LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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schksy_aa.f
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1*> \brief \b SCHKSY_AA
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 SCHKSY_AA( 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* REAL THRESH
19* ..
20* .. Array Arguments ..
21* LOGICAL DOTYPE( * )
22* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
23* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
24* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25* ..
26*
27*
28*> \par Purpose:
29* =============
30*>
31*> \verbatim
32*>
33*> SCHKSY_AA tests SSYTRF_AA, -TRS_AA.
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 REAL
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 REAL array, dimension (NMAX*NMAX)
107*> \endverbatim
108*>
109*> \param[out] AFAC
110*> \verbatim
111*> AFAC is REAL array, dimension (NMAX*NMAX)
112*> \endverbatim
113*>
114*> \param[out] AINV
115*> \verbatim
116*> AINV is REAL array, dimension (NMAX*NMAX)
117*> \endverbatim
118*>
119*> \param[out] B
120*> \verbatim
121*> B is REAL 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 REAL array, dimension (NMAX*NSMAX)
128*> \endverbatim
129*>
130*> \param[out] XACT
131*> \verbatim
132*> XACT is REAL array, dimension (NMAX*NSMAX)
133*> \endverbatim
134*>
135*> \param[out] WORK
136*> \verbatim
137*> WORK is REAL array, dimension (NMAX*max(3,NSMAX))
138*> \endverbatim
139*>
140*> \param[out] RWORK
141*> \verbatim
142*> RWORK is REAL array, dimension (max(NMAX,2*NSMAX))
143*> \endverbatim
144*>
145*> \param[out] IWORK
146*> \verbatim
147*> IWORK is INTEGER array, dimension (2*NMAX)
148*> \endverbatim
149*>
150*> \param[in] NOUT
151*> \verbatim
152*> NOUT is INTEGER
153*> The unit number for output.
154*> \endverbatim
155*
156* Authors:
157* ========
158*
159*> \author Univ. of Tennessee
160*> \author Univ. of California Berkeley
161*> \author Univ. of Colorado Denver
162*> \author NAG Ltd.
163*
164*> \ingroup real_lin
165*
166* =====================================================================
167 SUBROUTINE schksy_aa( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
168 $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
169 $ X, XACT, WORK, RWORK, IWORK, NOUT )
170*
171* -- LAPACK test routine --
172* -- LAPACK is a software package provided by Univ. of Tennessee, --
173* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174*
175 IMPLICIT NONE
176*
177* .. Scalar Arguments ..
178 LOGICAL TSTERR
179 INTEGER NN, NNB, NNS, NMAX, NOUT
180 REAL THRESH
181* ..
182* .. Array Arguments ..
183 LOGICAL DOTYPE( * )
184 INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
185 REAL A( * ), AFAC( * ), AINV( * ), B( * ),
186 $ rwork( * ), work( * ), x( * ), xact( * )
187* ..
188*
189* =====================================================================
190*
191* .. Parameters ..
192 REAL ZERO
193 PARAMETER ( ZERO = 0.0e+0 )
194 INTEGER NTYPES
195 parameter( ntypes = 10 )
196 INTEGER NTESTS
197 parameter( ntests = 9 )
198* ..
199* .. Local Scalars ..
200 LOGICAL ZEROT
201 CHARACTER DIST, TYPE, UPLO, XTYPE
202 CHARACTER*3 PATH, MATPATH
203 INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
204 $ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
205 $ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
206 REAL ANORM, CNDNUM
207* ..
208* .. Local Arrays ..
209 CHARACTER UPLOS( 2 )
210 INTEGER ISEED( 4 ), ISEEDY( 4 )
211 REAL RESULT( NTESTS )
212* ..
213* .. External Subroutines ..
214 EXTERNAL alaerh, alahd, alasum, serrsy, slacpy, slarhs,
215 $ slatb4, slatms, spot02, ssyt01_aa, ssytrf_aa,
216 $ ssytrs_aa, xlaenv
217* ..
218* .. Intrinsic Functions ..
219 INTRINSIC max, min
220* ..
221* .. Scalars in Common ..
