LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
zchksy_aa.f
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1 *> \brief \b ZCHKSY_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 ZCHKSY_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 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION RWORK( * )
24 * COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZCHKSY_AA tests ZSYTRF_AA, -TRS_AA.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] DOTYPE
41 *> \verbatim
42 *> DOTYPE is LOGICAL array, dimension (NTYPES)
43 *> The matrix types to be used for testing. Matrices of type j
44 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46 *> \endverbatim
47 *>
48 *> \param[in] NN
49 *> \verbatim
50 *> NN is INTEGER
51 *> The number of values of N contained in the vector NVAL.
52 *> \endverbatim
53 *>
54 *> \param[in] NVAL
55 *> \verbatim
56 *> NVAL is INTEGER array, dimension (NN)
57 *> The values of the matrix dimension N.
58 *> \endverbatim
59 *>
60 *> \param[in] NNB
61 *> \verbatim
62 *> NNB is INTEGER
63 *> The number of values of NB contained in the vector NBVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NBVAL
67 *> \verbatim
68 *> NBVAL is INTEGER array, dimension (NBVAL)
69 *> The values of the blocksize NB.
70 *> \endverbatim
71 *>
72 *> \param[in] NNS
73 *> \verbatim
74 *> NNS is INTEGER
75 *> The number of values of NRHS contained in the vector NSVAL.
76 *> \endverbatim
77 *>
78 *> \param[in] NSVAL
79 *> \verbatim
80 *> NSVAL is INTEGER array, dimension (NNS)
81 *> The values of the number of right hand sides NRHS.
82 *> \endverbatim
83 *>
84 *> \param[in] THRESH
85 *> \verbatim
86 *> THRESH is DOUBLE PRECISION
87 *> The threshold value for the test ratios. A result is
88 *> included in the output file if RESULT >= THRESH. To have
89 *> every test ratio printed, use THRESH = 0.
90 *> \endverbatim
91 *>
92 *> \param[in] TSTERR
93 *> \verbatim
94 *> TSTERR is LOGICAL
95 *> Flag that indicates whether error exits are to be tested.
96 *> \endverbatim
97 *>
98 *> \param[in] NMAX
99 *> \verbatim
100 *> NMAX is INTEGER
101 *> The maximum value permitted for N, used in dimensioning the
102 *> work arrays.
103 *> \endverbatim
104 *>
105 *> \param[out] A
106 *> \verbatim
107 *> A is COMPLEX*16 array, dimension (NMAX*NMAX)
108 *> \endverbatim
109 *>
110 *> \param[out] AFAC
111 *> \verbatim
112 *> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
113 *> \endverbatim
114 *>
115 *> \param[out] AINV
116 *> \verbatim
117 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
118 *> \endverbatim
119 *>
120 *> \param[out] B
121 *> \verbatim
122 *> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
123 *> where NSMAX is the largest entry in NSVAL.
124 *> \endverbatim
125 *>
126 *> \param[out] X
127 *> \verbatim
128 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
129 *> \endverbatim
130 *>
131 *> \param[out] XACT
132 *> \verbatim
133 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
134 *> \endverbatim
135 *>
136 *> \param[out] WORK
137 *> \verbatim
138 *> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
139 *> \endverbatim
140 *>
141 *> \param[out] RWORK
142 *> \verbatim
143 *> RWORK is COMPLEX*16 array, dimension (max(NMAX,2*NSMAX))
144 *> \endverbatim
145 *>
146 *> \param[out] IWORK
147 *> \verbatim
148 *> IWORK is INTEGER array, dimension (2*NMAX)
149 *> \endverbatim
150 *>
151 *> \param[in] NOUT
152 *> \verbatim
153 *> NOUT is INTEGER
154 *> The unit number for output.
155 *> \endverbatim
156 *
157 * Authors:
158 * ========
159 *
160 *> \author Univ. of Tennessee
161 *> \author Univ. of California Berkeley
162 *> \author Univ. of Colorado Denver
163 *> \author NAG Ltd.
164 *
165 *> \date November 2017
166 *
167 *> \ingroup complex16_lin
168 *
169 * =====================================================================
170  SUBROUTINE zchksy_aa( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
171  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
172  $ X, XACT, WORK, RWORK, IWORK, NOUT )
173 *
174 * -- LAPACK test routine (version 3.8.0) --
175 * -- LAPACK is a software package provided by Univ. of Tennessee, --
176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177 * November 2017
178 *
179  IMPLICIT NONE
180 *
181 * .. Scalar Arguments ..
