LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zdrvhe_rook.f
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1 *> \brief \b ZDRVHE_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 ZDRVHE_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 *> ZDRVHE_ROOK tests the driver routines ZHESV_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 zdrvhe_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 = 10, 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 ZLANHE
198  EXTERNAL ZLANHE
199 * ..
200 * .. External Subroutines ..
201  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx,
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 ) = 'HR'
230 *
231 * Path to generate matrices
232 *
233  matpath( 1: 1 ) = 'Zomplex precision'
234  matpath( 2: 3 ) = 'HE'
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 * Begin generate the test matrix A.
287 *
288 * Set up parameters with ZLATB4 for the matrix generator
289 * based on the type of matrix to be generated.
290 *
291  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
292  $ mode, cndnum, dist )
293 *
294 * Generate a matrix with ZLATMS.
295 *
296  srnamt = 'ZLATMS'
297  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
298  $ cndnum, anorm, kl, ku, uplo, a, lda,
299  $ work, info )
300 *
301 * Check error code from ZLATMS and handle error.
302 *
303  IF( info.NE.0 ) THEN
304  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
305  $ -1, -1, -1, imat, nfail, nerrs, nout )
306  GO TO 160
307  END IF
308 *
309 * For types 3-6, zero one or more rows and columns of
310 * the matrix to test that INFO is returned correctly.
311 *
312  IF( zerot ) THEN
313  IF( imat.EQ.3 ) THEN
314  izero = 1
315  ELSE IF( imat.EQ.4 ) THEN
316  izero = n
317  ELSE
318  izero = n / 2 + 1
319  END IF
320 *
321  IF( imat.LT.6 ) THEN
322 *
323 * Set row and column IZERO to zero.
324 *
325  IF( iuplo.EQ.1 ) THEN
326  ioff = ( izero-1 )*lda
327  DO 20 i = 1, izero - 1
328  a( ioff+i ) = zero
329  20 CONTINUE
330  ioff = ioff + izero
331  DO 30 i = izero, n
332  a( ioff ) = zero
333  ioff = ioff + lda
334  30 CONTINUE
335  ELSE
336  ioff = izero
337  DO 40 i = 1, izero - 1
338  a( ioff ) = zero
339  ioff = ioff + lda
340  40 CONTINUE
341  ioff = ioff - izero
342  DO 50 i = izero, n
343  a( ioff+i ) = zero
344  50 CONTINUE
345  END IF
346  ELSE
347  IF( iuplo.EQ.1 ) THEN
348 *
349 * Set the first IZERO rows and columns to zero.
350 *
351  ioff = 0
352  DO 70 j = 1, n
353  i2 = min( j, izero )
354  DO 60 i = 1, i2
355  a( ioff+i ) = zero
356  60 CONTINUE
357  ioff = ioff + lda
358  70 CONTINUE
359  ELSE
360 *
361 * Set the first IZERO rows and columns to zero.
362 *
363  ioff = 0
364  DO 90 j = 1, n
365  i1 = max( j, izero )
366  DO 80 i = i1, n
367  a( ioff+i ) = zero
368  80 CONTINUE
369  ioff = ioff + lda
370  90 CONTINUE
371  END IF
372  END IF
373  ELSE
374  izero = 0
375  END IF
376 *
377 * End generate the test matrix A.
378 *
379 *
380  DO 150 ifact = 1, nfact
381 *
382 * Do first for FACT = 'F', then for other values.
383 *
384  fact = facts( ifact )
385 *
386 * Compute the condition number for comparison with
387 * the value returned by ZHESVX_ROOK.
388 *
389  IF( zerot ) THEN
390  IF( ifact.EQ.1 )
391  $ GO TO 150
392  rcondc = zero
393 *
394  ELSE IF( ifact.EQ.1 ) THEN
395 *
396 * Compute the 1-norm of A.
397 *
398  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
399 *
400 * Factor the matrix A.
401 *
402 
403  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
404  CALL zhetrf_rook( uplo, n, afac, lda, iwork, work,
405  $ lwork, info )
406 *
407 * Compute inv(A) and take its norm.
