LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
zdrvsy_rk.f
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1 *> \brief \b ZDRVSY_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 ZDRVSY_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 *> ZDRVSY_RK tests the driver routines ZSYSV_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 zdrvsy_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 = 11, 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 ZLANSY
206  EXTERNAL ZLANSY
207 * ..
208 * .. External Subroutines ..
209  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
210  $ zlacpy, zlarhs, zlatb4, zlatms, zlatsy,
211  $ zsysv_rk, zsyt01_3, zsyt02, zsytrf_rk, zsytri_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 ) = 'SK'
237 *
238 * Path to generate matrices
239 *
240  matpath( 1: 1 ) = 'Zomplex precision'
241  matpath( 2: 3 ) = 'SY'
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  IF( imat.NE.ntypes ) THEN
294 *
295 * Begin generate the test matrix A.
296 *
297 * Set up parameters with ZLATB4 for the matrix generator
298 * based on the type of matrix to be generated.
299 *
300  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
301  $ mode, cndnum, dist )
302 *
303 * Generate a matrix with ZLATMS.
304 *
305  srnamt = 'ZLATMS'
306  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
307  $ cndnum, anorm, kl, ku, uplo, a, lda,
308  $ work, info )
309 *
310 * Check error code from DLATMS and handle error.
311 *
312  IF( info.NE.0 ) THEN
313  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
314  $ -1, -1, -1, imat, nfail, nerrs, nout )
315  GO TO 160
316  END IF
317 *
318 * For types 3-6, zero one or more rows and columns of
319 * the matrix to test that INFO is returned correctly.
320 *
321  IF( zerot ) THEN
322  IF( imat.EQ.3 ) THEN
323  izero = 1
324  ELSE IF( imat.EQ.4 ) THEN
325  izero = n
326  ELSE
327  izero = n / 2 + 1
328  END IF
329 *
330  IF( imat.LT.6 ) THEN
331 *
332 * Set row and column IZERO to zero.
333 *
334  IF( iuplo.EQ.1 ) THEN
335  ioff = ( izero-1 )*lda
336  DO 20 i = 1, izero - 1
337  a( ioff+i ) = zero
338  20 CONTINUE
339  ioff = ioff + izero
340  DO 30 i = izero, n
341  a( ioff ) = zero
342  ioff = ioff + lda
343  30 CONTINUE
344  ELSE
345  ioff = izero
346  DO 40 i = 1, izero - 1
347  a( ioff ) = zero
348  ioff = ioff + lda
349  40 CONTINUE
350  ioff = ioff - izero
351  DO 50 i = izero, n
352  a( ioff+i ) = zero
353  50 CONTINUE
354  END IF
355  ELSE
356  IF( iuplo.EQ.1 ) THEN
357 *
358 * Set the first IZERO rows and columns to zero.
359 *
360  ioff = 0
361  DO 70 j = 1, n
362  i2 = min( j, izero )
363  DO 60 i = 1, i2
364  a( ioff+i ) = zero
365  60 CONTINUE
366  ioff = ioff + lda
367  70 CONTINUE
368  ELSE
369 *
370 * Set the first IZERO rows and columns to zero.
371 *
372  ioff = 0
373  DO 90 j = 1, n
374  i1 = max( j, izero )
375  DO 80 i = i1, n
376  a( ioff+i ) = zero
377  80 CONTINUE
378  ioff = ioff + lda
379  90 CONTINUE
380  END IF
381  END IF
382  ELSE
383  izero = 0
384  END IF
385  ELSE
386 *
387 * IMAT = NTYPES: Use a special block diagonal matrix to
388 * test alternate code for the 2-by-2 blocks.
389 *
390  CALL zlatsy( uplo, n, a, lda, iseed )
391  END IF
392 *
393  DO 150 ifact = 1, nfact
394 *
395 * Do first for FACT = 'F', then for other values.
396 *
397  fact = facts( ifact )
398 *
399 * Compute the condition number for comparison with
400 * the value returned by ZSYSVX_ROOK.
401 *
402  IF( zerot ) THEN
403  IF( ifact.EQ.1 )
404  $ GO TO 150
405  rcondc = zero
406 *
407  ELSE IF( ifact.EQ.1 ) THEN
408 *
409 * Compute the 1-norm of A.
410 *
411  anorm = zlansy( '1', uplo, n, a, lda, rwork )
412 *
413 * Factor the matrix A.
414 *
415 
416  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
417  CALL zsytrf_rk( uplo, n, afac, lda, e, iwork, ainv,
418  $ lwork, info )
419 *
420 * Compute inv(A) and take its norm.