222 LOGICAL LERR, OK
223 CHARACTER*32 SRNAMT
224 INTEGER INFOT, NUNIT
225* ..
226* .. Common blocks ..
227 COMMON / infoc / infot, nunit, ok, lerr
228 COMMON / srnamc / srnamt
229* ..
230* .. Data statements ..
231 DATA iseedy / 1988, 1989, 1990, 1991 /
232 DATA uplos / 'U', 'L' /
233* ..
234* .. Executable Statements ..
235*
236* Initialize constants and the random number seed.
237*
238*
239* Test path
240*
241 path( 1: 1 ) = 'Single precision'
242 path( 2: 3 ) = 'SA'
243*
244* Path to generate matrices
245*
246 matpath( 1: 1 ) = 'Single precision'
247 matpath( 2: 3 ) = 'SY'
248 nrun = 0
249 nfail = 0
250 nerrs = 0
251 DO 10 i = 1, 4
252 iseed( i ) = iseedy( i )
253 10 CONTINUE
254*
255* Test the error exits
256*
257 IF( tsterr )
258 $ CALL serrsy( path, nout )
259 infot = 0
260*
261* Set the minimum block size for which the block routine should
262* be used, which will be later returned by ILAENV
263*
264 CALL xlaenv( 2, 2 )
265*
266* Do for each value of N in NVAL
267*
268 DO 180 in = 1, nn
269 n = nval( in )
270 IF( n .GT. nmax ) THEN
271 nfail = nfail + 1
272 WRITE(nout, 9995) 'M ', n, nmax
273 GO TO 180
274 END IF
275 lda = max( n, 1 )
276 xtype = 'N'
277 nimat = ntypes
278 IF( n.LE.0 )
279 $ nimat = 1
280*
281 izero = 0
282*
283* Do for each value of matrix type IMAT
284*
285 DO 170 imat = 1, nimat
286*
287* Do the tests only if DOTYPE( IMAT ) is true.
288*
289 IF( .NOT.dotype( imat ) )
290 $ GO TO 170
291*
292* Skip types 3, 4, 5, or 6 if the matrix size is too small.
293*
294 zerot = imat.GE.3 .AND. imat.LE.6
295 IF( zerot .AND. n.LT.imat-2 )
296 $ GO TO 170
297*
298* Do first for UPLO = 'U', then for UPLO = 'L'
299*
300 DO 160 iuplo = 1, 2
301 uplo = uplos( iuplo )
302*
303* Begin generate the test matrix A.
304*
305*
306* Set up parameters with SLATB4 for the matrix generator
307* based on the type of matrix to be generated.
308*
309 CALL slatb4( matpath, imat, n, n, TYPE, kl, ku,
310 $ anorm, mode, cndnum, dist )
311*
312* Generate a matrix with SLATMS.
313*
314 srnamt = 'SLATMS'
315 CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
316 $ cndnum, anorm, kl, ku, uplo, a, lda, work,
317 $ info )
318*
319* Check error code from SLATMS and handle error.
320*
321 IF( info.NE.0 ) THEN
322 CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
323 $ -1, -1, imat, nfail, nerrs, nout )
324*
325* Skip all tests for this generated matrix
326*
327 GO TO 160
328 END IF
329*
330* For matrix types 3-6, zero one or more rows and
331* columns of the matrix to test that INFO is returned
332* correctly.
333*
334 IF( zerot ) THEN
335 IF( imat.EQ.3 ) THEN
336 izero = 1
337 ELSE IF( imat.EQ.4 ) THEN
338 izero = n
339 ELSE
340 izero = n / 2 + 1
341 END IF
342*
343 IF( imat.LT.6 ) THEN
344*
345* Set row and column IZERO to zero.
