LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
zdrvsy_rook.f
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1 *> \brief \b ZDRVSY_ROOK
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_ROOK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
12 * NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
13 * 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( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZDRVSY_ROOK tests the driver routines ZSYSV_ROOK.
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 December 2016
148 *
149 *> \ingroup complex16_lin
150 *
151 * =====================================================================
152  SUBROUTINE zdrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
153  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
154  $ RWORK, IWORK, NOUT )
155 *
156 * -- LAPACK test routine (version 3.7.0) --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 * December 2016
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 = 3 )
181  INTEGER NFACT
182  parameter( nfact = 2 )
183 * ..
184 * .. Local Scalars ..
185  LOGICAL ZEROT
186  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
187  CHARACTER*3 MATPATH, PATH
188  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
189  $ izero, j, k, kl, ku, lda, lwork, mode, n,
190  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
191  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
192 * ..
193 * .. Local Arrays ..
194  CHARACTER FACTS( NFACT ), UPLOS( 2 )
195  INTEGER ISEED( 4 ), ISEEDY( 4 )
196  DOUBLE PRECISION RESULT( NTESTS )
197 
198 * ..
199 * .. External Functions ..
200  DOUBLE PRECISION ZLANSY
201  EXTERNAL ZLANSY
202 * ..
203 * .. External Subroutines ..
204  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
205  $ zlacpy, zlarhs, zlaset, zlatb4, zlatms, zlatsy,
206  $ zpot05, zsysv_rook, zsyt01_rook, zsyt02,
207  $ zsytrf_rook, zsytri_rook
208 * ..
209 * .. Scalars in Common ..
210  LOGICAL LERR, OK
211  CHARACTER*32 SRNAMT
212  INTEGER INFOT, NUNIT
213 * ..
214 * .. Common blocks ..
215  COMMON / infoc / infot, nunit, ok, lerr
216  COMMON / srnamc / srnamt
217 * ..
218 * .. Intrinsic Functions ..
219  INTRINSIC max, min
220 * ..
221 * .. Data statements ..
222  DATA iseedy / 1988, 1989, 1990, 1991 /
223  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
224 * ..
225 * .. Executable Statements ..
226 *
227 * Initialize constants and the random number seed.
228 *
229 * Test path
230 *
231  path( 1: 1 ) = 'Zomplex precision'
232  path( 2: 3 ) = 'SR'
233 *
234 * Path to generate matrices
235 *
236  matpath( 1: 1 ) = 'Zomplex precision'
237  matpath( 2: 3 ) = 'SY'
238 *
239  nrun = 0
240  nfail = 0
241  nerrs = 0
242  DO 10 i = 1, 4
243  iseed( i ) = iseedy( i )
244  10 CONTINUE
245  lwork = max( 2*nmax, nmax*nrhs )
246 *
247 * Test the error exits
248 *
249  IF( tsterr )
250  $ CALL zerrvx( path, nout )
251  infot = 0
252 *
253 * Set the block size and minimum block size for which the block
254 * routine should be used, which will be later returned by ILAENV.
255 *
256  nb = 1
257  nbmin = 2
258  CALL xlaenv( 1, nb )
259  CALL xlaenv( 2, nbmin )
260 *
261 * Do for each value of N in NVAL
262 *
263  DO 180 in = 1, nn
264  n = nval( in )
265  lda = max( n, 1 )
266  xtype = 'N'
267  nimat = ntypes
268  IF( n.LE.0 )
269  $ nimat = 1
270 *
271  DO 170 imat = 1, nimat
272 *
273 * Do the tests only if DOTYPE( IMAT ) is true.
274 *
275  IF( .NOT.dotype( imat ) )
276  $ GO TO 170
277 *
278 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
279 *
280  zerot = imat.GE.3 .AND. imat.LE.6
281  IF( zerot .AND. n.LT.imat-2 )
282  $ GO TO 170
283 *
284 * Do first for UPLO = 'U', then for UPLO = 'L'
285 *
286  DO 160 iuplo = 1, 2
287  uplo = uplos( iuplo )
288 *
289  IF( imat.NE.ntypes ) THEN
290 *
291 * Begin generate the test matrix A.
