LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
zdrvhe_rk.f
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1 *> \brief \b ZDRVHE_RK
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_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12 * NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
13 * RWORK, IWORK, 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( * ), E( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZDRVHE_RK tests the driver routines ZHESV_RK.
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] E
99 *> \verbatim
100 *> E is COMPLEX*16 array, dimension (NMAX)
101 *> \endverbatim
102 *>
103 *> \param[out] AINV
104 *> \verbatim
105 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
106 *> \endverbatim
107 *>
108 *> \param[out] B
109 *> \verbatim
110 *> B is COMPLEX*16 array, dimension (NMAX*NRHS)
111 *> \endverbatim
112 *>
113 *> \param[out] X
114 *> \verbatim
115 *> X is COMPLEX*16 array, dimension (NMAX*NRHS)
116 *> \endverbatim
117 *>
118 *> \param[out] XACT
119 *> \verbatim
120 *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
121 *> \endverbatim
122 *>
123 *> \param[out] WORK
124 *> \verbatim
125 *> WORK is COMPLEX*16 array, dimension (NMAX*max(2,NRHS))
126 *> \endverbatim
127 *>
128 *> \param[out] RWORK
129 *> \verbatim
130 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
131 *> \endverbatim
132 *>
133 *> \param[out] IWORK
134 *> \verbatim
135 *> IWORK is INTEGER array, dimension (NMAX)
136 *> \endverbatim
137 *>
138 *> \param[in] NOUT
139 *> \verbatim
140 *> NOUT is INTEGER
141 *> The unit number for output.
142 *> \endverbatim
143 *
144 * Authors:
145 * ========
146 *
147 *> \author Univ. of Tennessee
148 *> \author Univ. of California Berkeley
149 *> \author Univ. of Colorado Denver
150 *> \author NAG Ltd.
151 *
152 *> \date December 2016
153 *
154 *> \ingroup complex16_lin
155 *
156 * =====================================================================
157  SUBROUTINE zdrvhe_rk( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
158  $ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
159  $ RWORK, IWORK, NOUT )
160 *
161 * -- LAPACK test routine (version 3.7.0) --
162 * -- LAPACK is a software package provided by Univ. of Tennessee, --
163 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164 * December 2016
165 *
166 * .. Scalar Arguments ..
167  LOGICAL tsterr
168  INTEGER nmax, nn, nout, nrhs
169  DOUBLE PRECISION thresh
170 * ..
171 * .. Array Arguments ..
172  LOGICAL dotype( * )
173  INTEGER IWORK( * ), NVAL( * )
174  DOUBLE PRECISION RWORK( * )
175  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
176  $ work( * ), x( * ), xact( * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Parameters ..
182  DOUBLE PRECISION ONE, ZERO
183  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
184  INTEGER NTYPES, NTESTS
185  parameter( ntypes = 10, ntests = 3 )
186  INTEGER NFACT
187  parameter( nfact = 2 )
188 * ..
189 * .. Local Scalars ..
190  LOGICAL ZEROT
191  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
192  CHARACTER*3 MATPATH, PATH
193  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
194  $ izero, j, k, kl, ku, lda, lwork, mode, n,
195  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
196  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
197 * ..
198 * .. Local Arrays ..
199  CHARACTER FACTS( NFACT ), UPLOS( 2 )
200  INTEGER ISEED( 4 ), ISEEDY( 4 )
201  DOUBLE PRECISION RESULT( NTESTS )
202 
203 * ..
204 * .. External Functions ..
205  DOUBLE PRECISION ZLANHE
206  EXTERNAL ZLANHE
207 * ..
208 * .. External Subroutines ..
209  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx,
210  $ zget04, zlacpy, zlarhs, zlatb4, zlatms,
211  $ zhesv_rk, zhet01_3, zpot02, zhetrf_rk, zhetri_3
212 * ..
213 * .. Scalars in Common ..
214  LOGICAL LERR, OK
215  CHARACTER*32 SRNAMT
216  INTEGER INFOT, NUNIT
217 * ..
218 * .. Common blocks ..
219  COMMON / infoc / infot, nunit, ok, lerr
220  COMMON / srnamc / srnamt
221 * ..
222 * .. Intrinsic Functions ..
223  INTRINSIC max, min
224 * ..
225 * .. Data statements ..
226  DATA iseedy / 1988, 1989, 1990, 1991 /
227  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
228 * ..
229 * .. Executable Statements ..
230 *
231 * Initialize constants and the random number seed.
