LAPACK  3.10.1
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 *> \ingroup complex16_lin
148 *
149 * =====================================================================
150  SUBROUTINE zdrvsy_rook( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
151  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK,
152  $ RWORK, IWORK, NOUT )
153 *
154 * -- LAPACK test routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  LOGICAL TSTERR
160  INTEGER NMAX, NN, NOUT, NRHS
161  DOUBLE PRECISION THRESH
162 * ..
163 * .. Array Arguments ..
164  LOGICAL DOTYPE( * )
165  INTEGER IWORK( * ), NVAL( * )
166  DOUBLE PRECISION RWORK( * )
167  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
168  $ work( * ), x( * ), xact( * )
169 * ..
170 *
171 * =====================================================================
172 *
173 * .. Parameters ..
174  DOUBLE PRECISION ONE, ZERO
175  PARAMETER ( ONE = 1.0d+0, zero = 0.0d+0 )
176  INTEGER NTYPES, NTESTS
177  parameter( ntypes = 11, ntests = 3 )
178  INTEGER NFACT
179  parameter( nfact = 2 )
180 * ..
181 * .. Local Scalars ..
182  LOGICAL ZEROT
183  CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
184  CHARACTER*3 MATPATH, PATH
185  INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
186  $ izero, j, k, kl, ku, lda, lwork, mode, n,
187  $ nb, nbmin, nerrs, nfail, nimat, nrun, nt
188  DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
189 * ..
190 * .. Local Arrays ..
191  CHARACTER FACTS( NFACT ), UPLOS( 2 )
192  INTEGER ISEED( 4 ), ISEEDY( 4 )
193  DOUBLE PRECISION RESULT( NTESTS )
194 
195 * ..
196 * .. External Functions ..
197  DOUBLE PRECISION ZLANSY
198  EXTERNAL ZLANSY
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx, zget04,
205 * ..
206 * .. Scalars in Common ..
207  LOGICAL LERR, OK
208  CHARACTER*32 SRNAMT
209  INTEGER INFOT, NUNIT
210 * ..
211 * .. Common blocks ..
212  COMMON / infoc / infot, nunit, ok, lerr
213  COMMON / srnamc / srnamt
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max, min
217 * ..
218 * .. Data statements ..
219  DATA iseedy / 1988, 1989, 1990, 1991 /
220  DATA uplos / 'U', 'L' / , facts / 'F', 'N' /
221 * ..
222 * .. Executable Statements ..
223 *
224 * Initialize constants and the random number seed.
225 *
226 * Test path
227 *
228  path( 1: 1 ) = 'Zomplex precision'
229  path( 2: 3 ) = 'SR'
230 *
231 * Path to generate matrices
232 *
233  matpath( 1: 1 ) = 'Zomplex precision'
234  matpath( 2: 3 ) = 'SY'
235 *
236  nrun = 0
237  nfail = 0
238  nerrs = 0
239  DO 10 i = 1, 4
240  iseed( i ) = iseedy( i )
241  10 CONTINUE
242  lwork = max( 2*nmax, nmax*nrhs )
243 *
244 * Test the error exits
245 *
246  IF( tsterr )
247  $ CALL zerrvx( path, nout )
248  infot = 0
249 *
250 * Set the block size and minimum block size for which the block
251 * routine should be used, which will be later returned by ILAENV.
252 *
253  nb = 1
254  nbmin = 2
255  CALL xlaenv( 1, nb )
256  CALL xlaenv( 2, nbmin )
257 *
258 * Do for each value of N in NVAL
259 *
260  DO 180 in = 1, nn
261  n = nval( in )
262  lda = max( n, 1 )
263  xtype = 'N'
264  nimat = ntypes
265  IF( n.LE.0 )
266  $ nimat = 1
267 *
268  DO 170 imat = 1, nimat
269 *
270 * Do the tests only if DOTYPE( IMAT ) is true.
