LAPACK  3.4.2
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zchkhp.f
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1 *> \brief \b ZCHKHP
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 ZCHKHP( DOTYPE, NN, NVAL, NNS, NSVAL, 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, NNS, NOUT
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NSVAL( * ), 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 *> ZCHKHP tests ZHPTRF, -TRI, -TRS, -RFS, and -CON
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] NNS
61 *> \verbatim
62 *> NNS is INTEGER
63 *> The number of values of NRHS contained in the vector NSVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NSVAL
67 *> \verbatim
68 *> NSVAL is INTEGER array, dimension (NNS)
69 *> The values of the number of right hand sides NRHS.
70 *> \endverbatim
71 *>
72 *> \param[in] THRESH
73 *> \verbatim
74 *> THRESH is DOUBLE PRECISION
75 *> The threshold value for the test ratios. A result is
76 *> included in the output file if RESULT >= THRESH. To have
77 *> every test ratio printed, use THRESH = 0.
78 *> \endverbatim
79 *>
80 *> \param[in] TSTERR
81 *> \verbatim
82 *> TSTERR is LOGICAL
83 *> Flag that indicates whether error exits are to be tested.
84 *> \endverbatim
85 *>
86 *> \param[in] NMAX
87 *> \verbatim
88 *> NMAX is INTEGER
89 *> The maximum value permitted for N, used in dimensioning the
90 *> work arrays.
91 *> \endverbatim
92 *>
93 *> \param[out] A
94 *> \verbatim
95 *> A is COMPLEX*16 array, dimension
96 *> (NMAX*(NMAX+1)/2)
97 *> \endverbatim
98 *>
99 *> \param[out] AFAC
100 *> \verbatim
101 *> AFAC is COMPLEX*16 array, dimension
102 *> (NMAX*(NMAX+1)/2)
103 *> \endverbatim
104 *>
105 *> \param[out] AINV
106 *> \verbatim
107 *> AINV is COMPLEX*16 array, dimension
108 *> (NMAX*(NMAX+1)/2)
109 *> \endverbatim
110 *>
111 *> \param[out] B
112 *> \verbatim
113 *> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
114 *> where NSMAX is the largest entry in NSVAL.
115 *> \endverbatim
116 *>
117 *> \param[out] X
118 *> \verbatim
119 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
120 *> \endverbatim
121 *>
122 *> \param[out] XACT
123 *> \verbatim
124 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
125 *> \endverbatim
126 *>
127 *> \param[out] WORK
128 *> \verbatim
129 *> WORK is COMPLEX*16 array, dimension
130 *> (NMAX*max(2,NSMAX))
131 *> \endverbatim
132 *>
133 *> \param[out] RWORK
134 *> \verbatim
135 *> RWORK is DOUBLE PRECISION array,
136 *> dimension (NMAX+2*NSMAX)
137 *> \endverbatim
138 *>
139 *> \param[out] IWORK
140 *> \verbatim
141 *> IWORK is INTEGER array, dimension (NMAX)
142 *> \endverbatim
143 *>
144 *> \param[in] NOUT
145 *> \verbatim
146 *> NOUT is INTEGER
147 *> The unit number for output.
148 *> \endverbatim
149 *
150 * Authors:
151 * ========
152 *
153 *> \author Univ. of Tennessee
154 *> \author Univ. of California Berkeley
155 *> \author Univ. of Colorado Denver
156 *> \author NAG Ltd.
157 *
158 *> \date November 2011
159 *
160 *> \ingroup complex16_lin
161 *
162 * =====================================================================
163  SUBROUTINE zchkhp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
164  $ nmax, a, afac, ainv, b, x, xact, work, rwork,
165  $ iwork, nout )
166 *
167 * -- LAPACK test routine (version 3.4.0) --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 * November 2011
171 *
172 * .. Scalar Arguments ..
173  LOGICAL tsterr
174  INTEGER nmax, nn, nns, nout
175  DOUBLE PRECISION thresh
176 * ..
177 * .. Array Arguments ..
178  LOGICAL dotype( * )
179  INTEGER iwork( * ), nsval( * ), nval( * )
180  DOUBLE PRECISION rwork( * )
181  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
182  $ work( * ), x( * ), xact( * )
183 * ..
184 *
185 * =====================================================================
186 *
187 * .. Parameters ..
188  DOUBLE PRECISION zero
189  parameter( zero = 0.0d+0 )
190  INTEGER ntypes
191  parameter( ntypes = 10 )
192  INTEGER ntests
193  parameter( ntests = 8 )
194 * ..
195 * .. Local Scalars ..
