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zdrvhp.f
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1 *> \brief \b ZDRVHP
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 ZDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
13 * 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 *> ZDRVHP tests the driver routines ZHPSV and -SVX.
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
91 *> (NMAX*(NMAX+1)/2)
92 *> \endverbatim
93 *>
94 *> \param[out] AFAC
95 *> \verbatim
96 *> AFAC is COMPLEX*16 array, dimension
97 *> (NMAX*(NMAX+1)/2)
98 *> \endverbatim
99 *>
100 *> \param[out] AINV
101 *> \verbatim
102 *> AINV is COMPLEX*16 array, dimension
103 *> (NMAX*(NMAX+1)/2)
104 *> \endverbatim
105 *>
106 *> \param[out] B
107 *> \verbatim
108 *> B is COMPLEX*16 array, dimension (NMAX*NRHS)
109 *> \endverbatim
110 *>
111 *> \param[out] X
112 *> \verbatim
113 *> X is COMPLEX*16 array, dimension (NMAX*NRHS)
114 *> \endverbatim
115 *>
116 *> \param[out] XACT
117 *> \verbatim
118 *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
119 *> \endverbatim
120 *>
121 *> \param[out] WORK
122 *> \verbatim
123 *> WORK is COMPLEX*16 array, dimension
124 *> (NMAX*max(2,NRHS))
125 *> \endverbatim
126 *>
127 *> \param[out] RWORK
128 *> \verbatim
129 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
130 *> \endverbatim
131 *>
132 *> \param[out] IWORK
133 *> \verbatim
134 *> IWORK is INTEGER array, dimension (NMAX)
135 *> \endverbatim
136 *>
137 *> \param[in] NOUT
138 *> \verbatim
139 *> NOUT is INTEGER
140 *> The unit number for output.
141 *> \endverbatim
142 *
143 * Authors:
144 * ========
145 *
146 *> \author Univ. of Tennessee
147 *> \author Univ. of California Berkeley
148 *> \author Univ. of Colorado Denver
149 *> \author NAG Ltd.
150 *
151 *> \date November 2011
152 *
153 *> \ingroup complex16_lin
154 *
155 * =====================================================================
156  SUBROUTINE zdrvhp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
157  $ a, afac, ainv, b, x, xact, work, rwork, iwork,
158  $ nout )
159 *
160 * -- LAPACK test routine (version 3.4.0) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 * November 2011
164 *
165 * .. Scalar Arguments ..
166  LOGICAL tsterr
167  INTEGER nmax, nn, nout, nrhs
168  DOUBLE PRECISION thresh
169 * ..
170 * .. Array Arguments ..
171  LOGICAL dotype( * )
172  INTEGER iwork( * ), nval( * )
173  DOUBLE PRECISION rwork( * )
174  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
175  $ work( * ), x( * ), xact( * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. Parameters ..
181  DOUBLE PRECISION one, zero
182  parameter( one = 1.0d+0, zero = 0.0d+0 )
183  INTEGER ntypes, ntests
184  parameter( ntypes = 10, ntests = 6 )
185  INTEGER nfact
186  parameter( nfact = 2 )
187 * ..
188 * .. Local Scalars ..
189  LOGICAL zerot
190  CHARACTER dist, fact, packit, type, uplo, xtype
191  CHARACTER*3 path
192  INTEGER i, i1, i2, ifact, imat, in, info, ioff, iuplo,
193  $ izero, j, k, k1, kl, ku, lda, mode, n, nb,
194  $ nbmin, nerrs, nfail, nimat, npp, nrun, nt
195  DOUBLE PRECISION ainvnm, anorm, cndnum, rcond, rcondc
196 * ..
197 * .. Local Arrays ..
198  CHARACTER facts( nfact )
199  INTEGER iseed( 4 ), iseedy( 4 )
200  DOUBLE PRECISION result( ntests )
201 * ..
202 * .. External Functions ..
203  DOUBLE PRECISION dget06, zlanhp
204  EXTERNAL dget06, zlanhp
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zcopy, zerrvx,
208  $ zget04, zhpsv, zhpsvx, zhpt01, zhptrf, zhptri,
209  $ zlacpy, zlaipd, zlarhs, zlaset, zlatb4, zlatms,
210  $ zppt02, zppt05
211 * ..