292 *
293 * Set up parameters with ZLATB4 for the matrix generator
294 * based on the type of matrix to be generated.
295 *
296  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
297  $ mode, cndnum, dist )
298 *
299 * Generate a matrix with ZLATMS.
300 *
301  srnamt = 'ZLATMS'
302  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
303  $ cndnum, anorm, kl, ku, uplo, a, lda,
304  $ work, info )
305 *
306 * Check error code from DLATMS and handle error.
307 *
308  IF( info.NE.0 ) THEN
309  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
310  $ -1, -1, -1, imat, nfail, nerrs, nout )
311  GO TO 160
312  END IF
313 *
314 * For types 3-6, zero one or more rows and columns of
315 * the matrix to test that INFO is returned correctly.
316 *
317  IF( zerot ) THEN
318  IF( imat.EQ.3 ) THEN
319  izero = 1
320  ELSE IF( imat.EQ.4 ) THEN
321  izero = n
322  ELSE
323  izero = n / 2 + 1
324  END IF
325 *
326  IF( imat.LT.6 ) THEN
327 *
328 * Set row and column IZERO to zero.
329 *
330  IF( iuplo.EQ.1 ) THEN
331  ioff = ( izero-1 )*lda
332  DO 20 i = 1, izero - 1
333  a( ioff+i ) = zero
334  20 CONTINUE
335  ioff = ioff + izero
336  DO 30 i = izero, n
337  a( ioff ) = zero
338  ioff = ioff + lda
339  30 CONTINUE
340  ELSE
341  ioff = izero
342  DO 40 i = 1, izero - 1
343  a( ioff ) = zero
344  ioff = ioff + lda
345  40 CONTINUE
346  ioff = ioff - izero
347  DO 50 i = izero, n
348  a( ioff+i ) = zero
349  50 CONTINUE
350  END IF
351  ELSE
352  IF( iuplo.EQ.1 ) THEN
353 *
354 * Set the first IZERO rows and columns to zero.
355 *
356  ioff = 0
357  DO 70 j = 1, n
358  i2 = min( j, izero )
359  DO 60 i = 1, i2
360  a( ioff+i ) = zero
361  60 CONTINUE
362  ioff = ioff + lda
363  70 CONTINUE
364  ELSE
365 *
366 * Set the first IZERO rows and columns to zero.
367 *
368  ioff = 0
369  DO 90 j = 1, n
370  i1 = max( j, izero )
371  DO 80 i = i1, n
372  a( ioff+i ) = zero
373  80 CONTINUE
374  ioff = ioff + lda
375  90 CONTINUE
376  END IF
377  END IF
378  ELSE
379  izero = 0
380  END IF
381  ELSE
382 *
383 * IMAT = NTYPES: Use a special block diagonal matrix to
384 * test alternate code for the 2-by-2 blocks.
385 *
386  CALL zlatsy( uplo, n, a, lda, iseed )
387  END IF
388 *
389  DO 150 ifact = 1, nfact
390 *
391 * Do first for FACT = 'F', then for other values.
392 *
393  fact = facts( ifact )
394 *
395 * Compute the condition number for comparison with
396 * the value returned by ZSYSVX_ROOK.
397 *
398  IF( zerot ) THEN
399  IF( ifact.EQ.1 )
400  $ GO TO 150
401  rcondc = zero
402 *
403  ELSE IF( ifact.EQ.1 ) THEN
404 *
405 * Compute the 1-norm of A.
406 *
407  anorm = zlansy( '1', uplo, n, a, lda, rwork )
408 *
409 * Factor the matrix A.
410 *
411 
412  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
413  CALL zsytrf_rook( uplo, n, afac, lda, iwork, work,
414  $ lwork, info )
415 *
416 * Compute inv(A) and take its norm.
417 *
418  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
419  lwork = (n+nb+1)*(nb+3)
420  CALL zsytri_rook( uplo, n, ainv, lda, iwork,
421  $ work, info )
422  ainvnm = zlansy( '1', uplo, n, ainv, lda, rwork )
423 *
424 * Compute the 1-norm condition number of A.
