LAPACK  3.7.1
LAPACK: Linear Algebra PACKage
schksy_aa.f
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1 *> \brief \b SCHKSY_AA
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 SCHKSY_AA( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, IWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * REAL THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * REAL A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> SCHKSY_AA tests SSYTRF_AA, -TRS_AA.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NN
48 *> \verbatim
49 *> NN is INTEGER
50 *> The number of values of N contained in the vector NVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] NVAL
54 *> \verbatim
55 *> NVAL is INTEGER array, dimension (NN)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NNB
60 *> \verbatim
61 *> NNB is INTEGER
62 *> The number of values of NB contained in the vector NBVAL.
63 *> \endverbatim
64 *>
65 *> \param[in] NBVAL
66 *> \verbatim
67 *> NBVAL is INTEGER array, dimension (NBVAL)
68 *> The values of the blocksize NB.
69 *> \endverbatim
70 *>
71 *> \param[in] NNS
72 *> \verbatim
73 *> NNS is INTEGER
74 *> The number of values of NRHS contained in the vector NSVAL.
75 *> \endverbatim
76 *>
77 *> \param[in] NSVAL
78 *> \verbatim
79 *> NSVAL is INTEGER array, dimension (NNS)
80 *> The values of the number of right hand sides NRHS.
81 *> \endverbatim
82 *>
83 *> \param[in] THRESH
84 *> \verbatim
85 *> THRESH is REAL
86 *> The threshold value for the test ratios. A result is
87 *> included in the output file if RESULT >= THRESH. To have
88 *> every test ratio printed, use THRESH = 0.
89 *> \endverbatim
90 *>
91 *> \param[in] TSTERR
92 *> \verbatim
93 *> TSTERR is LOGICAL
94 *> Flag that indicates whether error exits are to be tested.
95 *> \endverbatim
96 *>
97 *> \param[in] NMAX
98 *> \verbatim
99 *> NMAX is INTEGER
100 *> The maximum value permitted for N, used in dimensioning the
101 *> work arrays.
102 *> \endverbatim
103 *>
104 *> \param[out] A
105 *> \verbatim
106 *> A is REAL array, dimension (NMAX*NMAX)
107 *> \endverbatim
108 *>
109 *> \param[out] AFAC
110 *> \verbatim
111 *> AFAC is REAL array, dimension (NMAX*NMAX)
112 *> \endverbatim
113 *>
114 *> \param[out] AINV
115 *> \verbatim
116 *> AINV is REAL array, dimension (NMAX*NMAX)
117 *> \endverbatim
118 *>
119 *> \param[out] B
120 *> \verbatim
121 *> B is REAL array, dimension (NMAX*NSMAX)
122 *> where NSMAX is the largest entry in NSVAL.
123 *> \endverbatim
124 *>
125 *> \param[out] X
126 *> \verbatim
127 *> X is REAL array, dimension (NMAX*NSMAX)
128 *> \endverbatim
129 *>
130 *> \param[out] XACT
131 *> \verbatim
132 *> XACT is REAL array, dimension (NMAX*NSMAX)
133 *> \endverbatim
134 *>
135 *> \param[out] WORK
136 *> \verbatim
137 *> WORK is REAL array, dimension (NMAX*max(3,NSMAX))
138 *> \endverbatim
139 *>
140 *> \param[out] RWORK
141 *> \verbatim
142 *> RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
143 *> \endverbatim
144 *>
145 *> \param[out] IWORK
146 *> \verbatim
147 *> IWORK is INTEGER array, dimension (2*NMAX)
148 *> \endverbatim
149 *>
150 *> \param[in] NOUT
151 *> \verbatim
152 *> NOUT is INTEGER
153 *> The unit number for output.
154 *> \endverbatim
155 *
156 * Authors:
157 * ========
158 *
159 *> \author Univ. of Tennessee
160 *> \author Univ. of California Berkeley
161 *> \author Univ. of Colorado Denver
162 *> \author NAG Ltd.
163 *
164 *> \date June 2017
165 *
166 * @precisions fortran d -> z c
167 *
168 *> \ingroup real_lin
169 *
170 * =====================================================================
171  SUBROUTINE schksy_aa( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
172  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
173  $ X, XACT, WORK, RWORK, IWORK, NOUT )
174 *
175 * -- LAPACK test routine (version 3.7.1) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * June 2017
179 *
180  IMPLICIT NONE
181 *
182 * .. Scalar Arguments ..
