LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
zchkpo.f
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1 *> \brief \b ZCHKPO
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 ZCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, NOUT )
14 *
15 * .. Scalar Arguments ..
16 * LOGICAL TSTERR
17 * INTEGER NMAX, NN, NNB, NNS, NOUT
18 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER NBVAL( * ), 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 *> ZCHKPO tests ZPOTRF, -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] NNB
61 *> \verbatim
62 *> NNB is INTEGER
63 *> The number of values of NB contained in the vector NBVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NBVAL
67 *> \verbatim
68 *> NBVAL is INTEGER array, dimension (NNB)
69 *> The values of the blocksize NB.
70 *> \endverbatim
71 *>
72 *> \param[in] NNS
73 *> \verbatim
74 *> NNS is INTEGER
75 *> The number of values of NRHS contained in the vector NSVAL.
76 *> \endverbatim
77 *>
78 *> \param[in] NSVAL
79 *> \verbatim
80 *> NSVAL is INTEGER array, dimension (NNS)
81 *> The values of the number of right hand sides NRHS.
82 *> \endverbatim
83 *>
84 *> \param[in] THRESH
85 *> \verbatim
86 *> THRESH is DOUBLE PRECISION
87 *> The threshold value for the test ratios. A result is
88 *> included in the output file if RESULT >= THRESH. To have
89 *> every test ratio printed, use THRESH = 0.
90 *> \endverbatim
91 *>
92 *> \param[in] TSTERR
93 *> \verbatim
94 *> TSTERR is LOGICAL
95 *> Flag that indicates whether error exits are to be tested.
96 *> \endverbatim
97 *>
98 *> \param[in] NMAX
99 *> \verbatim
100 *> NMAX is INTEGER
101 *> The maximum value permitted for N, used in dimensioning the
102 *> work arrays.
103 *> \endverbatim
104 *>
105 *> \param[out] A
106 *> \verbatim
107 *> A is COMPLEX*16 array, dimension (NMAX*NMAX)
108 *> \endverbatim
109 *>
110 *> \param[out] AFAC
111 *> \verbatim
112 *> AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)
113 *> \endverbatim
114 *>
115 *> \param[out] AINV
116 *> \verbatim
117 *> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
118 *> \endverbatim
119 *>
120 *> \param[out] B
121 *> \verbatim
122 *> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
123 *> where NSMAX is the largest entry in NSVAL.
124 *> \endverbatim
125 *>
126 *> \param[out] X
127 *> \verbatim
128 *> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
129 *> \endverbatim
130 *>
131 *> \param[out] XACT
132 *> \verbatim
133 *> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
134 *> \endverbatim
135 *>
136 *> \param[out] WORK
137 *> \verbatim
138 *> WORK is COMPLEX*16 array, dimension
139 *> (NMAX*max(3,NSMAX))
140 *> \endverbatim
141 *>
142 *> \param[out] RWORK
143 *> \verbatim
144 *> RWORK is DOUBLE PRECISION array, dimension
145 *> (NMAX+2*NSMAX)
146 *> \endverbatim
147 *>
148 *> \param[in] NOUT
149 *> \verbatim
150 *> NOUT is INTEGER
151 *> The unit number for output.
152 *> \endverbatim
153 *
154 * Authors:
155 * ========
156 *
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
160 *> \author NAG Ltd.
161 *
162 *> \ingroup complex16_lin
163 *
164 * =====================================================================
165  SUBROUTINE zchkpo( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
166  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
167  $ XACT, WORK, RWORK, NOUT )
168 *
169 * -- LAPACK test routine --
170 * -- LAPACK is a software package provided by Univ. of Tennessee, --
171 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172 *
173 * .. Scalar Arguments ..
174  LOGICAL TSTERR
175  INTEGER NMAX, NN, NNB, NNS, NOUT
176  DOUBLE PRECISION THRESH
177 * ..
178 * .. Array Arguments ..
179  LOGICAL DOTYPE( * )
180  INTEGER NBVAL( * ), NSVAL( * ), NVAL( * )
181  DOUBLE PRECISION RWORK( * )
182  COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
183  $ work( * ), x( * ), xact( * )
184 * ..
185 *
186 * =====================================================================
187 *
188 * .. Parameters ..
189  COMPLEX*16 CZERO
190  PARAMETER ( CZERO = ( 0.0d+0, 0.0d+0 ) )
191  INTEGER NTYPES
192  parameter( ntypes = 9 )
193  INTEGER NTESTS
194  parameter( ntests = 8 )
195 * ..
196 * .. Local Scalars ..
197  LOGICAL ZEROT
198  CHARACTER DIST, TYPE, UPLO, XTYPE
199  CHARACTER*3 PATH
200  INTEGER I, IMAT, IN, INB, INFO, IOFF, IRHS, IUPLO,
201  $ izero, k, kl, ku, lda, mode, n, nb, nerrs,
202  $ nfail, nimat, nrhs, nrun
203  DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
204 * ..
205 * .. Local Arrays ..
