LAPACK  3.7.0
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 December 2016
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 3.7.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * December 2016
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 Functions ..
219  REAL DGET06, SLANSY
220  EXTERNAL dget06, slansy
221 * ..
222 * .. External Subroutines ..
223  EXTERNAL alaerh, alahd, alasum, serrsy, sget04, slacpy,
224  $ slarhs, slatb4, slatms, spot02, dpot03, dpot05,
225  $ dsycon, ssyrfs, ssyt01_aa, ssytrf_aa,
226  $ dsytri2, ssytrs_aa, xlaenv
227 * ..
228 * .. Intrinsic Functions ..
229  INTRINSIC max, min
230 * ..
231 * .. Scalars in Common ..
232  LOGICAL LERR, OK
233  CHARACTER*32 SRNAMT
234  INTEGER INFOT, NUNIT
235 * ..
236 * .. Common blocks ..
237  COMMON / infoc / infot, nunit, ok, lerr
238  COMMON / srnamc / srnamt
239 * ..
240 * .. Data statements ..
241  DATA iseedy / 1988, 1989, 1990, 1991 /
242  DATA uplos / 'U', 'L' /
243 * ..
244 * .. Executable Statements ..
245 *
246 * Initialize constants and the random number seed.
247 *
248 *
249 * Test path
250 *
251  path( 1: 1 ) = 'Single precision'
252  path( 2: 3 ) = 'SA'
253 *
254 * Path to generate matrices
255 *
256  matpath( 1: 1 ) = 'Single precision'
257  matpath( 2: 3 ) = 'SY'
258  nrun = 0
259  nfail = 0
260  nerrs = 0
261  DO 10 i = 1, 4
262  iseed( i ) = iseedy( i )
263  10 CONTINUE
264 *
265 * Test the error exits
266 *
267  IF( tsterr )
268  $ CALL serrsy( path, nout )
269  infot = 0
270 *
271 * Set the minimum block size for which the block routine should
272 * be used, which will be later returned by ILAENV
273 *
274  CALL xlaenv( 2, 2 )
275 *
276 * Do for each value of N in NVAL
277 *
278  DO 180 in = 1, nn
279  n = nval( in )
280  IF( n .GT. nmax ) THEN
281  nfail = nfail + 1
282  WRITE(nout, 9995) 'M ', n, nmax
283  GO TO 180
284  END IF
285  lda = max( n, 1 )
286  xtype = 'N'
287  nimat = ntypes
288  IF( n.LE.0 )
289  $ nimat = 1
290 *
291  izero = 0
292 *
293 * Do for each value of matrix type IMAT
294 *
295  DO 170 imat = 1, nimat
296 *
297 * Do the tests only if DOTYPE( IMAT ) is true.
298 *
299  IF( .NOT.dotype( imat ) )
300  $ GO TO 170
301 *
302 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
303 *
304  zerot = imat.GE.3 .AND. imat.LE.6
305  IF( zerot .AND. n.LT.imat-2 )
306  $ GO TO 170
307 *
308 * Do first for UPLO = 'U', then for UPLO = 'L'
309 *
310  DO 160 iuplo = 1, 2
311  uplo = uplos( iuplo )
312 *
313 * Begin generate the test matrix A.
314 *
315 *
316 * Set up parameters with SLATB4 for the matrix generator
317 * based on the type of matrix to be generated.
318 *
319  CALL slatb4( matpath, imat, n, n, TYPE, KL, KU,
320  $ anorm, mode, cndnum, dist )
321 *
322 * Generate a matrix with SLATMS.
323 *
324  srnamt = 'SLATMS'
325  CALL slatms( n, n, dist, iseed, TYPE, RWORK, MODE,
326  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
327  $ info )
328 *
329 * Check error code from SLATMS and handle error.
