LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
schkpo.f
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1 *> \brief \b SCHKPO
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 SCHKPO( 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 *> SCHKPO tests SPOTRF, -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 (NBVAL)
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
138 *> (NMAX*max(3,NSMAX))
139 *> \endverbatim
140 *>
141 *> \param[out] RWORK
142 *> \verbatim
143 *> RWORK is REAL 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 *> \date December 2016
167 *
168 *> \ingroup single_lin
169 *
170 * =====================================================================
171  SUBROUTINE schkpo( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
172  $ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
173  $ XACT, WORK, RWORK, IWORK, NOUT )
174 *
175 * -- LAPACK test routine (version 3.7.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * December 2016
179 *
180 * .. Scalar Arguments ..
181  LOGICAL TSTERR
182  INTEGER NMAX, NN, NNB, NNS, NOUT
183  REAL THRESH
184 * ..
185 * .. Array Arguments ..
186  LOGICAL DOTYPE( * )
187  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
188  REAL A( * ), AFAC( * ), AINV( * ), B( * ),
189  $ rwork( * ), work( * ), x( * ), xact( * )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  REAL ZERO
196  parameter( zero = 0.0e+0 )
197  INTEGER NTYPES
198  parameter( ntypes = 9 )
199  INTEGER NTESTS
200  parameter( ntests = 8 )
201 * ..
202 * .. Local Scalars ..
203  LOGICAL ZEROT
204  CHARACTER DIST, TYPE, UPLO, XTYPE
205  CHARACTER*3 PATH
206  INTEGER I, IMAT, IN, INB, INFO, IOFF, IRHS, IUPLO,
207  $ izero, k, kl, ku, lda, mode, n, nb, nerrs,
208  $ nfail, nimat, nrhs, nrun
209  REAL ANORM, CNDNUM, RCOND, RCONDC
210 * ..
211 * .. Local Arrays ..
212  CHARACTER UPLOS( 2 )
213  INTEGER ISEED( 4 ), ISEEDY( 4 )
214  REAL RESULT( ntests )
215 * ..
216 * .. External Functions ..
217  REAL SGET06, SLANSY
218  EXTERNAL sget06, slansy
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL alaerh, alahd, alasum, serrpo, sget04, slacpy,
224  $ xlaenv
225 * ..
226 * .. Scalars in Common ..
227  LOGICAL LERR, OK
228  CHARACTER*32 SRNAMT
229  INTEGER INFOT, NUNIT
230 * ..
231 * .. Common blocks ..
232  COMMON / infoc / infot, nunit, ok, lerr
233  COMMON / srnamc / srnamt
234 * ..
235 * .. Intrinsic Functions ..
236  INTRINSIC max
237 * ..
238 * .. Data statements ..
239  DATA iseedy / 1988, 1989, 1990, 1991 /
240  DATA uplos / 'U', 'L' /
241 * ..
242 * .. Executable Statements ..
243 *
244 * Initialize constants and the random number seed.
245 *
246  path( 1: 1 ) = 'Single precision'
247  path( 2: 3 ) = 'PO'
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 serrpo( path, nout )
259  infot = 0
260  CALL xlaenv( 2, 2 )
261 *
262 * Do for each value of N in NVAL
263 *
264  DO 120 in = 1, nn
265  n = nval( in )
266  lda = max( n, 1 )
267  xtype = 'N'
268  nimat = ntypes
269  IF( n.LE.0 )
270  $ nimat = 1
271 *
272  izero = 0
273  DO 110 imat = 1, nimat
274 *
275 * Do the tests only if DOTYPE( IMAT ) is true.
276 *
277  IF( .NOT.dotype( imat ) )
278  $ GO TO 110
279 *
280 * Skip types 3, 4, or 5 if the matrix size is too small.
281 *
282  zerot = imat.GE.3 .AND. imat.LE.5
283  IF( zerot .AND. n.LT.imat-2 )
284  $ GO TO 110
285 *
286 * Do first for UPLO = 'U', then for UPLO = 'L'
287 *
288  DO 100 iuplo = 1, 2
289  uplo = uplos( iuplo )
290 *
291 * Set up parameters with SLATB4 and generate a test matrix
292 * with SLATMS.
