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zdrvsp.f
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1 *> \brief \b ZDRVSP
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 ZDRVSP( 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 *> ZDRVSP tests the driver routines ZSPSV 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 zdrvsp( 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 = 11, 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, zlansp
204  EXTERNAL dget06, zlansp
205 * ..
206 * .. External Subroutines ..
207  EXTERNAL aladhd, alaerh, alasvm, xlaenv, zcopy, zerrvx,
208  $ zget04, zlacpy, zlarhs, zlaset, zlatb4, zlatms,
209  $ zlatsp, zppt05, zspsv, zspsvx, zspt01, zspt02,
210  $ zsptrf, zsptri
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 ) = 'Zomplex precision'
233  path( 2: 3 ) = 'SP'
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  IF( imat.NE.ntypes ) THEN
290 *
291 * Set up parameters with ZLATB4 and generate a test
292 * matrix with ZLATMS.
293 *
294  CALL zlatb4( path, imat, n, n, type, kl, ku, anorm,
295  $ mode, cndnum, dist )
296 *
297  srnamt = 'ZLATMS'
298  CALL zlatms( n, n, dist, iseed, type, rwork, mode,
299  $ cndnum, anorm, kl, ku, packit, a, lda,
300  $ work, info )
301 *
302 * Check error code from ZLATMS.
303 *
304  IF( info.NE.0 ) THEN
305  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n,
306  $ -1, -1, -1, imat, nfail, nerrs, nout )
307  go to 160
308  END IF
309 *
310 * For types 3-6, zero one or more rows and columns of
311 * the matrix to test that INFO is returned correctly.
312 *
313  IF( zerot ) THEN
314  IF( imat.EQ.3 ) THEN
315  izero = 1
316  ELSE IF( imat.EQ.4 ) THEN
317  izero = n
318  ELSE
319  izero = n / 2 + 1
320  END IF
321 *
322  IF( imat.LT.6 ) THEN
323 *
324 * Set row and column IZERO to zero.
325 *
326  IF( iuplo.EQ.1 ) THEN
327  ioff = ( izero-1 )*izero / 2
328  DO 20 i = 1, izero - 1
329  a( ioff+i ) = zero
330  20 continue
331  ioff = ioff + izero
332  DO 30 i = izero, n
333  a( ioff ) = zero
334  ioff = ioff + i
335  30 continue
336  ELSE
337  ioff = izero
338  DO 40 i = 1, izero - 1
339  a( ioff ) = zero
340  ioff = ioff + n - i
341  40 continue
342  ioff = ioff - izero
343  DO 50 i = izero, n
344  a( ioff+i ) = zero
345  50 continue
346  END IF
347  ELSE
348  IF( iuplo.EQ.1 ) THEN
349 *
350 * Set the first IZERO rows and columns to zero.
351 *
352  ioff = 0
353  DO 70 j = 1, n
354  i2 = min( j, izero )
355  DO 60 i = 1, i2
356  a( ioff+i ) = zero
357  60 continue
358  ioff = ioff + j
359  70 continue
360  ELSE
361 *
362 * Set the last IZERO rows and columns to zero.
363 *
364  ioff = 0
365  DO 90 j = 1, n
366  i1 = max( j, izero )
367  DO 80 i = i1, n
368  a( ioff+i ) = zero
369  80 continue
370  ioff = ioff + n - j
371  90 continue
372  END IF
373  END IF
374  ELSE
375  izero = 0
376  END IF
377  ELSE
378 *
379 * Use a special block diagonal matrix to test alternate
380 * code for the 2-by-2 blocks.
381 *
382  CALL zlatsp( uplo, n, a, iseed )
383  END IF
384 *
385  DO 150 ifact = 1, nfact
386 *
387 * Do first for FACT = 'F', then for other values.
388 *
389  fact = facts( ifact )
390 *
391 * Compute the condition number for comparison with
392 * the value returned by ZSPSVX.
393 *
394  IF( zerot ) THEN
395  IF( ifact.EQ.1 )
396  $ go to 150
397  rcondc = zero
398 *
399  ELSE IF( ifact.EQ.1 ) THEN
400 *
401 * Compute the 1-norm of A.
402 *
403  anorm = zlansp( '1', uplo, n, a, rwork )
404 *
405 * Factor the matrix A.
406 *
407  CALL zcopy( npp, a, 1, afac, 1 )
408  CALL zsptrf( uplo, n, afac, iwork, info )
409 *
410 * Compute inv(A) and take its norm.
411 *
412  CALL zcopy( npp, afac, 1, ainv, 1 )
413  CALL zsptri( uplo, n, ainv, iwork, work, info )
414  ainvnm = zlansp( '1', uplo, n, ainv, rwork )
415 *
416 * Compute the 1-norm condition number of A.
417 *
418  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
419  rcondc = one
420  ELSE
421  rcondc = ( one / anorm ) / ainvnm
422  END IF
423  END IF
424 *
425 * Form an exact solution and set the right hand side.
426 *
427  srnamt = 'ZLARHS'
428  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
429  $ nrhs, a, lda, xact, lda, b, lda, iseed,
430  $ info )
431  xtype = 'C'
432 *
433 * --- Test ZSPSV ---
434 *
435  IF( ifact.EQ.2 ) THEN
436  CALL zcopy( npp, a, 1, afac, 1 )
437  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
438 *
439 * Factor the matrix and solve the system using ZSPSV.
