LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
zdrvhe_aa.f
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1 *> \brief \b ZDRVHE_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 ZDRVHE_AA( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13 * NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NOUT, NRHS
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), 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 *> ZDRVHE_AA tests the driver routine ZHESV_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] NRHS
61 *> \verbatim
62 *> NRHS is INTEGER
63 *> The number of right hand side vectors to be generated for
64 *> each linear system.
65 *> \endverbatim
66 *>
67 *> \param[in] THRESH
68 *> \verbatim
69 *> THRESH is DOUBLE PRECISION
70 *> The threshold value for the test ratios. A result is
71 *> included in the output file if RESULT >= THRESH. To have
72 *> every test ratio printed, use THRESH = 0.
73 *> \endverbatim
74 *>
75 *> \param[in] TSTERR
76 *> \verbatim
77 *> TSTERR is LOGICAL
78 *> Flag that indicates whether error exits are to be tested.
79 *> \endverbatim
80 *>
81 *> \param[in] NMAX
82 *> \verbatim
83 *> NMAX is INTEGER
84 *> The maximum value permitted for N, used in dimensioning the
85 *> work arrays.
86 *> \endverbatim
87 *>
88 *> \param[out] A
89 *> \verbatim
90 *> A is COMPLEX*16 array, dimension (NMAX*NMAX)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
96 *> \endverbatim
97 *>
98 *> \param[out] AINV
99 *> \verbatim
100 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
101 *> \endverbatim
102 *>
103 *> \param[out] B
104 *> \verbatim
105 *> B is COMPLEX*16 array, dimension (NMAX*NRHS)
106 *> \endverbatim
107 *>
108 *> \param[out] X
109 *> \verbatim
110 *> X is COMPLEX*16 array, dimension (NMAX*NRHS)
111 *> \endverbatim
112 *>
113 *> \param[out] XACT
114 *> \verbatim
115 *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
116 *> \endverbatim
117 *>
118 *> \param[out] WORK
119 *> \verbatim
120 *> WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))
121 *> \endverbatim
122 *>
123 *> \param[out] RWORK
124 *> \verbatim
125 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
126 *> \endverbatim
127 *>
128 *> \param[out] IWORK
129 *> \verbatim
130 *> IWORK is INTEGER array, dimension (NMAX)
131 *> \endverbatim
132 *>
133 *> \param[in] NOUT
134 *> \verbatim
135 *> NOUT is INTEGER
136 *> The unit number for output.
137 *> \endverbatim
138 *
139 * Authors:
140 * ========
141 *
142 *> \author Univ. of Tennessee
143 *> \author Univ. of California Berkeley
144 *> \author Univ. of Colorado Denver
145 *> \author NAG Ltd.
146 *
147 *> \date November 2017
148 *
149 *> \ingroup complex16_lin
150 *
151 * =====================================================================
152  SUBROUTINE zdrvhe_aa( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
153  \$ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
154  \$ RWORK, IWORK, NOUT )
155 *
156 * -- LAPACK test routine (version 3.8.0) --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 * November 2017
160 *
161 * .. Scalar Arguments ..
162  LOGICAL tsterr
163  INTEGER nmax, nn, nout, nrhs
164  DOUBLE PRECISION thresh
165 * ..
166 * .. Array Arguments ..
167  LOGICAL dotype( * )
168  INTEGER IWORK( * ), NVAL( * )
169  DOUBLE PRECISION RWORK( * )
170  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
171  \$ work( * ), x( * ), xact( * )
172 * ..
173 *
174 * =====================================================================
175 *
176 * .. Parameters ..
177  DOUBLE PRECISION ONE, ZERO
178  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
179  INTEGER NTYPES, NTESTS
180  parameter( ntypes = 10, ntests = 3 )
181  INTEGER NFACT
182  parameter( nfact = 2 )
183 * ..
184 * .. Local Scalars ..
185  LOGICAL ZEROT
186  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
187  CHARACTER*3 MATPATH, PATH
188  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
189  \$ izero, j, k, kl, ku, lda, lwork, mode, n,
190  \$ nb, nbmin, nerrs, nfail, nimat, nrun, nt
191  DOUBLE PRECISION ANORM, CNDNUM
192 * ..
193 * .. Local Arrays ..
194  CHARACTER FACTS( NFACT ), UPLOS( 2 )
195  INTEGER ISEED( 4 ), ISEEDY( 4 )
196  DOUBLE PRECISION RESULT( NTESTS )
197 * ..
198 * .. External Functions ..