293 *
294  CALL slatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
295  $ cndnum, dist )
296 *
297  srnamt = 'SLATMS'
298  CALL slatms( n, n, dist, iseed, TYPE, RWORK, MODE,
299  $ cndnum, anorm, kl, ku, uplo, a, lda, work,
300  $ info )
301 *
302 * Check error code from SLATMS.
303 *
304  IF( info.NE.0 ) THEN
305  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
306  $ -1, -1, imat, nfail, nerrs, nout )
307  GO TO 100
308  END IF
309 *
310 * For types 3-5, zero one row and column of the matrix to
311 * test that INFO is returned correctly.
312 *
313  IF( zerot ) THEN
314  IF( imat.EQ.3 ) THEN
315  izero = 1
316  ELSE IF( imat.EQ.4 ) THEN
317  izero = n
318  ELSE
319  izero = n / 2 + 1
320  END IF
321  ioff = ( izero-1 )*lda
322 *
323 * Set row and column IZERO of A to 0.
324 *
325  IF( iuplo.EQ.1 ) THEN
326  DO 20 i = 1, izero - 1
327  a( ioff+i ) = zero
328  20 CONTINUE
329  ioff = ioff + izero
330  DO 30 i = izero, n
331  a( ioff ) = zero
332  ioff = ioff + lda
333  30 CONTINUE
334  ELSE
335  ioff = izero
336  DO 40 i = 1, izero - 1
337  a( ioff ) = zero
338  ioff = ioff + lda
339  40 CONTINUE
340  ioff = ioff - izero
341  DO 50 i = izero, n
342  a( ioff+i ) = zero
343  50 CONTINUE
344  END IF
345  ELSE
346  izero = 0
347  END IF
348 *
349 * Do for each value of NB in NBVAL
350 *
351  DO 90 inb = 1, nnb
352  nb = nbval( inb )
353  CALL xlaenv( 1, nb )
354 *
355 * Compute the L*L' or U'*U factorization of the matrix.
356 *
357  CALL slacpy( uplo, n, n, a, lda, afac, lda )
358  srnamt = 'SPOTRF'
359  CALL spotrf( uplo, n, afac, lda, info )
360 *
361 * Check error code from SPOTRF.
362 *
363  IF( info.NE.izero ) THEN
364  CALL alaerh( path, 'SPOTRF', info, izero, uplo, n,
365  $ n, -1, -1, nb, imat, nfail, nerrs,
366  $ nout )
367  GO TO 90
368  END IF
369 *
370 * Skip the tests if INFO is not 0.
371 *
372  IF( info.NE.0 )
373  $ GO TO 90
374 *
375 *+ TEST 1
376 * Reconstruct matrix from factors and compute residual.
377 *
378  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
379  CALL spot01( uplo, n, a, lda, ainv, lda, rwork,
380  $ result( 1 ) )
381 *
382 *+ TEST 2
383 * Form the inverse and compute the residual.
384 *
385  CALL slacpy( uplo, n, n, afac, lda, ainv, lda )
386  srnamt = 'SPOTRI'
387  CALL spotri( uplo, n, ainv, lda, info )
388 *
389 * Check error code from SPOTRI.
390 *
391  IF( info.NE.0 )
392  $ CALL alaerh( path, 'SPOTRI', info, 0, uplo, n, n,
393  $ -1, -1, -1, imat, nfail, nerrs, nout )
394 *
395  CALL spot03( uplo, n, a, lda, ainv, lda, work, lda,
396  $ rwork, rcondc, result( 2 ) )
397 *
398 * Print information about the tests that did not pass
399 * the threshold.
400 *
401  DO 60 k = 1, 2
402  IF( result( k ).GE.thresh ) THEN
403  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
404  $ CALL alahd( nout, path )
405  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
406  $ result( k )
407  nfail = nfail + 1
408  END IF
409  60 CONTINUE
410  nrun = nrun + 2
411 *
412 * Skip the rest of the tests unless this is the first
413 * blocksize.
414 *
415  IF( inb.NE.1 )
416  $ GO TO 90
417 *
418  DO 80 irhs = 1, nns
419  nrhs = nsval( irhs )
420 *
421 *+ TEST 3
422 * Solve and compute residual for A * X = B .
423 *
424  srnamt = 'SLARHS'
425  CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
426  $ nrhs, a, lda, xact, lda, b, lda,
427  $ iseed, info )
428  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
429 *
430  srnamt = 'SPOTRS'
431  CALL spotrs( uplo, n, nrhs, afac, lda, x, lda,
432  $ info )
433 *
434 * Check error code from SPOTRS.
