LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zchktp.f
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1 *> \brief \b ZCHKTP
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 ZCHKTP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
12 * NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
13 * 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 NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION RWORK( * )
24 * COMPLEX*16 AINVP( * ), AP( * ), B( * ), WORK( * ), X( * ),
25 * \$ XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> ZCHKTP tests ZTPTRI, -TRS, -RFS, and -CON, and ZLATPS
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 column 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 leading dimension of the work arrays. NMAX >= the
90 *> maximumm value of N in NVAL.
91 *> \endverbatim
92 *>
93 *> \param[out] AP
94 *> \verbatim
95 *> AP is COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2)
96 *> \endverbatim
97 *>
98 *> \param[out] AINVP
99 *> \verbatim
100 *> AINVP 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*NSMAX)
106 *> where NSMAX is the largest entry in NSVAL.
107 *> \endverbatim
108 *>
109 *> \param[out] X
110 *> \verbatim
111 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
112 *> \endverbatim
113 *>
114 *> \param[out] XACT
115 *> \verbatim
116 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
117 *> \endverbatim
118 *>
119 *> \param[out] WORK
120 *> \verbatim
121 *> WORK is COMPLEX*16 array, dimension
122 *> (NMAX*max(3,NSMAX))
123 *> \endverbatim
124 *>
125 *> \param[out] RWORK
126 *> \verbatim
127 *> RWORK is DOUBLE PRECISION array, dimension
128 *> (max(NMAX,2*NSMAX))
129 *> \endverbatim
130 *>
131 *> \param[in] NOUT
132 *> \verbatim
133 *> NOUT is INTEGER
134 *> The unit number for output.
135 *> \endverbatim
136 *
137 * Authors:
138 * ========
139 *
140 *> \author Univ. of Tennessee
141 *> \author Univ. of California Berkeley
142 *> \author Univ. of Colorado Denver
143 *> \author NAG Ltd.
144 *
145 *> \ingroup complex16_lin
146 *
147 * =====================================================================
148  SUBROUTINE zchktp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
149  \$ NMAX, AP, AINVP, B, X, XACT, WORK, RWORK,
150  \$ NOUT )
151 *
152 * -- LAPACK test routine --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 *
156 * .. Scalar Arguments ..
157  LOGICAL TSTERR
158  INTEGER NMAX, NN, NNS, NOUT
159  DOUBLE PRECISION THRESH
160 * ..
161 * .. Array Arguments ..
162  LOGICAL DOTYPE( * )
163  INTEGER NSVAL( * ), NVAL( * )
164  DOUBLE PRECISION RWORK( * )
165  COMPLEX*16 AINVP( * ), AP( * ), B( * ), WORK( * ), X( * ),
166  \$ xact( * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  INTEGER NTYPE1, NTYPES
173  PARAMETER ( NTYPE1 = 10, ntypes = 18 )
174  INTEGER NTESTS
175  parameter( ntests = 9 )
176  INTEGER NTRAN
177  parameter( ntran = 3 )
178  DOUBLE PRECISION ONE, ZERO
179  parameter( one = 1.0d+0, zero = 0.0d+0 )
180 * ..
181 * .. Local Scalars ..
182  CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
183  CHARACTER*3 PATH
184  INTEGER I, IDIAG, IMAT, IN, INFO, IRHS, ITRAN, IUPLO,
185  \$ k, lap, lda, n, nerrs, nfail, nrhs, nrun
186  DOUBLE PRECISION AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
187  \$ SCALE
188 * ..
189 * .. Local Arrays ..
190  CHARACTER TRANSS( NTRAN ), UPLOS( 2 )
191  INTEGER ISEED( 4 ), ISEEDY( 4 )
192  DOUBLE PRECISION RESULT( NTESTS )
193 * ..
194 * .. External Functions ..
195  LOGICAL LSAME
196  DOUBLE PRECISION ZLANTP
197  EXTERNAL lsame, zlantp
198 * ..
199 * .. External Subroutines ..
200  EXTERNAL alaerh, alahd, alasum, zcopy, zerrtr, zget04,
203  \$ ztptrs
204 * ..
205 * .. Scalars in Common ..
206  LOGICAL LERR, OK
207  CHARACTER*32 SRNAMT
208  INTEGER INFOT, IOUNIT
209 * ..
210 * .. Common blocks ..
211  COMMON / infoc / infot, iounit, ok, lerr
212  COMMON / srnamc / srnamt
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC max
216 * ..
217 * .. Data statements ..
