LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zdrvsy_rk.f
Go to the documentation of this file.
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 *> \ingroup complex16_lin
153 *
154 * =====================================================================
155  SUBROUTINE zdrvsy_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 = 11, 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 ZLANSY
203  EXTERNAL ZLANSY
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
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 ) = 'SK'
234 *
235 * Path to generate matrices
236 *
237  matpath( 1: 1 ) = 'Zomplex precision'
238  matpath( 2: 3 ) = 'SY'
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  IF( imat.NE.ntypes ) THEN
291 *
292 * Begin generate the test matrix A.
293 *
294 * Set up parameters with ZLATB4 for the matrix generator
295 * based on the type of matrix to be generated.
296 *
297  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
298  $ mode, cndnum, dist )
299 *
300 * Generate a matrix with ZLATMS.
301 *
302  srnamt = 'ZLATMS'
303  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
304  $ cndnum, anorm, kl, ku, uplo, a, lda,
305  $ work, info )
306 *
307 * Check error code from DLATMS and handle error.
308 *
309  IF( info.NE.0 ) THEN
310  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
311  $ -1, -1, -1, imat, nfail, nerrs, nout )
312  GO TO 160
313  END IF
314 *
315 * For types 3-6, zero one or more rows and columns of
316 * the matrix to test that INFO is returned correctly.
317 *
318  IF( zerot ) THEN
319  IF( imat.EQ.3 ) THEN
320  izero = 1
321  ELSE IF( imat.EQ.4 ) THEN
322  izero = n
323  ELSE
324  izero = n / 2 + 1
325  END IF
326 *
327  IF( imat.LT.6 ) THEN
328 *
329 * Set row and column IZERO to zero.
330 *
331  IF( iuplo.EQ.1 ) THEN
332  ioff = ( izero-1 )*lda
333  DO 20 i = 1, izero - 1
334  a( ioff+i ) = zero
335  20 CONTINUE
336  ioff = ioff + izero
337  DO 30 i = izero, n
338  a( ioff ) = zero
339  ioff = ioff + lda
340  30 CONTINUE
341  ELSE
342  ioff = izero
343  DO 40 i = 1, izero - 1
344  a( ioff ) = zero
345  ioff = ioff + lda
346  40 CONTINUE
347  ioff = ioff - izero
348  DO 50 i = izero, n
349  a( ioff+i ) = zero
350  50 CONTINUE
351  END IF
352  ELSE
353  IF( iuplo.EQ.1 ) THEN
354 *
355 * Set the first IZERO rows and columns to zero.
356 *
357  ioff = 0
358  DO 70 j = 1, n
359  i2 = min( j, izero )
360  DO 60 i = 1, i2
361  a( ioff+i ) = zero
362  60 CONTINUE
363  ioff = ioff + lda
364  70 CONTINUE
365  ELSE
366 *
367 * Set the first IZERO rows and columns to zero.
368 *
369  ioff = 0
370  DO 90 j = 1, n
371  i1 = max( j, izero )
372  DO 80 i = i1, n
373  a( ioff+i ) = zero
374  80 CONTINUE
375  ioff = ioff + lda
376  90 CONTINUE
377  END IF
378  END IF
379  ELSE
380  izero = 0
381  END IF
382  ELSE
383 *
384 * IMAT = NTYPES: Use a special block diagonal matrix to
385 * test alternate code for the 2-by-2 blocks.
386 *
387  CALL zlatsy( uplo, n, a, lda, iseed )
388  END IF
389 *
390  DO 150 ifact = 1, nfact
391 *
392 * Do first for FACT = 'F', then for other values.
393 *
394  fact = facts( ifact )
395 *
396 * Compute the condition number for comparison with
397 * the value returned by ZSYSVX_ROOK.
398 *
399  IF( zerot ) THEN
400  IF( ifact.EQ.1 )
401  $ GO TO 150
402  rcondc = zero
403 *
404  ELSE IF( ifact.EQ.1 ) THEN
405 *
406 * Compute the 1-norm of A.
407 *
408  anorm = zlansy( '1', uplo, n, a, lda, rwork )
409 *
410 * Factor the matrix A.
411 *
412 
413  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
414  CALL zsytrf_rk( uplo, n, afac, lda, e, iwork, ainv,
415  $ lwork, info )
416 *
417 * Compute inv(A) and take its norm.