271 *
272  IF( .NOT.dotype( imat ) )
273  $ GO TO 170
274 *
275 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
276 *
277  zerot = imat.GE.3 .AND. imat.LE.6
278  IF( zerot .AND. n.LT.imat-2 )
279  $ GO TO 170
280 *
281 * Do first for UPLO = 'U', then for UPLO = 'L'
282 *
283  DO 160 iuplo = 1, 2
284  uplo = uplos( iuplo )
285 *
286  IF( imat.NE.ntypes ) THEN
287 *
288 * Begin generate the test matrix A.
289 *
290 * Set up parameters with ZLATB4 for the matrix generator
291 * based on the type of matrix to be generated.
292 *
293  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
294  $ mode, cndnum, dist )
295 *
296 * Generate a matrix with ZLATMS.
297 *
298  srnamt = 'ZLATMS'
299  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
300  $ cndnum, anorm, kl, ku, uplo, a, lda,
301  $ work, info )
302 *
303 * Check error code from DLATMS and handle error.
304 *
305  IF( info.NE.0 ) THEN
306  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
307  $ -1, -1, -1, imat, nfail, nerrs, nout )
308  GO TO 160
309  END IF
310 *
311 * For types 3-6, zero one or more rows and columns of
312 * the matrix to test that INFO is returned correctly.
313 *
314  IF( zerot ) THEN
315  IF( imat.EQ.3 ) THEN
316  izero = 1
317  ELSE IF( imat.EQ.4 ) THEN
318  izero = n
319  ELSE
320  izero = n / 2 + 1
321  END IF
322 *
323  IF( imat.LT.6 ) THEN
324 *
325 * Set row and column IZERO to zero.
326 *
327  IF( iuplo.EQ.1 ) THEN
328  ioff = ( izero-1 )*lda
329  DO 20 i = 1, izero - 1
330  a( ioff+i ) = zero
331  20 CONTINUE
332  ioff = ioff + izero
333  DO 30 i = izero, n
334  a( ioff ) = zero
335  ioff = ioff + lda
336  30 CONTINUE
337  ELSE
338  ioff = izero
339  DO 40 i = 1, izero - 1
340  a( ioff ) = zero
341  ioff = ioff + lda
342  40 CONTINUE
343  ioff = ioff - izero
344  DO 50 i = izero, n
345  a( ioff+i ) = zero
346  50 CONTINUE
347  END IF
348  ELSE
349  IF( iuplo.EQ.1 ) THEN
350 *
351 * Set the first IZERO rows and columns to zero.
352 *
353  ioff = 0
354  DO 70 j = 1, n
355  i2 = min( j, izero )
356  DO 60 i = 1, i2
357  a( ioff+i ) = zero
358  60 CONTINUE
359  ioff = ioff + lda
360  70 CONTINUE
361  ELSE
362 *
363 * Set the first IZERO rows and columns to zero.
364 *
365  ioff = 0
366  DO 90 j = 1, n
367  i1 = max( j, izero )
368  DO 80 i = i1, n
369  a( ioff+i ) = zero
370  80 CONTINUE
371  ioff = ioff + lda
372  90 CONTINUE
373  END IF
374  END IF
375  ELSE
376  izero = 0
377  END IF
378  ELSE
379 *
380 * IMAT = NTYPES: Use a special block diagonal matrix to
381 * test alternate code for the 2-by-2 blocks.
382 *
383  CALL zlatsy( uplo, n, a, lda, iseed )
384  END IF
385 *
386  DO 150 ifact = 1, nfact
387 *
388 * Do first for FACT = 'F', then for other values.
389 *
390  fact = facts( ifact )
391 *
392 * Compute the condition number for comparison with
393 * the value returned by ZSYSVX_ROOK.
394 *
395  IF( zerot ) THEN
396  IF( ifact.EQ.1 )
397  $ GO TO 150
398  rcondc = zero
399 *
400  ELSE IF( ifact.EQ.1 ) THEN
401 *
402 * Compute the 1-norm of A.
403 *
404  anorm = zlansy( '1', uplo, n, a, lda, rwork )
405 *
406 * Factor the matrix A.
407 *
408 
409  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
410  CALL zsytrf_rook( uplo, n, afac, lda, iwork, work,
411  $ lwork, info )
412 *
413 * Compute inv(A) and take its norm.