218  DATA iseedy / 1988, 1989, 1990, 1991 /
219  DATA uplos / 'U', 'L' / , transs / 'N', 'T', 'C' /
220 * ..
221 * .. Executable Statements ..
222 *
223 * Initialize constants and the random number seed.
224 *
225  path( 1: 1 ) = 'Zomplex precision'
226  path( 2: 3 ) = 'TP'
227  nrun = 0
228  nfail = 0
229  nerrs = 0
230  DO 10 i = 1, 4
231  iseed( i ) = iseedy( i )
232  10 CONTINUE
233 *
234 * Test the error exits
235 *
236  IF( tsterr )
237  \$ CALL zerrtr( path, nout )
238  infot = 0
239 *
240  DO 110 in = 1, nn
241 *
242 * Do for each value of N in NVAL
243 *
244  n = nval( in )
245  lda = max( 1, n )
246  lap = lda*( lda+1 ) / 2
247  xtype = 'N'
248 *
249  DO 70 imat = 1, ntype1
250 *
251 * Do the tests only if DOTYPE( IMAT ) is true.
252 *
253  IF( .NOT.dotype( imat ) )
254  \$ GO TO 70
255 *
256  DO 60 iuplo = 1, 2
257 *
258 * Do first for UPLO = 'U', then for UPLO = 'L'
259 *
260  uplo = uplos( iuplo )
261 *
262 * Call ZLATTP to generate a triangular test matrix.
263 *
264  srnamt = 'ZLATTP'
265  CALL zlattp( imat, uplo, 'No transpose', diag, iseed, n,
266  \$ ap, x, work, rwork, info )
267 *
268 * Set IDIAG = 1 for non-unit matrices, 2 for unit.
269 *
270  IF( lsame( diag, 'N' ) ) THEN
271  idiag = 1
272  ELSE
273  idiag = 2
274  END IF
275 *
276 *+ TEST 1
277 * Form the inverse of A.
278 *
279  IF( n.GT.0 )
280  \$ CALL zcopy( lap, ap, 1, ainvp, 1 )
281  srnamt = 'ZTPTRI'
282  CALL ztptri( uplo, diag, n, ainvp, info )
283 *
284 * Check error code from ZTPTRI.
285 *
286  IF( info.NE.0 )
287  \$ CALL alaerh( path, 'ZTPTRI', info, 0, uplo // diag, n,
288  \$ n, -1, -1, -1, imat, nfail, nerrs, nout )
289 *
290 * Compute the infinity-norm condition number of A.
291 *
292  anorm = zlantp( 'I', uplo, diag, n, ap, rwork )
293  ainvnm = zlantp( 'I', uplo, diag, n, ainvp, rwork )
294  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
295  rcondi = one
296  ELSE
297  rcondi = ( one / anorm ) / ainvnm
298  END IF
299 *
300 * Compute the residual for the triangular matrix times its
301 * inverse. Also compute the 1-norm condition number of A.
302 *
303  CALL ztpt01( uplo, diag, n, ap, ainvp, rcondo, rwork,
304  \$ result( 1 ) )
305 *
306 * Print the test ratio if it is .GE. THRESH.
307 *
308  IF( result( 1 ).GE.thresh ) THEN
309  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
310  \$ CALL alahd( nout, path )
311  WRITE( nout, fmt = 9999 )uplo, diag, n, imat, 1,
312  \$ result( 1 )
313  nfail = nfail + 1
314  END IF
315  nrun = nrun + 1
316 *
317  DO 40 irhs = 1, nns
318  nrhs = nsval( irhs )
319  xtype = 'N'
320 *
321  DO 30 itran = 1, ntran
322 *
323 * Do for op(A) = A, A**T, or A**H.
324 *
325  trans = transs( itran )
326  IF( itran.EQ.1 ) THEN
327  norm = 'O'
328  rcondc = rcondo
329  ELSE
330  norm = 'I'
331  rcondc = rcondi
332  END IF
333 *
334 *+ TEST 2
335 * Solve and compute residual for op(A)*x = b.
336 *
337  srnamt = 'ZLARHS'
338  CALL zlarhs( path, xtype, uplo, trans, n, n, 0,
339  \$ idiag, nrhs, ap, lap, xact, lda, b,
340  \$ lda, iseed, info )
341  xtype = 'C'
342  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
343 *
344  srnamt = 'ZTPTRS'
345  CALL ztptrs( uplo, trans, diag, n, nrhs, ap, x,
346  \$ lda, info )
347 *
348 * Check error code from ZTPTRS.
