LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dchkpo.f
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1 *> \brief \b DCHKPO
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 DCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
12 * THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
13 * XACT, WORK, RWORK, IWORK, 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 IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] DOTYPE
40 *> \verbatim
41 *> DOTYPE is LOGICAL array, dimension (NTYPES)
42 *> The matrix types to be used for testing. Matrices of type j
43 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
44 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
45 *> \endverbatim
46 *>
47 *> \param[in] NN
48 *> \verbatim
49 *> NN is INTEGER
50 *> The number of values of N contained in the vector NVAL.
51 *> \endverbatim
52 *>
53 *> \param[in] NVAL
54 *> \verbatim
55 *> NVAL is INTEGER array, dimension (NN)
56 *> The values of the matrix dimension N.
57 *> \endverbatim
58 *>
59 *> \param[in] NNB
60 *> \verbatim
61 *> NNB is INTEGER
62 *> The number of values of NB contained in the vector NBVAL.
63 *> \endverbatim
64 *>
65 *> \param[in] NBVAL
66 *> \verbatim
67 *> NBVAL is INTEGER array, dimension (NNB)
68 *> The values of the blocksize NB.
69 *> \endverbatim
70 *>
71 *> \param[in] NNS
72 *> \verbatim
73 *> NNS is INTEGER
74 *> The number of values of NRHS contained in the vector NSVAL.
75 *> \endverbatim
76 *>
77 *> \param[in] NSVAL
78 *> \verbatim
79 *> NSVAL is INTEGER array, dimension (NNS)
80 *> The values of the number of right hand sides NRHS.
81 *> \endverbatim
82 *>
83 *> \param[in] THRESH
84 *> \verbatim
85 *> THRESH is DOUBLE PRECISION
86 *> The threshold value for the test ratios. A result is
87 *> included in the output file if RESULT >= THRESH. To have
88 *> every test ratio printed, use THRESH = 0.
89 *> \endverbatim
90 *>
91 *> \param[in] TSTERR
92 *> \verbatim
93 *> TSTERR is LOGICAL
94 *> Flag that indicates whether error exits are to be tested.
95 *> \endverbatim
96 *>
97 *> \param[in] NMAX
98 *> \verbatim
99 *> NMAX is INTEGER
100 *> The maximum value permitted for N, used in dimensioning the
101 *> work arrays.
102 *> \endverbatim
103 *>
104 *> \param[out] A
105 *> \verbatim
106 *> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
107 *> \endverbatim
108 *>
109 *> \param[out] AFAC
110 *> \verbatim
111 *> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
112 *> \endverbatim
113 *>
114 *> \param[out] AINV
115 *> \verbatim
116 *> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
117 *> \endverbatim
118 *>
119 *> \param[out] B
120 *> \verbatim
121 *> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
122 *> where NSMAX is the largest entry in NSVAL.
123 *> \endverbatim
124 *>
125 *> \param[out] X
126 *> \verbatim
127 *> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
128 *> \endverbatim
129 *>
130 *> \param[out] XACT
131 *> \verbatim
132 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
133 *> \endverbatim
134 *>
135 *> \param[out] WORK
136 *> \verbatim
137 *> WORK is DOUBLE PRECISION array, dimension
138 *> (NMAX*max(3,NSMAX))
139 *> \endverbatim
140 *>
141 *> \param[out] RWORK
142 *> \verbatim
143 *> RWORK is DOUBLE PRECISION array, dimension
144 *> (max(NMAX,2*NSMAX))
145 *> \endverbatim
146 *>
147 *> \param[out] IWORK
148 *> \verbatim
149 *> IWORK is INTEGER array, dimension (NMAX)
150 *> \endverbatim
151 *>
152 *> \param[in] NOUT
153 *> \verbatim
154 *> NOUT is INTEGER
155 *> The unit number for output.
156 *> \endverbatim
157 *
158 * Authors:
159 * ========
160 *
161 *> \author Univ. of Tennessee
162 *> \author Univ. of California Berkeley
163 *> \author Univ. of Colorado Denver
164 *> \author NAG Ltd.
