LAPACK  3.9.0
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 *> \date November 2013
148 *
149 *> \ingroup complex16_lin
150 *
151 * =====================================================================
152  SUBROUTINE zdrvhe_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 3.5.0) --
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 = 10, 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 ZLANHE
201  EXTERNAL ZLANHE
202 * ..
203 * .. External Subroutines ..
204  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zerrvx,
205  $ zget04, zlacpy, zlarhs, zlatb4, zlatms,
206  $ zhesv_rook, zhet01_rook, zpot02,
207  $ zhetrf_rook, zhetri_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 ) = 'HR'
233 *
234 * Path to generate matrices
235 *
236  matpath( 1: 1 ) = 'Zomplex precision'
237  matpath( 2: 3 ) = 'HE'
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 * Begin generate the test matrix A.
290 *
291 * Set up parameters with ZLATB4 for the matrix generator
292 * based on the type of matrix to be generated.
293 *
294  CALL zlatb4( matpath, imat, n, n, TYPE, kl, ku, anorm,
295  $ mode, cndnum, dist )
296 *
297 * Generate a matrix with ZLATMS.
298 *
299  srnamt = 'ZLATMS'
300  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
301  $ cndnum, anorm, kl, ku, uplo, a, lda,
302  $ work, info )
303 *
304 * Check error code from ZLATMS and handle error.
305 *
306  IF( info.NE.0 ) THEN
307  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
308  $ -1, -1, -1, imat, nfail, nerrs, nout )
309  GO TO 160
310  END IF
311 *
312 * For types 3-6, zero one or more rows and columns of
313 * the matrix to test that INFO is returned correctly.
314 *
315  IF( zerot ) THEN
316  IF( imat.EQ.3 ) THEN
317  izero = 1
318  ELSE IF( imat.EQ.4 ) THEN
319  izero = n
320  ELSE
321  izero = n / 2 + 1
322  END IF
323 *
324  IF( imat.LT.6 ) THEN
325 *
326 * Set row and column IZERO to zero.
327 *
328  IF( iuplo.EQ.1 ) THEN
329  ioff = ( izero-1 )*lda
330  DO 20 i = 1, izero - 1
331  a( ioff+i ) = zero
332  20 CONTINUE
333  ioff = ioff + izero
334  DO 30 i = izero, n
335  a( ioff ) = zero
336  ioff = ioff + lda
337  30 CONTINUE
338  ELSE
339  ioff = izero
340  DO 40 i = 1, izero - 1
341  a( ioff ) = zero
342  ioff = ioff + lda
343  40 CONTINUE
344  ioff = ioff - izero
345  DO 50 i = izero, n
346  a( ioff+i ) = zero
347  50 CONTINUE
348  END IF
349  ELSE
350  IF( iuplo.EQ.1 ) THEN
351 *
352 * Set the first IZERO rows and columns to zero.
353 *
354  ioff = 0
355  DO 70 j = 1, n
356  i2 = min( j, izero )
357  DO 60 i = 1, i2
358  a( ioff+i ) = zero
359  60 CONTINUE
360  ioff = ioff + lda
361  70 CONTINUE
362  ELSE
363 *
364 * Set the first IZERO rows and columns to zero.
365 *
366  ioff = 0
367  DO 90 j = 1, n
368  i1 = max( j, izero )
369  DO 80 i = i1, n
370  a( ioff+i ) = zero
371  80 CONTINUE
372  ioff = ioff + lda
373  90 CONTINUE
374  END IF
375  END IF
376  ELSE
377  izero = 0
378  END IF
379 *
380 * End generate the test matrix A.
381 *
382 *
383  DO 150 ifact = 1, nfact
384 *
385 * Do first for FACT = 'F', then for other values.
386 *
387  fact = facts( ifact )
388 *
389 * Compute the condition number for comparison with
390 * the value returned by ZHESVX_ROOK.
391 *
392  IF( zerot ) THEN
393  IF( ifact.EQ.1 )
394  $ GO TO 150
395  rcondc = zero
396 *
397  ELSE IF( ifact.EQ.1 ) THEN
398 *
399 * Compute the 1-norm of A.
400 *
401  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
402 *
403 * Factor the matrix A.
404 *
405 
406  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
407  CALL zhetrf_rook( uplo, n, afac, lda, iwork, work,
408  $ lwork, info )
409 *
410 * Compute inv(A) and take its norm.