349 *
350  IF( info.NE.0 )
351  \$ CALL alaerh( path, 'ZTPTRS', info, 0,
352  \$ uplo // trans // diag, n, n, -1,
353  \$ -1, -1, imat, nfail, nerrs, nout )
354 *
355  CALL ztpt02( uplo, trans, diag, n, nrhs, ap, x,
356  \$ lda, b, lda, work, rwork,
357  \$ result( 2 ) )
358 *
359 *+ TEST 3
360 * Check solution from generated exact solution.
361 *
362  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
363  \$ result( 3 ) )
364 *
365 *+ TESTS 4, 5, and 6
366 * Use iterative refinement to improve the solution and
367 * compute error bounds.
368 *
369  srnamt = 'ZTPRFS'
370  CALL ztprfs( uplo, trans, diag, n, nrhs, ap, b,
371  \$ lda, x, lda, rwork, rwork( nrhs+1 ),
372  \$ work, rwork( 2*nrhs+1 ), info )
373 *
374 * Check error code from ZTPRFS.
375 *
376  IF( info.NE.0 )
377  \$ CALL alaerh( path, 'ZTPRFS', info, 0,
378  \$ uplo // trans // diag, n, n, -1,
379  \$ -1, nrhs, imat, nfail, nerrs,
380  \$ nout )
381 *
382  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
383  \$ result( 4 ) )
384  CALL ztpt05( uplo, trans, diag, n, nrhs, ap, b,
385  \$ lda, x, lda, xact, lda, rwork,
386  \$ rwork( nrhs+1 ), result( 5 ) )
387 *
388 * Print information about the tests that did not pass
389 * the threshold.
390 *
391  DO 20 k = 2, 6
392  IF( result( k ).GE.thresh ) THEN
393  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
394  \$ CALL alahd( nout, path )
395  WRITE( nout, fmt = 9998 )uplo, trans, diag,
396  \$ n, nrhs, imat, k, result( k )
397  nfail = nfail + 1
398  END IF
399  20 CONTINUE
400  nrun = nrun + 5
401  30 CONTINUE
402  40 CONTINUE
403 *
404 *+ TEST 7
405 * Get an estimate of RCOND = 1/CNDNUM.
406 *
407  DO 50 itran = 1, 2
408  IF( itran.EQ.1 ) THEN
409  norm = 'O'
410  rcondc = rcondo
411  ELSE
412  norm = 'I'
413  rcondc = rcondi
414  END IF
415  srnamt = 'ZTPCON'
416  CALL ztpcon( norm, uplo, diag, n, ap, rcond, work,
417  \$ rwork, info )
418 *
419 * Check error code from ZTPCON.
420 *
421  IF( info.NE.0 )
422  \$ CALL alaerh( path, 'ZTPCON', info, 0,
423  \$ norm // uplo // diag, n, n, -1, -1,
424  \$ -1, imat, nfail, nerrs, nout )
425 *
426  CALL ztpt06( rcond, rcondc, uplo, diag, n, ap, rwork,
427  \$ result( 7 ) )
428 *
429 * Print the test ratio if it is .GE. THRESH.
430 *
431  IF( result( 7 ).GE.thresh ) THEN
432  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
433  \$ CALL alahd( nout, path )
434  WRITE( nout, fmt = 9997 ) 'ZTPCON', norm, uplo,
435  \$ diag, n, imat, 7, result( 7 )
436  nfail = nfail + 1
437  END IF
438  nrun = nrun + 1
439  50 CONTINUE
440  60 CONTINUE
441  70 CONTINUE
442 *
443 * Use pathological test matrices to test ZLATPS.
444 *
445  DO 100 imat = ntype1 + 1, ntypes
446 *
447 * Do the tests only if DOTYPE( IMAT ) is true.
448 *
449  IF( .NOT.dotype( imat ) )
450  \$ GO TO 100
451 *
452  DO 90 iuplo = 1, 2
453 *
454 * Do first for UPLO = 'U', then for UPLO = 'L'
455 *
456  uplo = uplos( iuplo )
457  DO 80 itran = 1, ntran
458 *
459 * Do for op(A) = A, A**T, or A**H.
460 *
461  trans = transs( itran )
462 *
463 * Call ZLATTP to generate a triangular test matrix.
464 *
465  srnamt = 'ZLATTP'
466  CALL zlattp( imat, uplo, trans, diag, iseed, n, ap, x,
467  \$ work, rwork, info )
468 *
469 *+ TEST 8
470 * Solve the system op(A)*x = b.
471 *
472  srnamt = 'ZLATPS'
473  CALL zcopy( n, x, 1, b, 1 )
474  CALL zlatps( uplo, trans, diag, 'N', n, ap, b, scale,
475  \$ rwork, info )
476 *
477 * Check error code from ZLATPS.