440 *
441  srnamt = 'ZSPSV '
442  CALL zspsv( uplo, n, nrhs, afac, iwork, x, lda,
443  $ 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 ZSPSV .
463 *
464  IF( info.NE.k ) THEN
465  CALL alaerh( path, 'ZSPSV ', info, k, uplo, n,
466  $ 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 * Reconstruct matrix from factors and compute
474 * residual.
475 *
476  CALL zspt01( uplo, n, a, afac, iwork, ainv, lda,
477  $ rwork, result( 1 ) )
478 *
479 * Compute residual of the computed solution.
480 *
481  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
482  CALL zspt02( uplo, n, nrhs, a, x, lda, work, lda,
483  $ rwork, result( 2 ) )
484 *
485 * Check solution from generated exact solution.
486 *
487  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
488  $ result( 3 ) )
489  nt = 3
490 *
491 * Print information about the tests that did not pass
492 * the threshold.
493 *
494  DO 110 k = 1, nt
495  IF( result( k ).GE.thresh ) THEN
496  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
497  $ CALL aladhd( nout, path )
498  WRITE( nout, fmt = 9999 )'ZSPSV ', uplo, n,
499  $ imat, k, result( k )
500  nfail = nfail + 1
501  END IF
502  110 continue
503  nrun = nrun + nt
504  120 continue
505  END IF
506 *
507 * --- Test ZSPSVX ---
508 *
509  IF( ifact.EQ.2 .AND. npp.GT.0 )
510  $ CALL zlaset( 'Full', npp, 1, dcmplx( zero ),
511  $ dcmplx( zero ), afac, npp )
512  CALL zlaset( 'Full', n, nrhs, dcmplx( zero ),
513  $ dcmplx( zero ), x, lda )
514 *
515 * Solve the system and compute the condition number and
516 * error bounds using ZSPSVX.
517 *
518  srnamt = 'ZSPSVX'
519  CALL zspsvx( fact, uplo, n, nrhs, a, afac, iwork, b,
520  $ lda, x, lda, rcond, rwork,
521  $ rwork( nrhs+1 ), work, rwork( 2*nrhs+1 ),
522  $ info )
523 *
524 * Adjust the expected value of INFO to account for
525 * pivoting.
526 *
527  k = izero
528  IF( k.GT.0 ) THEN
529  130 continue
530  IF( iwork( k ).LT.0 ) THEN
531  IF( iwork( k ).NE.-k ) THEN
532  k = -iwork( k )
533  go to 130
534  END IF
535  ELSE IF( iwork( k ).NE.k ) THEN
536  k = iwork( k )
537  go to 130
538  END IF
539  END IF
540 *
541 * Check the error code from ZSPSVX.
542 *
543  IF( info.NE.k ) THEN
544  CALL alaerh( path, 'ZSPSVX', info, k, fact // uplo,
545  $ n, n, -1, -1, nrhs, imat, nfail,
546  $ nerrs, nout )
547  go to 150
548  END IF
549 *
550  IF( info.EQ.0 ) THEN
551  IF( ifact.GE.2 ) THEN
552 *
553 * Reconstruct matrix from factors and compute
554 * residual.
555 *
556  CALL zspt01( uplo, n, a, afac, iwork, ainv, lda,
557  $ rwork( 2*nrhs+1 ), result( 1 ) )
558  k1 = 1
559  ELSE
560  k1 = 2
561  END IF
562 *
563 * Compute residual of the computed solution.
564 *
565  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
566  CALL zspt02( uplo, n, nrhs, a, x, lda, work, lda,
567  $ rwork( 2*nrhs+1 ), result( 2 ) )
568 *
569 * Check solution from generated exact solution.
570 *
571  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
572  $ result( 3 ) )
573 *
574 * Check the error bounds from iterative refinement.
575 *
576  CALL zppt05( uplo, n, nrhs, a, b, lda, x, lda,
577  $ xact, lda, rwork, rwork( nrhs+1 ),
578  $ result( 4 ) )
579  ELSE
580  k1 = 6
581  END IF
582 *
583 * Compare RCOND from ZSPSVX with the computed value
584 * in RCONDC.
585 *
586  result( 6 ) = dget06( rcond, rcondc )
587 *
588 * Print information about the tests that did not pass
589 * the threshold.
590 *
591  DO 140 k = k1, 6
592  IF( result( k ).GE.thresh ) THEN
593  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
594  $ CALL aladhd( nout, path )
595  WRITE( nout, fmt = 9998 )'ZSPSVX', fact, uplo,
596  $ n, imat, k, result( k )
597  nfail = nfail + 1
598  END IF
599  140 continue
600  nrun = nrun + 7 - k1
601 *
602  150 continue
603 *
604  160 continue
605  170 continue
606  180 continue
607 *
608 * Print a summary of the results.
609 *
610  CALL alasvm( path, nout, nfail, nrun, nerrs )
611 *
612  9999 format( 1x, a, ', UPLO=''', a1, ''', N =', i5, ', type ', i2,
613  $ ', test ', i2, ', ratio =', g12.5 )
614  9998 format( 1x, a, ', FACT=''', a1, ''', UPLO=''', a1, ''', N =', i5,
615  $ ', type ', i2, ', test ', i2, ', ratio =', g12.5 )
616  return
617 *
618 * End of ZDRVSP
619 *
620  END