LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
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 *> \date December 2016
158 *
159 *> \ingroup single_lin
160 *
161 * =====================================================================
162  SUBROUTINE schkpp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
163  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
164  $ IWORK, NOUT )
165 *
166 * -- LAPACK test routine (version 3.7.0) --
167 * -- LAPACK is a software package provided by Univ. of Tennessee, --
168 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169 * December 2016
170 *
171 * .. Scalar Arguments ..
172  LOGICAL tsterr
173  INTEGER nmax, nn, nns, nout
174  REAL thresh
175 * ..
176 * .. Array Arguments ..
177  LOGICAL dotype( * )
178  INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
179  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
180  $ rwork( * ), work( * ), x( * ), xact( * )
181 * ..
182 *
183 * =====================================================================
184 *
185 * .. Parameters ..
186  REAL ZERO
187  PARAMETER ( ZERO = 0.0e+0 )
188  INTEGER NTYPES
189  parameter( ntypes = 9 )
190  INTEGER NTESTS
191  parameter( ntests = 8 )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL ZEROT
195  CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
196  CHARACTER*3 PATH
197  INTEGER I, IMAT, IN, INFO, IOFF, IRHS, IUPLO, IZERO, K,
198  $ kl, ku, lda, mode, n, nerrs, nfail, nimat, npp,
199  $ nrhs, nrun
200  REAL ANORM, CNDNUM, RCOND, RCONDC
201 * ..
202 * .. Local Arrays ..
203  CHARACTER PACKS( 2 ), UPLOS( 2 )
204  INTEGER ISEED( 4 ), ISEEDY( 4 )
205  REAL RESULT( NTESTS )
206 * ..
207 * .. External Functions ..
208  REAL SGET06, SLANSP
209  EXTERNAL SGET06, SLANSP
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL alaerh, alahd, alasum, scopy, serrpo, sget04,
213  $ slacpy, slarhs, slatb4, slatms, sppcon, spprfs,
214  $ sppt01, sppt02, sppt03, sppt05, spptrf, spptri,
215  $ spptrs
216 * ..
217 * .. Scalars in Common ..
218  LOGICAL LERR, OK
219  CHARACTER*32 SRNAMT
220  INTEGER INFOT, NUNIT
221 * ..
222 * .. Common blocks ..
223  COMMON / infoc / infot, nunit, ok, lerr
224  COMMON / srnamc / srnamt
225 * ..
226 * .. Intrinsic Functions ..
227  INTRINSIC max
228 * ..
229 * .. Data statements ..
230  DATA iseedy / 1988, 1989, 1990, 1991 /
231  DATA uplos / 'U', 'L' / , packs / 'C', 'R' /
232 * ..
233 * .. Executable Statements ..
234 *
235 * Initialize constants and the random number seed.
236 *
237  path( 1: 1 ) = 'Single precision'
238  path( 2: 3 ) = 'PP'
239  nrun = 0
240  nfail = 0
241  nerrs = 0
242  DO 10 i = 1, 4
243  iseed( i ) = iseedy( i )
244  10 CONTINUE
245 *
246 * Test the error exits
247 *
248  IF( tsterr )
249  $ CALL serrpo( path, nout )
250  infot = 0
251 *
252 * Do for each value of N in NVAL
253 *
254  DO 110 in = 1, nn
255  n = nval( in )
256  lda = max( n, 1 )
257  xtype = 'N'
258  nimat = ntypes
259  IF( n.LE.0 )
260  $ nimat = 1
261 *
262  DO 100 imat = 1, nimat
263 *
264 * Do the tests only if DOTYPE( IMAT ) is true.
265 *
266  IF( .NOT.dotype( imat ) )
267  $ GO TO 100
268 *
269 * Skip types 3, 4, or 5 if the matrix size is too small.
270 *
271  zerot = imat.GE.3 .AND. imat.LE.5
272  IF( zerot .AND. n.LT.imat-2 )
273  $ GO TO 100
274 *
275 * Do first for UPLO = 'U', then for UPLO = 'L'
276 *
277  DO 90 iuplo = 1, 2
278  uplo = uplos( iuplo )
279  packit = packs( iuplo )
280 *
281 * Set up parameters with SLATB4 and generate a test matrix
282 * with SLATMS.