206  CHARACTER UPLOS( 2 )
207  INTEGER ISEED( 4 ), ISEEDY( 4 )
208  DOUBLE PRECISION RESULT( NTESTS )
209 * ..
210 * .. External Functions ..
211  DOUBLE PRECISION DGET06, ZLANHE
212  EXTERNAL DGET06, ZLANHE
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL alaerh, alahd, alasum, xlaenv, zerrpo, zget04,
218  $ zpotri, zpotrs
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 * .. Intrinsic Functions ..
230  INTRINSIC max
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 ) = 'PO'
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 zerrpo( path, nout )
253  infot = 0
254 *
255 * Do for each value of N in NVAL
256 *
257  DO 120 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 110 imat = 1, nimat
267 *
268 * Do the tests only if DOTYPE( IMAT ) is true.
269 *
270  IF( .NOT.dotype( imat ) )
271  $ GO TO 110
272 *
273 * Skip types 3, 4, or 5 if the matrix size is too small.
274 *
275  zerot = imat.GE.3 .AND. imat.LE.5
276  IF( zerot .AND. n.LT.imat-2 )
277  $ GO TO 110
278 *
279 * Do first for UPLO = 'U', then for UPLO = 'L'
280 *
281  DO 100 iuplo = 1, 2
282  uplo = uplos( iuplo )
283 *
284 * Set up parameters with ZLATB4 and generate a test matrix
285 * with ZLATMS.
286 *
287  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
288  $ cndnum, dist )
289 *
290  srnamt = 'ZLATMS'
291  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
292  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
293  $ info )
294 *
295 * Check error code from ZLATMS.
296 *
297  IF( info.NE.0 ) THEN
298  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
299  $ -1, -1, imat, nfail, nerrs, nout )
300  GO TO 100
301  END IF
302 *
303 * For types 3-5, zero one row and column of the matrix to
304 * test that INFO is returned correctly.
305 *
306  IF( zerot ) THEN
307  IF( imat.EQ.3 ) THEN
308  izero = 1
309  ELSE IF( imat.EQ.4 ) THEN
310  izero = n
311  ELSE
312  izero = n / 2 + 1
313  END IF
314  ioff = ( izero-1 )*lda
315 *
316 * Set row and column IZERO of A to 0.
317 *
318  IF( iuplo.EQ.1 ) THEN
319  DO 20 i = 1, izero - 1
320  a( ioff+i ) = czero
321  20 CONTINUE
322  ioff = ioff + izero
323  DO 30 i = izero, n
324  a( ioff ) = czero
325  ioff = ioff + lda
326  30 CONTINUE
327  ELSE
328  ioff = izero
329  DO 40 i = 1, izero - 1
330  a( ioff ) = czero
331  ioff = ioff + lda
332  40 CONTINUE
333  ioff = ioff - izero
334  DO 50 i = izero, n
335  a( ioff+i ) = czero
336  50 CONTINUE
337  END IF
338  ELSE
339  izero = 0
340  END IF
341 *
342 * Set the imaginary part of the diagonals.
343 *
344  CALL zlaipd( n, a, lda+1, 0 )
345 *
346 * Do for each value of NB in NBVAL
347 *
348  DO 90 inb = 1, nnb
349  nb = nbval( inb )
350  CALL xlaenv( 1, nb )
351 *
352 * Compute the L*L' or U'*U factorization of the matrix.
353 *
354  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
355  srnamt = 'ZPOTRF'
356  CALL zpotrf( uplo, n, afac, lda, info )
357 *
358 * Check error code from ZPOTRF.
359 *
360  IF( info.NE.izero ) THEN
361  CALL alaerh( path, 'ZPOTRF', info, izero, uplo, n,
362  $ n, -1, -1, nb, imat, nfail, nerrs,
363  $ nout )
364  GO TO 90
365  END IF
366 *
367 * Skip the tests if INFO is not 0.
368 *
369  IF( info.NE.0 )
370  $ GO TO 90
371 *
372 *+ TEST 1
373 * Reconstruct matrix from factors and compute residual.
374 *
375  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
376  CALL zpot01( uplo, n, a, lda, ainv, lda, rwork,
377  $ result( 1 ) )
378 *
379 *+ TEST 2
380 * Form the inverse and compute the residual.
381 *
382  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
383  srnamt = 'ZPOTRI'
384  CALL zpotri( uplo, n, ainv, lda, info )
385 *
386 * Check error code from ZPOTRI.
387 *
388  IF( info.NE.0 )
389  $ CALL alaerh( path, 'ZPOTRI', info, 0, uplo, n, n,
390  $ -1, -1, -1, imat, nfail, nerrs, nout )
391 *
392  CALL zpot03( uplo, n, a, lda, ainv, lda, work, lda,
393  $ rwork, rcondc, result( 2 ) )
394 *
395 * Print information about the tests that did not pass
396 * the threshold.
