )
510  WRITE( nout, fmt = 9999 )trans, m,
511  $ n, nrhs, nb, itype, k,
512  $ result( k )
513  nfail = nfail + 1
514  END IF
515  20 CONTINUE
516  nrun = nrun + 2
517  30 CONTINUE
518  40 CONTINUE
519 *
520 *
521 * Test SGETSLS
522 *
523 * Generate a matrix of scaling type ISCALE
524 *
525  CALL sqrt13( iscale, m, n, copya, lda, norma,
526  $ iseed )
527  DO 65 inb = 1, nnb
528  mb = nbval( inb )
529  CALL xlaenv( 1, mb )
530  DO 62 imb = 1, nnb
531  nb = nbval( imb )
532  CALL xlaenv( 2, nb )
533 *
534  DO 60 itran = 1, 2
535  IF( itran.EQ.1 ) THEN
536  trans = 'N'
537  nrows = m
538  ncols = n
539  ELSE
540  trans = 'T'
541  nrows = n
542  ncols = m
543  END IF
544  ldwork = max( 1, ncols )
545 *
546 * Set up a consistent rhs
547 *
548  IF( ncols.GT.0 ) THEN
549  CALL slarnv( 2, iseed, ncols*nrhs,
550  $ work )
551  CALL sscal( ncols*nrhs,
552  $ one / real( ncols ), work,
553  $ 1 )
554  END IF
555  CALL sgemm( trans, 'No transpose', nrows,
556  $ nrhs, ncols, one, copya, lda,
557  $ work, ldwork, zero, b, ldb )
558  CALL slacpy( 'Full', nrows, nrhs, b, ldb,
559  $ copyb, ldb )
560 *
561 * Solve LS or overdetermined system
562 *
563  IF( m.GT.0 .AND. n.GT.0 ) THEN
564  CALL slacpy( 'Full', m, n, copya, lda,
565  $ a, lda )
566  CALL slacpy( 'Full', nrows, nrhs,
567  $ copyb, ldb, b, ldb )
568  END IF
569  srnamt = 'SGETSLS '
570  CALL sgetsls( trans, m, n, nrhs, a,
571  $ lda, b, ldb, work, lwork, info )
572  IF( info.NE.0 )
573  $ CALL alaerh( path, 'SGETSLS ', info, 0,
574  $ trans, m, n, nrhs, -1, nb,
575  $ itype, nfail, nerrs,
576  $ nout )
577 *
578 * Check correctness of results
579 *
580  ldwork = max( 1, nrows )
581  IF( nrows.GT.0 .AND. nrhs.GT.0 )
582  $ CALL slacpy( 'Full', nrows, nrhs,
583  $ copyb, ldb, c, ldb )
584  CALL sqrt16( trans, m, n, nrhs, copya,
585  $ lda, b, ldb, c, ldb, work,
586  $ result( 15 ) )
587 *
588  IF( ( itran.EQ.1 .AND. m.GE.n ) .OR.
589  $ ( itran.EQ.2 .AND. m.LT.n ) ) THEN
590 *
591 * Solving LS system
592 *
593  result( 16 ) = sqrt17( trans, 1, m, n,
594  $ nrhs, copya, lda, b, ldb,
595  $ copyb, ldb, c, work,
596  $ lwork )
597  ELSE
598 *
599 * Solving overdetermined system
600 *
601  result( 16 ) = sqrt14( trans, m, n,
602  $ nrhs, copya, lda, b, ldb,
603  $ work, lwork )
604  END IF
605 *
606 * Print information about the tests that
607 * did not pass the threshold.
608 *
609  DO 50 k = 15, 16
610  IF( result( k ).GE.thresh ) THEN
611  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
612  $ CALL alahd( nout, path )
613  WRITE( nout, fmt = 9997 )trans, m,
614  $ n, nrhs, mb, nb, itype, k,
615  $ result( k )
616  nfail = nfail + 1
617  END IF
618  50 CONTINUE
619  nrun = nrun + 2
620  60 CONTINUE
621  62 CONTINUE
622  65 CONTINUE
623  END IF
624 *
625 * Generate a matrix of scaling type ISCALE and rank
626 * type IRANK.
627 *
628  CALL sqrt15( iscale, irank, m, n, nrhs, copya, lda,
629  $ copyb, ldb, copys, rank, norma, normb,
630  $ iseed, work, lwork )
631 *
632 * workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
633 *
634  ldwork = max( 1, m )
635 *
636 * Loop for testing different block sizes.
637 *
638  DO 100 inb = 1, nnb
639  nb = nbval( inb )
640  CALL xlaenv( 1, nb )
641  CALL xlaenv( 3, nxval( inb ) )
642 *
643 * Test SGELSY
644 *
645 * SGELSY: Compute the minimum-norm solution X
646 * to min( norm( A * X - B ) )
647 * using the rank-revealing orthogonal
648 * factorization.
649 *
650 * Initialize vector IWORK.
