LAPACK  3.10.1
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 (NNB)
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 *> \ingroup real_lin
165 *
166 * =====================================================================
167  SUBROUTINE schksy_aa( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
168  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
169  $ X, XACT, WORK, RWORK, IWORK, NOUT )
170 *
171 * -- LAPACK test routine --
172 * -- LAPACK is a software package provided by Univ. of Tennessee, --
173 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174 *
175  IMPLICIT NONE
176 *
177 * .. Scalar Arguments ..
178  LOGICAL TSTERR
179  INTEGER NN, NNB, NNS, NMAX, NOUT
180  REAL THRESH
181 * ..
182 * .. Array Arguments ..
183  LOGICAL DOTYPE( * )
184  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
185  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
186  $ rwork( * ), work( * ), x( * ), xact( * )
187 * ..
188 *
189 * =====================================================================
190 *
191 * .. Parameters ..
192  REAL ZERO
193  PARAMETER ( ZERO = 0.0e+0 )
194  INTEGER NTYPES
195  parameter( ntypes = 10 )
196  INTEGER NTESTS
197  parameter( ntests = 9 )
198 * ..
199 * .. Local Scalars ..
200  LOGICAL ZEROT
201  CHARACTER DIST, TYPE, UPLO, XTYPE
202  CHARACTER*3 PATH, MATPATH
203  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
204  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
205  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
206  REAL ANORM, CNDNUM
207 * ..
208 * .. Local Arrays ..
209  CHARACTER UPLOS( 2 )
210  INTEGER ISEED( 4 ), ISEEDY( 4 )
211  REAL RESULT( NTESTS )
212 * ..
213 * .. External Subroutines ..
214  EXTERNAL alaerh, alahd, alasum, serrsy, slacpy, slarhs,
216  $ ssytrs_aa, xlaenv
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max, min
220 * ..
221 * .. Scalars in Common ..
222  LOGICAL LERR, OK
223  CHARACTER*32 SRNAMT
224  INTEGER INFOT, NUNIT
225 * ..
226 * .. Common blocks ..
227  COMMON / infoc / infot, nunit, ok, lerr
228  COMMON / srnamc / srnamt
229 * ..
230 * .. Data statements ..
231  DATA iseedy / 1988, 1989, 1990, 1991 /
232  DATA uplos / 'U', 'L' /
233 * ..
234 * .. Executable Statements ..
235 *
236 * Initialize constants and the random number seed.
237 *
238 *
239 * Test path
240 *
241  path( 1: 1 ) = 'Single precision'
242  path( 2: 3 ) = 'SA'
243 *
244 * Path to generate matrices
245 *
246  matpath( 1: 1 ) = 'Single precision'
247  matpath( 2: 3 ) = 'SY'
248  nrun = 0
249  nfail = 0
250  nerrs = 0
251  DO 10 i = 1, 4
252  iseed( i ) = iseedy( i )
253  10 CONTINUE
254 *
255 * Test the error exits
256 *
257  IF( tsterr )
258  $ CALL serrsy( path, nout )
259  infot = 0
260 *
261 * Set the minimum block size for which the block routine should
262 * be used, which will be later returned by ILAENV
263 *
264  CALL xlaenv( 2, 2 )
265 *
266 * Do for each value of N in NVAL
267 *
268  DO 180 in = 1, nn
269  n = nval( in )
270  IF( n .GT. nmax ) THEN
271  nfail = nfail + 1
272  WRITE(nout, 9995) 'M ', n, nmax
273  GO TO 180
274  END IF
275  lda = max( n, 1 )
276  xtype = 'N'
277  nimat = ntypes
278  IF( n.LE.0 )
279  $ nimat = 1
280 *
281  izero = 0
282 *
283 * Do for each value of matrix type IMAT
284 *
285  DO 170 imat = 1, nimat
286 *
287 * Do the tests only if DOTYPE( IMAT ) is true.
288 *
289  IF( .NOT.dotype( imat ) )
290  $ GO TO 170
291 *
292 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
293 *
294  zerot = imat.GE.3 .AND. imat.LE.6
295  IF( zerot .AND. n.LT.imat-2 )
296  $ GO TO 170
297 *
298 * Do first for UPLO = 'U', then for UPLO = 'L'
299 *
300  DO 160 iuplo = 1, 2
301  uplo = uplos( iuplo )
302 *
303 * Begin generate the test matrix A.