418 *
419  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
420  lwork = (n+nb+1)*(nb+3)
421 *
422 * We need to compute the inverse to compute
423 * RCONDC that is used later in TEST3.
424 *
425  CALL zsytri_3( uplo, n, ainv, lda, e, iwork,
426  $ work, lwork, info )
427  ainvnm = zlansy( '1', uplo, n, ainv, lda, rwork )
428 *
429 * Compute the 1-norm condition number of A.
430 *
431  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
432  rcondc = one
433  ELSE
434  rcondc = ( one / anorm ) / ainvnm
435  END IF
436  END IF
437 *
438 * Form an exact solution and set the right hand side.
439 *
440  srnamt = 'ZLARHS'
441  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
442  $ nrhs, a, lda, xact, lda, b, lda, iseed,
443  $ info )
444  xtype = 'C'
445 *
446 * --- Test ZSYSV_RK ---
447 *
448  IF( ifact.EQ.2 ) THEN
449  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
450  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
451 *
452 * Factor the matrix and solve the system using
453 * ZSYSV_RK.
454 *
455  srnamt = 'ZSYSV_RK'
456  CALL zsysv_rk( uplo, n, nrhs, afac, lda, e, iwork,
457  $ x, lda, work, lwork, info )
458 *
459 * Adjust the expected value of INFO to account for
460 * pivoting.
461 *
462  k = izero
463  IF( k.GT.0 ) THEN
464  100 CONTINUE
465  IF( iwork( k ).LT.0 ) THEN
466  IF( iwork( k ).NE.-k ) THEN
467  k = -iwork( k )
468  GO TO 100
469  END IF
470  ELSE IF( iwork( k ).NE.k ) THEN
471  k = iwork( k )
472  GO TO 100
473  END IF
474  END IF
475 *
476 * Check error code from ZSYSV_RK and handle error.
477 *
478  IF( info.NE.k ) THEN
479  CALL alaerh( path, 'ZSYSV_RK', info, k, uplo,
480  $ n, n, -1, -1, nrhs, imat, nfail,
481  $ nerrs, nout )
482  GO TO 120
483  ELSE IF( info.NE.0 ) THEN
484  GO TO 120
485  END IF
486 *
487 *+ TEST 1 Reconstruct matrix from factors and compute
488 * residual.
489 *
490  CALL zsyt01_3( uplo, n, a, lda, afac, lda, e,
491  $ iwork, ainv, lda, rwork,
492  $ result( 1 ) )
493 *
494 *+ TEST 2 Compute residual of the computed solution.
495 *
496  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
497  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
498  $ lda, rwork, result( 2 ) )
499 *
500 *+ TEST 3
501 * Check solution from generated exact solution.
502 *
503  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
504  $ result( 3 ) )
505  nt = 3
506 *
507 * Print information about the tests that did not pass
508 * the threshold.
509 *
510  DO 110 k = 1, nt
511  IF( result( k ).GE.thresh ) THEN
512  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
513  $ CALL aladhd( nout, path )
514  WRITE( nout, fmt = 9999 )'ZSYSV_RK', uplo,
515  $ n, imat, k, result( k )
516  nfail = nfail + 1
517  END IF
518  110 CONTINUE
519  nrun = nrun + nt
520  120 CONTINUE
521  END IF
522 *
523  150 CONTINUE
524 *
525  160 CONTINUE
526  170 CONTINUE
527  180 CONTINUE
528 *
529 * Print a summary of the results.
530 *
531  CALL alasvm( path, nout, nfail, nrun, nerrs )
532 *
533  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
534  $ ', test ', i2, ', ratio =', g12.5 )
535  RETURN
536 *
537 * End of ZDRVSY_RK
538 *
539  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 zsyt02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZSYT02
Definition: zsyt02.f:127
subroutine zlatsy(UPLO, N, X, LDX, ISEED)
ZLATSY
Definition: zlatsy.f:89
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:158
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 zsyt01_3(UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C, LDC, RWORK, RESID)
ZSYT01_3
Definition: zsyt01_3.f:141
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:121
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
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
subroutine zsytri_3(UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
ZSYTRI_3
Definition: zsytri_3.f:170
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:259
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:228