232 *
233 * Test path
234 *
235  path( 1: 1 ) = 'Zomplex precision'
236  path( 2: 3 ) = 'HK'
237 *
238 * Path to generate matrices
239 *
240  matpath( 1: 1 ) = 'Zomplex precision'
241  matpath( 2: 3 ) = 'HE'
242 *
243  nrun = 0
244  nfail = 0
245  nerrs = 0
246  DO 10 i = 1, 4
247  iseed( i ) = iseedy( i )
248  10 CONTINUE
249  lwork = max( 2*nmax, nmax*nrhs )
250 *
251 * Test the error exits
252 *
253  IF( tsterr )
254  $ CALL zerrvx( path, nout )
255  infot = 0
256 *
257 * Set the block size and minimum block size for which the block
258 * routine should be used, which will be later returned by ILAENV.
259 *
260  nb = 1
261  nbmin = 2
262  CALL xlaenv( 1, nb )
263  CALL xlaenv( 2, nbmin )
264 *
265 * Do for each value of N in NVAL
266 *
267  DO 180 in = 1, nn
268  n = nval( in )
269  lda = max( n, 1 )
270  xtype = 'N'
271  nimat = ntypes
272  IF( n.LE.0 )
273  $ nimat = 1
274 *
275  DO 170 imat = 1, nimat
276 *
277 * Do the tests only if DOTYPE( IMAT ) is true.
278 *
279  IF( .NOT.dotype( imat ) )
280  $ GO TO 170
281 *
282 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
283 *
284  zerot = imat.GE.3 .AND. imat.LE.6
285  IF( zerot .AND. n.LT.imat-2 )
286  $ GO TO 170
287 *
288 * Do first for UPLO = 'U', then for UPLO = 'L'
289 *
290  DO 160 iuplo = 1, 2
291  uplo = uplos( iuplo )
292 *
293 * Begin generate the test matrix A.
294 *
295 * Set up parameters with ZLATB4 for the matrix generator
296 * based on the type of matrix to be generated.
297 *
298  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
299  $ mode, cndnum, dist )
300 *
301 * Generate a matrix with ZLATMS.
302 *
303  srnamt = 'ZLATMS'
304  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
305  $ cndnum, anorm, kl, ku, uplo, a, lda,
306  $ work, info )
307 *
308 * Check error code from ZLATMS and handle error.
309 *
310  IF( info.NE.0 ) THEN
311  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
312  $ -1, -1, -1, imat, nfail, nerrs, nout )
313  GO TO 160
314  END IF
315 *
316 * For types 3-6, zero one or more rows and columns of
317 * the matrix to test that INFO is returned correctly.
318 *
319  IF( zerot ) THEN
320  IF( imat.EQ.3 ) THEN
321  izero = 1
322  ELSE IF( imat.EQ.4 ) THEN
323  izero = n
324  ELSE
325  izero = n / 2 + 1
326  END IF
327 *
328  IF( imat.LT.6 ) THEN
329 *
330 * Set row and column IZERO to zero.
331 *
332  IF( iuplo.EQ.1 ) THEN
333  ioff = ( izero-1 )*lda
334  DO 20 i = 1, izero - 1
335  a( ioff+i ) = zero
336  20 CONTINUE
337  ioff = ioff + izero
338  DO 30 i = izero, n
339  a( ioff ) = zero
340  ioff = ioff + lda
341  30 CONTINUE
342  ELSE
343  ioff = izero
344  DO 40 i = 1, izero - 1
345  a( ioff ) = zero
346  ioff = ioff + lda
347  40 CONTINUE
348  ioff = ioff - izero
349  DO 50 i = izero, n
350  a( ioff+i ) = zero
351  50 CONTINUE
352  END IF
353  ELSE
354  IF( iuplo.EQ.1 ) THEN
355 *
356 * Set the first IZERO rows and columns to zero.
357 *
358  ioff = 0
359  DO 70 j = 1, n
360  i2 = min( j, izero )
361  DO 60 i = 1, i2
362  a( ioff+i ) = zero
363  60 CONTINUE
364  ioff = ioff + lda
365  70 CONTINUE
366  ELSE
367 *
368 * Set the first IZERO rows and columns to zero.
369 *
370  ioff = 0
371  DO 90 j = 1, n
372  i1 = max( j, izero )
373  DO 80 i = i1, n
374  a( ioff+i ) = zero
375  80 CONTINUE
376  ioff = ioff + lda
377  90 CONTINUE
378  END IF
379  END IF
380  ELSE
381  izero = 0
382  END IF
383 *
384 * End generate the test matrix A.
385 *
386 *
387  DO 150 ifact = 1, nfact
388 *
389 * Do first for FACT = 'F', then for other values.
390 *
391  fact = facts( ifact )
392 *
393 * Compute the condition number
394 *
395  IF( zerot ) THEN
396  IF( ifact.EQ.1 )
397  $ GO TO 150
398  rcondc = zero
399 *
400  ELSE IF( ifact.EQ.1 ) THEN
401 *
402 * Compute the 1-norm of A.