330 *
331  IF( info.NE.0 ) THEN
332  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
333  $ -1, -1, imat, nfail, nerrs, nout )
334 *
335 * Skip all tests for this generated matrix
336 *
337  GO TO 160
338  END IF
339 *
340 * For matrix types 3-6, zero one or more rows and
341 * columns of the matrix to test that INFO is returned
342 * correctly.
343 *
344  IF( zerot ) THEN
345  IF( imat.EQ.3 ) THEN
346  izero = 1
347  ELSE IF( imat.EQ.4 ) THEN
348  izero = n
349  ELSE
350  izero = n / 2 + 1
351  END IF
352 *
353  IF( imat.LT.6 ) THEN
354 *
355 * Set row and column IZERO to zero.
356 *
357  IF( iuplo.EQ.1 ) THEN
358  ioff = ( izero-1 )*lda
359  DO 20 i = 1, izero - 1
360  a( ioff+i ) = zero
361  20 CONTINUE
362  ioff = ioff + izero
363  DO 30 i = izero, n
364  a( ioff ) = zero
365  ioff = ioff + lda
366  30 CONTINUE
367  ELSE
368  ioff = izero
369  DO 40 i = 1, izero - 1
370  a( ioff ) = zero
371  ioff = ioff + lda
372  40 CONTINUE
373  ioff = ioff - izero
374  DO 50 i = izero, n
375  a( ioff+i ) = zero
376  50 CONTINUE
377  END IF
378  ELSE
379  IF( iuplo.EQ.1 ) THEN
380 *
381 * Set the first IZERO rows and columns to zero.
382 *
383  ioff = 0
384  DO 70 j = 1, n
385  i2 = min( j, izero )
386  DO 60 i = 1, i2
387  a( ioff+i ) = zero
388  60 CONTINUE
389  ioff = ioff + lda
390  70 CONTINUE
391  izero = 1
392  ELSE
393 *
394 * Set the last IZERO rows and columns to zero.
395 *
396  ioff = 0
397  DO 90 j = 1, n
398  i1 = max( j, izero )
399  DO 80 i = i1, n
400  a( ioff+i ) = zero
401  80 CONTINUE
402  ioff = ioff + lda
403  90 CONTINUE
404  END IF
405  END IF
406  ELSE
407  izero = 0
408  END IF
409 *
410 * End generate the test matrix A.
411 *
412 * Do for each value of NB in NBVAL
413 *
414  DO 150 inb = 1, nnb
415 *
416 * Set the optimal blocksize, which will be later
417 * returned by ILAENV.
418 *
419  nb = nbval( inb )
420  CALL xlaenv( 1, nb )
421 *
422 * Copy the test matrix A into matrix AFAC which
423 * will be factorized in place. This is needed to
424 * preserve the test matrix A for subsequent tests.
425 *
426  CALL slacpy( uplo, n, n, a, lda, afac, lda )
427 *
428 * Compute the L*D*L**T or U*D*U**T factorization of the
429 * matrix. IWORK stores details of the interchanges and
430 * the block structure of D. AINV is a work array for
431 * block factorization, LWORK is the length of AINV.
432 *
433  srnamt = 'SSYTRF_AA'
434  lwork = max( 1, n*nb + n )
435  CALL ssytrf_aa( uplo, n, afac, lda, iwork, ainv,
436  $ lwork, info )
437 *
438 * Adjust the expected value of INFO to account for
439 * pivoting.
440 *
441  IF( izero.GT.0 ) THEN
442  j = 1
443  k = izero
444  100 CONTINUE
445  IF( j.EQ.k ) THEN
446  k = iwork( j )
447  ELSE IF( iwork( j ).EQ.k ) THEN
448  k = j
449  END IF
450  IF( j.LT.k ) THEN
451  j = j + 1
452  GO TO 100
453  END IF
454  ELSE
455  k = 0
456  END IF
457 *
458 * Check error code from SSYTRF and handle error.
459 *
460  IF( info.NE.k ) THEN
461  CALL alaerh( path, 'SSYTRF_AA', info, k, uplo,
462  $ n, n, -1, -1, nb, imat, nfail, nerrs,
463  $ nout )
464  END IF
465 *
466 *+ TEST 1
467 * Reconstruct matrix from factors and compute residual.