304 *
305 *
306 * Set up parameters with SLATB4 for the matrix generator
307 * based on the type of matrix to be generated.
308 *
309  CALL slatb4( matpath, imat, n, n, TYPE, kl, ku,
310  $ anorm, mode, cndnum, dist )
311 *
312 * Generate a matrix with SLATMS.
313 *
314  srnamt = 'SLATMS'
315  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
316  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
317  $ info )
318 *
319 * Check error code from SLATMS and handle error.
320 *
321  IF( info.NE.0 ) THEN
322  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
323  $ -1, -1, imat, nfail, nerrs, nout )
324 *
325 * Skip all tests for this generated matrix
326 *
327  GO TO 160
328  END IF
329 *
330 * For matrix types 3-6, zero one or more rows and
331 * columns of the matrix to test that INFO is returned
332 * correctly.
333 *
334  IF( zerot ) THEN
335  IF( imat.EQ.3 ) THEN
336  izero = 1
337  ELSE IF( imat.EQ.4 ) THEN
338  izero = n
339  ELSE
340  izero = n / 2 + 1
341  END IF
342 *
343  IF( imat.LT.6 ) THEN
344 *
345 * Set row and column IZERO to zero.
346 *
347  IF( iuplo.EQ.1 ) THEN
348  ioff = ( izero-1 )*lda
349  DO 20 i = 1, izero - 1
350  a( ioff+i ) = zero
351  20 CONTINUE
352  ioff = ioff + izero
353  DO 30 i = izero, n
354  a( ioff ) = zero
355  ioff = ioff + lda
356  30 CONTINUE
357  ELSE
358  ioff = izero
359  DO 40 i = 1, izero - 1
360  a( ioff ) = zero
361  ioff = ioff + lda
362  40 CONTINUE
363  ioff = ioff - izero
364  DO 50 i = izero, n
365  a( ioff+i ) = zero
366  50 CONTINUE
367  END IF
368  ELSE
369  IF( iuplo.EQ.1 ) THEN
370 *
371 * Set the first IZERO rows and columns to zero.
372 *
373  ioff = 0
374  DO 70 j = 1, n
375  i2 = min( j, izero )
376  DO 60 i = 1, i2
377  a( ioff+i ) = zero
378  60 CONTINUE
379  ioff = ioff + lda
380  70 CONTINUE
381  izero = 1
382  ELSE
383 *
384 * Set the last IZERO rows and columns to zero.
385 *
386  ioff = 0
387  DO 90 j = 1, n
388  i1 = max( j, izero )
389  DO 80 i = i1, n
390  a( ioff+i ) = zero
391  80 CONTINUE
392  ioff = ioff + lda
393  90 CONTINUE
394  END IF
395  END IF
396  ELSE
397  izero = 0
398  END IF
399 *
400 * End generate the test matrix A.
401 *
402 * Do for each value of NB in NBVAL
403 *
404  DO 150 inb = 1, nnb
405 *
406 * Set the optimal blocksize, which will be later
407 * returned by ILAENV.
408 *
409  nb = nbval( inb )
410  CALL xlaenv( 1, nb )
411 *
412 * Copy the test matrix A into matrix AFAC which
413 * will be factorized in place. This is needed to
414 * preserve the test matrix A for subsequent tests.
415 *
416  CALL slacpy( uplo, n, n, a, lda, afac, lda )
417 *
418 * Compute the L*D*L**T or U*D*U**T factorization of the
419 * matrix. IWORK stores details of the interchanges and
420 * the block structure of D. AINV is a work array for
421 * block factorization, LWORK is the length of AINV.
422 *
423  srnamt = 'SSYTRF_AA'
424  lwork = max( 1, n*nb + n )
425  CALL ssytrf_aa( uplo, n, afac, lda, iwork, ainv,
426  $ lwork, info )
427 *
428 * Adjust the expected value of INFO to account for
429 * pivoting.
