LAPACK  3.4.2
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zdrvpp.f
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1 *> \brief \b ZDRVPP
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 ZDRVPP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
12 * A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
13 * RWORK, 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 NVAL( * )
23 * DOUBLE PRECISION RWORK( * ), S( * )
24 * COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ),
25 * $ BSAV( * ), WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZDRVPP tests the driver routines ZPPSV 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 (NMAX*(NMAX+1)/2)
91 *> \endverbatim
92 *>
93 *> \param[out] AFAC
94 *> \verbatim
95 *> AFAC is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2)
96 *> \endverbatim
97 *>
98 *> \param[out] ASAV
99 *> \verbatim
100 *> ASAV is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2)
101 *> \endverbatim
102 *>
103 *> \param[out] B
104 *> \verbatim
105 *> B is COMPLEX*16 array, dimension (NMAX*NRHS)
106 *> \endverbatim
107 *>
108 *> \param[out] BSAV
109 *> \verbatim
110 *> BSAV is COMPLEX*16 array, dimension (NMAX*NRHS)
111 *> \endverbatim
112 *>
113 *> \param[out] X
114 *> \verbatim
115 *> X is COMPLEX*16 array, dimension (NMAX*NRHS)
116 *> \endverbatim
117 *>
118 *> \param[out] XACT
119 *> \verbatim
120 *> XACT is COMPLEX*16 array, dimension (NMAX*NRHS)
121 *> \endverbatim
122 *>
123 *> \param[out] S
124 *> \verbatim
125 *> S is DOUBLE PRECISION array, dimension (NMAX)
126 *> \endverbatim
127 *>
128 *> \param[out] WORK
129 *> \verbatim
130 *> WORK is COMPLEX*16 array, dimension
131 *> (NMAX*max(3,NRHS))
132 *> \endverbatim
133 *>
134 *> \param[out] RWORK
135 *> \verbatim
136 *> RWORK is DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
137 *> \endverbatim
138 *>
139 *> \param[in] NOUT
140 *> \verbatim
141 *> NOUT is INTEGER
142 *> The unit number for output.
143 *> \endverbatim
144 *
145 * Authors:
146 * ========
147 *
148 *> \author Univ. of Tennessee
149 *> \author Univ. of California Berkeley
150 *> \author Univ. of Colorado Denver
151 *> \author NAG Ltd.
152 *
153 *> \date November 2011
154 *
155 *> \ingroup complex16_lin
156 *
157 * =====================================================================
158  SUBROUTINE zdrvpp( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
159  $ a, afac, asav, b, bsav, x, xact, s, work,
160  $ rwork, nout )
161 *
162 * -- LAPACK test routine (version 3.4.0) --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * November 2011
166 *
167 * .. Scalar Arguments ..
168  LOGICAL tsterr
169  INTEGER nmax, nn, nout, nrhs
170  DOUBLE PRECISION thresh
171 * ..
172 * .. Array Arguments ..
173  LOGICAL dotype( * )
174  INTEGER nval( * )
175  DOUBLE PRECISION rwork( * ), s( * )
176  COMPLEX*16 a( * ), afac( * ), asav( * ), b( * ),
177  $ bsav( * ), work( * ), x( * ), xact( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  DOUBLE PRECISION one, zero
184  parameter( one = 1.0d+0, zero = 0.0d+0 )
185  INTEGER ntypes
186  parameter( ntypes = 9 )
187  INTEGER ntests
188  parameter( ntests = 6 )
189 * ..
190 * .. Local Scalars ..
191  LOGICAL equil, nofact, prefac, zerot
192  CHARACTER dist, equed, fact, packit, type, uplo, xtype
193  CHARACTER*3 path
194  INTEGER i, iequed, ifact, imat, in, info, ioff, iuplo,
195  $ izero, k, k1, kl, ku, lda, mode, n, nerrs,
196  $ nfact, nfail, nimat, npp, nrun, nt
197  DOUBLE PRECISION ainvnm, amax, anorm, cndnum, rcond, rcondc,
198  $ roldc, scond
199 * ..
200 * .. Local Arrays ..
201  CHARACTER equeds( 2 ), facts( 3 ), packs( 2 ), uplos( 2 )
202  INTEGER iseed( 4 ), iseedy( 4 )
203  DOUBLE PRECISION result( ntests )
204 * ..
205 * .. External Functions ..
206  LOGICAL lsame
207  DOUBLE PRECISION dget06, zlanhp
208  EXTERNAL lsame, dget06, zlanhp
209 * ..
210 * .. External Subroutines ..
