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zdrvsy.f
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1 *> \brief \b ZDRVSY
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( 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 *> ZDRVSY tests the driver routines ZSYSV and -SVX.
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 2013
148 *
149 *> \ingroup complex16_lin
150 *
151 * =====================================================================
152  SUBROUTINE zdrvsy( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
153  $ a, afac, ainv, b, x, xact, work, rwork, iwork,
154  $ nout )
155 *
156 * -- LAPACK test routine (version 3.5.0) --
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 2013
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 = 11, ntests = 6 )
181  INTEGER nfact
182  parameter( nfact = 2 )
183 * ..
184 * .. Local Scalars ..
185  LOGICAL zerot
186  CHARACTER dist, fact, type, uplo, xtype
187  CHARACTER*3 path
188  INTEGER i, i1, i2, ifact, imat, in, info, ioff, iuplo,
189  $ izero, j, k, k1, kl, ku, lda, lwork, mode, n,
190  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
191  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
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, zlansy
200  EXTERNAL dget06, zlansy
201 * ..
202 * .. External Subroutines ..
203  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
206  $ zsytri2
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  path( 1: 1 ) = 'Zomplex precision'
229  path( 2: 3 ) = 'SY'
230  nrun = 0
231  nfail = 0
232  nerrs = 0
233  DO 10 i = 1, 4
234  iseed( i ) = iseedy( i )
235  10 CONTINUE
236  lwork = max( 2*nmax, nmax*nrhs )
237 *
238 * Test the error exits
239 *
240  IF( tsterr )
241  $ CALL zerrvx( path, nout )
242  infot = 0
243 *
244 * Set the block size and minimum block size for testing.
245 *
246  nb = 1
247  nbmin = 2
248  CALL xlaenv( 1, nb )
249  CALL xlaenv( 2, nbmin )
250 *
251 * Do for each value of N in NVAL
252 *
253  DO 180 in = 1, nn
254  n = nval( in )
255  lda = max( n, 1 )
256  xtype = 'N'
257  nimat = ntypes
258  IF( n.LE.0 )
259  $ nimat = 1
260 *
261  DO 170 imat = 1, nimat
262 *
263 * Do the tests only if DOTYPE( IMAT ) is true.
264 *
265  IF( .NOT.dotype( imat ) )
266  $ go to 170
267 *
268 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
269 *
270  zerot = imat.GE.3 .AND. imat.LE.6
271  IF( zerot .AND. n.LT.imat-2 )
272  $ go to 170
273 *
274 * Do first for UPLO = 'U', then for UPLO = 'L'
275 *
276  DO 160 iuplo = 1, 2
277  uplo = uplos( iuplo )
278 *
279  IF( imat.NE.ntypes ) THEN
280 *
281 * Set up parameters with ZLATB4 and generate a test
282 * matrix with ZLATMS.
283 *
284  CALL zlatb4( path, imat, n, n, type, kl, ku, anorm,
285  $ mode, cndnum, dist )
286 *
287  srnamt = 'ZLATMS'
288  CALL zlatms( n, n, dist, iseed, type, rwork, mode,
289  $ cndnum, anorm, kl, ku, uplo, a, lda,
290  $ work, info )
291 *
292 * Check error code from ZLATMS.
293 *
294  IF( info.NE.0 ) THEN
295  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
296  $ -1, -1, -1, imat, nfail, nerrs, nout )
297  go to 160
298  END IF
299 *
300 * For types 3-6, zero one or more rows and columns of
301 * the matrix to test that INFO is returned correctly.
302 *
303  IF( zerot ) THEN
304  IF( imat.EQ.3 ) THEN
305  izero = 1
306  ELSE IF( imat.EQ.4 ) THEN
307  izero = n
308  ELSE
309  izero = n / 2 + 1
310  END IF
311 *
312  IF( imat.LT.6 ) THEN
313 *
314 * Set row and column IZERO to zero.
315 *
316  IF( iuplo.EQ.1 ) THEN
317  ioff = ( izero-1 )*lda
318  DO 20 i = 1, izero - 1
319  a( ioff+i ) = zero
320  20 CONTINUE
321  ioff = ioff + izero
322  DO 30 i = izero, n
323  a( ioff ) = zero
324  ioff = ioff + lda
325  30 CONTINUE
326  ELSE
327  ioff = izero
328  DO 40 i = 1, izero - 1
329  a( ioff ) = zero
330  ioff = ioff + lda
331  40 CONTINUE
332  ioff = ioff - izero
333  DO 50 i = izero, n
334  a( ioff+i ) = zero
335  50 CONTINUE
336  END IF
337  ELSE
338  IF( iuplo.EQ.1 ) THEN
339 *
340 * Set the first IZERO rows to zero.
