LAPACK  3.7.1
LAPACK: Linear Algebra PACKage
zchkhe_aa.f
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1 *> \brief \b ZCHKHE_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 ZCHKHE_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 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 *> ZCHKHE_AA tests ZHETRF_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 DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX))
144 *> \endverbatim
145 *>
146 *> \param[out] IWORK
147 *> \verbatim
148 *> IWORK is INTEGER array, dimension (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 June 2017
166 *
167 *
168 *> \ingroup complex16_lin
169 *
170 * =====================================================================
171  SUBROUTINE zchkhe_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 NMAX, NN, NNB, NNS, NOUT
185  DOUBLE PRECISION THRESH
186 * ..
187 * .. Array Arguments ..
188  LOGICAL DOTYPE( * )
189  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
190  DOUBLE PRECISION RWORK( * )
191  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
192  $ work( * ), x( * ), xact( * )
193 * ..
194 *
195 * =====================================================================
196 *
197 * .. Parameters ..
198  DOUBLE PRECISION ZERO
199  parameter( zero = 0.0d+0 )
200  COMPLEX*16 CZERO
201  parameter( czero = ( 0.0d+0, 0.0d+0 ) )
202  INTEGER NTYPES
203  parameter( ntypes = 10 )
204  INTEGER NTESTS
205  parameter( ntests = 9 )
206 * ..
207 * .. Local Scalars ..
208  LOGICAL ZEROT
209  CHARACTER DIST, TYPE, UPLO, XTYPE
210  CHARACTER*3 PATH, MATPATH
211  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
212  $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
213  $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
214  DOUBLE PRECISION ANORM, CNDNUM
215 * ..
216 * .. Local Arrays ..
217  CHARACTER UPLOS( 2 )
218  INTEGER ISEED( 4 ), ISEEDY( 4 )
219  DOUBLE PRECISION RESULT( ntests )
220 * ..
221 * .. External Subroutines ..
222  EXTERNAL alaerh, alahd, alasum, xlaenv, zerrhe,
223  $ zhet01_aa, zhetrf_aa, zhetrs_aa, zlacpy,
224  $ zlaipd, zlarhs, zlatb4, zlatms, zpot02
225 * ..
226 * .. Intrinsic Functions ..
227  INTRINSIC max, min
228 * ..
229 * .. Scalars in Common ..
230  LOGICAL LERR, OK
231  CHARACTER*32 SRNAMT
232  INTEGER INFOT, NUNIT
233 * ..
234 * .. Common blocks ..
235  COMMON / infoc / infot, nunit, ok, lerr
236  COMMON / srnamc / srnamt
237 * ..
238 * .. Data statements ..
239  DATA iseedy / 1988, 1989, 1990, 1991 /
240  DATA uplos / 'U', 'L' /
241 * ..
242 * .. Executable Statements ..
243 *
244 * Initialize constants and the random number seed.
245 *
246 * Test path
247 *
248  path( 1: 1 ) = 'Zomplex precision'
249  path( 2: 3 ) = 'HA'
250 *
251 * Path to generate matrices
252 *
253  matpath( 1: 1 ) = 'Zomplex precision'
254  matpath( 2: 3 ) = 'HE'
255  nrun = 0
256  nfail = 0
257  nerrs = 0
258  DO 10 i = 1, 4
259  iseed( i ) = iseedy( i )
260  10 CONTINUE
261 *
262 * Test the error exits
263 *
264  IF( tsterr )
265  $ CALL zerrhe( path, nout )
266  infot = 0
267 *
268 * Set the minimum block size for which the block routine should
269 * be used, which will be later returned by ILAENV
270 *
271  CALL xlaenv( 2, 2 )
272 *
273 * Do for each value of N in NVAL
274 *
275  DO 180 in = 1, nn
276  n = nval( in )
277  IF( n .GT. nmax ) THEN
278  nfail = nfail + 1
279  WRITE(nout, 9995) 'M ', n, nmax
280  GO TO 180
281  END IF
282  lda = max( n, 1 )
283  xtype = 'N'
284  nimat = ntypes
285  IF( n.LE.0 )
286  $ nimat = 1
287 *
288  izero = 0
289  DO 170 imat = 1, nimat
290 *
291 * Do the tests only if DOTYPE( IMAT ) is true.
292 *
293  IF( .NOT.dotype( imat ) )
294  $ GO TO 170
295 *
296 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
297 *
298  zerot = imat.GE.3 .AND. imat.LE.6
299  IF( zerot .AND. n.LT.imat-2 )
300  $ GO TO 170
301 *
302 * Do first for UPLO = 'U', then for UPLO = 'L'
303 *
304  DO 160 iuplo = 1, 2
305  uplo = uplos( iuplo )
306 *
307 * Set up parameters with ZLATB4 for the matrix generator
308 * based on the type of matrix to be generated.