199  DOUBLE PRECISION DGET06, ZLANHE
200  EXTERNAL DGET06, ZLANHE
201 * ..
202 * .. External Subroutines ..
203  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
206  \$ zlatms, zpot02
207 * ..
208 * .. Scalars in Common ..
209  LOGICAL LERR, OK
210  CHARACTER*32 SRNAMT
211  INTEGER INFOT, NUNIT
212 * ..
213 * .. Common blocks ..
214  COMMON / infoc / infot, nunit, ok, lerr
215  COMMON / srnamc / srnamt
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC dcmplx, max, min
219 * ..
220 * .. Data statements ..
221  DATA iseedy / 1988, 1989, 1990, 1991 /
222  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
223 * ..
224 * .. Executable Statements ..
225 *
226 * Initialize constants and the random number seed.
227 *
228 * Test path
229 *
230  path( 1: 1 ) = 'Zomplex precision'
231  path( 2: 3 ) = 'HA'
232 *
233 * Path to generate matrices
234 *
235  matpath( 1: 1 ) = 'Zomplex precision'
236  matpath( 2: 3 ) = 'HE'
237 *
238  nrun = 0
239  nfail = 0
240  nerrs = 0
241  DO 10 i = 1, 4
242  iseed( i ) = iseedy( i )
243  10 CONTINUE
244 *
245 * Test the error exits
246 *
247  IF( tsterr )
248  \$ CALL zerrvx( path, nout )
249  infot = 0
250 *
251 * Set the block size and minimum block size for testing.
252 *
253  nb = 1
254  nbmin = 2
255  CALL xlaenv( 1, nb )
256  CALL xlaenv( 2, nbmin )
257 *
258 * Do for each value of N in NVAL
259 *
260  DO 180 in = 1, nn
261  n = nval( in )
262  lwork = max( 3*n-2, n*(1+nb) )
263  lwork = max( lwork, 1 )
264  lda = max( n, 1 )
265  xtype = 'N'
266  nimat = ntypes
267  IF( n.LE.0 )
268  \$ nimat = 1
269 *
270  DO 170 imat = 1, nimat
271 *
272 * Do the tests only if DOTYPE( IMAT ) is true.
273 *
274  IF( .NOT.dotype( imat ) )
275  \$ GO TO 170
276 *
277 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
278 *
279  zerot = imat.GE.3 .AND. imat.LE.6
280  IF( zerot .AND. n.LT.imat-2 )
281  \$ GO TO 170
282 *
283 * Do first for UPLO = 'U', then for UPLO = 'L'
284 *
285  DO 160 iuplo = 1, 2
286  uplo = uplos( iuplo )
287 *
288 * Begin generate the test matrix A.
289 *
290 * Set up parameters with ZLATB4 and generate a test matrix
291 * with ZLATMS.
292 *
293  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
294  \$ mode, cndnum, dist )
295 *
296  srnamt = 'ZLATMS'
297  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
298  \$ cndnum, anorm, kl, ku, uplo, a, lda, work,
299  \$ info )
300 *
301 * Check error code from ZLATMS.
302 *
303  IF( info.NE.0 ) THEN
304  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
305  \$ -1, -1, imat, nfail, nerrs, nout )
306  GO TO 160
307  END IF
308 *
309 * For types 3-6, zero one or more rows and columns of the
310 * matrix to test that INFO is returned correctly.
311 *
312  IF( zerot ) THEN
313  IF( imat.EQ.3 ) THEN
314  izero = 1
315  ELSE IF( imat.EQ.4 ) THEN
316  izero = n
317  ELSE
318  izero = n / 2 + 1
319  END IF
320 *
321  IF( imat.LT.6 ) THEN
322 *
323 * Set row and column IZERO to zero.
324 *
325  IF( iuplo.EQ.1 ) THEN
326  ioff = ( izero-1 )*lda
327  DO 20 i = 1, izero - 1
328  a( ioff+i ) = zero
329  20 CONTINUE
330  ioff = ioff + izero
331  DO 30 i = izero, n
332  a( ioff ) = zero
333  ioff = ioff + lda
334  30 CONTINUE
335  ELSE
336  ioff = izero
337  DO 40 i = 1, izero - 1
338  a( ioff ) = zero
339  ioff = ioff + lda
340  40 CONTINUE
341  ioff = ioff - izero
342  DO 50 i = izero, n
343  a( ioff+i ) = zero
344  50 CONTINUE
345  END IF
346  ELSE
347  ioff = 0
348  IF( iuplo.EQ.1 ) THEN
349 *
350 * Set the first IZERO rows and columns to zero.