425 *
426  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
427  rcondc = one
428  ELSE
429  rcondc = ( one / anorm ) / ainvnm
430  END IF
431  END IF
432 *
433 * Form an exact solution and set the right hand side.
434 *
435  srnamt = 'ZLARHS'
436  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
437  $ nrhs, a, lda, xact, lda, b, lda, iseed,
438  $ info )
439  xtype = 'C'
440 *
441 * --- Test ZSYSV_ROOK ---
442 *
443  IF( ifact.EQ.2 ) THEN
444  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
445  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
446 *
447 * Factor the matrix and solve the system using
448 * ZSYSV_ROOK.
449 *
450  srnamt = 'ZSYSV_ROOK'
451  CALL zsysv_rook( uplo, n, nrhs, afac, lda, iwork,
452  $ x, lda, work, lwork, info )
453 *
454 * Adjust the expected value of INFO to account for
455 * pivoting.
456 *
457  k = izero
458  IF( k.GT.0 ) THEN
459  100 CONTINUE
460  IF( iwork( k ).LT.0 ) THEN
461  IF( iwork( k ).NE.-k ) THEN
462  k = -iwork( k )
463  GO TO 100
464  END IF
465  ELSE IF( iwork( k ).NE.k ) THEN
466  k = iwork( k )
467  GO TO 100
468  END IF
469  END IF
470 *
471 * Check error code from ZSYSV_ROOK and handle error.
472 *
473  IF( info.NE.k ) THEN
474  CALL alaerh( path, 'ZSYSV_ROOK', info, k, uplo,
475  $ n, n, -1, -1, nrhs, imat, nfail,
476  $ nerrs, nout )
477  GO TO 120
478  ELSE IF( info.NE.0 ) THEN
479  GO TO 120
480  END IF
481 *
482 *+ TEST 1 Reconstruct matrix from factors and compute
483 * residual.
484 *
485  CALL zsyt01_rook( uplo, n, a, lda, afac, lda,
486  $ iwork, ainv, lda, rwork,
487  $ result( 1 ) )
488 *
489 *+ TEST 2 Compute residual of the computed solution.
490 *
491  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
492  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
493  $ lda, rwork, result( 2 ) )
494 *
495 *+ TEST 3
496 * Check solution from generated exact solution.
497 *
498  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
499  $ result( 3 ) )
500  nt = 3
501 *
502 * Print information about the tests that did not pass
503 * the threshold.
504 *
505  DO 110 k = 1, nt
506  IF( result( k ).GE.thresh ) THEN
507  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
508  $ CALL aladhd( nout, path )
509  WRITE( nout, fmt = 9999 )'ZSYSV_ROOK', uplo,
510  $ n, imat, k, result( k )
511  nfail = nfail + 1
512  END IF
513  110 CONTINUE
514  nrun = nrun + nt
515  120 CONTINUE
516  END IF
517 *
518  150 CONTINUE
519 *
520  160 CONTINUE
521  170 CONTINUE
522  180 CONTINUE
523 *
524 * Print a summary of the results.
525 *
526  CALL alasvm( path, nout, nfail, nrun, nerrs )
527 *
528  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
529  $ ', test ', i2, ', ratio =', g12.5 )
530  RETURN
531 *
532 * End of ZDRVSY_ROOK
533 *
534  END
zerrvx
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
zsytrf_rook
subroutine zsytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_ROOK
Definition: zsytrf_rook.f:210
zsytri_rook
subroutine zsytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZSYTRI_ROOK
Definition: zsytri_rook.f:131
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_rook
subroutine zsyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZSYT01_ROOK
Definition: zsyt01_rook.f:127
zpot05
subroutine zpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPOT05
Definition: zpot05.f:167
zlaset
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:108
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
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
zdrvsy_rook
subroutine zdrvsy_rook(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZDRVSY_ROOK
Definition: zdrvsy_rook.f:155
zsysv_rook
subroutine zsysv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
Definition: zsysv_rook.f:206
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
zlatms
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334