283 *
284  CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
285  $ cndnum, dist )
286 *
287  srnamt = 'SLATMS'
288  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
289  $ cndnum, anorm, kl, ku, packit, a, lda, work,
290  $ info )
291 *
292 * Check error code from SLATMS.
293 *
294  IF( info.NE.0 ) THEN
295  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
296  $ -1, -1, imat, nfail, nerrs, nout )
297  GO TO 90
298  END IF
299 *
300 * For types 3-5, zero one row and column of the matrix to
301 * test that INFO is returned correctly.
302 *
303  IF( zerot ) THEN
304  IF( imat.EQ.3 ) THEN
305  izero = 1
306  ELSE IF( imat.EQ.4 ) THEN
307  izero = n
308  ELSE
309  izero = n / 2 + 1
310  END IF
311 *
312 * Set row and column IZERO of A to 0.
313 *
314  IF( iuplo.EQ.1 ) THEN
315  ioff = ( izero-1 )*izero / 2
316  DO 20 i = 1, izero - 1
317  a( ioff+i ) = zero
318  20 CONTINUE
319  ioff = ioff + izero
320  DO 30 i = izero, n
321  a( ioff ) = zero
322  ioff = ioff + i
323  30 CONTINUE
324  ELSE
325  ioff = izero
326  DO 40 i = 1, izero - 1
327  a( ioff ) = zero
328  ioff = ioff + n - i
329  40 CONTINUE
330  ioff = ioff - izero
331  DO 50 i = izero, n
332  a( ioff+i ) = zero
333  50 CONTINUE
334  END IF
335  ELSE
336  izero = 0
337  END IF
338 *
339 * Compute the L*L' or U'*U factorization of the matrix.
340 *
341  npp = n*( n+1 ) / 2
342  CALL scopy( npp, a, 1, afac, 1 )
343  srnamt = 'SPPTRF'
344  CALL spptrf( uplo, n, afac, info )
345 *
346 * Check error code from SPPTRF.
347 *
348  IF( info.NE.izero ) THEN
349  CALL alaerh( path, 'SPPTRF', info, izero, uplo, n, n,
350  $ -1, -1, -1, imat, nfail, nerrs, nout )
351  GO TO 90
352  END IF
353 *
354 * Skip the tests if INFO is not 0.
355 *
356  IF( info.NE.0 )
357  $ GO TO 90
358 *
359 *+ TEST 1
360 * Reconstruct matrix from factors and compute residual.
361 *
362  CALL scopy( npp, afac, 1, ainv, 1 )
363  CALL sppt01( uplo, n, a, ainv, rwork, result( 1 ) )
364 *
365 *+ TEST 2
366 * Form the inverse and compute the residual.
367 *
368  CALL scopy( npp, afac, 1, ainv, 1 )
369  srnamt = 'SPPTRI'
370  CALL spptri( uplo, n, ainv, info )
371 *
372 * Check error code from SPPTRI.
373 *
374  IF( info.NE.0 )
375  $ CALL alaerh( path, 'SPPTRI', info, 0, uplo, n, n, -1,
376  $ -1, -1, imat, nfail, nerrs, nout )
377 *
378  CALL sppt03( uplo, n, a, ainv, work, lda, rwork, rcondc,
379  $ result( 2 ) )
380 *
381 * Print information about the tests that did not pass
382 * the threshold.
383 *
384  DO 60 k = 1, 2
385  IF( result( k ).GE.thresh ) THEN
386  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
387  $ CALL alahd( nout, path )
388  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
389  $ result( k )
390  nfail = nfail + 1
391  END IF
392  60 CONTINUE
393  nrun = nrun + 2
394 *
395  DO 80 irhs = 1, nns
396  nrhs = nsval( irhs )
397 *
398 *+ TEST 3
399 * Solve and compute residual for A * X = B.
400 *
401  srnamt = 'SLARHS'
402  CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
403  $ nrhs, a, lda, xact, lda, b, lda, iseed,
404  $ info )
405  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
406 *
407  srnamt = 'SPPTRS'
408  CALL spptrs( uplo, n, nrhs, afac, x, lda, info )
409 *
410 * Check error code from SPPTRS.