212 * .. Scalars in Common ..
213  LOGICAL lerr, ok
214  CHARACTER*32 srnamt
215  INTEGER infot, nunit
216 * ..
217 * .. Common blocks ..
218  common / infoc / infot, nunit, ok, lerr
219  common / srnamc / srnamt
220 * ..
221 * .. Intrinsic Functions ..
222  INTRINSIC dcmplx, max, min
223 * ..
224 * .. Data statements ..
225  DATA iseedy / 1988, 1989, 1990, 1991 /
226  DATA facts / 'F', 'N' /
227 * ..
228 * .. Executable Statements ..
229 *
230 * Initialize constants and the random number seed.
231 *
232  path( 1: 1 ) = 'Z'
233  path( 2: 3 ) = 'HP'
234  nrun = 0
235  nfail = 0
236  nerrs = 0
237  DO 10 i = 1, 4
238  iseed( i ) = iseedy( i )
239  10 continue
240 *
241 * Test the error exits
242 *
243  IF( tsterr )
244  $ CALL zerrvx( path, nout )
245  infot = 0
246 *
247 * Set the block size and minimum block size for testing.
248 *
249  nb = 1
250  nbmin = 2
251  CALL xlaenv( 1, nb )
252  CALL xlaenv( 2, nbmin )
253 *
254 * Do for each value of N in NVAL
255 *
256  DO 180 in = 1, nn
257  n = nval( in )
258  lda = max( n, 1 )
259  npp = n*( n+1 ) / 2
260  xtype = 'N'
261  nimat = ntypes
262  IF( n.LE.0 )
263  $ nimat = 1
264 *
265  DO 170 imat = 1, nimat
266 *
267 * Do the tests only if DOTYPE( IMAT ) is true.
268 *
269  IF( .NOT.dotype( imat ) )
270  $ go to 170
271 *
272 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
273 *
274  zerot = imat.GE.3 .AND. imat.LE.6
275  IF( zerot .AND. n.LT.imat-2 )
276  $ go to 170
277 *
278 * Do first for UPLO = 'U', then for UPLO = 'L'
279 *
280  DO 160 iuplo = 1, 2
281  IF( iuplo.EQ.1 ) THEN
282  uplo = 'U'
283  packit = 'C'
284  ELSE
285  uplo = 'L'
286  packit = 'R'
287  END IF
288 *
289 * Set up parameters with ZLATB4 and generate a test matrix
290 * with ZLATMS.
291 *
292  CALL zlatb4( path, imat, n, n, type, kl, ku, anorm, mode,
293  $ cndnum, dist )
294 *
295  srnamt = 'ZLATMS'
296  CALL zlatms( n, n, dist, iseed, type, rwork, mode,
297  $ cndnum, anorm, kl, ku, packit, a, lda, work,
298  $ info )
299 *
300 * Check error code from ZLATMS.
301 *
302  IF( info.NE.0 ) THEN
303  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
304  $ -1, -1, imat, nfail, nerrs, nout )
305  go to 160
306  END IF
307 *
308 * For types 3-6, zero one or more rows and columns of the
309 * matrix to test that INFO is returned correctly.
310 *
311  IF( zerot ) THEN
312  IF( imat.EQ.3 ) THEN
313  izero = 1
314  ELSE IF( imat.EQ.4 ) THEN
315  izero = n
316  ELSE
317  izero = n / 2 + 1
318  END IF
319 *
320  IF( imat.LT.6 ) THEN
321 *
322 * Set row and column IZERO to zero.
323 *
324  IF( iuplo.EQ.1 ) THEN
325  ioff = ( izero-1 )*izero / 2
326  DO 20 i = 1, izero - 1
327  a( ioff+i ) = zero
328  20 continue
329  ioff = ioff + izero
330  DO 30 i = izero, n
331  a( ioff ) = zero
332  ioff = ioff + i
333  30 continue
334  ELSE
335  ioff = izero
336  DO 40 i = 1, izero - 1
337  a( ioff ) = zero
338  ioff = ioff + n - i
339  40 continue
340  ioff = ioff - izero
341  DO 50 i = izero, n
342  a( ioff+i ) = zero
343  50 continue
344  END IF
345  ELSE
346  ioff = 0
347  IF( iuplo.EQ.1 ) THEN
348 *
349 * Set the first IZERO rows and columns to zero.
