LAPACK  3.9.0
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 November 2017
165 *
166 *> \ingroup real_lin
167 *
168 * =====================================================================
169  SUBROUTINE schksy_aa( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
170  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
171  $ X, XACT, WORK, RWORK, IWORK, NOUT )
172 *
173 * -- LAPACK test routine (version 3.8.0) --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 * November 2017
177 *
178  IMPLICIT NONE
179 *
180 * .. Scalar Arguments ..
181  LOGICAL tsterr
182  INTEGER nn, nnb, nns, nmax, nout
183  REAL thresh
184 * ..
185 * .. Array Arguments ..
186  LOGICAL dotype( * )
187  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
188  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
189  $ rwork( * ), work( * ), x( * ), xact( * )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  REAL ZERO
196  PARAMETER ( ZERO = 0.0e+0 )
197  INTEGER NTYPES
198  parameter( ntypes = 10 )
199  INTEGER NTESTS
200  parameter( ntests = 9 )
201 * ..
202 * .. Local Scalars ..
203  LOGICAL ZEROT
204  CHARACTER DIST, TYPE, UPLO, XTYPE
205  CHARACTER*3 PATH, MATPATH
206  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
207  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
208  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
209  REAL ANORM, CNDNUM
210 * ..
211 * .. Local Arrays ..
212  CHARACTER UPLOS( 2 )
213  INTEGER ISEED( 4 ), ISEEDY( 4 )
214  REAL RESULT( NTESTS )
215 * ..
216 * .. External Subroutines ..
217  EXTERNAL alaerh, alahd, alasum, serrsy, slacpy, slarhs,
218  $ slatb4, slatms, spot02, ssyt01_aa, ssytrf_aa,
219  $ ssytrs_aa, xlaenv
220 * ..
221 * .. Intrinsic Functions ..
222  INTRINSIC max, min
223 * ..
224 * .. Scalars in Common ..
225  LOGICAL LERR, OK
226  CHARACTER*32 SRNAMT
227  INTEGER INFOT, NUNIT
228 * ..
229 * .. Common blocks ..
230  COMMON / infoc / infot, nunit, ok, lerr
231  COMMON / srnamc / srnamt
232 * ..
233 * .. Data statements ..
234  DATA iseedy / 1988, 1989, 1990, 1991 /
235  DATA uplos / 'U', 'L' /
236 * ..
237 * .. Executable Statements ..
238 *
239 * Initialize constants and the random number seed.
240 *
241 *
242 * Test path
243 *
244  path( 1: 1 ) = 'Single precision'
245  path( 2: 3 ) = 'SA'
246 *
247 * Path to generate matrices
248 *
249  matpath( 1: 1 ) = 'Single precision'
250  matpath( 2: 3 ) = 'SY'
251  nrun = 0
252  nfail = 0
253  nerrs = 0
254  DO 10 i = 1, 4
255  iseed( i ) = iseedy( i )
256  10 CONTINUE
257 *
258 * Test the error exits
259 *
260  IF( tsterr )
261  $ CALL serrsy( path, nout )
262  infot = 0
263 *
264 * Set the minimum block size for which the block routine should
265 * be used, which will be later returned by ILAENV
266 *
267  CALL xlaenv( 2, 2 )
268 *
269 * Do for each value of N in NVAL
270 *
271  DO 180 in = 1, nn
272  n = nval( in )
273  IF( n .GT. nmax ) THEN
274  nfail = nfail + 1
275  WRITE(nout, 9995) 'M ', n, nmax
276  GO TO 180
277  END IF
278  lda = max( n, 1 )
279  xtype = 'N'
280  nimat = ntypes
281  IF( n.LE.0 )
282  $ nimat = 1
283 *
284  izero = 0
285 *
286 * Do for each value of matrix type IMAT
287 *
288  DO 170 imat = 1, nimat
289 *
290 * Do the tests only if DOTYPE( IMAT ) is true.
291 *
292  IF( .NOT.dotype( imat ) )
293  $ GO TO 170
294 *
295 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
296 *
297  zerot = imat.GE.3 .AND. imat.LE.6
298  IF( zerot .AND. n.LT.imat-2 )
299  $ GO TO 170
300 *
301 * Do first for UPLO = 'U', then for UPLO = 'L'
302 *
303  DO 160 iuplo = 1, 2
304  uplo = uplos( iuplo )
305 *
306 * Begin generate the test matrix A.