183  LOGICAL TSTERR
184  INTEGER NN, NNB, NNS, NMAX, NOUT
185  REAL THRESH
186 * ..
187 * .. Array Arguments ..
188  LOGICAL DOTYPE( * )
189  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
190  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
191  $ rwork( * ), work( * ), x( * ), xact( * )
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. Parameters ..
197  REAL ZERO
198  parameter( zero = 0.0e+0 )
199  INTEGER NTYPES
200  parameter( ntypes = 10 )
201  INTEGER NTESTS
202  parameter( ntests = 9 )
203 * ..
204 * .. Local Scalars ..
205  LOGICAL ZEROT
206  CHARACTER DIST, TYPE, UPLO, XTYPE
207  CHARACTER*3 PATH, MATPATH
208  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
209  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
210  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
211  REAL ANORM, CNDNUM
212 * ..
213 * .. Local Arrays ..
214  CHARACTER UPLOS( 2 )
215  INTEGER ISEED( 4 ), ISEEDY( 4 )
216  REAL RESULT( ntests )
217 * ..
218 * .. External Subroutines ..
219  EXTERNAL alaerh, alahd, alasum, serrsy, slacpy, slarhs,
220  $ slatb4, slatms, spot02, ssyt01_aa, ssytrf_aa,
221  $ ssytrs_aa, xlaenv
222 * ..
223 * .. Intrinsic Functions ..
224  INTRINSIC max, min
225 * ..
226 * .. Scalars in Common ..
227  LOGICAL LERR, OK
228  CHARACTER*32 SRNAMT
229  INTEGER INFOT, NUNIT
230 * ..
231 * .. Common blocks ..
232  COMMON / infoc / infot, nunit, ok, lerr
233  COMMON / srnamc / srnamt
234 * ..
235 * .. Data statements ..
236  DATA iseedy / 1988, 1989, 1990, 1991 /
237  DATA uplos / 'U', 'L' /
238 * ..
239 * .. Executable Statements ..
240 *
241 * Initialize constants and the random number seed.
242 *
243 *
244 * Test path
245 *
246  path( 1: 1 ) = 'Single precision'
247  path( 2: 3 ) = 'SA'
248 *
249 * Path to generate matrices
250 *
251  matpath( 1: 1 ) = 'Single precision'
252  matpath( 2: 3 ) = 'SY'
253  nrun = 0
254  nfail = 0
255  nerrs = 0
256  DO 10 i = 1, 4
257  iseed( i ) = iseedy( i )
258  10 CONTINUE
259 *
260 * Test the error exits
261 *
262  IF( tsterr )
263  $ CALL serrsy( path, nout )
264  infot = 0
265 *
266 * Set the minimum block size for which the block routine should
267 * be used, which will be later returned by ILAENV
268 *
269  CALL xlaenv( 2, 2 )
270 *
271 * Do for each value of N in NVAL
272 *
273  DO 180 in = 1, nn
274  n = nval( in )
275  IF( n .GT. nmax ) THEN
276  nfail = nfail + 1
277  WRITE(nout, 9995) 'M ', n, nmax
278  GO TO 180
279  END IF
280  lda = max( n, 1 )
281  xtype = 'N'
282  nimat = ntypes
283  IF( n.LE.0 )
284  $ nimat = 1
285 *
286  izero = 0
287 *
288 * Do for each value of matrix type IMAT
289 *
290  DO 170 imat = 1, nimat
291 *
292 * Do the tests only if DOTYPE( IMAT ) is true.
293 *
294  IF( .NOT.dotype( imat ) )
295  $ GO TO 170
296 *
297 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
298 *
299  zerot = imat.GE.3 .AND. imat.LE.6
300  IF( zerot .AND. n.LT.imat-2 )
301  $ GO TO 170
302 *
303 * Do first for UPLO = 'U', then for UPLO = 'L'
304 *
305  DO 160 iuplo = 1, 2
306  uplo = uplos( iuplo )
307 *
308 * Begin generate the test matrix A.
309 *
310 *
311 * Set up parameters with SLATB4 for the matrix generator
312 * based on the type of matrix to be generated.