478 *
479  IF( info.NE.0 )
480  \$ CALL alaerh( path, 'ZLATPS', info, 0,
481  \$ uplo // trans // diag // 'N', n, n,
482  \$ -1, -1, -1, imat, nfail, nerrs, nout )
483 *
484  CALL ztpt03( uplo, trans, diag, n, 1, ap, scale,
485  \$ rwork, one, b, lda, x, lda, work,
486  \$ result( 8 ) )
487 *
488 *+ TEST 9
489 * Solve op(A)*x = b again with NORMIN = 'Y'.
490 *
491  CALL zcopy( n, x, 1, b( n+1 ), 1 )
492  CALL zlatps( uplo, trans, diag, 'Y', n, ap, b( n+1 ),
493  \$ scale, rwork, info )
494 *
495 * Check error code from ZLATPS.
496 *
497  IF( info.NE.0 )
498  \$ CALL alaerh( path, 'ZLATPS', info, 0,
499  \$ uplo // trans // diag // 'Y', n, n,
500  \$ -1, -1, -1, imat, nfail, nerrs, nout )
501 *
502  CALL ztpt03( uplo, trans, diag, n, 1, ap, scale,
503  \$ rwork, one, b( n+1 ), lda, x, lda, work,
504  \$ result( 9 ) )
505 *
506 * Print information about the tests that did not pass
507 * the threshold.
508 *
509  IF( result( 8 ).GE.thresh ) THEN
510  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
511  \$ CALL alahd( nout, path )
512  WRITE( nout, fmt = 9996 )'ZLATPS', uplo, trans,
513  \$ diag, 'N', n, imat, 8, result( 8 )
514  nfail = nfail + 1
515  END IF
516  IF( result( 9 ).GE.thresh ) THEN
517  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
518  \$ CALL alahd( nout, path )
519  WRITE( nout, fmt = 9996 )'ZLATPS', uplo, trans,
520  \$ diag, 'Y', n, imat, 9, result( 9 )
521  nfail = nfail + 1
522  END IF
523  nrun = nrun + 2
524  80 CONTINUE
525  90 CONTINUE
526  100 CONTINUE
527  110 CONTINUE
528 *
529 * Print a summary of the results.
530 *
531  CALL alasum( path, nout, nfail, nrun, nerrs )
532 *
533  9999 FORMAT( ' UPLO=''', a1, ''', DIAG=''', a1, ''', N=', i5,
534  \$ ', type ', i2, ', test(', i2, ')= ', g12.5 )
535  9998 FORMAT( ' UPLO=''', a1, ''', TRANS=''', a1, ''', DIAG=''', a1,
536  \$ ''', N=', i5, ''', NRHS=', i5, ', type ', i2, ', test(',
537  \$ i2, ')= ', g12.5 )
538  9997 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ''', a1, ''',',
539  \$ i5, ', ... ), type ', i2, ', test(', i2, ')=', g12.5 )
540  9996 FORMAT( 1x, a, '( ''', a1, ''', ''', a1, ''', ''', a1, ''', ''',
541  \$ a1, ''',', i5, ', ... ), type ', i2, ', test(', i2, ')=',
542  \$ g12.5 )
543  RETURN
544 *
545 * End of ZCHKTP
546 *
547  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 zchktp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, NOUT)
ZCHKTP
Definition: zchktp.f:151
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:102
subroutine ztpt05(UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZTPT05
Definition: ztpt05.f:175
subroutine ztpt01(UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID)
ZTPT01
Definition: ztpt01.f:109
subroutine ztpt02(UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RWORK, RESID)
ZTPT02
Definition: ztpt02.f:147
subroutine zlattp(IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK, RWORK, INFO)
ZLATTP
Definition: zlattp.f:131
subroutine ztpt03(UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
ZTPT03
Definition: ztpt03.f:162
subroutine ztpt06(RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
ZTPT06
Definition: ztpt06.f:112
subroutine zerrtr(PATH, NUNIT)
ZERRTR
Definition: zerrtr.f:54
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 zlatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
ZLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: zlatps.f:231
subroutine ztprfs(UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZTPRFS
Definition: ztprfs.f:174
subroutine ztptri(UPLO, DIAG, N, AP, INFO)
ZTPTRI
Definition: ztptri.f:117
subroutine ztpcon(NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO)
ZTPCON
Definition: ztpcon.f:130
subroutine ztptrs(UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO)
ZTPTRS
Definition: ztptrs.f:130