350 *
351  DO 70 j = 1, n
352  i2 = min( j, izero )
353  DO 60 i = 1, i2
354  a( ioff+i ) = zero
355  60 continue
356  ioff = ioff + j
357  70 continue
358  ELSE
359 *
360 * Set the last IZERO rows and columns to zero.
361 *
362  DO 90 j = 1, n
363  i1 = max( j, izero )
364  DO 80 i = i1, n
365  a( ioff+i ) = zero
366  80 continue
367  ioff = ioff + n - j
368  90 continue
369  END IF
370  END IF
371  ELSE
372  izero = 0
373  END IF
374 *
375 * Set the imaginary part of the diagonals.
376 *
377  IF( iuplo.EQ.1 ) THEN
378  CALL zlaipd( n, a, 2, 1 )
379  ELSE
380  CALL zlaipd( n, a, n, -1 )
381  END IF
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 ZHPSVX.
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 = zlanhp( '1', uplo, n, a, rwork )
402 *
403 * Factor the matrix A.
404 *
405  CALL zcopy( npp, a, 1, afac, 1 )
406  CALL zhptrf( uplo, n, afac, iwork, info )
407 *
408 * Compute inv(A) and take its norm.
409 *
410  CALL zcopy( npp, afac, 1, ainv, 1 )
411  CALL zhptri( uplo, n, ainv, iwork, work, info )
412  ainvnm = zlanhp( '1', uplo, n, ainv, rwork )
413 *
414 * Compute the 1-norm condition number of A.
415 *
416  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
417  rcondc = one
418  ELSE
419  rcondc = ( one / anorm ) / ainvnm
420  END IF
421  END IF
422 *
423 * Form an exact solution and set the right hand side.
424 *
425  srnamt = 'ZLARHS'
426  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
427  $ nrhs, a, lda, xact, lda, b, lda, iseed,
428  $ info )
429  xtype = 'C'
430 *
431 * --- Test ZHPSV ---
432 *
433  IF( ifact.EQ.2 ) THEN
434  CALL zcopy( npp, a, 1, afac, 1 )
435  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
436 *
437 * Factor the matrix and solve the system using ZHPSV.
438 *
439  srnamt = 'ZHPSV '
440  CALL zhpsv( uplo, n, nrhs, afac, iwork, x, lda,
441  $ info )
442 *
443 * Adjust the expected value of INFO to account for
444 * pivoting.
445 *
446  k = izero
447  IF( k.GT.0 ) THEN
448  100 continue
449  IF( iwork( k ).LT.0 ) THEN
450  IF( iwork( k ).NE.-k ) THEN
451  k = -iwork( k )
452  go to 100
453  END IF
454  ELSE IF( iwork( k ).NE.k ) THEN
455  k = iwork( k )
456  go to 100
457  END IF
458  END IF
459 *
460 * Check error code from ZHPSV .
461 *
462  IF( info.NE.k ) THEN
463  CALL alaerh( path, 'ZHPSV ', info, k, uplo, n,
464  $ n, -1, -1, nrhs, imat, nfail,
465  $ nerrs, nout )
466  go to 120
467  ELSE IF( info.NE.0 ) THEN
468  go to 120
469  END IF
470 *
471 * Reconstruct matrix from factors and compute
472 * residual.
473 *
474  CALL zhpt01( uplo, n, a, afac, iwork, ainv, lda,
475  $ rwork, result( 1 ) )
476 *
477 * Compute residual of the computed solution.
478 *
479  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
480  CALL zppt02( uplo, n, nrhs, a, x, lda, work, lda,
481  $ rwork, result( 2 ) )
482 *
483 * Check solution from generated exact solution.