211  EXTERNAL aladhd, alaerh, alasvm, zcopy, zerrvx, zget04,
212  $ zlacpy, zlaipd, zlaqhp, zlarhs, zlaset, zlatb4,
213  $ zlatms, zppequ, zppsv, zppsvx, zppt01, zppt02,
214  $ zppt05, zpptrf, zpptri
215 * ..
216 * .. Scalars in Common ..
217  LOGICAL lerr, ok
218  CHARACTER*32 srnamt
219  INTEGER infot, nunit
220 * ..
221 * .. Common blocks ..
222  common / infoc / infot, nunit, ok, lerr
223  common / srnamc / srnamt
224 * ..
225 * .. Intrinsic Functions ..
226  INTRINSIC dcmplx, max
227 * ..
228 * .. Data statements ..
229  DATA iseedy / 1988, 1989, 1990, 1991 /
230  DATA uplos / 'U', 'L' / , facts / 'F', 'N', 'E' / ,
231  $ packs / 'C', 'R' / , equeds / 'N', 'Y' /
232 * ..
233 * .. Executable Statements ..
234 *
235 * Initialize constants and the random number seed.
236 *
237  path( 1: 1 ) = 'Zomplex precision'
238  path( 2: 3 ) = 'PP'
239  nrun = 0
240  nfail = 0
241  nerrs = 0
242  DO 10 i = 1, 4
243  iseed( i ) = iseedy( i )
244  10 continue
245 *
246 * Test the error exits
247 *
248  IF( tsterr )
249  $ CALL zerrvx( path, nout )
250  infot = 0
251 *
252 * Do for each value of N in NVAL
253 *
254  DO 140 in = 1, nn
255  n = nval( in )
256  lda = max( n, 1 )
257  npp = n*( n+1 ) / 2
258  xtype = 'N'
259  nimat = ntypes
260  IF( n.LE.0 )
261  $ nimat = 1
262 *
263  DO 130 imat = 1, nimat
264 *
265 * Do the tests only if DOTYPE( IMAT ) is true.
266 *
267  IF( .NOT.dotype( imat ) )
268  $ go to 130
269 *
270 * Skip types 3, 4, or 5 if the matrix size is too small.
271 *
272  zerot = imat.GE.3 .AND. imat.LE.5
273  IF( zerot .AND. n.LT.imat-2 )
274  $ go to 130
275 *
276 * Do first for UPLO = 'U', then for UPLO = 'L'
277 *
278  DO 120 iuplo = 1, 2
279  uplo = uplos( iuplo )
280  packit = packs( iuplo )
281 *
282 * Set up parameters with ZLATB4 and generate a test matrix
283 * with ZLATMS.
284 *
285  CALL zlatb4( path, imat, n, n, type, kl, ku, anorm, mode,
286  $ cndnum, dist )
287  rcondc = one / cndnum
288 *
289  srnamt = 'ZLATMS'
290  CALL zlatms( n, n, dist, iseed, type, rwork, mode,
291  $ cndnum, anorm, kl, ku, packit, a, lda, work,
292  $ info )
293 *
294 * Check error code from ZLATMS.
295 *
296  IF( info.NE.0 ) THEN
297  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
298  $ -1, -1, imat, nfail, nerrs, nout )
299  go to 120
300  END IF
301 *
302 * For types 3-5, zero one row and column of the matrix to
303 * test that INFO is returned correctly.
304 *
305  IF( zerot ) THEN
306  IF( imat.EQ.3 ) THEN
307  izero = 1
308  ELSE IF( imat.EQ.4 ) THEN
309  izero = n
310  ELSE
311  izero = n / 2 + 1
312  END IF
313 *
314 * Set row and column IZERO of A to 0.
315 *
316  IF( iuplo.EQ.1 ) THEN
317  ioff = ( izero-1 )*izero / 2
318  DO 20 i = 1, izero - 1
319  a( ioff+i ) = zero
320  20 continue
321  ioff = ioff + izero
322  DO 30 i = izero, n
323  a( ioff ) = zero
324  ioff = ioff + i
325  30 continue
326  ELSE
327  ioff = izero
328  DO 40 i = 1, izero - 1
329  a( ioff ) = zero
330  ioff = ioff + n - i
331  40 continue
332  ioff = ioff - izero
333  DO 50 i = izero, n
334  a( ioff+i ) = zero
335  50 continue
336  END IF
337  ELSE
338  izero = 0
339  END IF
340 *
341 * Set the imaginary part of the diagonals.