341 *
342  ioff = 0
343  DO 70 j = 1, n
344  i2 = min( j, izero )
345  DO 60 i = 1, i2
346  a( ioff+i ) = zero
347  60 CONTINUE
348  ioff = ioff + lda
349  70 CONTINUE
350  ELSE
351 *
352 * Set the last IZERO rows to zero.
353 *
354  ioff = 0
355  DO 90 j = 1, n
356  i1 = max( j, izero )
357  DO 80 i = i1, n
358  a( ioff+i ) = zero
359  80 CONTINUE
360  ioff = ioff + lda
361  90 CONTINUE
362  END IF
363  END IF
364  ELSE
365  izero = 0
366  END IF
367  ELSE
368 *
369 * IMAT = NTYPES: Use a special block diagonal matrix to
370 * test alternate code for the 2-by-2 blocks.
371 *
372  CALL zlatsy( uplo, n, a, lda, iseed )
373  END IF
374 *
375  DO 150 ifact = 1, nfact
376 *
377 * Do first for FACT = 'F', then for other values.
378 *
379  fact = facts( ifact )
380 *
381 * Compute the condition number for comparison with
382 * the value returned by ZSYSVX.
383 *
384  IF( zerot ) THEN
385  IF( ifact.EQ.1 )
386  $ go to 150
387  rcondc = zero
388 *
389  ELSE IF( ifact.EQ.1 ) THEN
390 *
391 * Compute the 1-norm of A.
392 *
393  anorm = zlansy( '1', uplo, n, a, lda, rwork )
394 *
395 * Factor the matrix A.
396 *
397  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
398  CALL zsytrf( uplo, n, afac, lda, iwork, work,
399  $ lwork, info )
400 *
401 * Compute inv(A) and take its norm.
402 *
403  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
404  lwork = (n+nb+1)*(nb+3)
405  CALL zsytri2( uplo, n, ainv, lda, iwork, work,
406  $ lwork, info )
407  ainvnm = zlansy( '1', uplo, n, ainv, lda, rwork )
408 *
409 * Compute the 1-norm condition number of A.
410 *
411  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
412  rcondc = one
413  ELSE
414  rcondc = ( one / anorm ) / ainvnm
415  END IF
416  END IF
417 *
418 * Form an exact solution and set the right hand side.
419 *
420  srnamt = 'ZLARHS'
421  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
422  $ nrhs, a, lda, xact, lda, b, lda, iseed,
423  $ info )
424  xtype = 'C'
425 *
426 * --- Test ZSYSV ---
427 *
428  IF( ifact.EQ.2 ) THEN
429  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
430  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
431 *
432 * Factor the matrix and solve the system using ZSYSV.
433 *
434  srnamt = 'ZSYSV '
435  CALL zsysv( uplo, n, nrhs, afac, lda, iwork, x,
436  $ lda, work, lwork, info )
437 *
438 * Adjust the expected value of INFO to account for
439 * pivoting.
440 *
441  k = izero
442  IF( k.GT.0 ) THEN
443  100 CONTINUE
444  IF( iwork( k ).LT.0 ) THEN
445  IF( iwork( k ).NE.-k ) THEN
446  k = -iwork( k )
447  go to 100
448  END IF
449  ELSE IF( iwork( k ).NE.k ) THEN
450  k = iwork( k )
451  go to 100
452  END IF
453  END IF
454 *
455 * Check error code from ZSYSV .
456 *
457  IF( info.NE.k ) THEN
458  CALL alaerh( path, 'ZSYSV ', info, k, uplo, n,
459  $ n, -1, -1, nrhs, imat, nfail,
460  $ nerrs, nout )
461  go to 120
462  ELSE IF( info.NE.0 ) THEN
463  go to 120
464  END IF
465 *
466 * Reconstruct matrix from factors and compute
467 * residual.
468 *
469  CALL zsyt01( uplo, n, a, lda, afac, lda, iwork,
470  $ ainv, lda, rwork, result( 1 ) )
471 *
472 * Compute residual of the computed solution.