435 *
436  IF( info.NE.0 )
437  $ CALL alaerh( path, 'SPOTRS', info, 0, uplo, n,
438  $ n, -1, -1, nrhs, imat, nfail,
439  $ nerrs, nout )
440 *
441  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
442  CALL spot02( uplo, n, nrhs, a, lda, x, lda, work,
443  $ lda, rwork, result( 3 ) )
444 *
445 *+ TEST 4
446 * Check solution from generated exact solution.
447 *
448  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
449  $ result( 4 ) )
450 *
451 *+ TESTS 5, 6, and 7
452 * Use iterative refinement to improve the solution.
453 *
454  srnamt = 'SPORFS'
455  CALL sporfs( uplo, n, nrhs, a, lda, afac, lda, b,
456  $ lda, x, lda, rwork, rwork( nrhs+1 ),
457  $ work, iwork, info )
458 *
459 * Check error code from SPORFS.
460 *
461  IF( info.NE.0 )
462  $ CALL alaerh( path, 'SPORFS', info, 0, uplo, n,
463  $ n, -1, -1, nrhs, imat, nfail,
464  $ nerrs, nout )
465 *
466  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
467  $ result( 5 ) )
468  CALL spot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
469  $ xact, lda, rwork, rwork( nrhs+1 ),
470  $ result( 6 ) )
471 *
472 * Print information about the tests that did not pass
473 * the threshold.
474 *
475  DO 70 k = 3, 7
476  IF( result( k ).GE.thresh ) THEN
477  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
478  $ CALL alahd( nout, path )
479  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
480  $ imat, k, result( k )
481  nfail = nfail + 1
482  END IF
483  70 CONTINUE
484  nrun = nrun + 5
485  80 CONTINUE
486 *
487 *+ TEST 8
488 * Get an estimate of RCOND = 1/CNDNUM.
489 *
490  anorm = slansy( '1', uplo, n, a, lda, rwork )
491  srnamt = 'SPOCON'
492  CALL spocon( uplo, n, afac, lda, anorm, rcond, work,
493  $ iwork, info )
494 *
495 * Check error code from SPOCON.
496 *
497  IF( info.NE.0 )
498  $ CALL alaerh( path, 'SPOCON', info, 0, uplo, n, n,
499  $ -1, -1, -1, imat, nfail, nerrs, nout )
500 *
501  result( 8 ) = sget06( rcond, rcondc )
502 *
503 * Print the test ratio if it is .GE. THRESH.
504 *
505  IF( result( 8 ).GE.thresh ) THEN
506  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
507  $ CALL alahd( nout, path )
508  WRITE( nout, fmt = 9997 )uplo, n, imat, 8,
509  $ result( 8 )
510  nfail = nfail + 1
511  END IF
512  nrun = nrun + 1
513  90 CONTINUE
514  100 CONTINUE
515  110 CONTINUE
516  120 CONTINUE
517 *
518 * Print a summary of the results.
519 *
520  CALL alasum( path, nout, nfail, nrun, nerrs )
521 *
522  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
523  $ i2, ', test ', i2, ', ratio =', g12.5 )
524  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
525  $ i2, ', test(', i2, ') =', g12.5 )
526  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
527  $ ', test(', i2, ') =', g12.5 )
528  RETURN
529 *
530 * End of SCHKPO
531 *
532  END
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:107
subroutine spot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPOT02
Definition: spot02.f:129
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:149
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:122
subroutine spot01(UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
SPOT01
Definition: spot01.f:106
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine spot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
SPOT03
Definition: spot03.f:127
subroutine spotrf(UPLO, N, A, LDA, INFO)
SPOTRF
Definition: spotrf.f:109
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
subroutine spocon(UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO)
SPOCON
Definition: spocon.f:123
subroutine schkpo(DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKPO
Definition: schkpo.f:174
subroutine spotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
SPOTRS
Definition: spotrs.f:112
subroutine sporfs(UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SPORFS
Definition: sporfs.f:185
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
subroutine slarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
SLARHS
Definition: slarhs.f:206
subroutine serrpo(PATH, NUNIT)
SERRPO
Definition: serrpo.f:57
subroutine spot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPOT05
Definition: spot05.f:166
subroutine spotri(UPLO, N, A, LDA, INFO)
SPOTRI
Definition: spotri.f:97
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75