403 *
404  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
405 *
406 * Factor the matrix A.
407 *
408 
409  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
410  CALL zhetrf_rk( uplo, n, afac, lda, e, iwork, work,
411  $ lwork, info )
412 *
413 * Compute inv(A) and take its norm.
414 *
415  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
416  lwork = (n+nb+1)*(nb+3)
417 *
418 * We need to copute the invesrse to compute
419 * RCONDC that is used later in TEST3.
420 *
421  CALL zhetri_3( uplo, n, ainv, lda, e, iwork,
422  $ work, lwork, info )
423  ainvnm = zlanhe( '1', uplo, n, ainv, lda, rwork )
424 *
425 * Compute the 1-norm condition number of A.
426 *
427  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
428  rcondc = one
429  ELSE
430  rcondc = ( one / anorm ) / ainvnm
431  END IF
432  END IF
433 *
434 * Form an exact solution and set the right hand side.
435 *
436  srnamt = 'ZLARHS'
437  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
438  $ nrhs, a, lda, xact, lda, b, lda, iseed,
439  $ info )
440  xtype = 'C'
441 *
442 * --- Test ZHESV_RK ---
443 *
444  IF( ifact.EQ.2 ) THEN
445  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
446  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
447 *
448 * Factor the matrix and solve the system using
449 * ZHESV_RK.
450 *
451  srnamt = 'ZHESV_RK'
452  CALL zhesv_rk( uplo, n, nrhs, afac, lda, e, iwork,
453  $ x, lda, work, lwork, info )
454 *
455 * Adjust the expected value of INFO to account for
456 * pivoting.
457 *
458  k = izero
459  IF( k.GT.0 ) THEN
460  100 CONTINUE
461  IF( iwork( k ).LT.0 ) THEN
462  IF( iwork( k ).NE.-k ) THEN
463  k = -iwork( k )
464  GO TO 100
465  END IF
466  ELSE IF( iwork( k ).NE.k ) THEN
467  k = iwork( k )
468  GO TO 100
469  END IF
470  END IF
471 *
472 * Check error code from ZHESV_RK and handle error.
473 *
474  IF( info.NE.k ) THEN
475  CALL alaerh( path, 'ZHESV_RK', info, k, uplo,
476  $ n, n, -1, -1, nrhs, imat, nfail,
477  $ nerrs, nout )
478  GO TO 120
479  ELSE IF( info.NE.0 ) THEN
480  GO TO 120
481  END IF
482 *
483 *+ TEST 1 Reconstruct matrix from factors and compute
484 * residual.
485 *
486  CALL zhet01_3( uplo, n, a, lda, afac, lda, e,
487  $ iwork, ainv, lda, rwork,
488  $ result( 1 ) )
489 *
490 *+ TEST 2 Compute residual of the computed solution.
491 *
492  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
493  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
494  $ lda, rwork, result( 2 ) )
495 *
496 *+ TEST 3
497 * Check solution from generated exact solution.
498 *
499  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
500  $ result( 3 ) )
501  nt = 3
502 *
503 * Print information about the tests that did not pass
504 * the threshold.
505 *
506  DO 110 k = 1, nt
507  IF( result( k ).GE.thresh ) THEN
508  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
509  $ CALL aladhd( nout, path )
510  WRITE( nout, fmt = 9999 )'ZHESV_RK', uplo,
511  $ n, imat, k, result( k )
512  nfail = nfail + 1
513  END IF
514  110 CONTINUE
515  nrun = nrun + nt
516  120 CONTINUE
517  END IF
518 *
519  150 CONTINUE
520 *
521  160 CONTINUE
522  170 CONTINUE
523  180 CONTINUE
524 *
525 * Print a summary of the results.
526 *
527  CALL alasvm( path, nout, nfail, nrun, nerrs )
528 *
529  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
530  $ ', test ', i2, ', ratio =', g12.5 )
531  RETURN
532 *
533 * End of ZDRVHE_RK
534 *
535  END
zerrvx
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
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
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
zhetrf_rk
subroutine zhetrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZHETRF_RK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch...
Definition: zhetrf_rk.f:261
zhesv_rk
subroutine zhesv_rk(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
ZHESV_RK computes the solution to system of linear equations A * X = B for SY matrices
Definition: zhesv_rk.f:230
zdrvhe_rk
subroutine zdrvhe_rk(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZDRVHE_RK
Definition: zdrvhe_rk.f:160
zhetri_3
subroutine zhetri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZHETRI_3
Definition: zhetri_3.f:172
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
aladhd
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
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
zhet01_3
subroutine zhet01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZHET01_3
Definition: zhet01_3.f:143
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