307 *
308 *
309 * Set up parameters with SLATB4 for the matrix generator
310 * based on the type of matrix to be generated.
311 *
312  CALL slatb4( matpath, imat, n, n, TYPE, kl, ku,
313  $ anorm, mode, cndnum, dist )
314 *
315 * Generate a matrix with SLATMS.
316 *
317  srnamt = 'SLATMS'
318  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
319  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
320  $ info )
321 *
322 * Check error code from SLATMS and handle error.
323 *
324  IF( info.NE.0 ) THEN
325  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
326  $ -1, -1, imat, nfail, nerrs, nout )
327 *
328 * Skip all tests for this generated matrix
329 *
330  GO TO 160
331  END IF
332 *
333 * For matrix types 3-6, zero one or more rows and
334 * columns of the matrix to test that INFO is returned
335 * correctly.
336 *
337  IF( zerot ) THEN
338  IF( imat.EQ.3 ) THEN
339  izero = 1
340  ELSE IF( imat.EQ.4 ) THEN
341  izero = n
342  ELSE
343  izero = n / 2 + 1
344  END IF
345 *
346  IF( imat.LT.6 ) THEN
347 *
348 * Set row and column IZERO to zero.
349 *
350  IF( iuplo.EQ.1 ) THEN
351  ioff = ( izero-1 )*lda
352  DO 20 i = 1, izero - 1
353  a( ioff+i ) = zero
354  20 CONTINUE
355  ioff = ioff + izero
356  DO 30 i = izero, n
357  a( ioff ) = zero
358  ioff = ioff + lda
359  30 CONTINUE
360  ELSE
361  ioff = izero
362  DO 40 i = 1, izero - 1
363  a( ioff ) = zero
364  ioff = ioff + lda
365  40 CONTINUE
366  ioff = ioff - izero
367  DO 50 i = izero, n
368  a( ioff+i ) = zero
369  50 CONTINUE
370  END IF
371  ELSE
372  IF( iuplo.EQ.1 ) THEN
373 *
374 * Set the first IZERO rows and columns to zero.
375 *
376  ioff = 0
377  DO 70 j = 1, n
378  i2 = min( j, izero )
379  DO 60 i = 1, i2
380  a( ioff+i ) = zero
381  60 CONTINUE
382  ioff = ioff + lda
383  70 CONTINUE
384  izero = 1
385  ELSE
386 *
387 * Set the last IZERO rows and columns to zero.
388 *
389  ioff = 0
390  DO 90 j = 1, n
391  i1 = max( j, izero )
392  DO 80 i = i1, n
393  a( ioff+i ) = zero
394  80 CONTINUE
395  ioff = ioff + lda
396  90 CONTINUE
397  END IF
398  END IF
399  ELSE
400  izero = 0
401  END IF
402 *
403 * End generate the test matrix A.
404 *
405 * Do for each value of NB in NBVAL
406 *
407  DO 150 inb = 1, nnb
408 *
409 * Set the optimal blocksize, which will be later
410 * returned by ILAENV.
411 *
412  nb = nbval( inb )
413  CALL xlaenv( 1, nb )
414 *
415 * Copy the test matrix A into matrix AFAC which
416 * will be factorized in place. This is needed to
417 * preserve the test matrix A for subsequent tests.
418 *
419  CALL slacpy( uplo, n, n, a, lda, afac, lda )
420 *
421 * Compute the L*D*L**T or U*D*U**T factorization of the
422 * matrix. IWORK stores details of the interchanges and
423 * the block structure of D. AINV is a work array for
424 * block factorization, LWORK is the length of AINV.
425 *
426  srnamt = 'SSYTRF_AA'
427  lwork = max( 1, n*nb + n )
428  CALL ssytrf_aa( uplo, n, afac, lda, iwork, ainv,
429  $ lwork, info )
430 *
431 * Adjust the expected value of INFO to account for
432 * pivoting.
