LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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schkpp.f
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1*> \brief \b SCHKPP
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 SCHKPP( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
12* NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
13* IWORK, NOUT )
14*
15* .. Scalar Arguments ..
16* LOGICAL TSTERR
17* INTEGER NMAX, NN, NNS, NOUT
18* REAL THRESH
19* ..
20* .. Array Arguments ..
21* LOGICAL DOTYPE( * )
22* INTEGER IWORK( * ), 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*> SCHKPP tests SPPTRF, -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] NNS
60*> \verbatim
61*> NNS is INTEGER
62*> The number of values of NRHS contained in the vector NSVAL.
63*> \endverbatim
64*>
65*> \param[in] NSVAL
66*> \verbatim
67*> NSVAL is INTEGER array, dimension (NNS)
68*> The values of the number of right hand sides NRHS.
69*> \endverbatim
70*>
71*> \param[in] THRESH
72*> \verbatim
73*> THRESH is REAL
74*> The threshold value for the test ratios. A result is
75*> included in the output file if RESULT >= THRESH. To have
76*> every test ratio printed, use THRESH = 0.
77*> \endverbatim
78*>
79*> \param[in] TSTERR
80*> \verbatim
81*> TSTERR is LOGICAL
82*> Flag that indicates whether error exits are to be tested.
83*> \endverbatim
84*>
85*> \param[in] NMAX
86*> \verbatim
87*> NMAX is INTEGER
88*> The maximum value permitted for N, used in dimensioning the
89*> work arrays.
90*> \endverbatim
91*>
92*> \param[out] A
93*> \verbatim
94*> A is REAL array, dimension
95*> (NMAX*(NMAX+1)/2)
96*> \endverbatim
97*>
98*> \param[out] AFAC
99*> \verbatim
100*> AFAC is REAL array, dimension
101*> (NMAX*(NMAX+1)/2)
102*> \endverbatim
103*>
104*> \param[out] AINV
105*> \verbatim
106*> AINV is REAL array, dimension
107*> (NMAX*(NMAX+1)/2)
108*> \endverbatim
109*>
110*> \param[out] B
111*> \verbatim
112*> B is REAL array, dimension (NMAX*NSMAX)
113*> where NSMAX is the largest entry in NSVAL.
114*> \endverbatim
115*>
116*> \param[out] X
117*> \verbatim
118*> X is REAL array, dimension (NMAX*NSMAX)
119*> \endverbatim
120*>
121*> \param[out] XACT
122*> \verbatim
123*> XACT is REAL array, dimension (NMAX*NSMAX)
124*> \endverbatim
125*>
126*> \param[out] WORK
127*> \verbatim
128*> WORK is REAL array, dimension
129*> (NMAX*max(3,NSMAX))
130*> \endverbatim
131*>
132*> \param[out] RWORK
133*> \verbatim
134*> RWORK is REAL array, dimension
135*> (max(NMAX,2*NSMAX))
136*> \endverbatim
137*>
138*> \param[out] IWORK
139*> \verbatim
140*> IWORK is INTEGER array, dimension (NMAX)
141*> \endverbatim
142*>
143*> \param[in] NOUT
144*> \verbatim
145*> NOUT is INTEGER
146*> The unit number for output.
147*> \endverbatim
148*
149* Authors:
150* ========
151*
152*> \author Univ. of Tennessee
153*> \author Univ. of California Berkeley
154*> \author Univ. of Colorado Denver
155*> \author NAG Ltd.
156*
157*> \ingroup single_lin
158*
159* =====================================================================
160 SUBROUTINE schkpp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
161 \$ NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
162 \$ IWORK, NOUT )
163*
164* -- LAPACK test routine --
165* -- LAPACK is a software package provided by Univ. of Tennessee, --
166* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167*
168* .. Scalar Arguments ..
169 LOGICAL TSTERR
170 INTEGER NMAX, NN, NNS, NOUT
171 REAL THRESH
172* ..