313 *
314  CALL slatb4( matpath, imat, n, n, TYPE, KL, KU,
315  $ anorm, mode, cndnum, dist )
316 *
317 * Generate a matrix with SLATMS.
318 *
319  srnamt = 'SLATMS'
320  CALL slatms( n, n, dist, iseed, TYPE, RWORK, MODE,
321  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
322  $ info )
323 *
324 * Check error code from SLATMS and handle error.
325 *
326  IF( info.NE.0 ) THEN
327  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
328  $ -1, -1, imat, nfail, nerrs, nout )
329 *
330 * Skip all tests for this generated matrix
331 *
332  GO TO 160
333  END IF
334 *
335 * For matrix types 3-6, zero one or more rows and
336 * columns of the matrix to test that INFO is returned
337 * correctly.
338 *
339  IF( zerot ) THEN
340  IF( imat.EQ.3 ) THEN
341  izero = 1
342  ELSE IF( imat.EQ.4 ) THEN
343  izero = n
344  ELSE
345  izero = n / 2 + 1
346  END IF
347 *
348  IF( imat.LT.6 ) THEN
349 *
350 * Set row and column IZERO to zero.
351 *
352  IF( iuplo.EQ.1 ) THEN
353  ioff = ( izero-1 )*lda
354  DO 20 i = 1, izero - 1
355  a( ioff+i ) = zero
356  20 CONTINUE
357  ioff = ioff + izero
358  DO 30 i = izero, n
359  a( ioff ) = zero
360  ioff = ioff + lda
361  30 CONTINUE
362  ELSE
363  ioff = izero
364  DO 40 i = 1, izero - 1
365  a( ioff ) = zero
366  ioff = ioff + lda
367  40 CONTINUE
368  ioff = ioff - izero
369  DO 50 i = izero, n
370  a( ioff+i ) = zero
371  50 CONTINUE
372  END IF
373  ELSE
374  IF( iuplo.EQ.1 ) THEN
375 *
376 * Set the first IZERO rows and columns to zero.
377 *
378  ioff = 0
379  DO 70 j = 1, n
380  i2 = min( j, izero )
381  DO 60 i = 1, i2
382  a( ioff+i ) = zero
383  60 CONTINUE
384  ioff = ioff + lda
385  70 CONTINUE
386  izero = 1
387  ELSE
388 *
389 * Set the last IZERO rows and columns to zero.
390 *
391  ioff = 0
392  DO 90 j = 1, n
393  i1 = max( j, izero )
394  DO 80 i = i1, n
395  a( ioff+i ) = zero
396  80 CONTINUE
397  ioff = ioff + lda
398  90 CONTINUE
399  END IF
400  END IF
401  ELSE
402  izero = 0
403  END IF
404 *
405 * End generate the test matrix A.
406 *
407 * Do for each value of NB in NBVAL
408 *
409  DO 150 inb = 1, nnb
410 *
411 * Set the optimal blocksize, which will be later
412 * returned by ILAENV.
413 *
414  nb = nbval( inb )
415  CALL xlaenv( 1, nb )
416 *
417 * Copy the test matrix A into matrix AFAC which
418 * will be factorized in place. This is needed to
419 * preserve the test matrix A for subsequent tests.
420 *
421  CALL slacpy( uplo, n, n, a, lda, afac, lda )
422 *
423 * Compute the L*D*L**T or U*D*U**T factorization of the
424 * matrix. IWORK stores details of the interchanges and
425 * the block structure of D. AINV is a work array for
426 * block factorization, LWORK is the length of AINV.
427 *
428  srnamt = 'SSYTRF_AA'
429  lwork = max( 1, n*nb + n )
430  CALL ssytrf_aa( uplo, n, afac, lda, iwork, ainv,
431  $ lwork, info )
432 *
433 * Adjust the expected value of INFO to account for
434 * pivoting.
435 *
436 c IF( IZERO.GT.0 ) THEN
437 c J = 1
438 c K = IZERO
439 c 100 CONTINUE
440 c IF( J.EQ.K ) THEN
441 c K = IWORK( J )
442 c ELSE IF( IWORK( J ).EQ.K ) THEN
443 c K = J
444 c END IF
445 c IF( J.LT.K ) THEN
446 c J = J + 1
447 c GO TO 100
448 c END IF
449 c ELSE
450  k = 0
451 c END IF
452 *
453 * Check error code from SSYTRF and handle error.