433 *
434 c IF( IZERO.GT.0 ) THEN
435 c J = 1
436 c K = IZERO
437 c 100 CONTINUE
438 c IF( J.EQ.K ) THEN
439 c K = IWORK( J )
440 c ELSE IF( IWORK( J ).EQ.K ) THEN
441 c K = J
442 c END IF
443 c IF( J.LT.K ) THEN
444 c J = J + 1
445 c GO TO 100
446 c END IF
447 c ELSE
448  k = 0
449 c END IF
450 *
451 * Check error code from SSYTRF and handle error.
452 *
453  IF( info.NE.k ) THEN
454  CALL alaerh( path, 'SSYTRF_AA', info, k, uplo,
455  $ n, n, -1, -1, nb, imat, nfail, nerrs,
456  $ nout )
457  END IF
458 *
459 *+ TEST 1
460 * Reconstruct matrix from factors and compute residual.
461 *
462  CALL ssyt01_aa( uplo, n, a, lda, afac, lda, iwork,
463  $ ainv, lda, rwork, result( 1 ) )
464  nt = 1
465 *
466 *
467 * Print information about the tests that did not pass
468 * the threshold.
469 *
470  DO 110 k = 1, nt
471  IF( result( k ).GE.thresh ) THEN
472  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
473  $ CALL alahd( nout, path )
474  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
475  $ result( k )
476  nfail = nfail + 1
477  END IF
478  110 CONTINUE
479  nrun = nrun + nt
480 *
481 * Skip solver test if INFO is not 0.
482 *
483  IF( info.NE.0 ) THEN
484  GO TO 140
485  END IF
486 *
487 * Do for each value of NRHS in NSVAL.
488 *
489  DO 130 irhs = 1, nns
490  nrhs = nsval( irhs )
491 *
492 *+ TEST 2 (Using TRS)
493 * Solve and compute residual for A * X = B.
494 *
495 * Choose a set of NRHS random solution vectors
496 * stored in XACT and set up the right hand side B
497 *
498  srnamt = 'SLARHS'
499  CALL slarhs( matpath, xtype, uplo, ' ', n, n,
500  $ kl, ku, nrhs, a, lda, xact, lda,
501  $ b, lda, iseed, info )
502  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
503 *
504  srnamt = 'SSYTRS_AA'
505  lwork = max( 1, 3*n-2 )
506  CALL ssytrs_aa( uplo, n, nrhs, afac, lda,
507  $ iwork, x, lda, work, lwork,
508  $ info )
509 *
510 * Check error code from SSYTRS and handle error.
511 *
512  IF( info.NE.0 ) THEN
513  IF( izero.EQ.0 ) THEN
514  CALL alaerh( path, 'SSYTRS_AA', info, 0,
515  $ uplo, n, n, -1, -1, nrhs, imat,
516  $ nfail, nerrs, nout )
517  END IF
518  ELSE
519  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda
520  $ )
521 *
522 * Compute the residual for the solution
523 *
524  CALL spot02( uplo, n, nrhs, a, lda, x, lda,
525  $ work, lda, rwork, result( 2 ) )
526 *
527 *
528 * Print information about the tests that did not pass
529 * the threshold.
530 *
531  DO 120 k = 2, 2
532  IF( result( k ).GE.thresh ) THEN
533  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
534  $ CALL alahd( nout, path )
535  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
536  $ imat, k, result( k )
537  nfail = nfail + 1
538  END IF
539  120 CONTINUE
540  END IF
541  nrun = nrun + 1
542 *
543 * End do for each value of NRHS in NSVAL.
544 *
545  130 CONTINUE
546  140 CONTINUE
547  150 CONTINUE
548  160 CONTINUE
549  170 CONTINUE
550  180 CONTINUE
551 *
552 * Print a summary of the results.
553 *
554  CALL alasum( path, nout, nfail, nrun, nerrs )
555 *
556  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
557  $ i2, ', test ', i2, ', ratio =', g12.5 )
558  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
559  $ i2, ', test(', i2, ') =', g12.5 )
560  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
561  $ i6 )
562  RETURN
563 *
564 * End of SCHKSY_AA
565 *
566  END
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
spot02
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
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:172
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
ssytrs_aa
subroutine ssytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYTRS_AA
Definition: ssytrs_aa.f:133
serrsy
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:57
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
slatms
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
ssytrf_aa
subroutine ssytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_AA
Definition: ssytrf_aa.f:134
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75
ssyt01_aa
subroutine ssyt01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_AA
Definition: ssyt01_aa.f:127
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83