473 *
474  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
475  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
476  $ lda, rwork, result( 2 ) )
477 *
478 * Check solution from generated exact solution.
479 *
480  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
481  $ result( 3 ) )
482  nt = 3
483 *
484 * Print information about the tests that did not pass
485 * the threshold.
486 *
487  DO 110 k = 1, nt
488  IF( result( k ).GE.thresh ) THEN
489  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
490  $ CALL aladhd( nout, path )
491  WRITE( nout, fmt = 9999 )'ZSYSV ', uplo, n,
492  $ imat, k, result( k )
493  nfail = nfail + 1
494  END IF
495  110 CONTINUE
496  nrun = nrun + nt
497  120 CONTINUE
498  END IF
499 *
500 * --- Test ZSYSVX ---
501 *
502  IF( ifact.EQ.2 )
503  $ CALL zlaset( uplo, n, n, dcmplx( zero ),
504  $ dcmplx( zero ), afac, lda )
505  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
506  $ dcmplx( zero ), x, lda )
507 *
508 * Solve the system and compute the condition number and
509 * error bounds using ZSYSVX.
510 *
511  srnamt = 'ZSYSVX'
512  CALL zsysvx( fact, uplo, n, nrhs, a, lda, afac, lda,
513  $ iwork, b, lda, x, lda, rcond, rwork,
514  $ rwork( nrhs+1 ), work, lwork,
515  $ rwork( 2*nrhs+1 ), info )
516 *
517 * Adjust the expected value of INFO to account for
518 * pivoting.
519 *
520  k = izero
521  IF( k.GT.0 ) THEN
522  130 CONTINUE
523  IF( iwork( k ).LT.0 ) THEN
524  IF( iwork( k ).NE.-k ) THEN
525  k = -iwork( k )
526  go to 130
527  END IF
528  ELSE IF( iwork( k ).NE.k ) THEN
529  k = iwork( k )
530  go to 130
531  END IF
532  END IF
533 *
534 * Check the error code from ZSYSVX.
535 *
536  IF( info.NE.k ) THEN
537  CALL alaerh( path, 'ZSYSVX', info, k, fact // uplo,
538  $ n, n, -1, -1, nrhs, imat, nfail,
539  $ nerrs, nout )
540  go to 150
541  END IF
542 *
543  IF( info.EQ.0 ) THEN
544  IF( ifact.GE.2 ) THEN
545 *
546 * Reconstruct matrix from factors and compute
547 * residual.
548 *
549  CALL zsyt01( uplo, n, a, lda, afac, lda, iwork,
550  $ ainv, lda, rwork( 2*nrhs+1 ),
551  $ result( 1 ) )
552  k1 = 1
553  ELSE
554  k1 = 2
555  END IF
556 *
557 * Compute residual of the computed solution.
558 *
559  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
560  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
561  $ lda, rwork( 2*nrhs+1 ), result( 2 ) )
562 *
563 * Check solution from generated exact solution.
564 *
565  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
566  $ result( 3 ) )
567 *
568 * Check the error bounds from iterative refinement.
569 *
570  CALL zpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
571  $ xact, lda, rwork, rwork( nrhs+1 ),
572  $ result( 4 ) )
573  ELSE
574  k1 = 6
575  END IF
576 *
577 * Compare RCOND from ZSYSVX with the computed value
578 * in RCONDC.
579 *
580  result( 6 ) = dget06( rcond, rcondc )
581 *
582 * Print information about the tests that did not pass
583 * the threshold.
584 *
585  DO 140 k = k1, 6
586  IF( result( k ).GE.thresh ) THEN
587  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
588  $ CALL aladhd( nout, path )
589  WRITE( nout, fmt = 9998 )'ZSYSVX', fact, uplo,
590  $ n, imat, k, result( k )
591  nfail = nfail + 1
592  END IF
593  140 CONTINUE
594  nrun = nrun + 7 - k1
595 *
596  150 CONTINUE
597 *
598  160 CONTINUE
599  170 CONTINUE
600  180 CONTINUE
601 *
602 * Print a summary of the results.
603 *
604  CALL alasvm( path, nout, nfail, nrun, nerrs )
605 *
606  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
607  $ ', test ', i2, ', ratio =', g12.5 )
608  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
609  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
610  RETURN
611 *
612 * End of ZDRVSY
613 *
614  END