346*
347 IF( iuplo.EQ.1 ) THEN
348 ioff = ( izero-1 )*lda
349 DO 20 i = 1, izero - 1
350 a( ioff+i ) = zero
351 20 CONTINUE
352 ioff = ioff + izero
353 DO 30 i = izero, n
354 a( ioff ) = zero
355 ioff = ioff + lda
356 30 CONTINUE
357 ELSE
358 ioff = izero
359 DO 40 i = 1, izero - 1
360 a( ioff ) = zero
361 ioff = ioff + lda
362 40 CONTINUE
363 ioff = ioff - izero
364 DO 50 i = izero, n
365 a( ioff+i ) = zero
366 50 CONTINUE
367 END IF
368 ELSE
369 IF( iuplo.EQ.1 ) THEN
370*
371* Set the first IZERO rows and columns to zero.
372*
373 ioff = 0
374 DO 70 j = 1, n
375 i2 = min( j, izero )
376 DO 60 i = 1, i2
377 a( ioff+i ) = zero
378 60 CONTINUE
379 ioff = ioff + lda
380 70 CONTINUE
381 izero = 1
382 ELSE
383*
384* Set the last IZERO rows and columns to zero.
385*
386 ioff = 0
387 DO 90 j = 1, n
388 i1 = max( j, izero )
389 DO 80 i = i1, n
390 a( ioff+i ) = zero
391 80 CONTINUE
392 ioff = ioff + lda
393 90 CONTINUE
394 END IF
395 END IF
396 ELSE
397 izero = 0
398 END IF
399*
400* End generate the test matrix A.
401*
402* Do for each value of NB in NBVAL
403*
404 DO 150 inb = 1, nnb
405*
406* Set the optimal blocksize, which will be later
407* returned by ILAENV.
408*
409 nb = nbval( inb )
410 CALL xlaenv( 1, nb )
411*
412* Copy the test matrix A into matrix AFAC which
413* will be factorized in place. This is needed to
414* preserve the test matrix A for subsequent tests.
415*
416 CALL slacpy( uplo, n, n, a, lda, afac, lda )
417*
418* Compute the L*D*L**T or U*D*U**T factorization of the
419* matrix. IWORK stores details of the interchanges and
420* the block structure of D. AINV is a work array for
421* block factorization, LWORK is the length of AINV.
422*
423 srnamt = 'SSYTRF_AA'
424 lwork = max( 1, n*nb + n )
425 CALL ssytrf_aa( uplo, n, afac, lda, iwork, ainv,
426 $ lwork, info )
427*
428* Adjust the expected value of INFO to account for
429* pivoting.
430*
431c IF( IZERO.GT.0 ) THEN
432c J = 1
433c K = IZERO
434c 100 CONTINUE
435c IF( J.EQ.K ) THEN
436c K = IWORK( J )
437c ELSE IF( IWORK( J ).EQ.K ) THEN
438c K = J
439c END IF
440c IF( J.LT.K ) THEN
441c J = J + 1
442c GO TO 100
443c END IF
444c ELSE
445 k = 0
446c END IF
447*
448* Check error code from SSYTRF and handle error.
449*
450 IF( info.NE.k ) THEN
451 CALL alaerh( path, 'SSYTRF_AA', info, k, uplo,
452 $ n, n, -1, -1, nb, imat, nfail, nerrs,
453 $ nout )
454 END IF
455*
456*+ TEST 1
457* Reconstruct matrix from factors and compute residual.
458*
459 CALL ssyt01_aa( uplo, n, a, lda, afac, lda, iwork,
460 $ ainv, lda, rwork, result( 1 ) )
461 nt = 1
462*
463*
464* Print information about the tests that did not pass
465* the threshold.
466*
467 DO 110 k = 1, nt
468 IF( result( k ).GE.thresh ) THEN
469 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
470 $ CALL alahd( nout, path )
471 WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
472 $ result( k )
473 nfail = nfail + 1
474 END IF
475 110 CONTINUE
476 nrun = nrun + nt
477*
478* Skip solver test if INFO is not 0.
479*
480 IF( info.NE.0 ) THEN
481 GO TO 140
482 END IF
483*
484* Do for each value of NRHS in NSVAL.
485*
486 DO 130 irhs = 1, nns
487 nrhs = nsval( irhs )
488*
489*+ TEST 2 (Using TRS)
490* Solve and compute residual for A * X = B.