414 *
415  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
416  lwork = (n+nb+1)*(nb+3)
417  CALL zsytri_rook( uplo, n, ainv, lda, iwork,
418  $ work, info )
419  ainvnm = zlansy( '1', uplo, n, ainv, lda, rwork )
420 *
421 * Compute the 1-norm condition number of A.
422 *
423  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
424  rcondc = one
425  ELSE
426  rcondc = ( one / anorm ) / ainvnm
427  END IF
428  END IF
429 *
430 * Form an exact solution and set the right hand side.
431 *
432  srnamt = 'ZLARHS'
433  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
434  $ nrhs, a, lda, xact, lda, b, lda, iseed,
435  $ info )
436  xtype = 'C'
437 *
438 * --- Test ZSYSV_ROOK ---
439 *
440  IF( ifact.EQ.2 ) THEN
441  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
442  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
443 *
444 * Factor the matrix and solve the system using
445 * ZSYSV_ROOK.
446 *
447  srnamt = 'ZSYSV_ROOK'
448  CALL zsysv_rook( uplo, n, nrhs, afac, lda, iwork,
449  $ x, lda, work, lwork, info )
450 *
451 * Adjust the expected value of INFO to account for
452 * pivoting.
453 *
454  k = izero
455  IF( k.GT.0 ) THEN
456  100 CONTINUE
457  IF( iwork( k ).LT.0 ) THEN
458  IF( iwork( k ).NE.-k ) THEN
459  k = -iwork( k )
460  GO TO 100
461  END IF
462  ELSE IF( iwork( k ).NE.k ) THEN
463  k = iwork( k )
464  GO TO 100
465  END IF
466  END IF
467 *
468 * Check error code from ZSYSV_ROOK and handle error.
469 *
470  IF( info.NE.k ) THEN
471  CALL alaerh( path, 'ZSYSV_ROOK', info, k, uplo,
472  $ n, n, -1, -1, nrhs, imat, nfail,
473  $ nerrs, nout )
474  GO TO 120
475  ELSE IF( info.NE.0 ) THEN
476  GO TO 120
477  END IF
478 *
479 *+ TEST 1 Reconstruct matrix from factors and compute
480 * residual.
481 *
482  CALL zsyt01_rook( uplo, n, a, lda, afac, lda,
483  $ iwork, ainv, lda, rwork,
484  $ result( 1 ) )
485 *
486 *+ TEST 2 Compute residual of the computed solution.
487 *
488  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
489  CALL zsyt02( uplo, n, nrhs, a, lda, x, lda, work,
490  $ lda, rwork, result( 2 ) )
491 *
492 *+ TEST 3
493 * Check solution from generated exact solution.
494 *
495  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
496  $ result( 3 ) )
497  nt = 3
498 *
499 * Print information about the tests that did not pass
500 * the threshold.
501 *
502  DO 110 k = 1, nt
503  IF( result( k ).GE.thresh ) THEN
504  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
505  $ CALL aladhd( nout, path )
506  WRITE( nout, fmt = 9999 )'ZSYSV_ROOK', uplo,
507  $ n, imat, k, result( k )
508  nfail = nfail + 1
509  END IF
510  110 CONTINUE
511  nrun = nrun + nt
512  120 CONTINUE
513  END IF
514 *
515  150 CONTINUE
516 *
517  160 CONTINUE
518  170 CONTINUE
519  180 CONTINUE
520 *
521 * Print a summary of the results.
522 *
523  CALL alasvm( path, nout, nfail, nrun, nerrs )
524 *
525  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
526  $ ', test ', i2, ', ratio =', g12.5 )
527  RETURN
528 *
529 * End of ZDRVSY_ROOK
530 *
531  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 zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:55
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:102
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:153
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:121
subroutine zsyt01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZSYT01_ROOK
Definition: zsyt01_rook.f:125
subroutine zpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPOT05
Definition: zpot05.f:165
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 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:106
subroutine zsytri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZSYTRI_ROOK
Definition: zsytri_rook.f:129
subroutine zsytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF_ROOK
Definition: zsytrf_rook.f:208
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:204