182  LOGICAL tsterr
183  INTEGER nn, nnb, nns, nmax, nout
184  DOUBLE PRECISION thresh
185 * ..
186 * .. Array Arguments ..
187  LOGICAL dotype( * )
188  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
189  DOUBLE PRECISION RWORK( * )
190  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
191  $ work( * ), x( * ), xact( * )
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. Parameters ..
197  DOUBLE PRECISION ZERO
198  PARAMETER ( ZERO = 0.0d+0 )
199  COMPLEX*16 CZERO
200  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
201  INTEGER NTYPES
202  parameter( ntypes = 10 )
203  INTEGER NTESTS
204  parameter( ntests = 9 )
205 * ..
206 * .. Local Scalars ..
207  LOGICAL ZEROT
208  CHARACTER DIST, TYPE, UPLO, XTYPE
209  CHARACTER*3 PATH, MATPATH
210  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
211  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
212  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
213  DOUBLE PRECISION ANORM, CNDNUM
214 * ..
215 * .. Local Arrays ..
216  CHARACTER UPLOS( 2 )
217  INTEGER ISEED( 4 ), ISEEDY( 4 )
218  DOUBLE PRECISION RESULT( NTESTS )
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL alaerh, alahd, alasum, zerrsy, zlacpy, zlarhs,
222  $ zlatb4, zlatms, zsyt02, zsyt01_aa, zsytrf_aa,
223  $ zsytrs_aa, xlaenv
224 * ..
225 * .. Intrinsic Functions ..
226  INTRINSIC max, min
227 * ..
228 * .. Scalars in Common ..
229  LOGICAL LERR, OK
230  CHARACTER*32 SRNAMT
231  INTEGER INFOT, NUNIT
232 * ..
233 * .. Common blocks ..
234  COMMON / infoc / infot, nunit, ok, lerr
235  COMMON / srnamc / srnamt
236 * ..
237 * .. Data statements ..
238  DATA iseedy / 1988, 1989, 1990, 1991 /
239  DATA uplos / 'U', 'L' /
240 * ..
241 * .. Executable Statements ..
242 *
243 * Initialize constants and the random number seed.
244 *
245 * Test path
246 *
247  path( 1: 1 ) = 'Zomplex precision'
248  path( 2: 3 ) = 'SA'
249 *
250 * Path to generate matrices
251 *
252  matpath( 1: 1 ) = 'Zomplex precision'
253  matpath( 2: 3 ) = 'SY'
254  nrun = 0
255  nfail = 0
256  nerrs = 0
257  DO 10 i = 1, 4
258  iseed( i ) = iseedy( i )
259  10 CONTINUE
260 *
261 * Test the error exits
262 *
263  IF( tsterr )
264  $ CALL zerrsy( path, nout )
265  infot = 0
266 *
267 * Set the minimum block size for which the block routine should
268 * be used, which will be later returned by ILAENV
269 *
270  CALL xlaenv( 2, 2 )
271 *
272 * Do for each value of N in NVAL
273 *
274  DO 180 in = 1, nn
275  n = nval( in )
276  IF( n .GT. nmax ) THEN
277  nfail = nfail + 1
278  WRITE(nout, 9995) 'M ', n, nmax
279  GO TO 180
280  END IF
281  lda = max( n, 1 )
282  xtype = 'N'
283  nimat = ntypes
284  IF( n.LE.0 )
285  $ nimat = 1
286 *
287  izero = 0
288 *
289 * Do for each value of matrix type IMAT
290 *
291  DO 170 imat = 1, nimat
292 *
293 * Do the tests only if DOTYPE( IMAT ) is true.
294 *
295  IF( .NOT.dotype( imat ) )
296  $ GO TO 170
297 *
298 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
299 *
300  zerot = imat.GE.3 .AND. imat.LE.6
301  IF( zerot .AND. n.LT.imat-2 )
302  $ GO TO 170
303 *
304 * Do first for UPLO = 'U', then for UPLO = 'L'
305 *
306  DO 160 iuplo = 1, 2
307  uplo = uplos( iuplo )
308 *
309 * Begin generate the test matrix A.