491*
492* Choose a set of NRHS random solution vectors
493* stored in XACT and set up the right hand side B
494*
495 srnamt = 'SLARHS'
496 CALL slarhs( matpath, xtype, uplo, ' ', n, n,
497 $ kl, ku, nrhs, a, lda, xact, lda,
498 $ b, lda, iseed, info )
499 CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
500*
501 srnamt = 'SSYTRS_AA'
502 lwork = max( 1, 3*n-2 )
503 CALL ssytrs_aa( uplo, n, nrhs, afac, lda,
504 $ iwork, x, lda, work, lwork,
505 $ info )
506*
507* Check error code from SSYTRS and handle error.
508*
509 IF( info.NE.0 ) THEN
510 IF( izero.EQ.0 ) THEN
511 CALL alaerh( path, 'SSYTRS_AA', info, 0,
512 $ uplo, n, n, -1, -1, nrhs, imat,
513 $ nfail, nerrs, nout )
514 END IF
515 ELSE
516 CALL slacpy( 'Full', n, nrhs, b, lda, work, lda
517 $ )
518*
519* Compute the residual for the solution
520*
521 CALL spot02( uplo, n, nrhs, a, lda, x, lda,
522 $ work, lda, rwork, result( 2 ) )
523*
524*
525* Print information about the tests that did not pass
526* the threshold.
527*
528 DO 120 k = 2, 2
529 IF( result( k ).GE.thresh ) THEN
530 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
531 $ CALL alahd( nout, path )
532 WRITE( nout, fmt = 9998 )uplo, n, nrhs,
533 $ imat, k, result( k )
534 nfail = nfail + 1
535 END IF
536 120 CONTINUE
537 END IF
538 nrun = nrun + 1
539*
540* End do for each value of NRHS in NSVAL.
541*
542 130 CONTINUE
543 140 CONTINUE
544 150 CONTINUE
545 160 CONTINUE
546 170 CONTINUE
547 180 CONTINUE
548*
549* Print a summary of the results.
550*
551 CALL alasum( path, nout, nfail, nrun, nerrs )
552*
553 9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
554 $ i2, ', test ', i2, ', ratio =', g12.5 )
555 9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
556 $ i2, ', test(', i2, ') =', g12.5 )
557 9995 FORMAT( ' Invalid input value: ', a4, '=', i6, '; must be <=',
558 $ i6 )
559 RETURN
560*
561* End of SCHKSY_AA
562*
563 END
alasum
subroutine alasum(type, nout, nfail, nrun, nerrs)
ALASUM
Definition alasum.f:73
slarhs
subroutine slarhs(path, xtype, uplo, trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, iseed, info)
SLARHS
Definition slarhs.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
ssytrf_aa
subroutine ssytrf_aa(uplo, n, a, lda, ipiv, work, lwork, info)
SSYTRF_AA
Definition ssytrf_aa.f:132
ssytrs_aa
subroutine ssytrs_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYTRS_AA
Definition ssytrs_aa.f:131
slacpy
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
schksy_aa
subroutine schksy_aa(dotype, nn, nval, nnb, nbval, nns, nsval, thresh, tsterr, nmax, a, afac, ainv, b, x, xact, work, rwork, iwork, nout)
SCHKSY_AA
Definition schksy_aa.f:170
serrsy
subroutine serrsy(path, nunit)
SERRSY
Definition serrsy.f:55
slatb4
subroutine slatb4(path, imat, m, n, type, kl, ku, anorm, mode, cndnum, dist)
SLATB4
Definition slatb4.f:120
slatms
subroutine slatms(m, n, dist, iseed, sym, d, mode, cond, dmax, kl, ku, pack, a, lda, work, info)
SLATMS
Definition slatms.f:321
spot02
subroutine spot02(uplo, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
SPOT02
Definition spot02.f:127
ssyt01_aa
subroutine ssyt01_aa(uplo, n, a, lda, afac, ldafac, ipiv, c, ldc, rwork, resid)
SSYT01_AA
Definition ssyt01_aa.f:124