397 *
398  DO 60 k = 1, 2
399  IF( result( k ).GE.thresh ) THEN
400  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
401  $ CALL alahd( nout, path )
402  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
403  $ result( k )
404  nfail = nfail + 1
405  END IF
406  60 CONTINUE
407  nrun = nrun + 2
408 *
409 * Skip the rest of the tests unless this is the first
410 * blocksize.
411 *
412  IF( inb.NE.1 )
413  $ GO TO 90
414 *
415  DO 80 irhs = 1, nns
416  nrhs = nsval( irhs )
417 *
418 *+ TEST 3
419 * Solve and compute residual for A * X = B .
420 *
421  srnamt = 'ZLARHS'
422  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
423  $ nrhs, a, lda, xact, lda, b, lda,
424  $ iseed, info )
425  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
426 *
427  srnamt = 'ZPOTRS'
428  CALL zpotrs( uplo, n, nrhs, afac, lda, x, lda,
429  $ info )
430 *
431 * Check error code from ZPOTRS.
432 *
433  IF( info.NE.0 )
434  $ CALL alaerh( path, 'ZPOTRS', info, 0, uplo, n,
435  $ n, -1, -1, nrhs, imat, nfail,
436  $ nerrs, nout )
437 *
438  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
439  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
440  $ lda, rwork, result( 3 ) )
441 *
442 *+ TEST 4
443 * Check solution from generated exact solution.
444 *
445  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
446  $ result( 4 ) )
447 *
448 *+ TESTS 5, 6, and 7
449 * Use iterative refinement to improve the solution.
450 *
451  srnamt = 'ZPORFS'
452  CALL zporfs( uplo, n, nrhs, a, lda, afac, lda, b,
453  $ lda, x, lda, rwork, rwork( nrhs+1 ),
454  $ work, rwork( 2*nrhs+1 ), info )
455 *
456 * Check error code from ZPORFS.
457 *
458  IF( info.NE.0 )
459  $ CALL alaerh( path, 'ZPORFS', info, 0, uplo, n,
460  $ n, -1, -1, nrhs, imat, nfail,
461  $ nerrs, nout )
462 *
463  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
464  $ result( 5 ) )
465  CALL zpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
466  $ xact, lda, rwork, rwork( nrhs+1 ),
467  $ result( 6 ) )
468 *
469 * Print information about the tests that did not pass
470 * the threshold.
471 *
472  DO 70 k = 3, 7
473  IF( result( k ).GE.thresh ) THEN
474  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
475  $ CALL alahd( nout, path )
476  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
477  $ imat, k, result( k )
478  nfail = nfail + 1
479  END IF
480  70 CONTINUE
481  nrun = nrun + 5
482  80 CONTINUE
483 *
484 *+ TEST 8
485 * Get an estimate of RCOND = 1/CNDNUM.
486 *
487  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
488  srnamt = 'ZPOCON'
489  CALL zpocon( uplo, n, afac, lda, anorm, rcond, work,
490  $ rwork, info )
491 *
492 * Check error code from ZPOCON.
493 *
494  IF( info.NE.0 )
495  $ CALL alaerh( path, 'ZPOCON', info, 0, uplo, n, n,
496  $ -1, -1, -1, imat, nfail, nerrs, nout )
497 *
498  result( 8 ) = dget06( rcond, rcondc )
499 *
500 * Print the test ratio if it is .GE. THRESH.
501 *
502  IF( result( 8 ).GE.thresh ) THEN
503  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
504  $ CALL alahd( nout, path )
505  WRITE( nout, fmt = 9997 )uplo, n, imat, 8,
506  $ result( 8 )
507  nfail = nfail + 1
508  END IF
509  nrun = nrun + 1
510  90 CONTINUE
511  100 CONTINUE
512  110 CONTINUE
513  120 CONTINUE
514 *
515 * Print a summary of the results.
516 *
517  CALL alasum( path, nout, nfail, nrun, nerrs )
518 *
519  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
520  $ i2, ', test ', i2, ', ratio =', g12.5 )
521  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
522  $ i2, ', test(', i2, ') =', g12.5 )
523  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
524  $ ', test(', i2, ') =', g12.5 )
525  RETURN
526 *
527 * End of ZCHKPO
528 *
529  END
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
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 zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:208
subroutine zpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPOT03
Definition: zpot03.f:126
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:102
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:83
subroutine zerrpo(PATH, NUNIT)
ZERRPO
Definition: zerrpo.f:55
subroutine zpot01(UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
ZPOT01
Definition: zpot01.f:106
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:127
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:121
subroutine zpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPOT05
Definition: zpot05.f:165
subroutine zchkpo(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
ZCHKPO
Definition: zchkpo.f:168
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 zpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
ZPOTRS
Definition: zpotrs.f:110
subroutine zpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO)
ZPOCON
Definition: zpocon.f:121
subroutine zporfs(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPORFS
Definition: zporfs.f:183
subroutine zpotri(UPLO, N, A, LDA, INFO)
ZPOTRI
Definition: zpotri.f:95
subroutine zpotrf(UPLO, N, A, LDA, INFO)
ZPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.
Definition: zpotrf.f:102