173* .. Array Arguments ..
174 LOGICAL DOTYPE( * )
175 INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
176 REAL A( * ), AFAC( * ), AINV( * ), B( * ),
177 \$ rwork( * ), work( * ), x( * ), xact( * )
178* ..
179*
180* =====================================================================
181*
182* .. Parameters ..
183 REAL ZERO
184 PARAMETER ( ZERO = 0.0e+0 )
185 INTEGER NTYPES
186 parameter( ntypes = 9 )
187 INTEGER NTESTS
188 parameter( ntests = 8 )
189* ..
190* .. Local Scalars ..
191 LOGICAL ZEROT
192 CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
193 CHARACTER*3 PATH
194 INTEGER I, IMAT, IN, INFO, IOFF, IRHS, IUPLO, IZERO, K,
195 \$ kl, ku, lda, mode, n, nerrs, nfail, nimat, npp,
196 \$ nrhs, nrun
197 REAL ANORM, CNDNUM, RCOND, RCONDC
198* ..
199* .. Local Arrays ..
200 CHARACTER PACKS( 2 ), UPLOS( 2 )
201 INTEGER ISEED( 4 ), ISEEDY( 4 )
202 REAL RESULT( NTESTS )
203* ..
204* .. External Functions ..
205 REAL SGET06, SLANSP
206 EXTERNAL SGET06, SLANSP
207* ..
208* .. External Subroutines ..
209 EXTERNAL alaerh, alahd, alasum, scopy, serrpo, sget04,
212 \$ spptrs
213* ..
214* .. Scalars in Common ..
215 LOGICAL LERR, OK
216 CHARACTER*32 SRNAMT
217 INTEGER INFOT, NUNIT
218* ..
219* .. Common blocks ..
220 COMMON / infoc / infot, nunit, ok, lerr
221 COMMON / srnamc / srnamt
222* ..
223* .. Intrinsic Functions ..
224 INTRINSIC max
225* ..
226* .. Data statements ..
227 DATA iseedy / 1988, 1989, 1990, 1991 /
228 DATA uplos / 'U', 'L' / , packs / 'C', 'R' /
229* ..
230* .. Executable Statements ..
231*
232* Initialize constants and the random number seed.
233*
234 path( 1: 1 ) = 'Single precision'
235 path( 2: 3 ) = 'PP'
236 nrun = 0
237 nfail = 0
238 nerrs = 0
239 DO 10 i = 1, 4
240 iseed( i ) = iseedy( i )
241 10 CONTINUE
242*
243* Test the error exits
244*
245 IF( tsterr )
246 \$ CALL serrpo( path, nout )
247 infot = 0
248*
249* Do for each value of N in NVAL
250*
251 DO 110 in = 1, nn
252 n = nval( in )
253 lda = max( n, 1 )
254 xtype = 'N'
255 nimat = ntypes
256 IF( n.LE.0 )
257 \$ nimat = 1
258*
259 DO 100 imat = 1, nimat
260*
261* Do the tests only if DOTYPE( IMAT ) is true.
262*
263 IF( .NOT.dotype( imat ) )
264 \$ GO TO 100
265*
266* Skip types 3, 4, or 5 if the matrix size is too small.
267*
268 zerot = imat.GE.3 .AND. imat.LE.5
269 IF( zerot .AND. n.LT.imat-2 )
270 \$ GO TO 100
271*
272* Do first for UPLO = 'U', then for UPLO = 'L'
273*
274 DO 90 iuplo = 1, 2
275 uplo = uplos( iuplo )
276 packit = packs( iuplo )
277*
278* Set up parameters with SLATB4 and generate a test matrix
279* with SLATMS.
280*
281 CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
282 \$ cndnum, dist )
283*
284 srnamt = 'SLATMS'
285 CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
286 \$ cndnum, anorm, kl, ku, packit, a, lda, work,
287 \$ info )
288*
289* Check error code from SLATMS.