165 *
166 *> \ingroup double_lin
167 *
168 * =====================================================================
169  SUBROUTINE dchkpo( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
170  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
171  $ XACT, WORK, RWORK, IWORK, NOUT )
172 *
173 * -- LAPACK test routine --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 *
177 * .. Scalar Arguments ..
178  LOGICAL TSTERR
179  INTEGER NMAX, NN, NNB, NNS, NOUT
180  DOUBLE PRECISION THRESH
181 * ..
182 * .. Array Arguments ..
183  LOGICAL DOTYPE( * )
184  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
185  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
186  $ rwork( * ), work( * ), x( * ), xact( * )
187 * ..
188 *
189 * =====================================================================
190 *
191 * .. Parameters ..
192  DOUBLE PRECISION ZERO
193  PARAMETER ( ZERO = 0.0d+0 )
194  INTEGER NTYPES
195  parameter( ntypes = 9 )
196  INTEGER NTESTS
197  parameter( ntests = 8 )
198 * ..
199 * .. Local Scalars ..
200  LOGICAL ZEROT
201  CHARACTER DIST, TYPE, UPLO, XTYPE
202  CHARACTER*3 PATH
203  INTEGER I, IMAT, IN, INB, INFO, IOFF, IRHS, IUPLO,
204  $ izero, k, kl, ku, lda, mode, n, nb, nerrs,
205  $ nfail, nimat, nrhs, nrun
206  DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
207 * ..
208 * .. Local Arrays ..
209  CHARACTER UPLOS( 2 )
210  INTEGER ISEED( 4 ), ISEEDY( 4 )
211  DOUBLE PRECISION RESULT( NTESTS )
212 * ..
213 * .. External Functions ..
214  DOUBLE PRECISION DGET06, DLANSY
215  EXTERNAL DGET06, DLANSY
216 * ..
217 * .. External Subroutines ..
218  EXTERNAL alaerh, alahd, alasum, derrpo, dget04, dlacpy,
221  $ xlaenv
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 * .. Intrinsic Functions ..
233  INTRINSIC max
234 * ..
235 * .. Data statements ..
236  DATA iseedy / 1988, 1989, 1990, 1991 /
237  DATA uplos / 'U', 'L' /
238 * ..
239 * .. Executable Statements ..
240 *
241 * Initialize constants and the random number seed.
242 *
243  path( 1: 1 ) = 'Double precision'
244  path( 2: 3 ) = 'PO'
245  nrun = 0
246  nfail = 0
247  nerrs = 0
248  DO 10 i = 1, 4
249  iseed( i ) = iseedy( i )
250  10 CONTINUE
251 *
252 * Test the error exits
253 *
254  IF( tsterr )
255  $ CALL derrpo( path, nout )
256  infot = 0
257  CALL xlaenv( 2, 2 )
258 *
259 * Do for each value of N in NVAL
260 *
261  DO 120 in = 1, nn
262  n = nval( in )
263  lda = max( n, 1 )
264  xtype = 'N'
265  nimat = ntypes
266  IF( n.LE.0 )
267  $ nimat = 1
268 *
269  izero = 0
270  DO 110 imat = 1, nimat
271 *
272 * Do the tests only if DOTYPE( IMAT ) is true.
273 *
274  IF( .NOT.dotype( imat ) )
275  $ GO TO 110
276 *
277 * Skip types 3, 4, or 5 if the matrix size is too small.
278 *
279  zerot = imat.GE.3 .AND. imat.LE.5
280  IF( zerot .AND. n.LT.imat-2 )
281  $ GO TO 110
282 *
283 * Do first for UPLO = 'U', then for UPLO = 'L'
284 *
285  DO 100 iuplo = 1, 2
286  uplo = uplos( iuplo )
287 *
288 * Set up parameters with DLATB4 and generate a test matrix
289 * with DLATMS.
290 *
291  CALL dlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
292  $ cndnum, dist )
293 *
294  srnamt = 'DLATMS'
295  CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
296  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
297  $ info )
298 *
299 * Check error code from DLATMS.
300 *
301  IF( info.NE.0 ) THEN
302  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
303  $ -1, -1, imat, nfail, nerrs, nout )
304  GO TO 100
305  END IF
306 *
307 * For types 3-5, zero one row and column of the matrix to
308 * test that INFO is returned correctly.
