LAPACK  3.10.1
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 *> \ingroup complex16_lin
153 *
154 * =====================================================================
155  SUBROUTINE zdrvhe_rk( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
156  $ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
157  $ RWORK, IWORK, NOUT )
158 *
159 * -- LAPACK test routine --
160 * -- LAPACK is a software package provided by Univ. of Tennessee, --
161 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162 *
163 * .. Scalar Arguments ..
164  LOGICAL TSTERR
165  INTEGER NMAX, NN, NOUT, NRHS
166  DOUBLE PRECISION THRESH
167 * ..
168 * .. Array Arguments ..
169  LOGICAL DOTYPE( * )
170  INTEGER IWORK( * ), NVAL( * )
171  DOUBLE PRECISION RWORK( * )
172  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
173  $ work( * ), x( * ), xact( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  DOUBLE PRECISION ONE, ZERO
180  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
181  INTEGER NTYPES, NTESTS
182  parameter( ntypes = 10, ntests = 3 )
183  INTEGER NFACT
184  parameter( nfact = 2 )
185 * ..
186 * .. Local Scalars ..
187  LOGICAL ZEROT
188  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
189  CHARACTER*3 MATPATH, PATH
190  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
191  $ izero, j, k, kl, ku, lda, lwork, mode, n,
192  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
193  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
194 * ..
195 * .. Local Arrays ..
196  CHARACTER FACTS( NFACT ), UPLOS( 2 )
197  INTEGER ISEED( 4 ), ISEEDY( 4 )
198  DOUBLE PRECISION RESULT( NTESTS )
199 
200 * ..
201 * .. External Functions ..
202  DOUBLE PRECISION ZLANHE
203  EXTERNAL ZLANHE
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx,
209 * ..
210 * .. Scalars in Common ..
211  LOGICAL LERR, OK
212  CHARACTER*32 SRNAMT
213  INTEGER INFOT, NUNIT
214 * ..
215 * .. Common blocks ..
216  COMMON / infoc / infot, nunit, ok, lerr
217  COMMON / srnamc / srnamt
218 * ..
219 * .. Intrinsic Functions ..
220  INTRINSIC max, min
221 * ..
222 * .. Data statements ..
223  DATA iseedy / 1988, 1989, 1990, 1991 /
224  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
225 * ..
226 * .. Executable Statements ..
227 *
228 * Initialize constants and the random number seed.
229 *
230 * Test path
231 *
232  path( 1: 1 ) = 'Zomplex precision'
233  path( 2: 3 ) = 'HK'
234 *
235 * Path to generate matrices
236 *
237  matpath( 1: 1 ) = 'Zomplex precision'
238  matpath( 2: 3 ) = 'HE'
239 *
240  nrun = 0
241  nfail = 0
242  nerrs = 0
243  DO 10 i = 1, 4
244  iseed( i ) = iseedy( i )
245  10 CONTINUE
246  lwork = max( 2*nmax, nmax*nrhs )
247 *
248 * Test the error exits
249 *
250  IF( tsterr )
251  $ CALL zerrvx( path, nout )
252  infot = 0
253 *
254 * Set the block size and minimum block size for which the block
255 * routine should be used, which will be later returned by ILAENV.
256 *
257  nb = 1
258  nbmin = 2
259  CALL xlaenv( 1, nb )
260  CALL xlaenv( 2, nbmin )
261 *
262 * Do for each value of N in NVAL
263 *
264  DO 180 in = 1, nn
265  n = nval( in )
266  lda = max( n, 1 )
267  xtype = 'N'
268  nimat = ntypes
269  IF( n.LE.0 )
270  $ nimat = 1
271 *
272  DO 170 imat = 1, nimat
273 *
274 * Do the tests only if DOTYPE( IMAT ) is true.