651 *
652  DO 70 j = 1, n
653  iwork( j ) = 0
654  70 CONTINUE
655 *
656  CALL slacpy( 'Full', m, n, copya, lda, a, lda )
657  CALL slacpy( 'Full', m, nrhs, copyb, ldb, b,
658  $ ldb )
659 *
660  srnamt = 'SGELSY'
661  CALL sgelsy( m, n, nrhs, a, lda, b, ldb, iwork,
662  $ rcond, crank, work, lwlsy, info )
663  IF( info.NE.0 )
664  $ CALL alaerh( path, 'SGELSY', info, 0, ' ', m,
665  $ n, nrhs, -1, nb, itype, nfail,
666  $ nerrs, nout )
667 *
668 * Test 3: Compute relative error in svd
669 * workspace: M*N + 4*MIN(M,N) + MAX(M,N)
670 *
671  result( 3 ) = sqrt12( crank, crank, a, lda,
672  $ copys, work, lwork )
673 *
674 * Test 4: Compute error in solution
675 * workspace: M*NRHS + M
676 *
677  CALL slacpy( 'Full', m, nrhs, copyb, ldb, work,
678  $ ldwork )
679  CALL sqrt16( 'No transpose', m, n, nrhs, copya,
680  $ lda, b, ldb, work, ldwork,
681  $ work( m*nrhs+1 ), result( 4 ) )
682 *
683 * Test 5: Check norm of r'*A
684 * workspace: NRHS*(M+N)
685 *
686  result( 5 ) = zero
687  IF( m.GT.crank )
688  $ result( 5 ) = sqrt17( 'No transpose', 1, m,
689  $ n, nrhs, copya, lda, b, ldb,
690  $ copyb, ldb, c, work, lwork )
691 *
692 * Test 6: Check if x is in the rowspace of A
693 * workspace: (M+NRHS)*(N+2)
694 *
695  result( 6 ) = zero
696 *
697  IF( n.GT.crank )
698  $ result( 6 ) = sqrt14( 'No transpose', m, n,
699  $ nrhs, copya, lda, b, ldb,
700  $ work, lwork )
701 *
702 * Test SGELSS
703 *
704 * SGELSS: Compute the minimum-norm solution X
705 * to min( norm( A * X - B ) )
706 * using the SVD.
707 *
708  CALL slacpy( 'Full', m, n, copya, lda, a, lda )
709  CALL slacpy( 'Full', m, nrhs, copyb, ldb, b,
710  $ ldb )
711  srnamt = 'SGELSS'
712  CALL sgelss( m, n, nrhs, a, lda, b, ldb, s,
713  $ rcond, crank, work, lwork, info )
714  IF( info.NE.0 )
715  $ CALL alaerh( path, 'SGELSS', info, 0, ' ', m,
716  $ n, nrhs, -1, nb, itype, nfail,
717  $ nerrs, nout )
718 *
719 * workspace used: 3*min(m,n) +
720 * max(2*min(m,n),nrhs,max(m,n))
721 *
722 * Test 7: Compute relative error in svd
723 *
724  IF( rank.GT.0 ) THEN
725  CALL saxpy( mnmin, -one, copys, 1, s, 1 )
726  result( 7 ) = sasum( mnmin, s, 1 ) /
727  $ sasum( mnmin, copys, 1 ) /
728  $ ( eps*real( mnmin ) )
729  ELSE
730  result( 7 ) = zero
731  END IF
732 *
733 * Test 8: Compute error in solution
734 *
735  CALL slacpy( 'Full', m, nrhs, copyb, ldb, work,
736  $ ldwork )
737  CALL sqrt16( 'No transpose', m, n, nrhs, copya,
738  $ lda, b, ldb, work, ldwork,
739  $ work( m*nrhs+1 ), result( 8 ) )
740 *
741 * Test 9: Check norm of r'*A
742 *
743  result( 9 ) = zero
744  IF( m.GT.crank )
745  $ result( 9 ) = sqrt17( 'No transpose', 1, m,
746  $ n, nrhs, copya, lda, b, ldb,
747  $ copyb, ldb, c, work, lwork )
748 *
749 * Test 10: Check if x is in the rowspace of A
750 *
751  result( 10 ) = zero
752  IF( n.GT.crank )
753  $ result( 10 ) = sqrt14( 'No transpose', m, n,
754  $ nrhs, copya, lda, b, ldb,
755  $ work, lwork )
756 *
757 * Test SGELSD
758 *
759 * SGELSD: Compute the minimum-norm solution X
760 * to min( norm( A * X - B ) ) using a
761 * divide and conquer SVD.
762 *
763 * Initialize vector IWORK.