196  LOGICAL trfcon, zerot
197  CHARACTER dist, packit, type, uplo, xtype
198  CHARACTER*3 path
199  INTEGER i, i1, i2, imat, in, info, ioff, irhs, iuplo,
200  $ izero, j, k, kl, ku, lda, mode, n, nerrs,
201  $ nfail, nimat, npp, nrhs, nrun, nt
202  DOUBLE PRECISION anorm, cndnum, rcond, rcondc
203 * ..
204 * .. Local Arrays ..
205  CHARACTER uplos( 2 )
206  INTEGER iseed( 4 ), iseedy( 4 )
207  DOUBLE PRECISION result( ntests )
208 * ..
209 * .. External Functions ..
210  LOGICAL lsame
211  DOUBLE PRECISION dget06, zlanhp
212  EXTERNAL lsame, dget06, zlanhp
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL alaerh, alahd, alasum, zcopy, zerrsy, zget04,
216  $ zhpcon, zhprfs, zhpt01, zhptrf, zhptri, zhptrs,
217  $ zlacpy, zlaipd, zlarhs, zlatb4, zlatms, zppt02,
218  $ zppt03, zppt05
219 * ..
220 * .. Intrinsic Functions ..
221  INTRINSIC max, min
222 * ..
223 * .. Scalars in Common ..
224  LOGICAL lerr, ok
225  CHARACTER*32 srnamt
226  INTEGER infot, nunit
227 * ..
228 * .. Common blocks ..
229  common / infoc / infot, nunit, ok, lerr
230  common / srnamc / srnamt
231 * ..
232 * .. Data statements ..
233  DATA iseedy / 1988, 1989, 1990, 1991 /
234  DATA uplos / 'U', 'L' /
235 * ..
236 * .. Executable Statements ..
237 *
238 * Initialize constants and the random number seed.
239 *
240  path( 1: 1 ) = 'Zomplex precision'
241  path( 2: 3 ) = 'HP'
242  nrun = 0
243  nfail = 0
244  nerrs = 0
245  DO 10 i = 1, 4
246  iseed( i ) = iseedy( i )
247  10 continue
248 *
249 * Test the error exits
250 *
251  IF( tsterr )
252  $ CALL zerrsy( path, nout )
253  infot = 0
254 *
255 * Do for each value of N in NVAL
256 *
257  DO 170 in = 1, nn
258  n = nval( in )
259  lda = max( n, 1 )
260  xtype = 'N'
261  nimat = ntypes
262  IF( n.LE.0 )
263  $ nimat = 1
264 *
265  izero = 0
266  DO 160 imat = 1, nimat
267 *
268 * Do the tests only if DOTYPE( IMAT ) is true.
269 *
270  IF( .NOT.dotype( imat ) )
271  $ go to 160
272 *
273 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
274 *
275  zerot = imat.GE.3 .AND. imat.LE.6
276  IF( zerot .AND. n.LT.imat-2 )
277  $ go to 160
278 *
279 * Do first for UPLO = 'U', then for UPLO = 'L'
280 *
281  DO 150 iuplo = 1, 2
282  uplo = uplos( iuplo )
283  IF( lsame( uplo, 'U' ) ) THEN
284  packit = 'C'
285  ELSE
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 150
306  END IF
307 *
308 * For types 3-6, zero one or more rows and columns of
309 * the 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 * Compute the L*D*L' or U*D*U' factorization of the matrix.
384 *
385  npp = n*( n+1 ) / 2
386  CALL zcopy( npp, a, 1, afac, 1 )
387  srnamt = 'ZHPTRF'
388  CALL zhptrf( uplo, n, afac, iwork, info )
389 *
390 * Adjust the expected value of INFO to account for
391 * pivoting.
392 *
393  k = izero
394  IF( k.GT.0 ) THEN
395  100 continue
396  IF( iwork( k ).LT.0 ) THEN
397  IF( iwork( k ).NE.-k ) THEN
398  k = -iwork( k )
399  go to 100
400  END IF
401  ELSE IF( iwork( k ).NE.k ) THEN
402  k = iwork( k )
403  go to 100
404  END IF
405  END IF
406 *
407 * Check error code from ZHPTRF.
408 *
409  IF( info.NE.k )
410  $ CALL alaerh( path, 'ZHPTRF', info, k, uplo, n, n, -1,
411  $ -1, -1, imat, nfail, nerrs, nout )
412  IF( info.NE.0 ) THEN
413  trfcon = .true.
414  ELSE
415  trfcon = .false.
416  END IF
417 *
418 *+ TEST 1
419 * Reconstruct matrix from factors and compute residual.
420 *
421  CALL zhpt01( uplo, n, a, afac, iwork, ainv, lda, rwork,
422  $ result( 1 ) )
423  nt = 1
424 *
425 *+ TEST 2
426 * Form the inverse and compute the residual.