310 *
311 *
312 * Set up parameters with ZLATB4 for the matrix generator
313 * based on the type of matrix to be generated.
314 *
315  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku,
316  $ anorm, mode, cndnum, dist )
317 *
318 * Generate a matrix with ZLATMS.
319 *
320  srnamt = 'ZLATMS'
321  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
322  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
323  $ info )
324 *
325 * Check error code from ZLATMS and handle error.
326 *
327  IF( info.NE.0 ) THEN
328  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
329  $ -1, -1, imat, nfail, nerrs, nout )
330 *
331 * Skip all tests for this generated matrix
332 *
333  GO TO 160
334  END IF
335 *
336 * For matrix types 3-6, zero one or more rows and
337 * columns of the matrix to test that INFO is returned
338 * correctly.
339 *
340  IF( zerot ) THEN
341  IF( imat.EQ.3 ) THEN
342  izero = 1
343  ELSE IF( imat.EQ.4 ) THEN
344  izero = n
345  ELSE
346  izero = n / 2 + 1
347  END IF
348 *
349  IF( imat.LT.6 ) THEN
350 *
351 * Set row and column IZERO to zero.
352 *
353  IF( iuplo.EQ.1 ) THEN
354  ioff = ( izero-1 )*lda
355  DO 20 i = 1, izero - 1
356  a( ioff+i ) = czero
357  20 CONTINUE
358  ioff = ioff + izero
359  DO 30 i = izero, n
360  a( ioff ) = czero
361  ioff = ioff + lda
362  30 CONTINUE
363  ELSE
364  ioff = izero
365  DO 40 i = 1, izero - 1
366  a( ioff ) = czero
367  ioff = ioff + lda
368  40 CONTINUE
369  ioff = ioff - izero
370  DO 50 i = izero, n
371  a( ioff+i ) = czero
372  50 CONTINUE
373  END IF
374  ELSE
375  IF( iuplo.EQ.1 ) THEN
376 *
377 * Set the first IZERO rows and columns to zero.
378 *
379  ioff = 0
380  DO 70 j = 1, n
381  i2 = min( j, izero )
382  DO 60 i = 1, i2
383  a( ioff+i ) = czero
384  60 CONTINUE
385  ioff = ioff + lda
386  70 CONTINUE
387  izero = 1
388  ELSE
389 *
390 * Set the last IZERO rows and columns to zero.
391 *
392  ioff = 0
393  DO 90 j = 1, n
394  i1 = max( j, izero )
395  DO 80 i = i1, n
396  a( ioff+i ) = czero
397  80 CONTINUE
398  ioff = ioff + lda
399  90 CONTINUE
400  END IF
401  END IF
402  ELSE
403  izero = 0
404  END IF
405 *
406 * End generate the test matrix A.
407 *
408 * Do for each value of NB in NBVAL
409 *
410  DO 150 inb = 1, nnb
411 *
412 * Set the optimal blocksize, which will be later
413 * returned by ILAENV.
414 *
415  nb = nbval( inb )
416  CALL xlaenv( 1, nb )
417 *
418 * Copy the test matrix A into matrix AFAC which
419 * will be factorized in place. This is needed to
420 * preserve the test matrix A for subsequent tests.
421 *
422  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
423 *
424 * Compute the L*D*L**T or U*D*U**T factorization of the
425 * matrix. IWORK stores details of the interchanges and
426 * the block structure of D. AINV is a work array for
427 * block factorization, LWORK is the length of AINV.
428 *
429  srnamt = 'ZSYTRF_AA'
430  lwork = max( 1, n*nb + n )
431  CALL zsytrf_aa( uplo, n, afac, lda, iwork, ainv,
432  $ lwork, info )
433 *
434 * Adjust the expected value of INFO to account for
435 * pivoting.
436 *
437 c IF( IZERO.GT.0 ) THEN
438 c J = 1
439 c K = IZERO
440 c 100 CONTINUE
441 c IF( J.EQ.K ) THEN
442 c K = IWORK( J )
443 c ELSE IF( IWORK( J ).EQ.K ) THEN
444 c K = J
445 c END IF
446 c IF( J.LT.K ) THEN
447 c J = J + 1
448 c GO TO 100
449 c END IF
450 c ELSE
451  k = 0
452 c END IF
453 *
454 * Check error code from ZSYTRF and handle error.