408 *
409  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
410  lwork = (n+nb+1)*(nb+3)
411  CALL zhetri_rook( uplo, n, ainv, lda, iwork,
412  $ work, info )
413  ainvnm = zlanhe( '1', uplo, n, ainv, lda, rwork )
414 *
415 * Compute the 1-norm condition number of A.
416 *
417  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
418  rcondc = one
419  ELSE
420  rcondc = ( one / anorm ) / ainvnm
421  END IF
422  END IF
423 *
424 * Form an exact solution and set the right hand side.
425 *
426  srnamt = 'ZLARHS'
427  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
428  $ nrhs, a, lda, xact, lda, b, lda, iseed,
429  $ info )
430  xtype = 'C'
431 *
432 * --- Test ZHESV_ROOK ---
433 *
434  IF( ifact.EQ.2 ) THEN
435  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
436  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
437 *
438 * Factor the matrix and solve the system using
439 * ZHESV_ROOK.
440 *
441  srnamt = 'ZHESV_ROOK'
442  CALL zhesv_rook( uplo, n, nrhs, afac, lda, iwork,
443  $ x, lda, work, lwork, info )
444 *
445 * Adjust the expected value of INFO to account for
446 * pivoting.
447 *
448  k = izero
449  IF( k.GT.0 ) THEN
450  100 CONTINUE
451  IF( iwork( k ).LT.0 ) THEN
452  IF( iwork( k ).NE.-k ) THEN
453  k = -iwork( k )
454  GO TO 100
455  END IF
456  ELSE IF( iwork( k ).NE.k ) THEN
457  k = iwork( k )
458  GO TO 100
459  END IF
460  END IF
461 *
462 * Check error code from ZHESV_ROOK and handle error.
463 *
464  IF( info.NE.k ) THEN
465  CALL alaerh( path, 'ZHESV_ROOK', info, k, uplo,
466  $ n, n, -1, -1, nrhs, imat, nfail,
467  $ nerrs, nout )
468  GO TO 120
469  ELSE IF( info.NE.0 ) THEN
470  GO TO 120
471  END IF
472 *
473 *+ TEST 1 Reconstruct matrix from factors and compute
474 * residual.
475 *
476  CALL zhet01_rook( uplo, n, a, lda, afac, lda,
477  $ iwork, ainv, lda, rwork,
478  $ result( 1 ) )
479 *
480 *+ TEST 2 Compute residual of the computed solution.
481 *
482  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
483  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
484  $ lda, rwork, result( 2 ) )
485 *
486 *+ TEST 3
487 * Check solution from generated exact solution.
488 *
489  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
490  $ result( 3 ) )
491  nt = 3
492 *
493 * Print information about the tests that did not pass
494 * the threshold.
495 *
496  DO 110 k = 1, nt
497  IF( result( k ).GE.thresh ) THEN
498  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
499  $ CALL aladhd( nout, path )
500  WRITE( nout, fmt = 9999 )'ZHESV_ROOK', uplo,
501  $ n, imat, k, result( k )
502  nfail = nfail + 1
503  END IF
504  110 CONTINUE
505  nrun = nrun + nt
506  120 CONTINUE
507  END IF
508 *
509  150 CONTINUE
510 *
511  160 CONTINUE
512  170 CONTINUE
513  180 CONTINUE
514 *
515 * Print a summary of the results.
516 *
517  CALL alasvm( path, nout, nfail, nrun, nerrs )
518 *
519  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
520  $ ', test ', i2, ', ratio =', g12.5 )
521  RETURN
522 *
523 * End of ZDRVHE_ROOK
524 *
525  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 zhet01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01_ROOK
Definition: zhet01_rook.f:125
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 zdrvhe_rook(DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZDRVHE_ROOK
Definition: zdrvhe_rook.f:153
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:127
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 zhetri_rook(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch...
Definition: zhetri_rook.f:128
subroutine zhetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: zhetrf_rook.f:212
subroutine zhesv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the ...
Definition: zhesv_rook.f:205
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