454 *
455  IF( info.NE.k ) THEN
456  CALL alaerh( path, 'SSYTRF_AA', info, k, uplo,
457  $ n, n, -1, -1, nb, imat, nfail, nerrs,
458  $ nout )
459  END IF
460 *
461 *+ TEST 1
462 * Reconstruct matrix from factors and compute residual.
463 *
464  CALL ssyt01_aa( uplo, n, a, lda, afac, lda, iwork,
465  $ ainv, lda, rwork, result( 1 ) )
466  nt = 1
467 *
468 *
469 * Print information about the tests that did not pass
470 * the threshold.
471 *
472  DO 110 k = 1, nt
473  IF( result( k ).GE.thresh ) THEN
474  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
475  $ CALL alahd( nout, path )
476  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
477  $ result( k )
478  nfail = nfail + 1
479  END IF
480  110 CONTINUE
481  nrun = nrun + nt
482 *
483 * Skip solver test if INFO is not 0.
484 *
485  IF( info.NE.0 ) THEN
486  GO TO 140
487  END IF
488 *
489 * Do for each value of NRHS in NSVAL.
490 *
491  DO 130 irhs = 1, nns
492  nrhs = nsval( irhs )
493 *
494 *+ TEST 2 (Using TRS)
495 * Solve and compute residual for A * X = B.
496 *
497 * Choose a set of NRHS random solution vectors
498 * stored in XACT and set up the right hand side B
499 *
500  srnamt = 'SLARHS'
501  CALL slarhs( matpath, xtype, uplo, ' ', n, n,
502  $ kl, ku, nrhs, a, lda, xact, lda,
503  $ b, lda, iseed, info )
504  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
505 *
506  srnamt = 'SSYTRS_AA'
507  lwork = max( 1, 3*n-2 )
508  CALL ssytrs_aa( uplo, n, nrhs, afac, lda,
509  $ iwork, x, lda, work, lwork,
510  $ info )
511 *
512 * Check error code from SSYTRS and handle error.
513 *
514  IF( info.NE.0 ) THEN
515  IF( izero.EQ.0 ) THEN
516  CALL alaerh( path, 'SSYTRS_AA', info, 0,
517  $ uplo, n, n, -1, -1, nrhs, imat,
518  $ nfail, nerrs, nout )
519  END IF
520  ELSE
521  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda
522  $ )
523 *
524 * Compute the residual for the solution
525 *
526  CALL spot02( uplo, n, nrhs, a, lda, x, lda,
527  $ work, lda, rwork, result( 2 ) )
528 *
529 *
530 * Print information about the tests that did not pass
531 * the threshold.
532 *
533  DO 120 k = 2, 2
534  IF( result( k ).GE.thresh ) THEN
535  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
536  $ CALL alahd( nout, path )
537  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
538  $ imat, k, result( k )
539  nfail = nfail + 1
540  END IF
541  120 CONTINUE
542  END IF
543  nrun = nrun + 1
544 *
545 * End do for each value of NRHS in NSVAL.
546 *
547  130 CONTINUE
548  140 CONTINUE
549  150 CONTINUE
550  160 CONTINUE
551  170 CONTINUE
552  180 CONTINUE
553 *
554 * Print a summary of the results.
555 *
556  CALL alasum( path, nout, nfail, nrun, nerrs )
557 *
558  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
559  $ i2, ', test ', i2, ', ratio =', g12.5 )
560  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
561  $ i2, ', test(', i2, ') =', g12.5 )
562  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
563  $ i6 )
564  RETURN
565 *
566 * End of SCHKSY_AA
567 *
568  END
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
ssytrf_aa
subroutine ssytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_AA
Definition: ssytrf_aa.f:134
spot02
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
ssyt01_aa
subroutine ssyt01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_AA
Definition: ssyt01_aa.f:127
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
schksy_aa
subroutine schksy_aa(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKSY_AA
Definition: schksy_aa.f:174
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
slatms
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
serrsy
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:57
ssytrs_aa
subroutine ssytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYTRS_AA
Definition: ssytrs_aa.f:131
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
slarhs
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:206
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75