LAPACK  3.10.1
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 *> \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