275 *
276  IF( .NOT.dotype( imat ) )
277  $ GO TO 170
278 *
279 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
280 *
281  zerot = imat.GE.3 .AND. imat.LE.6
282  IF( zerot .AND. n.LT.imat-2 )
283  $ GO TO 170
284 *
285 * Do first for UPLO = 'U', then for UPLO = 'L'
286 *
287  DO 160 iuplo = 1, 2
288  uplo = uplos( iuplo )
289 *
290 * Begin generate the test matrix A.
291 *
292 * Set up parameters with ZLATB4 for the matrix generator
293 * based on the type of matrix to be generated.
294 *
295  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
296  $ mode, cndnum, dist )
297 *
298 * Generate a matrix with ZLATMS.
299 *
300  srnamt = 'ZLATMS'
301  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
302  $ cndnum, anorm, kl, ku, uplo, a, lda,
303  $ work, info )
304 *
305 * Check error code from ZLATMS and handle error.
306 *
307  IF( info.NE.0 ) THEN
308  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
309  $ -1, -1, -1, imat, nfail, nerrs, nout )
310  GO TO 160
311  END IF
312 *
313 * For types 3-6, zero one or more rows and columns of
314 * the matrix to test that INFO is returned correctly.
315 *
316  IF( zerot ) THEN
317  IF( imat.EQ.3 ) THEN
318  izero = 1
319  ELSE IF( imat.EQ.4 ) THEN
320  izero = n
321  ELSE
322  izero = n / 2 + 1
323  END IF
324 *
325  IF( imat.LT.6 ) THEN
326 *
327 * Set row and column IZERO to zero.
328 *
329  IF( iuplo.EQ.1 ) THEN
330  ioff = ( izero-1 )*lda
331  DO 20 i = 1, izero - 1
332  a( ioff+i ) = zero
333  20 CONTINUE
334  ioff = ioff + izero
335  DO 30 i = izero, n
336  a( ioff ) = zero
337  ioff = ioff + lda
338  30 CONTINUE
339  ELSE
340  ioff = izero
341  DO 40 i = 1, izero - 1
342  a( ioff ) = zero
343  ioff = ioff + lda
344  40 CONTINUE
345  ioff = ioff - izero
346  DO 50 i = izero, n
347  a( ioff+i ) = zero
348  50 CONTINUE
349  END IF
350  ELSE
351  IF( iuplo.EQ.1 ) THEN
352 *
353 * Set the first IZERO rows and columns to zero.
354 *
355  ioff = 0
356  DO 70 j = 1, n
357  i2 = min( j, izero )
358  DO 60 i = 1, i2
359  a( ioff+i ) = zero
360  60 CONTINUE
361  ioff = ioff + lda
362  70 CONTINUE
363  ELSE
364 *
365 * Set the first IZERO rows and columns to zero.
366 *
367  ioff = 0
368  DO 90 j = 1, n
369  i1 = max( j, izero )
370  DO 80 i = i1, n
371  a( ioff+i ) = zero
372  80 CONTINUE
373  ioff = ioff + lda
374  90 CONTINUE
375  END IF
376  END IF
377  ELSE
378  izero = 0
379  END IF
380 *
381 * End generate the test matrix A.
382 *
383 *
384  DO 150 ifact = 1, nfact
385 *
386 * Do first for FACT = 'F', then for other values.
387 *
388  fact = facts( ifact )
389 *
390 * Compute the condition number
391 *
392  IF( zerot ) THEN
393  IF( ifact.EQ.1 )
394  $ GO TO 150
395  rcondc = zero
396 *
397  ELSE IF( ifact.EQ.1 ) THEN
398 *
399 * Compute the 1-norm of A.
400 *
401  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
402 *
403 * Factor the matrix A.
404 *
405 
406  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
407  CALL zhetrf_rk( uplo, n, afac, lda, e, iwork, work,
408  $ lwork, info )
409 *
410 * Compute inv(A) and take its norm.