309 *
310  IF( zerot ) THEN
311  IF( imat.EQ.3 ) THEN
312  izero = 1
313  ELSE IF( imat.EQ.4 ) THEN
314  izero = n
315  ELSE
316  izero = n / 2 + 1
317  END IF
318  ioff = ( izero-1 )*lda
319 *
320 * Set row and column IZERO of A to 0.
321 *
322  IF( iuplo.EQ.1 ) THEN
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 + lda
330  30 CONTINUE
331  ELSE
332  ioff = izero
333  DO 40 i = 1, izero - 1
334  a( ioff ) = zero
335  ioff = ioff + lda
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  izero = 0
344  END IF
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 dlacpy( uplo, n, n, a, lda, afac, lda )
355  srnamt = 'DPOTRF'
356  CALL dpotrf( uplo, n, afac, lda, info )
357 *
358 * Check error code from DPOTRF.
359 *
360  IF( info.NE.izero ) THEN
361  CALL alaerh( path, 'DPOTRF', 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 dlacpy( uplo, n, n, afac, lda, ainv, lda )
376  CALL dpot01( 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 dlacpy( uplo, n, n, afac, lda, ainv, lda )
383  srnamt = 'DPOTRI'
384  CALL dpotri( uplo, n, ainv, lda, info )
385 *
386 * Check error code from DPOTRI.
387 *
388  IF( info.NE.0 )
389  $ CALL alaerh( path, 'DPOTRI', info, 0, uplo, n, n,
390  $ -1, -1, -1, imat, nfail, nerrs, nout )
391 *
392  CALL dpot03( 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 = 'DLARHS'
422  CALL dlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
423  $ nrhs, a, lda, xact, lda, b, lda,
424  $ iseed, info )
425  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
426 *
427  srnamt = 'DPOTRS'
428  CALL dpotrs( uplo, n, nrhs, afac, lda, x, lda,
429  $ info )
430 *
431 * Check error code from DPOTRS.
432 *
433  IF( info.NE.0 )
434  $ CALL alaerh( path, 'DPOTRS', info, 0, uplo, n,
435  $ n, -1, -1, nrhs, imat, nfail,
436  $ nerrs, nout )
437 *
438  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
439  CALL dpot02( 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 dget04( 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 = 'DPORFS'
452  CALL dporfs( uplo, n, nrhs, a, lda, afac, lda, b,
453  $ lda, x, lda, rwork, rwork( nrhs+1 ),
454  $ work, iwork, info )
455 *
456 * Check error code from DPORFS.
457 *
458  IF( info.NE.0 )
459  $ CALL alaerh( path, 'DPORFS', info, 0, uplo, n,
460  $ n, -1, -1, nrhs, imat, nfail,
461  $ nerrs, nout )
462 *
463  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
464  $ result( 5 ) )
465  CALL dpot05( 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 = dlansy( '1', uplo, n, a, lda, rwork )
488  srnamt = 'DPOCON'
489  CALL dpocon( uplo, n, afac, lda, anorm, rcond, work,
490  $ iwork, info )
491 *
492 * Check error code from DPOCON.
493 *
494  IF( info.NE.0 )
495  $ CALL alaerh( path, 'DPOCON', 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 DCHKPO
528 *
529  END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
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 dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:205
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:102
subroutine dpot01(UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
DPOT01
Definition: dpot01.f:104
subroutine derrpo(PATH, NUNIT)
DERRPO
Definition: derrpo.f:55
subroutine dpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DPOT02
Definition: dpot02.f:127
subroutine dpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
DPOT03
Definition: dpot03.f:125
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:120
subroutine dpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPOT05
Definition: dpot05.f:164
subroutine dchkpo(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKPO
Definition: dchkpo.f:172
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dporfs(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DPORFS
Definition: dporfs.f:183
subroutine dpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOTRS
Definition: dpotrs.f:110
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:107
subroutine dpocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
DPOCON
Definition: dpocon.f:121
subroutine dpotri(UPLO, N, A, LDA, INFO)
DPOTRI
Definition: dpotri.f:95