LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zchkhp.f
Go to the documentation of this file.
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 *> \ingroup complex16_lin
159 *
160 * =====================================================================
161  SUBROUTINE zchkhp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
162  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
163  $ IWORK, NOUT )
164 *
165 * -- LAPACK test routine --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 *
169 * .. Scalar Arguments ..
170  LOGICAL TSTERR
171  INTEGER NMAX, NN, NNS, NOUT
172  DOUBLE PRECISION THRESH
173 * ..
174 * .. Array Arguments ..
175  LOGICAL DOTYPE( * )
176  INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
177  DOUBLE PRECISION RWORK( * )
178  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
179  $ work( * ), x( * ), xact( * )
180 * ..
181 *
182 * =====================================================================
183 *
184 * .. Parameters ..
185  DOUBLE PRECISION ZERO
186  PARAMETER ( ZERO = 0.0d+0 )
187  INTEGER NTYPES
188  parameter( ntypes = 10 )
189  INTEGER NTESTS
190  parameter( ntests = 8 )
191 * ..
192 * .. Local Scalars ..
193  LOGICAL TRFCON, ZEROT
194  CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
195  CHARACTER*3 PATH
196  INTEGER I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
197  $ izero, j, k, kl, ku, lda, mode, n, nerrs,
198  $ nfail, nimat, npp, nrhs, nrun, nt
199  DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
200 * ..
201 * .. Local Arrays ..
202  CHARACTER UPLOS( 2 )
203  INTEGER ISEED( 4 ), ISEEDY( 4 )
204  DOUBLE PRECISION RESULT( NTESTS )
205 * ..
206 * .. External Functions ..
207  LOGICAL LSAME
208  DOUBLE PRECISION DGET06, ZLANHP
209  EXTERNAL lsame, dget06, zlanhp
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL alaerh, alahd, alasum, zcopy, zerrsy, zget04,
215  $ zppt03, zppt05
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC max, min
219 * ..
220 * .. Scalars in Common ..
221  LOGICAL LERR, OK
222  CHARACTER*32 SRNAMT
223  INTEGER INFOT, NUNIT
224 * ..
225 * .. Common blocks ..
226  COMMON / infoc / infot, nunit, ok, lerr
227  COMMON / srnamc / srnamt
228 * ..
229 * .. Data statements ..
230  DATA iseedy / 1988, 1989, 1990, 1991 /
231  DATA uplos / 'U', 'L' /
232 * ..
233 * .. Executable Statements ..
234 *
235 * Initialize constants and the random number seed.
236 *
237  path( 1: 1 ) = 'Zomplex precision'
238  path( 2: 3 ) = 'HP'
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 zerrsy( path, nout )
250  infot = 0
251 *
252 * Do for each value of N in NVAL
253 *
254  DO 170 in = 1, nn
255  n = nval( in )
256  lda = max( n, 1 )
257  xtype = 'N'
258  nimat = ntypes
259  IF( n.LE.0 )
260  $ nimat = 1
261 *
262  izero = 0
263  DO 160 imat = 1, nimat
264 *
265 * Do the tests only if DOTYPE( IMAT ) is true.
266 *
267  IF( .NOT.dotype( imat ) )
268  $ GO TO 160
269 *
270 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
271 *
272  zerot = imat.GE.3 .AND. imat.LE.6
273  IF( zerot .AND. n.LT.imat-2 )
274  $ GO TO 160
275 *
276 * Do first for UPLO = 'U', then for UPLO = 'L'
277 *
278  DO 150 iuplo = 1, 2
279  uplo = uplos( iuplo )
280  IF( lsame( uplo, 'U' ) ) THEN
281  packit = 'C'
282  ELSE
283  packit = 'R'
284  END IF
285 *
286 * Set up parameters with ZLATB4 and generate a test matrix
287 * with ZLATMS.
288 *
289  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
290  $ cndnum, dist )
291 *
292  srnamt = 'ZLATMS'
293  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
294  $ cndnum, anorm, kl, ku, packit, a, lda, work,
295  $ info )
296 *
297 * Check error code from ZLATMS.
298 *
299  IF( info.NE.0 ) THEN
300  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
301  $ -1, -1, imat, nfail, nerrs, nout )
302  GO TO 150
303  END IF
304 *
305 * For types 3-6, zero one or more rows and columns of
306 * the matrix to test that INFO is returned correctly.
307 *
308  IF( zerot ) THEN
309  IF( imat.EQ.3 ) THEN
310  izero = 1
311  ELSE IF( imat.EQ.4 ) THEN
312  izero = n
313  ELSE
314  izero = n / 2 + 1
315  END IF
316 *
317  IF( imat.LT.6 ) THEN
318 *
319 * Set row and column IZERO to zero.