411 *
412  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
413  lwork = (n+nb+1)*(nb+3)
414 *
415 * We need to compute the inverse to compute
416 * RCONDC that is used later in TEST3.
417 *
418  CALL zhetri_3( uplo, n, ainv, lda, e, iwork,
419  $ work, lwork, info )
420  ainvnm = zlanhe( '1', uplo, n, ainv, lda, rwork )
421 *
422 * Compute the 1-norm condition number of A.
423 *
424  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
425  rcondc = one
426  ELSE
427  rcondc = ( one / anorm ) / ainvnm
428  END IF
429  END IF
430 *
431 * Form an exact solution and set the right hand side.
432 *
433  srnamt = 'ZLARHS'
434  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
435  $ nrhs, a, lda, xact, lda, b, lda, iseed,
436  $ info )
437  xtype = 'C'
438 *
439 * --- Test ZHESV_RK ---
440 *
441  IF( ifact.EQ.2 ) THEN
442  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
443  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
444 *
445 * Factor the matrix and solve the system using
446 * ZHESV_RK.
447 *
448  srnamt = 'ZHESV_RK'
449  CALL zhesv_rk( uplo, n, nrhs, afac, lda, e, iwork,
450  $ x, lda, work, lwork, info )
451 *
452 * Adjust the expected value of INFO to account for
453 * pivoting.
454 *
455  k = izero
456  IF( k.GT.0 ) THEN
457  100 CONTINUE
458  IF( iwork( k ).LT.0 ) THEN
459  IF( iwork( k ).NE.-k ) THEN
460  k = -iwork( k )
461  GO TO 100
462  END IF
463  ELSE IF( iwork( k ).NE.k ) THEN
464  k = iwork( k )
465  GO TO 100
466  END IF
467  END IF
468 *
469 * Check error code from ZHESV_RK and handle error.
470 *
471  IF( info.NE.k ) THEN
472  CALL alaerh( path, 'ZHESV_RK', info, k, uplo,
473  $ n, n, -1, -1, nrhs, imat, nfail,
474  $ nerrs, nout )
475  GO TO 120
476  ELSE IF( info.NE.0 ) THEN
477  GO TO 120
478  END IF
479 *
480 *+ TEST 1 Reconstruct matrix from factors and compute
481 * residual.
482 *
483  CALL zhet01_3( uplo, n, a, lda, afac, lda, e,
484  $ iwork, ainv, lda, rwork,
485  $ result( 1 ) )
486 *
487 *+ TEST 2 Compute residual of the computed solution.
488 *
489  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
490  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
491  $ lda, rwork, result( 2 ) )
492 *
493 *+ TEST 3
494 * Check solution from generated exact solution.
495 *
496  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
497  $ result( 3 ) )
498  nt = 3
499 *
500 * Print information about the tests that did not pass
501 * the threshold.
502 *
503  DO 110 k = 1, nt
504  IF( result( k ).GE.thresh ) THEN
505  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
506  $ CALL aladhd( nout, path )
507  WRITE( nout, fmt = 9999 )'ZHESV_RK', uplo,
508  $ n, imat, k, result( k )
509  nfail = nfail + 1
510  END IF
511  110 CONTINUE
512  nrun = nrun + nt
513  120 CONTINUE
514  END IF
515 *
516  150 CONTINUE
517 *
518  160 CONTINUE
519  170 CONTINUE
520  180 CONTINUE
521 *
522 * Print a summary of the results.
523 *
524  CALL alasvm( path, nout, nfail, nrun, nerrs )
525 *
526  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
527  $ ', test ', i2, ', ratio =', g12.5 )
528  RETURN
529 *
530 * End of ZDRVHE_RK
531 *
532  END
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:90
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:208
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:55
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:102
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:127
subroutine zhet01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZHET01_3
Definition: zhet01_3.f:141
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:121
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:158
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
subroutine zhetri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZHETRI_3
Definition: zhetri_3.f:170
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:259
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:228
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103