290*
291 IF( info.NE.0 ) THEN
292 CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
293 \$ -1, -1, imat, nfail, nerrs, nout )
294 GO TO 90
295 END IF
296*
297* For types 3-5, zero one row and column of the matrix to
298* test that INFO is returned correctly.
299*
300 IF( zerot ) THEN
301 IF( imat.EQ.3 ) THEN
302 izero = 1
303 ELSE IF( imat.EQ.4 ) THEN
304 izero = n
305 ELSE
306 izero = n / 2 + 1
307 END IF
308*
309* Set row and column IZERO of A to 0.
310*
311 IF( iuplo.EQ.1 ) THEN
312 ioff = ( izero-1 )*izero / 2
313 DO 20 i = 1, izero - 1
314 a( ioff+i ) = zero
315 20 CONTINUE
316 ioff = ioff + izero
317 DO 30 i = izero, n
318 a( ioff ) = zero
319 ioff = ioff + i
320 30 CONTINUE
321 ELSE
322 ioff = izero
323 DO 40 i = 1, izero - 1
324 a( ioff ) = zero
325 ioff = ioff + n - i
326 40 CONTINUE
327 ioff = ioff - izero
328 DO 50 i = izero, n
329 a( ioff+i ) = zero
330 50 CONTINUE
331 END IF
332 ELSE
333 izero = 0
334 END IF
335*
336* Compute the L*L' or U'*U factorization of the matrix.
337*
338 npp = n*( n+1 ) / 2
339 CALL scopy( npp, a, 1, afac, 1 )
340 srnamt = 'SPPTRF'
341 CALL spptrf( uplo, n, afac, info )
342*
343* Check error code from SPPTRF.
344*
345 IF( info.NE.izero ) THEN
346 CALL alaerh( path, 'SPPTRF', info, izero, uplo, n, n,
347 \$ -1, -1, -1, imat, nfail, nerrs, nout )
348 GO TO 90
349 END IF
350*
351* Skip the tests if INFO is not 0.
352*
353 IF( info.NE.0 )
354 \$ GO TO 90
355*
356*+ TEST 1
357* Reconstruct matrix from factors and compute residual.
358*
359 CALL scopy( npp, afac, 1, ainv, 1 )
360 CALL sppt01( uplo, n, a, ainv, rwork, result( 1 ) )
361*
362*+ TEST 2
363* Form the inverse and compute the residual.
364*
365 CALL scopy( npp, afac, 1, ainv, 1 )
366 srnamt = 'SPPTRI'
367 CALL spptri( uplo, n, ainv, info )
368*
369* Check error code from SPPTRI.
370*
371 IF( info.NE.0 )
372 \$ CALL alaerh( path, 'SPPTRI', info, 0, uplo, n, n, -1,
373 \$ -1, -1, imat, nfail, nerrs, nout )
374*
375 CALL sppt03( uplo, n, a, ainv, work, lda, rwork, rcondc,
376 \$ result( 2 ) )
377*
378* Print information about the tests that did not pass
379* the threshold.
380*
381 DO 60 k = 1, 2
382 IF( result( k ).GE.thresh ) THEN
383 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
384 \$ CALL alahd( nout, path )
385 WRITE( nout, fmt = 9999 )uplo, n, imat, k,
386 \$ result( k )
387 nfail = nfail + 1
388 END IF
389 60 CONTINUE
390 nrun = nrun + 2
391*
392 DO 80 irhs = 1, nns
393 nrhs = nsval( irhs )
394*
395*+ TEST 3
396* Solve and compute residual for A * X = B.
397*
398 srnamt = 'SLARHS'
399 CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
400 \$ nrhs, a, lda, xact, lda, b, lda, iseed,
401 \$ info )
402 CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
403*
404 srnamt = 'SPPTRS'
405 CALL spptrs( uplo, n, nrhs, afac, x, lda, info )
406*
407* Check error code from SPPTRS.
