LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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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,
219 $ dlarhs, dlatb4, dlatms, dpocon, dporfs, dpot01,
220 $ dpot02, dpot03, dpot05, dpotrf, dpotri, dpotrs,
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
alasum
subroutine alasum(type, nout, nfail, nrun, nerrs)
ALASUM
Definition alasum.f:73
dlarhs
subroutine dlarhs(path, xtype, uplo, trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, iseed, info)
DLARHS
Definition dlarhs.f:205
xlaenv
subroutine xlaenv(ispec, nvalue)
XLAENV
Definition xlaenv.f:81
alaerh
subroutine alaerh(path, subnam, info, infoe, opts, m, n, kl, ku, n5, imat, nfail, nerrs, nout)
ALAERH
Definition alaerh.f:147
alahd
subroutine alahd(iounit, path)
ALAHD
Definition alahd.f:107
dchkpo
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
derrpo
subroutine derrpo(path, nunit)
DERRPO
Definition derrpo.f:55
dget04
subroutine dget04(n, nrhs, x, ldx, xact, ldxact, rcond, resid)
DGET04
Definition dget04.f:102
dlatb4
subroutine dlatb4(path, imat, m, n, type, kl, ku, anorm, mode, cndnum, dist)
DLATB4
Definition dlatb4.f:120
dlatms
subroutine dlatms(m, n, dist, iseed, sym, d, mode, cond, dmax, kl, ku, pack, a, lda, work, info)
DLATMS
Definition dlatms.f:321
dpot01
subroutine dpot01(uplo, n, a, lda, afac, ldafac, rwork, resid)
DPOT01
Definition dpot01.f:104
dpot02
subroutine dpot02(uplo, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
DPOT02
Definition dpot02.f:127
dpot03
subroutine dpot03(uplo, n, a, lda, ainv, ldainv, work, ldwork, rwork, rcond, resid)
DPOT03
Definition dpot03.f:125
dpot05
subroutine dpot05(uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)
DPOT05
Definition dpot05.f:164
dlacpy
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
dpocon
subroutine dpocon(uplo, n, a, lda, anorm, rcond, work, iwork, info)
DPOCON
Definition dpocon.f:121
dporfs
subroutine dporfs(uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPORFS
Definition dporfs.f:183
dpotrf
subroutine dpotrf(uplo, n, a, lda, info)
DPOTRF
Definition dpotrf.f:107
dpotri
subroutine dpotri(uplo, n, a, lda, info)
DPOTRI
Definition dpotri.f:95
dpotrs
subroutine dpotrs(uplo, n, nrhs, a, lda, b, ldb, info)
DPOTRS
Definition dpotrs.f:110