427 *
428  IF( .NOT.trfcon ) THEN
429  CALL zcopy( npp, afac, 1, ainv, 1 )
430  srnamt = 'ZHPTRI'
431  CALL zhptri( uplo, n, ainv, iwork, work, info )
432 *
433 * Check error code from ZHPTRI.
434 *
435  IF( info.NE.0 )
436  $ CALL alaerh( path, 'ZHPTRI', info, 0, uplo, n, n,
437  $ -1, -1, -1, imat, nfail, nerrs, nout )
438 *
439  CALL zppt03( uplo, n, a, ainv, work, lda, rwork,
440  $ rcondc, result( 2 ) )
441  nt = 2
442  END IF
443 *
444 * Print information about the tests that did not pass
445 * the threshold.
446 *
447  DO 110 k = 1, nt
448  IF( result( k ).GE.thresh ) THEN
449  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
450  $ CALL alahd( nout, path )
451  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
452  $ result( k )
453  nfail = nfail + 1
454  END IF
455  110 continue
456  nrun = nrun + nt
457 *
458 * Do only the condition estimate if INFO is not 0.
459 *
460  IF( trfcon ) THEN
461  rcondc = zero
462  go to 140
463  END IF
464 *
465  DO 130 irhs = 1, nns
466  nrhs = nsval( irhs )
467 *
468 *+ TEST 3
469 * Solve and compute residual for A * X = B.
470 *
471  srnamt = 'ZLARHS'
472  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
473  $ nrhs, a, lda, xact, lda, b, lda, iseed,
474  $ info )
475  xtype = 'C'
476  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
477 *
478  srnamt = 'ZHPTRS'
479  CALL zhptrs( uplo, n, nrhs, afac, iwork, x, lda,
480  $ info )
481 *
482 * Check error code from ZHPTRS.
483 *
484  IF( info.NE.0 )
485  $ CALL alaerh( path, 'ZHPTRS', info, 0, uplo, n, n,
486  $ -1, -1, nrhs, imat, nfail, nerrs,
487  $ nout )
488 *
489  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
490  CALL zppt02( uplo, n, nrhs, a, x, lda, work, lda,
491  $ rwork, result( 3 ) )
492 *
493 *+ TEST 4
494 * Check solution from generated exact solution.
495 *
496  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
497  $ result( 4 ) )
498 *
499 *+ TESTS 5, 6, and 7
500 * Use iterative refinement to improve the solution.
501 *
502  srnamt = 'ZHPRFS'
503  CALL zhprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
504  $ lda, rwork, rwork( nrhs+1 ), work,
505  $ rwork( 2*nrhs+1 ), info )
506 *
507 * Check error code from ZHPRFS.
508 *
509  IF( info.NE.0 )
510  $ CALL alaerh( path, 'ZHPRFS', info, 0, uplo, n, n,
511  $ -1, -1, nrhs, imat, nfail, nerrs,
512  $ nout )
513 *
514  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
515  $ result( 5 ) )
516  CALL zppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
517  $ lda, rwork, rwork( nrhs+1 ),
518  $ result( 6 ) )
519 *
520 * Print information about the tests that did not pass
521 * the threshold.
522 *
523  DO 120 k = 3, 7
524  IF( result( k ).GE.thresh ) THEN
525  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
526  $ CALL alahd( nout, path )
527  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
528  $ k, result( k )
529  nfail = nfail + 1
530  END IF
531  120 continue
532  nrun = nrun + 5
533  130 continue
534 *
535 *+ TEST 8
536 * Get an estimate of RCOND = 1/CNDNUM.
537 *
538  140 continue
539  anorm = zlanhp( '1', uplo, n, a, rwork )
540  srnamt = 'ZHPCON'
541  CALL zhpcon( uplo, n, afac, iwork, anorm, rcond, work,
542  $ info )
543 *
544 * Check error code from ZHPCON.
545 *
546  IF( info.NE.0 )
547  $ CALL alaerh( path, 'ZHPCON', info, 0, uplo, n, n, -1,
548  $ -1, -1, imat, nfail, nerrs, nout )
549 *
550  result( 8 ) = dget06( rcond, rcondc )
551 *
552 * Print the test ratio if it is .GE. THRESH.
553 *
554  IF( result( 8 ).GE.thresh ) THEN
555  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
556  $ CALL alahd( nout, path )
557  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
558  $ result( 8 )
559  nfail = nfail + 1
560  END IF
561  nrun = nrun + 1
562  150 continue
563  160 continue
564  170 continue
565 *
566 * Print a summary of the results.
567 *
568  CALL alasum( path, nout, nfail, nrun, nerrs )
569 *
570  9999 format( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
571  $ i2, ', ratio =', g12.5 )
572  9998 format( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
573  $ i2, ', test(', i2, ') =', g12.5 )
574  return
575 *
576 * End of ZCHKHP
577 *
578  END