430 *
431 c IF( IZERO.GT.0 ) THEN
432 c J = 1
433 c K = IZERO
434 c 100 CONTINUE
435 c IF( J.EQ.K ) THEN
436 c K = IWORK( J )
437 c ELSE IF( IWORK( J ).EQ.K ) THEN
438 c K = J
439 c END IF
440 c IF( J.LT.K ) THEN
441 c J = J + 1
442 c GO TO 100
443 c END IF
444 c ELSE
445  k = 0
446 c END IF
447 *
448 * Check error code from SSYTRF and handle error.
449 *
450  IF( info.NE.k ) THEN
451  CALL alaerh( path, 'SSYTRF_AA', info, k, uplo,
452  $ n, n, -1, -1, nb, imat, nfail, nerrs,
453  $ nout )
454  END IF
455 *
456 *+ TEST 1
457 * Reconstruct matrix from factors and compute residual.
458 *
459  CALL ssyt01_aa( uplo, n, a, lda, afac, lda, iwork,
460  $ ainv, lda, rwork, result( 1 ) )
461  nt = 1
462 *
463 *
464 * Print information about the tests that did not pass
465 * the threshold.
466 *
467  DO 110 k = 1, nt
468  IF( result( k ).GE.thresh ) THEN
469  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
470  $ CALL alahd( nout, path )
471  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
472  $ result( k )
473  nfail = nfail + 1
474  END IF
475  110 CONTINUE
476  nrun = nrun + nt
477 *
478 * Skip solver test if INFO is not 0.
479 *
480  IF( info.NE.0 ) THEN
481  GO TO 140
482  END IF
483 *
484 * Do for each value of NRHS in NSVAL.
485 *
486  DO 130 irhs = 1, nns
487  nrhs = nsval( irhs )
488 *
489 *+ TEST 2 (Using TRS)
490 * Solve and compute residual for A * X = B.
491 *
492 * Choose a set of NRHS random solution vectors
493 * stored in XACT and set up the right hand side B
494 *
495  srnamt = 'SLARHS'
496  CALL slarhs( matpath, xtype, uplo, ' ', n, n,
497  $ kl, ku, nrhs, a, lda, xact, lda,
498  $ b, lda, iseed, info )
499  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
500 *
501  srnamt = 'SSYTRS_AA'
502  lwork = max( 1, 3*n-2 )
503  CALL ssytrs_aa( uplo, n, nrhs, afac, lda,
504  $ iwork, x, lda, work, lwork,
505  $ info )
506 *
507 * Check error code from SSYTRS and handle error.
508 *
509  IF( info.NE.0 ) THEN
510  IF( izero.EQ.0 ) THEN
511  CALL alaerh( path, 'SSYTRS_AA', info, 0,
512  $ uplo, n, n, -1, -1, nrhs, imat,
513  $ nfail, nerrs, nout )
514  END IF
515  ELSE
516  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda
517  $ )
518 *
519 * Compute the residual for the solution
520 *
521  CALL spot02( uplo, n, nrhs, a, lda, x, lda,
522  $ work, lda, rwork, result( 2 ) )
523 *
524 *
525 * Print information about the tests that did not pass
526 * the threshold.
527 *
528  DO 120 k = 2, 2
529  IF( result( k ).GE.thresh ) THEN
530  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
531  $ CALL alahd( nout, path )
532  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
533  $ imat, k, result( k )
534  nfail = nfail + 1
535  END IF
536  120 CONTINUE
537  END IF
538  nrun = nrun + 1
539 *
540 * End do for each value of NRHS in NSVAL.
541 *
542  130 CONTINUE
543  140 CONTINUE
544  150 CONTINUE
545  160 CONTINUE
546  170 CONTINUE
547  180 CONTINUE
548 *
549 * Print a summary of the results.
550 *
551  CALL alasum( path, nout, nfail, nrun, nerrs )
552 *
553  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
554  $ i2, ', test ', i2, ', ratio =', g12.5 )
555  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
556  $ i2, ', test(', i2, ') =', g12.5 )
557  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
558  $ i6 )
559  RETURN
560 *
561 * End of SCHKSY_AA
562 *
563  END
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine ssytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_AA
Definition: ssytrf_aa.f:132
subroutine ssytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
SSYTRS_AA
Definition: ssytrs_aa.f:131
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:205
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:120
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:55
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:127
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:170
subroutine ssyt01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
SSYT01_AA
Definition: ssyt01_aa.f:124