484 *
485  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
486  $ result( 3 ) )
487  nt = 3
488 *
489 * Print information about the tests that did not pass
490 * the threshold.
491 *
492  DO 110 k = 1, nt
493  IF( result( k ).GE.thresh ) THEN
494  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
495  $ CALL aladhd( nout, path )
496  WRITE( nout, fmt = 9999 )'ZHPSV ', uplo, n,
497  $ imat, k, result( k )
498  nfail = nfail + 1
499  END IF
500  110 continue
501  nrun = nrun + nt
502  120 continue
503  END IF
504 *
505 * --- Test ZHPSVX ---
506 *
507  IF( ifact.EQ.2 .AND. npp.GT.0 )
508  $ CALL zlaset( 'Full', npp, 1, dcmplx( zero ),
509  $ dcmplx( zero ), afac, npp )
510  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
511  $ dcmplx( zero ), x, lda )
512 *
513 * Solve the system and compute the condition number and
514 * error bounds using ZHPSVX.
515 *
516  srnamt = 'ZHPSVX'
517  CALL zhpsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
518  $ lda, x, lda, rcond, rwork,
519  $ rwork( nrhs+1 ), work, rwork( 2*nrhs+1 ),
520  $ info )
521 *
522 * Adjust the expected value of INFO to account for
523 * pivoting.
524 *
525  k = izero
526  IF( k.GT.0 ) THEN
527  130 continue
528  IF( iwork( k ).LT.0 ) THEN
529  IF( iwork( k ).NE.-k ) THEN
530  k = -iwork( k )
531  go to 130
532  END IF
533  ELSE IF( iwork( k ).NE.k ) THEN
534  k = iwork( k )
535  go to 130
536  END IF
537  END IF
538 *
539 * Check the error code from ZHPSVX.
540 *
541  IF( info.NE.k ) THEN
542  CALL alaerh( path, 'ZHPSVX', info, k, fact // uplo,
543  $ n, n, -1, -1, nrhs, imat, nfail,
544  $ nerrs, nout )
545  go to 150
546  END IF
547 *
548  IF( info.EQ.0 ) THEN
549  IF( ifact.GE.2 ) THEN
550 *
551 * Reconstruct matrix from factors and compute
552 * residual.
553 *
554  CALL zhpt01( uplo, n, a, afac, iwork, ainv, lda,
555  $ rwork( 2*nrhs+1 ), result( 1 ) )
556  k1 = 1
557  ELSE
558  k1 = 2
559  END IF
560 *
561 * Compute residual of the computed solution.
562 *
563  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
564  CALL zppt02( uplo, n, nrhs, a, x, lda, work, lda,
565  $ rwork( 2*nrhs+1 ), result( 2 ) )
566 *
567 * Check solution from generated exact solution.
568 *
569  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
570  $ result( 3 ) )
571 *
572 * Check the error bounds from iterative refinement.
573 *
574  CALL zppt05( uplo, n, nrhs, a, b, lda, x, lda,
575  $ xact, lda, rwork, rwork( nrhs+1 ),
576  $ result( 4 ) )
577  ELSE
578  k1 = 6
579  END IF
580 *
581 * Compare RCOND from ZHPSVX with the computed value
582 * in RCONDC.
583 *
584  result( 6 ) = dget06( rcond, rcondc )
585 *
586 * Print information about the tests that did not pass
587 * the threshold.
588 *
589  DO 140 k = k1, 6
590  IF( result( k ).GE.thresh ) THEN
591  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
592  $ CALL aladhd( nout, path )
593  WRITE( nout, fmt = 9998 )'ZHPSVX', fact, uplo,
594  $ n, imat, k, result( k )
595  nfail = nfail + 1
596  END IF
597  140 continue
598  nrun = nrun + 7 - k1
599 *
600  150 continue
601 *
602  160 continue
603  170 continue
604  180 continue
605 *
606 * Print a summary of the results.
607 *
608  CALL alasvm( path, nout, nfail, nrun, nerrs )
609 *
610  9999 format( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
611  $ ', test ', i2, ', ratio =', g12.5 )
612  9998 format( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
613  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
614  return
615 *
616 * End of ZDRVHP
617 *
618  END