309 *
310  CALL zlatb4( matpath, imat, n, n, TYPE, KL, KU,
311  $ anorm, mode, cndnum, dist )
312 *
313 * Generate a matrix with ZLATMS.
314 *
315  srnamt = 'ZLATMS'
316  CALL zlatms( n, n, dist, iseed, TYPE, RWORK, MODE,
317  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
318  $ info )
319 *
320 * Check error code from ZLATMS and handle error.
321 *
322  IF( info.NE.0 ) THEN
323  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
324  $ -1, -1, imat, nfail, nerrs, nout )
325 *
326 * Skip all tests for this generated matrix
327 *
328  GO TO 160
329  END IF
330 *
331 * For types 3-6, zero one or more rows and columns of
332 * the matrix to test that INFO is returned 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 ) = czero
351  20 CONTINUE
352  ioff = ioff + izero
353  DO 30 i = izero, n
354  a( ioff ) = czero
355  ioff = ioff + lda
356  30 CONTINUE
357  ELSE
358  ioff = izero
359  DO 40 i = 1, izero - 1
360  a( ioff ) = czero
361  ioff = ioff + lda
362  40 CONTINUE
363  ioff = ioff - izero
364  DO 50 i = izero, n
365  a( ioff+i ) = czero
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 ) = czero
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 ) = czero
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 test matrix A.
401 *
402 *
403 * Set the imaginary part of the diagonals.
404 *
405  CALL zlaipd( n, a, lda+1, 0 )
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 zlacpy( 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  lwork = max( 1, ( nb+1 )*lda )
429  srnamt = 'ZHETRF_AA'
430  CALL zhetrf_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 ZHETRF and handle error.
454 *
455  IF( info.NE.k ) THEN
456  CALL alaerh( path, 'ZHETRF_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 zhet01_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 = 'ZLARHS'
501  CALL zlarhs( matpath, xtype, uplo, ' ', n, n,
502  $ kl, ku, nrhs, a, lda, xact, lda,
503  $ b, lda, iseed, info )
504  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
505 *
506  srnamt = 'ZHETRS_AA'
507  lwork = max( 1, 3*n-2 )
508  CALL zhetrs_aa( uplo, n, nrhs, afac, lda, iwork,
509  $ x, lda, work, lwork, info )
510 *
511 * Check error code from ZHETRS and handle error.
512 *
513  IF( info.NE.0 ) THEN
514  IF( izero.EQ.0 ) THEN
515  CALL alaerh( path, 'ZHETRS_AA', info, 0,
516  $ uplo, n, n, -1, -1, nrhs, imat,
517  $ nfail, nerrs, nout )
518  END IF
519  ELSE
520 *
521  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda
522  $ )
523 *
524 * Compute the residual for the solution
525 *
526  CALL zpot02( uplo, n, nrhs, a, lda, x, lda,
527  $ work, lda, rwork, result( 2 ) )
528 *
529 * Print information about the tests that did not pass
530 * the threshold.
531 *
532  DO 120 k = 2, 2
533  IF( result( k ).GE.thresh ) THEN
534  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
535  $ CALL alahd( nout, path )
536  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
537  $ imat, k, result( k )
538  nfail = nfail + 1
539  END IF
540  120 CONTINUE
541  END IF
542  nrun = nrun + 1
543 *
544 * End do for each value of NRHS in NSVAL.
545 *
546  130 CONTINUE
547  140 CONTINUE
548  150 CONTINUE
549  160 CONTINUE
550  170 CONTINUE
551  180 CONTINUE
552 *
553 * Print a summary of the results.
554 *
555  CALL alasum( path, nout, nfail, nrun, nerrs )
556 *
557  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
558  $ i2, ', test ', i2, ', ratio =', g12.5 )
559  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
560  $ i2, ', test(', i2, ') =', g12.5 )
561 c 9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
562 c $ ', test(', I2, ') =', G12.5 )
563  9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
564  $ i6 )
565  RETURN
566 *
567 * End of ZCHKHE_AA
568 *
569  END
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
zchkhe_aa
subroutine zchkhe_aa(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZCHKHE_AA
Definition: zchkhe_aa.f:174
zerrhe
subroutine zerrhe(PATH, NUNIT)
ZERRHE
Definition: zerrhe.f:57
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
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
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
zlaipd
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:85
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
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
zpot02
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
zhet01_aa
subroutine zhet01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01_AA
Definition: zhet01_aa.f:127
zhetrf_aa
subroutine zhetrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_AA
Definition: zhetrf_aa.f:134
zhetrs_aa
subroutine zhetrs_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHETRS_AA
Definition: zhetrs_aa.f:132
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75