342 *
343  IF( iuplo.EQ.1 ) THEN
344  CALL zlaipd( n, a, 2, 1 )
345  ELSE
346  CALL zlaipd( n, a, n, -1 )
347  END IF
348 *
349 * Save a copy of the matrix A in ASAV.
350 *
351  CALL zcopy( npp, a, 1, asav, 1 )
352 *
353  DO 110 iequed = 1, 2
354  equed = equeds( iequed )
355  IF( iequed.EQ.1 ) THEN
356  nfact = 3
357  ELSE
358  nfact = 1
359  END IF
360 *
361  DO 100 ifact = 1, nfact
362  fact = facts( ifact )
363  prefac = lsame( fact, 'F' )
364  nofact = lsame( fact, 'N' )
365  equil = lsame( fact, 'E' )
366 *
367  IF( zerot ) THEN
368  IF( prefac )
369  $ go to 100
370  rcondc = zero
371 *
372  ELSE IF( .NOT.lsame( fact, 'N' ) ) THEN
373 *
374 * Compute the condition number for comparison with
375 * the value returned by ZPPSVX (FACT = 'N' reuses
376 * the condition number from the previous iteration
377 * with FACT = 'F').
378 *
379  CALL zcopy( npp, asav, 1, afac, 1 )
380  IF( equil .OR. iequed.GT.1 ) THEN
381 *
382 * Compute row and column scale factors to
383 * equilibrate the matrix A.
384 *
385  CALL zppequ( uplo, n, afac, s, scond, amax,
386  $ info )
387  IF( info.EQ.0 .AND. n.GT.0 ) THEN
388  IF( iequed.GT.1 )
389  $ scond = zero
390 *
391 * Equilibrate the matrix.
392 *
393  CALL zlaqhp( uplo, n, afac, s, scond,
394  $ amax, equed )
395  END IF
396  END IF
397 *
398 * Save the condition number of the
399 * non-equilibrated system for use in ZGET04.
400 *
401  IF( equil )
402  $ roldc = rcondc
403 *
404 * Compute the 1-norm of A.
405 *
406  anorm = zlanhp( '1', uplo, n, afac, rwork )
407 *
408 * Factor the matrix A.
409 *
410  CALL zpptrf( uplo, n, afac, info )
411 *
412 * Form the inverse of A.
413 *
414  CALL zcopy( npp, afac, 1, a, 1 )
415  CALL zpptri( uplo, n, a, info )
416 *
417 * Compute the 1-norm condition number of A.
418 *
419  ainvnm = zlanhp( '1', uplo, n, a, rwork )
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 * Restore the matrix A.
428 *
429  CALL zcopy( npp, asav, 1, a, 1 )
430 *
431 * Form an exact solution and set the right hand side.
432 *
433  srnamt = 'ZLARHS'
434  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
435  $ nrhs, a, lda, xact, lda, b, lda,
436  $ iseed, info )
437  xtype = 'C'
438  CALL zlacpy( 'Full', n, nrhs, b, lda, bsav, lda )
439 *
440  IF( nofact ) THEN
441 *
442 * --- Test ZPPSV ---
443 *
444 * Compute the L*L' or U'*U factorization of the
445 * matrix and solve the system.
446 *
447  CALL zcopy( npp, a, 1, afac, 1 )
448  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
449 *
450  srnamt = 'ZPPSV '
451  CALL zppsv( uplo, n, nrhs, afac, x, lda, info )
452 *
453 * Check error code from ZPPSV .
454 *
455  IF( info.NE.izero ) THEN
456  CALL alaerh( path, 'ZPPSV ', info, izero,
457  $ uplo, n, n, -1, -1, nrhs, imat,
458  $ nfail, nerrs, nout )
459  go to 70
460  ELSE IF( info.NE.0 ) THEN
461  go to 70
462  END IF
463 *
464 * Reconstruct matrix from factors and compute
465 * residual.
466 *
467  CALL zppt01( uplo, n, a, afac, rwork,
468  $ result( 1 ) )
469 *
470 * Compute residual of the computed solution.
471 *
472  CALL zlacpy( 'Full', n, nrhs, b, lda, work,
473  $ lda )
474  CALL zppt02( uplo, n, nrhs, a, x, lda, work,
475  $ lda, rwork, result( 2 ) )
476 *
477 * Check solution from generated exact solution.
478 *
479  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
480  $ result( 3 ) )
481  nt = 3
482 *
483 * Print information about the tests that did not
484 * pass the threshold.