411 *
412  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
413  lwork = (n+nb+1)*(nb+3)
414  CALL zhetri_rook( uplo, n, ainv, lda, iwork,
415  $ work, info )
416  ainvnm = zlanhe( '1', uplo, n, ainv, lda, rwork )
417 *
418 * Compute the 1-norm condition number of A.
419 *
420  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
421  rcondc = one
422  ELSE
423  rcondc = ( one / anorm ) / ainvnm
424  END IF
425  END IF
426 *
427 * Form an exact solution and set the right hand side.
428 *
429  srnamt = 'ZLARHS'
430  CALL zlarhs( matpath, xtype, uplo, ' ', n, n, kl, ku,
431  $ nrhs, a, lda, xact, lda, b, lda, iseed,
432  $ info )
433  xtype = 'C'
434 *
435 * --- Test ZHESV_ROOK ---
436 *
437  IF( ifact.EQ.2 ) THEN
438  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
439  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
440 *
441 * Factor the matrix and solve the system using
442 * ZHESV_ROOK.
443 *
444  srnamt = 'ZHESV_ROOK'
445  CALL zhesv_rook( uplo, n, nrhs, afac, lda, iwork,
446  $ x, lda, work, lwork, info )
447 *
448 * Adjust the expected value of INFO to account for
449 * pivoting.
450 *
451  k = izero
452  IF( k.GT.0 ) THEN
453  100 CONTINUE
454  IF( iwork( k ).LT.0 ) THEN
455  IF( iwork( k ).NE.-k ) THEN
456  k = -iwork( k )
457  GO TO 100
458  END IF
459  ELSE IF( iwork( k ).NE.k ) THEN
460  k = iwork( k )
461  GO TO 100
462  END IF
463  END IF
464 *
465 * Check error code from ZHESV_ROOK and handle error.
466 *
467  IF( info.NE.k ) THEN
468  CALL alaerh( path, 'ZHESV_ROOK', info, k, uplo,
469  $ n, n, -1, -1, nrhs, imat, nfail,
470  $ nerrs, nout )
471  GO TO 120
472  ELSE IF( info.NE.0 ) THEN
473  GO TO 120
474  END IF
475 *
476 *+ TEST 1 Reconstruct matrix from factors and compute
477 * residual.
478 *
479  CALL zhet01_rook( uplo, n, a, lda, afac, lda,
480  $ iwork, ainv, lda, rwork,
481  $ result( 1 ) )
482 *
483 *+ TEST 2 Compute residual of the computed solution.
484 *
485  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
486  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
487  $ lda, rwork, result( 2 ) )
488 *
489 *+ TEST 3
490 * Check solution from generated exact solution.
491 *
492  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
493  $ result( 3 ) )
494  nt = 3
495 *
496 * Print information about the tests that did not pass
497 * the threshold.
498 *
499  DO 110 k = 1, nt
500  IF( result( k ).GE.thresh ) THEN
501  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
502  $ CALL aladhd( nout, path )
503  WRITE( nout, fmt = 9999 )'ZHESV_ROOK', uplo,
504  $ n, imat, k, result( k )
505  nfail = nfail + 1
506  END IF
507  110 CONTINUE
508  nrun = nrun + nt
509  120 CONTINUE
510  END IF
511 *
512  150 CONTINUE
513 *
514  160 CONTINUE
515  170 CONTINUE
516  180 CONTINUE
517 *
518 * Print a summary of the results.
519 *
520  CALL alasvm( path, nout, nfail, nrun, nerrs )
521 *
522  9999 FORMAT( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
523  $ ', test ', i2, ', ratio =', g12.5 )
524  RETURN
525 *
526 * End of ZDRVHE_ROOK
527 *
528  END
zerrvx
subroutine zerrvx(PATH, NUNIT)
ZERRVX
Definition: zerrvx.f:57
zpot02
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
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
zdrvhe_rook
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:155
zget04
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
zhesv_rook
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:207
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
aladhd
subroutine aladhd(IOUNIT, PATH)
ALADHD
Definition: aladhd.f:92
zhet01_rook
subroutine zhet01_rook(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01_ROOK
Definition: zhet01_rook.f:127
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
zhetri_rook
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:130
zhetrf_rook
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:214
zlatb4
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
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