411 *
412  IF( info.NE.0 )
413  $ CALL alaerh( path, 'SPPTRS', info, 0, uplo, n, n,
414  $ -1, -1, nrhs, imat, nfail, nerrs,
415  $ nout )
416 *
417  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
418  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
419  $ rwork, result( 3 ) )
420 *
421 *+ TEST 4
422 * Check solution from generated exact solution.
423 *
424  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
425  $ result( 4 ) )
426 *
427 *+ TESTS 5, 6, and 7
428 * Use iterative refinement to improve the solution.
429 *
430  srnamt = 'SPPRFS'
431  CALL spprfs( uplo, n, nrhs, a, afac, b, lda, x, lda,
432  $ rwork, rwork( nrhs+1 ), work, iwork,
433  $ info )
434 *
435 * Check error code from SPPRFS.
436 *
437  IF( info.NE.0 )
438  $ CALL alaerh( path, 'SPPRFS', info, 0, uplo, n, n,
439  $ -1, -1, nrhs, imat, nfail, nerrs,
440  $ nout )
441 *
442  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
443  $ result( 5 ) )
444  CALL sppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
445  $ lda, rwork, rwork( nrhs+1 ),
446  $ result( 6 ) )
447 *
448 * Print information about the tests that did not pass
449 * the threshold.
450 *
451  DO 70 k = 3, 7
452  IF( result( k ).GE.thresh ) THEN
453  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
454  $ CALL alahd( nout, path )
455  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
456  $ k, result( k )
457  nfail = nfail + 1
458  END IF
459  70 CONTINUE
460  nrun = nrun + 5
461  80 CONTINUE
462 *
463 *+ TEST 8
464 * Get an estimate of RCOND = 1/CNDNUM.
465 *
466  anorm = slansp( '1', uplo, n, a, rwork )
467  srnamt = 'SPPCON'
468  CALL sppcon( uplo, n, afac, anorm, rcond, work, iwork,
469  $ info )
470 *
471 * Check error code from SPPCON.
472 *
473  IF( info.NE.0 )
474  $ CALL alaerh( path, 'SPPCON', info, 0, uplo, n, n, -1,
475  $ -1, -1, imat, nfail, nerrs, nout )
476 *
477  result( 8 ) = sget06( rcond, rcondc )
478 *
479 * Print the test ratio if greater than or equal to THRESH.
480 *
481  IF( result( 8 ).GE.thresh ) THEN
482  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
483  $ CALL alahd( nout, path )
484  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
485  $ result( 8 )
486  nfail = nfail + 1
487  END IF
488  nrun = nrun + 1
489  90 CONTINUE
490  100 CONTINUE
491  110 CONTINUE
492 *
493 * Print a summary of the results.
494 *
495  CALL alasum( path, nout, nfail, nrun, nerrs )
496 *
497  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
498  $ i2, ', ratio =', g12.5 )
499  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
500  $ i2, ', test(', i2, ') =', g12.5 )
501  RETURN
502 *
503 * End of SCHKPP
504 *
505  END
spprfs
subroutine spprfs(UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SPPRFS
Definition: spprfs.f:173
sppt01
subroutine sppt01(UPLO, N, A, AFAC, RWORK, RESID)
SPPT01
Definition: sppt01.f:95
slarhs
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:206
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
sppt02
subroutine sppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
SPPT02
Definition: sppt02.f:124
spptri
subroutine spptri(UPLO, N, AP, INFO)
SPPTRI
Definition: spptri.f:95
spptrs
subroutine spptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
SPPTRS
Definition: spptrs.f:110
sppt03
subroutine sppt03(UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
SPPT03
Definition: sppt03.f:112
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:105
scopy
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
sget04
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
alaerh
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
slatms
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
serrpo
subroutine serrpo(PATH, NUNIT)
SERRPO
Definition: serrpo.f:57
sppcon
subroutine sppcon(UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO)
SPPCON
Definition: sppcon.f:120
slatb4
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
alasum
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75
spptrf
subroutine spptrf(UPLO, N, AP, INFO)
SPPTRF
Definition: spptrf.f:121
schkpp
subroutine schkpp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKPP
Definition: schkpp.f:165
sppt05
subroutine sppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPPT05
Definition: sppt05.f:158