485 *
486  DO 60 k = 1, nt
487  IF( result( k ).GE.thresh ) THEN
488  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
489  $ CALL aladhd( nout, path )
490  WRITE( nout, fmt = 9999 )'ZPPSV ', uplo,
491  $ n, imat, k, result( k )
492  nfail = nfail + 1
493  END IF
494  60 continue
495  nrun = nrun + nt
496  70 continue
497  END IF
498 *
499 * --- Test ZPPSVX ---
500 *
501  IF( .NOT.prefac .AND. npp.GT.0 )
502  $ CALL zlaset( 'Full', npp, 1, dcmplx( zero ),
503  $ dcmplx( zero ), afac, npp )
504  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
505  $ dcmplx( zero ), x, lda )
506  IF( iequed.GT.1 .AND. n.GT.0 ) THEN
507 *
508 * Equilibrate the matrix if FACT='F' and
509 * EQUED='Y'.
510 *
511  CALL zlaqhp( uplo, n, a, s, scond, amax, equed )
512  END IF
513 *
514 * Solve the system and compute the condition number
515 * and error bounds using ZPPSVX.
516 *
517  srnamt = 'ZPPSVX'
518  CALL zppsvx( fact, uplo, n, nrhs, a, afac, equed,
519  $ s, b, lda, x, lda, rcond, rwork,
520  $ rwork( nrhs+1 ), work,
521  $ rwork( 2*nrhs+1 ), info )
522 *
523 * Check the error code from ZPPSVX.
524 *
525  IF( info.NE.izero ) THEN
526  CALL alaerh( path, 'ZPPSVX', info, izero,
527  $ fact // uplo, n, n, -1, -1, nrhs,
528  $ imat, nfail, nerrs, nout )
529  go to 90
530  END IF
531 *
532  IF( info.EQ.0 ) THEN
533  IF( .NOT.prefac ) THEN
534 *
535 * Reconstruct matrix from factors and compute
536 * residual.
537 *
538  CALL zppt01( uplo, n, a, afac,
539  $ rwork( 2*nrhs+1 ), result( 1 ) )
540  k1 = 1
541  ELSE
542  k1 = 2
543  END IF
544 *
545 * Compute residual of the computed solution.
546 *
547  CALL zlacpy( 'Full', n, nrhs, bsav, lda, work,
548  $ lda )
549  CALL zppt02( uplo, n, nrhs, asav, x, lda, work,
550  $ lda, rwork( 2*nrhs+1 ),
551  $ result( 2 ) )
552 *
553 * Check solution from generated exact solution.
554 *
555  IF( nofact .OR. ( prefac .AND. lsame( equed,
556  $ 'N' ) ) ) THEN
557  CALL zget04( n, nrhs, x, lda, xact, lda,
558  $ rcondc, result( 3 ) )
559  ELSE
560  CALL zget04( n, nrhs, x, lda, xact, lda,
561  $ roldc, result( 3 ) )
562  END IF
563 *
564 * Check the error bounds from iterative
565 * refinement.
566 *
567  CALL zppt05( uplo, n, nrhs, asav, b, lda, x,
568  $ lda, xact, lda, rwork,
569  $ rwork( nrhs+1 ), result( 4 ) )
570  ELSE
571  k1 = 6
572  END IF
573 *
574 * Compare RCOND from ZPPSVX with the computed value
575 * in RCONDC.
576 *
577  result( 6 ) = dget06( rcond, rcondc )
578 *
579 * Print information about the tests that did not pass
580 * the threshold.
581 *
582  DO 80 k = k1, 6
583  IF( result( k ).GE.thresh ) THEN
584  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
585  $ CALL aladhd( nout, path )
586  IF( prefac ) THEN
587  WRITE( nout, fmt = 9997 )'ZPPSVX', fact,
588  $ uplo, n, equed, imat, k, result( k )
589  ELSE
590  WRITE( nout, fmt = 9998 )'ZPPSVX', fact,
591  $ uplo, n, imat, k, result( k )
592  END IF
593  nfail = nfail + 1
594  END IF
595  80 continue
596  nrun = nrun + 7 - k1
597  90 continue
598  100 continue
599  110 continue
600  120 continue
601  130 continue
602  140 continue
603 *
604 * Print a summary of the results.
605 *
606  CALL alasvm( path, nout, nfail, nrun, nerrs )
607 *
608  9999 format( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i1,
609  $ ', test(', i1, ')=', g12.5 )
610  9998 format( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N=', i5,
611  $ ', type ', i1, ', test(', i1, ')=', g12.5 )
612  9997 format( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N=', i5,
613  $ ', EQUED=''', a1, ''', type ', i1, ', test(', i1, ')=',
614  $ g12.5 )
615  return
616 *
617 * End of ZDRVPP
618 *
619  END