351 *
352  DO 70 j = 1, n
353  i2 = min( j, izero )
354  DO 60 i = 1, i2
355  a( ioff+i ) = zero
356  60 CONTINUE
357  ioff = ioff + lda
358  70 CONTINUE
359  izero = 1
360  ELSE
361 *
362 * Set the last IZERO rows and columns to zero.
363 *
364  DO 90 j = 1, n
365  i1 = max( j, izero )
366  DO 80 i = i1, n
367  a( ioff+i ) = zero
368  80 CONTINUE
369  ioff = ioff + lda
370  90 CONTINUE
371  END IF
372  END IF
373  ELSE
374  izero = 0
375  END IF
376 *
377 * Set the imaginary part of the diagonals.
378 *
379  CALL zlaipd( n, a, lda+1, 0 )
380 *
381  DO 150 ifact = 1, nfact
382 *
383 * Do first for FACT = 'F', then for other values.
384 *
385  fact = facts( ifact )
386 *
387 * Form an exact solution and set the right hand side.
388 *
389  srnamt = 'ZLARHS'
390  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
391  \$ nrhs, a, lda, xact, lda, b, lda, iseed,
392  \$ info )
393  xtype = 'C'
394 *
395 * --- Test ZHESV_AA ---
396 *
397  IF( ifact.EQ.2 ) THEN
398  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
399  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
400 *
401 * Factor the matrix and solve the system using ZHESV.
402 *
403  srnamt = 'ZHESV_AA '
404  CALL zhesv_aa( uplo, n, nrhs, afac, lda, iwork,
405  \$ x, lda, work, lwork, info )
406 *
407 * Adjust the expected value of INFO to account for
408 * pivoting.
409 *
410  IF( izero.GT.0 ) THEN
411  j = 1
412  k = izero
413  100 CONTINUE
414  IF( j.EQ.k ) THEN
415  k = iwork( j )
416  ELSE IF( iwork( j ).EQ.k ) THEN
417  k = j
418  END IF
419  IF( j.LT.k ) THEN
420  j = j + 1
421  GO TO 100
422  END IF
423  ELSE
424  k = 0
425  END IF
426 *
427 * Check error code from ZHESV .
428 *
429  IF( info.NE.k ) THEN
430  CALL alaerh( path, 'ZHESV_AA', info, k, uplo, n,
431  \$ n, -1, -1, nrhs, imat, nfail,
432  \$ nerrs, nout )
433  GO TO 120
434  ELSE IF( info.NE.0 ) THEN
435  GO TO 120
436  END IF
437 *
438 * Reconstruct matrix from factors and compute
439 * residual.
440 *
441  CALL zhet01_aa( uplo, n, a, lda, afac, lda,
442  \$ iwork, ainv, lda, rwork,
443  \$ result( 1 ) )
444 *
445 * Compute residual of the computed solution.
446 *
447  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
448  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
449  \$ lda, rwork, result( 2 ) )
450  nt = 2
451 *
452 * Print information about the tests that did not pass
453 * the threshold.
454 *
455  DO 110 k = 1, nt
456  IF( result( k ).GE.thresh ) THEN
457  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
458  \$ CALL aladhd( nout, path )
459  WRITE( nout, fmt = 9999 )'ZHESV_AA', uplo, n,
460  \$ imat, k, result( k )
461  nfail = nfail + 1
462  END IF
463  110 CONTINUE
464  nrun = nrun + nt
465  120 CONTINUE
466  END IF
467 *
468  150 CONTINUE
469 *
470  160 CONTINUE
471  170 CONTINUE
472  180 CONTINUE
473 *
474 * Print a summary of the results.
475 *
476  CALL alasvm( path, nout, nfail, nrun, nerrs )
477 *
478  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
479  \$ ', test ', i2, ', ratio =', g12.5 )
480  RETURN
481 *
482 * End of ZDRVHE_AA
483 *
484  END
zerrvx
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
zhet01_aa
subroutine zhet01_aa(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01_AA
Definition: zhet01_aa.f:127
zpot02
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
alasvm
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:75
zhesv_aa
subroutine zhesv_aa(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
Definition: zhesv_aa.f:164
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
zhetri2
subroutine zhetri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRI2
Definition: zhetri2.f:129
zlaipd
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:85
zhetrf_aa
subroutine zhetrf_aa(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_AA
Definition: zhetrf_aa.f:134
zdrvhe_aa
subroutine zdrvhe_aa(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZDRVHE_AA
Definition: zdrvhe_aa.f:155
zget04
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
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
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
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