408*
409 IF( info.NE.0 )
410 \$ CALL alaerh( path, 'SPPTRS', info, 0, uplo, n, n,
411 \$ -1, -1, nrhs, imat, nfail, nerrs,
412 \$ nout )
413*
414 CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
415 CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
416 \$ rwork, result( 3 ) )
417*
418*+ TEST 4
419* Check solution from generated exact solution.
420*
421 CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
422 \$ result( 4 ) )
423*
424*+ TESTS 5, 6, and 7
425* Use iterative refinement to improve the solution.
426*
427 srnamt = 'SPPRFS'
428 CALL spprfs( uplo, n, nrhs, a, afac, b, lda, x, lda,
429 \$ rwork, rwork( nrhs+1 ), work, iwork,
430 \$ info )
431*
432* Check error code from SPPRFS.
433*
434 IF( info.NE.0 )
435 \$ CALL alaerh( path, 'SPPRFS', info, 0, uplo, n, n,
436 \$ -1, -1, nrhs, imat, nfail, nerrs,
437 \$ nout )
438*
439 CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
440 \$ result( 5 ) )
441 CALL sppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
442 \$ lda, rwork, rwork( nrhs+1 ),
443 \$ result( 6 ) )
444*
445* Print information about the tests that did not pass
446* the threshold.
447*
448 DO 70 k = 3, 7
449 IF( result( k ).GE.thresh ) THEN
450 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
451 \$ CALL alahd( nout, path )
452 WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
453 \$ k, result( k )
454 nfail = nfail + 1
455 END IF
456 70 CONTINUE
457 nrun = nrun + 5
458 80 CONTINUE
459*
460*+ TEST 8
461* Get an estimate of RCOND = 1/CNDNUM.
462*
463 anorm = slansp( '1', uplo, n, a, rwork )
464 srnamt = 'SPPCON'
465 CALL sppcon( uplo, n, afac, anorm, rcond, work, iwork,
466 \$ info )
467*
468* Check error code from SPPCON.
469*
470 IF( info.NE.0 )
471 \$ CALL alaerh( path, 'SPPCON', info, 0, uplo, n, n, -1,
472 \$ -1, -1, imat, nfail, nerrs, nout )
473*
474 result( 8 ) = sget06( rcond, rcondc )
475*
476* Print the test ratio if greater than or equal to THRESH.
477*
478 IF( result( 8 ).GE.thresh ) THEN
479 IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
480 \$ CALL alahd( nout, path )
481 WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
482 \$ result( 8 )
483 nfail = nfail + 1
484 END IF
485 nrun = nrun + 1
486 90 CONTINUE
487 100 CONTINUE
488 110 CONTINUE
489*
490* Print a summary of the results.
491*
492 CALL alasum( path, nout, nfail, nrun, nerrs )
493*
494 9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
495 \$ i2, ', ratio =', g12.5 )
496 9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
497 \$ i2, ', test(', i2, ') =', g12.5 )
498 RETURN
499*
500* End of SCHKPP
501*
502 END
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
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 slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine spptrf(UPLO, N, AP, INFO)
SPPTRF
Definition: spptrf.f:119
subroutine spptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
SPPTRS
Definition: spptrs.f:108
subroutine spprfs(UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SPPRFS
Definition: spprfs.f:171
subroutine sppcon(UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO)
SPPCON
Definition: sppcon.f:118
subroutine spptri(UPLO, N, AP, INFO)
SPPTRI
Definition: spptri.f:93
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:205
subroutine serrpo(PATH, NUNIT)
SERRPO
Definition: serrpo.f:55
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:120
subroutine sppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPPT05
Definition: sppt05.f:156
subroutine sppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
SPPT02
Definition: sppt02.f:122
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:102
subroutine sppt03(UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
SPPT03
Definition: sppt03.f:110
subroutine schkpp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKPP
Definition: schkpp.f:163
subroutine sppt01(UPLO, N, A, AFAC, RWORK, RESID)
SPPT01
Definition: sppt01.f:93