764 *
765  DO 80 j = 1, n
766  iwork( j ) = 0
767  80 CONTINUE
768 *
769  CALL slacpy( 'Full', m, n, copya, lda, a, lda )
770  CALL slacpy( 'Full', m, nrhs, copyb, ldb, b,
771  $ ldb )
772 *
773  srnamt = 'SGELSD'
774  CALL sgelsd( m, n, nrhs, a, lda, b, ldb, s,
775  $ rcond, crank, work, lwork, iwork,
776  $ info )
777  IF( info.NE.0 )
778  $ CALL alaerh( path, 'SGELSD', info, 0, ' ', m,
779  $ n, nrhs, -1, nb, itype, nfail,
780  $ nerrs, nout )
781 *
782 * Test 11: Compute relative error in svd
783 *
784  IF( rank.GT.0 ) THEN
785  CALL saxpy( mnmin, -one, copys, 1, s, 1 )
786  result( 11 ) = sasum( mnmin, s, 1 ) /
787  $ sasum( mnmin, copys, 1 ) /
788  $ ( eps*real( mnmin ) )
789  ELSE
790  result( 11 ) = zero
791  END IF
792 *
793 * Test 12: Compute error in solution
794 *
795  CALL slacpy( 'Full', m, nrhs, copyb, ldb, work,
796  $ ldwork )
797  CALL sqrt16( 'No transpose', m, n, nrhs, copya,
798  $ lda, b, ldb, work, ldwork,
799  $ work( m*nrhs+1 ), result( 12 ) )
800 *
801 * Test 13: Check norm of r'*A
802 *
803  result( 13 ) = zero
804  IF( m.GT.crank )
805  $ result( 13 ) = sqrt17( 'No transpose', 1, m,
806  $ n, nrhs, copya, lda, b, ldb,
807  $ copyb, ldb, c, work, lwork )
808 *
809 * Test 14: Check if x is in the rowspace of A
810 *
811  result( 14 ) = zero
812  IF( n.GT.crank )
813  $ result( 14 ) = sqrt14( 'No transpose', m, n,
814  $ nrhs, copya, lda, b, ldb,
815  $ work, lwork )
816 *
817 * Print information about the tests that did not
818 * pass the threshold.
819 *
820  DO 90 k = 3, 14
821  IF( result( k ).GE.thresh ) THEN
822  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
823  $ CALL alahd( nout, path )
824  WRITE( nout, fmt = 9998 )m, n, nrhs, nb,
825  $ itype, k, result( k )
826  nfail = nfail + 1
827  END IF
828  90 CONTINUE
829  nrun = nrun + 12
830 *
831  100 CONTINUE
832  110 CONTINUE
833  120 CONTINUE
834  130 CONTINUE
835  140 CONTINUE
836  150 CONTINUE
837 *
838 * Print a summary of the results.
839 *
840  CALL alasvm( path, nout, nfail, nrun, nerrs )
841 *
842  9999 FORMAT( ' TRANS=''', a1, ''', M=', i5, ', N=', i5, ', NRHS=', i4,
843  $ ', NB=', i4, ', type', i2, ', test(', i2, ')=', g12.5 )
844  9998 FORMAT( ' M=', i5, ', N=', i5, ', NRHS=', i4, ', NB=', i4,
845  $ ', type', i2, ', test(', i2, ')=', g12.5 )
846  9997 FORMAT( ' TRANS=''', a1,' M=', i5, ', N=', i5, ', NRHS=', i4,
847  $ ', MB=', i4,', NB=', i4,', type', i2,
848  $ ', test(', i2, ')=', g12.5 )
849 *
850  DEALLOCATE( work )
851  DEALLOCATE( iwork )
852  RETURN
853 *
854 * End of SDRVLS
855 *
856  END
slarnv
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:99
alasvm
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
sqrt16
subroutine sqrt16(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SQRT16
Definition: sqrt16.f:135
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
sgels
subroutine sgels(TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
SGELS solves overdetermined or underdetermined systems for GE matrices
Definition: sgels.f:185
sgelss
subroutine sgelss(M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO)
SGELSS solves overdetermined or underdetermined systems for GE matrices
Definition: sgelss.f:174
sgemm
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
sqrt15
subroutine sqrt15(SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK)
SQRT15
Definition: sqrt15.f:150
sdrvls
subroutine sdrvls(DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, COPYB, C, S, COPYS, NOUT)
SDRVLS
Definition: sdrvls.f:194
slacpy
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
sscal
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
serrls
subroutine serrls(PATH, NUNIT)
SERRLS
Definition: serrls.f:57
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
sgetsls
subroutine sgetsls(TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
SGETSLS
Definition: sgetsls.f:164
sgelsd
subroutine sgelsd(M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, IWORK, INFO)
SGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices
Definition: sgelsd.f:212
sqrt13
subroutine sqrt13(SCALE, M, N, A, LDA, NORMA, ISEED)
SQRT13
Definition: sqrt13.f:93
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
saxpy
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
sgelsy
subroutine sgelsy(M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, LWORK, INFO)
SGELSY solves overdetermined or underdetermined systems for GE matrices
Definition: sgelsy.f:206