455 *
456  IF( info.NE.k ) THEN
457  CALL alaerh( path, 'ZSYTRF_AA', info, k, uplo,
458  $ n, n, -1, -1, nb, imat, nfail, nerrs,
459  $ nout )
460  END IF
461 *
462 *+ TEST 1
463 * Reconstruct matrix from factors and compute residual.
464 *
465  CALL zsyt01_aa( uplo, n, a, lda, afac, lda, iwork,
466  $ ainv, lda, rwork, result( 1 ) )
467  nt = 1
468 *
469 *
470 * Print information about the tests that did not pass
471 * the threshold.
472 *
473  DO 110 k = 1, nt
474  IF( result( k ).GE.thresh ) THEN
475  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
476  $ CALL alahd( nout, path )
477  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
478  $ result( k )
479  nfail = nfail + 1
480  END IF
481  110 CONTINUE
482  nrun = nrun + nt
483 *
484 * Skip solver test if INFO is not 0.
485 *
486  IF( info.NE.0 ) THEN
487  GO TO 140
488  END IF
489 *
490 * Do for each value of NRHS in NSVAL.
491 *
492  DO 130 irhs = 1, nns
493  nrhs = nsval( irhs )
494 *
495 *+ TEST 2 (Using TRS)
496 * Solve and compute residual for A * X = B.
497 *
498 * Choose a set of NRHS random solution vectors
499 * stored in XACT and set up the right hand side B
500 *
501  srnamt = 'ZLARHS'
502  CALL zlarhs( matpath, xtype, uplo, ' ', n, n,
503  $ kl, ku, nrhs, a, lda, xact, lda,
504  $ b, lda, iseed, info )
505  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
506 *
507  srnamt = 'ZSYTRS_AA'
508  lwork = max( 1, 3*n-2 )
509  CALL zsytrs_aa( uplo, n, nrhs, afac, lda,
510  $ iwork, x, lda, work, lwork,
511  $ info )
512 *
513 * Check error code from ZSYTRS and handle error.
514 *
515  IF( info.NE.0 ) THEN
516  IF( izero.EQ.0 ) THEN
517  CALL alaerh( path, 'ZSYTRS_AA', info, 0,
518  $ uplo, n, n, -1, -1, nrhs, imat,
519  $ nfail, nerrs, nout )
520  END IF
521  ELSE
522  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda
523  $ )
524 *
525 * Compute the residual for the solution
526 *
527  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda,
528  $ work, lda, rwork, result( 2 ) )
529 *
530 *
531 * Print information about the tests that did not pass
532 * the threshold.
533 *
534  DO 120 k = 2, 2
535  IF( result( k ).GE.thresh ) THEN
536  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
537  $ CALL alahd( nout, path )
538  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
539  $ imat, k, result( k )
540  nfail = nfail + 1
541  END IF
542  120 CONTINUE
543  END IF
544  nrun = nrun + 1
545 *
546 * End do for each value of NRHS in NSVAL.
547 *
548  130 CONTINUE
549  140 CONTINUE
550  150 CONTINUE
551  160 CONTINUE
552  170 CONTINUE
553  180 CONTINUE
554 *
555 * Print a summary of the results.
556 *
557  CALL alasum( path, nout, nfail, nrun, nerrs )
558 *
559  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
560  $ i2, ', test ', i2, ', ratio =', g12.5 )
561  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
562  $ i2, ', test(', i2, ') =', g12.5 )
563  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
564  $ i6 )
565  RETURN
566 *
567 * End of ZCHKSY_AA
568 *
569  END
zlarhs
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
zsytrf_aa
subroutine zsytrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_AA
Definition: zsytrf_aa.f:134
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
zchksy_aa
subroutine zchksy_aa(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZCHKSY_AA
Definition: zchksy_aa.f:173
zsyt01_aa
subroutine zsyt01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZSYT01
Definition: zsyt01_aa.f:128
zlacpy
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
zsyt02
subroutine zsyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZSYT02
Definition: zsyt02.f:129
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
zerrsy
subroutine zerrsy(PATH, NUNIT)
ZERRSY
Definition: zerrsy.f:57
zsytrs_aa
subroutine zsytrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYTRS_AA
Definition: zsytrs_aa.f:133
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75
zlatb4
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334