320 *
321  IF( iuplo.EQ.1 ) THEN
322  ioff = ( izero-1 )*izero / 2
323  DO 20 i = 1, izero - 1
324  a( ioff+i ) = zero
325  20 CONTINUE
326  ioff = ioff + izero
327  DO 30 i = izero, n
328  a( ioff ) = zero
329  ioff = ioff + i
330  30 CONTINUE
331  ELSE
332  ioff = izero
333  DO 40 i = 1, izero - 1
334  a( ioff ) = zero
335  ioff = ioff + n - i
336  40 CONTINUE
337  ioff = ioff - izero
338  DO 50 i = izero, n
339  a( ioff+i ) = zero
340  50 CONTINUE
341  END IF
342  ELSE
343  ioff = 0
344  IF( iuplo.EQ.1 ) THEN
345 *
346 * Set the first IZERO rows and columns to zero.
347 *
348  DO 70 j = 1, n
349  i2 = min( j, izero )
350  DO 60 i = 1, i2
351  a( ioff+i ) = zero
352  60 CONTINUE
353  ioff = ioff + j
354  70 CONTINUE
355  ELSE
356 *
357 * Set the last IZERO rows and columns to zero.
358 *
359  DO 90 j = 1, n
360  i1 = max( j, izero )
361  DO 80 i = i1, n
362  a( ioff+i ) = zero
363  80 CONTINUE
364  ioff = ioff + n - j
365  90 CONTINUE
366  END IF
367  END IF
368  ELSE
369  izero = 0
370  END IF
371 *
372 * Set the imaginary part of the diagonals.
373 *
374  IF( iuplo.EQ.1 ) THEN
375  CALL zlaipd( n, a, 2, 1 )
376  ELSE
377  CALL zlaipd( n, a, n, -1 )
378  END IF
379 *
380 * Compute the L*D*L' or U*D*U' factorization of the matrix.
381 *
382  npp = n*( n+1 ) / 2
383  CALL zcopy( npp, a, 1, afac, 1 )
384  srnamt = 'ZHPTRF'
385  CALL zhptrf( uplo, n, afac, iwork, info )
386 *
387 * Adjust the expected value of INFO to account for
388 * pivoting.
389 *
390  k = izero
391  IF( k.GT.0 ) THEN
392  100 CONTINUE
393  IF( iwork( k ).LT.0 ) THEN
394  IF( iwork( k ).NE.-k ) THEN
395  k = -iwork( k )
396  GO TO 100
397  END IF
398  ELSE IF( iwork( k ).NE.k ) THEN
399  k = iwork( k )
400  GO TO 100
401  END IF
402  END IF
403 *
404 * Check error code from ZHPTRF.
405 *
406  IF( info.NE.k )
407  $ CALL alaerh( path, 'ZHPTRF', info, k, uplo, n, n, -1,
408  $ -1, -1, imat, nfail, nerrs, nout )
409  IF( info.NE.0 ) THEN
410  trfcon = .true.
411  ELSE
412  trfcon = .false.
413  END IF
414 *
415 *+ TEST 1
416 * Reconstruct matrix from factors and compute residual.
417 *
418  CALL zhpt01( uplo, n, a, afac, iwork, ainv, lda, rwork,
419  $ result( 1 ) )
420  nt = 1
421 *
422 *+ TEST 2
423 * Form the inverse and compute the residual.
424 *
425  IF( .NOT.trfcon ) THEN
426  CALL zcopy( npp, afac, 1, ainv, 1 )
427  srnamt = 'ZHPTRI'
428  CALL zhptri( uplo, n, ainv, iwork, work, info )
429 *
430 * Check error code from ZHPTRI.
431 *
432  IF( info.NE.0 )
433  $ CALL alaerh( path, 'ZHPTRI', info, 0, uplo, n, n,
434  $ -1, -1, -1, imat, nfail, nerrs, nout )
435 *
436  CALL zppt03( uplo, n, a, ainv, work, lda, rwork,
437  $ rcondc, result( 2 ) )
438  nt = 2
439  END IF
440 *
441 * Print information about the tests that did not pass
442 * the threshold.
443 *
444  DO 110 k = 1, nt
445  IF( result( k ).GE.thresh ) THEN
446  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
447  $ CALL alahd( nout, path )
448  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
449  $ result( k )
450  nfail = nfail + 1
451  END IF
452  110 CONTINUE
453  nrun = nrun + nt
454 *
455 * Do only the condition estimate if INFO is not 0.
456 *
457  IF( trfcon ) THEN
458  rcondc = zero
459  GO TO 140
460  END IF
461 *
462  DO 130 irhs = 1, nns
463  nrhs = nsval( irhs )
464 *
465 *+ TEST 3
466 * Solve and compute residual for A * X = B.