421 *
422  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
423  lwork = (n+nb+1)*(nb+3)
424 *
425 * We need to copute the invesrse to compute
426 * RCONDC that is used later in TEST3.
427 *
428  CALL zsytri_3( uplo, n, ainv, lda, e, iwork,
429  $ work, lwork, info )
430  ainvnm = zlansy( '1', uplo, n, ainv, lda, rwork )
431 *
432 * Compute the 1-norm condition number of A.
433 *
434  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
435  rcondc = one
436  ELSE
437  rcondc = ( one / anorm ) / ainvnm
438  END IF
439  END IF
440 *
441 * Form an exact solution and set the right hand side.
442 *
443  srnamt = 'ZLARHS'
444  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
445  $ nrhs, a, lda, xact, lda, b, lda, iseed,
446  $ info )
447  xtype = 'C'
448 *
449 * --- Test ZSYSV_RK ---
450 *
451  IF( ifact.EQ.2 ) THEN
452  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
453  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
454 *
455 * Factor the matrix and solve the system using
456 * ZSYSV_RK.
457 *
458  srnamt = 'ZSYSV_RK'
459  CALL zsysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
460  $ x, lda, work, lwork, info )
461 *
462 * Adjust the expected value of INFO to account for
463 * pivoting.
464 *
465  k = izero
466  IF( k.GT.0 ) THEN
467  100 CONTINUE
468  IF( iwork( k ).LT.0 ) THEN
469  IF( iwork( k ).NE.-k ) THEN
470  k = -iwork( k )
471  GO TO 100
472  END IF
473  ELSE IF( iwork( k ).NE.k ) THEN
474  k = iwork( k )
475  GO TO 100
476  END IF
477  END IF
478 *
479 * Check error code from ZSYSV_RK and handle error.
480 *
481  IF( info.NE.k ) THEN
482  CALL alaerh( path, 'ZSYSV_RK', info, k, uplo,
483  $ n, n, -1, -1, nrhs, imat, nfail,
484  $ nerrs, nout )
485  GO TO 120
486  ELSE IF( info.NE.0 ) THEN
487  GO TO 120
488  END IF
489 *
490 *+ TEST 1 Reconstruct matrix from factors and compute
491 * residual.
492 *
493  CALL zsyt01_3( uplo, n, a, lda, afac, lda, e,
494  $ iwork, ainv, lda, rwork,
495  $ result( 1 ) )
496 *
497 *+ TEST 2 Compute residual of the computed solution.
498 *
499  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
500  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
501  $ lda, rwork, result( 2 ) )
502 *
503 *+ TEST 3
504 * Check solution from generated exact solution.
505 *
506  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
507  $ result( 3 ) )
508  nt = 3
509 *
510 * Print information about the tests that did not pass
511 * the threshold.
512 *
513  DO 110 k = 1, nt
514  IF( result( k ).GE.thresh ) THEN
515  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
516  $ CALL aladhd( nout, path )
517  WRITE( nout, fmt = 9999 )'ZSYSV_RK', uplo,
518  $ n, imat, k, result( k )
519  nfail = nfail + 1
520  END IF
521  110 CONTINUE
522  nrun = nrun + nt
523  120 CONTINUE
524  END IF
525 *
526  150 CONTINUE
527 *
528  160 CONTINUE
529  170 CONTINUE
530  180 CONTINUE
531 *
532 * Print a summary of the results.
533 *
534  CALL alasvm( path, nout, nfail, nrun, nerrs )
535 *
536  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
537  $ ', test ', i2, ', ratio =', g12.5 )
538  RETURN
539 *
540 * End of ZDRVSY_RK
541 *
542  END
zerrvx
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
zsytri_3
subroutine zsytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZSYTRI_3
Definition: zsytri_3.f:172
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
zsyt01_3
subroutine zsyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZSYT01_3
Definition: zsyt01_3.f:143
zsytrf_rk
subroutine zsytrf_rk(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZSYTRF_RK computes the factorization of a complex symmetric indefinite matrix using the bounded Bunch...
Definition: zsytrf_rk.f:261
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
zsyt02
subroutine zsyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZSYT02
Definition: zsyt02.f:129
aladhd
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
zdrvsy_rk
subroutine zdrvsy_rk(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, E, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZDRVSY_RK
Definition: zdrvsy_rk.f:160
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
zlatsy
subroutine zlatsy(UPLO, N, X, LDX, ISEED)
ZLATSY
Definition: zlatsy.f:91
xlaenv
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
zsysv_rk
subroutine zsysv_rk(UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices
Definition: zsysv_rk.f:230
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334