468 *
469  CALL ssyt01_aa( uplo, n, a, lda, afac, lda, iwork,
470  $ ainv, lda, rwork, result( 1 ) )
471  nt = 1
472 *
473 *
474 * Print information about the tests that did not pass
475 * the threshold.
476 *
477  DO 110 k = 1, nt
478  IF( result( k ).GE.thresh ) THEN
479  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
480  $ CALL alahd( nout, path )
481  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
482  $ result( k )
483  nfail = nfail + 1
484  END IF
485  110 CONTINUE
486  nrun = nrun + nt
487 *
488 * Skip solver test if INFO is not 0.
489 *
490  IF( info.NE.0 ) THEN
491  GO TO 140
492  END IF
493 *
494 * Do for each value of NRHS in NSVAL.
495 *
496  DO 130 irhs = 1, nns
497  nrhs = nsval( irhs )
498 *
499 *+ TEST 2 (Using TRS)
500 * Solve and compute residual for A * X = B.
501 *
502 * Choose a set of NRHS random solution vectors
503 * stored in XACT and set up the right hand side B
504 *
505  srnamt = 'SLARHS'
506  CALL slarhs( matpath, xtype, uplo, ' ', n, n,
507  $ kl, ku, nrhs, a, lda, xact, lda,
508  $ b, lda, iseed, info )
509  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
510 *
511  srnamt = 'SSYTRS_AA'
512  lwork = max( 1, 3*n-2 )
513  CALL ssytrs_aa( uplo, n, nrhs, afac, lda,
514  $ iwork, x, lda, work, lwork,
515  $ info )
516 *
517 * Check error code from SSYTRS and handle error.
518 *
519  IF( info.NE.0 ) THEN
520  CALL alaerh( path, 'SSYTRS_AA', info, 0,
521  $ uplo, n, n, -1, -1, nrhs, imat,
522  $ nfail, nerrs, nout )
523  END IF
524 *
525  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
526 *
527 * Compute the residual for the solution
528 *
529  CALL spot02( uplo, n, nrhs, a, lda, x, lda, work,
530  $ lda, rwork, result( 2 ) )
531 *
532 *
533 * Print information about the tests that did not pass
534 * the threshold.
535 *
536  DO 120 k = 2, 2
537  IF( result( k ).GE.thresh ) THEN
538  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
539  $ CALL alahd( nout, path )
540  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
541  $ imat, k, result( k )
542  nfail = nfail + 1
543  END IF
544  120 CONTINUE
545  nrun = nrun + 1
546 *
547 * End do for each value of NRHS in NSVAL.
548 *
549  130 CONTINUE
550  140 CONTINUE
551  150 CONTINUE
552  160 CONTINUE
553  170 CONTINUE
554  180 CONTINUE
555 *
556 * Print a summary of the results.
557 *
558  CALL alasum( path, nout, nfail, nrun, nerrs )
559 *
560  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
561  $ i2, ', test ', i2, ', ratio =', g12.5 )
562  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
563  $ i2, ', test(', i2, ') =', g12.5 )
564  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
565  $ i6 )
566  RETURN
567 *
568 * End of SCHKSY_AA
569 *
570  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:138
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
ssyt01_aa
subroutine ssyt01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_AA
Definition: ssyt01_aa.f:127
dsytri2
subroutine dsytri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
DSYTRI2
Definition: dsytri2.f:129
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
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
dsycon
subroutine dsycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DSYCON
Definition: dsycon.f:132
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
dpot03
subroutine dpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DPOT03
Definition: dpot03.f:127
sget04
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
serrsy
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:57
dpot05
subroutine dpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPOT05
Definition: dpot05.f:166
spot02
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
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
ssyrfs
subroutine ssyrfs(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SSYRFS
Definition: ssyrfs.f:193
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75