467 *
468  srnamt = 'ZLARHS'
469  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
470  $ nrhs, a, lda, xact, lda, b, lda, iseed,
471  $ info )
472  xtype = 'C'
473  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
474 *
475  srnamt = 'ZHPTRS'
476  CALL zhptrs( uplo, n, nrhs, afac, iwork, x, lda,
477  $ info )
478 *
479 * Check error code from ZHPTRS.
480 *
481  IF( info.NE.0 )
482  $ CALL alaerh( path, 'ZHPTRS', info, 0, uplo, n, n,
483  $ -1, -1, nrhs, imat, nfail, nerrs,
484  $ nout )
485 *
486  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
487  CALL zppt02( uplo, n, nrhs, a, x, lda, work, lda,
488  $ rwork, result( 3 ) )
489 *
490 *+ TEST 4
491 * Check solution from generated exact solution.
492 *
493  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
494  $ result( 4 ) )
495 *
496 *+ TESTS 5, 6, and 7
497 * Use iterative refinement to improve the solution.
498 *
499  srnamt = 'ZHPRFS'
500  CALL zhprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
501  $ lda, rwork, rwork( nrhs+1 ), work,
502  $ rwork( 2*nrhs+1 ), info )
503 *
504 * Check error code from ZHPRFS.
505 *
506  IF( info.NE.0 )
507  $ CALL alaerh( path, 'ZHPRFS', info, 0, uplo, n, n,
508  $ -1, -1, nrhs, imat, nfail, nerrs,
509  $ nout )
510 *
511  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
512  $ result( 5 ) )
513  CALL zppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
514  $ lda, rwork, rwork( nrhs+1 ),
515  $ result( 6 ) )
516 *
517 * Print information about the tests that did not pass
518 * the threshold.
519 *
520  DO 120 k = 3, 7
521  IF( result( k ).GE.thresh ) THEN
522  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
523  $ CALL alahd( nout, path )
524  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
525  $ k, result( k )
526  nfail = nfail + 1
527  END IF
528  120 CONTINUE
529  nrun = nrun + 5
530  130 CONTINUE
531 *
532 *+ TEST 8
533 * Get an estimate of RCOND = 1/CNDNUM.
534 *
535  140 CONTINUE
536  anorm = zlanhp( '1', uplo, n, a, rwork )
537  srnamt = 'ZHPCON'
538  CALL zhpcon( uplo, n, afac, iwork, anorm, rcond, work,
539  $ info )
540 *
541 * Check error code from ZHPCON.
542 *
543  IF( info.NE.0 )
544  $ CALL alaerh( path, 'ZHPCON', info, 0, uplo, n, n, -1,
545  $ -1, -1, imat, nfail, nerrs, nout )
546 *
547  result( 8 ) = dget06( rcond, rcondc )
548 *
549 * Print the test ratio if it is .GE. THRESH.
550 *
551  IF( result( 8 ).GE.thresh ) THEN
552  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
553  $ CALL alahd( nout, path )
554  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
555  $ result( 8 )
556  nfail = nfail + 1
557  END IF
558  nrun = nrun + 1
559  150 CONTINUE
560  160 CONTINUE
561  170 CONTINUE
562 *
563 * Print a summary of the results.
564 *
565  CALL alasum( path, nout, nfail, nrun, nerrs )
566 *
567  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
568  $ i2, ', ratio =', g12.5 )
569  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
570  $ i2, ', test(', i2, ') =', g12.5 )
571  RETURN
572 *
573 * End of ZCHKHP
574 *
575  END
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:208
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:102
subroutine zppt03(UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPPT03
Definition: zppt03.f:110
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:83
subroutine zppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
ZPPT02
Definition: zppt02.f:123
subroutine zppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPPT05
Definition: zppt05.f:157
subroutine zchkhp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
ZCHKHP
Definition: zchkhp.f:164
subroutine zhpt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
ZHPT01
Definition: zhpt01.f:113
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:121
subroutine zerrsy(PATH, NUNIT)
ZERRSY
Definition: zerrsy.f:55
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:332
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
subroutine zhpcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO)
ZHPCON
Definition: zhpcon.f:118
subroutine zhptrf(UPLO, N, AP, IPIV, INFO)
ZHPTRF
Definition: zhptrf.f:159
subroutine zhptri(UPLO, N, AP, IPIV, WORK, INFO)
ZHPTRI
Definition: zhptri.f:109
subroutine zhprfs(UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZHPRFS
Definition: zhprfs.f:180
subroutine zhptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
ZHPTRS
Definition: zhptrs.f:115