LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
schksp.f
Go to the documentation of this file.
1 *> \brief \b SCHKSP
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 SCHKSP( 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 *> SCHKSP tests SSPTRF, -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(2,NSMAX))
130 *> \endverbatim
131 *>
132 *> \param[out] RWORK
133 *> \verbatim
134 *> RWORK is REAL array,
135 *> dimension (NMAX+2*NSMAX)
136 *> \endverbatim
137 *>
138 *> \param[out] IWORK
139 *> \verbatim
140 *> IWORK is INTEGER array, dimension (2*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 schksp( 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 = 10 )
190  INTEGER NTESTS
191  parameter( ntests = 8 )
192 * ..
193 * .. Local Scalars ..
194  LOGICAL TRFCON, ZEROT
195  CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
196  CHARACTER*3 PATH
197  INTEGER I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
198  $ izero, j, k, kl, ku, lda, mode, n, nerrs,
199  $ nfail, nimat, npp, nrhs, nrun, nt
200  REAL ANORM, CNDNUM, RCOND, RCONDC
201 * ..
202 * .. Local Arrays ..
203  CHARACTER UPLOS( 2 )
204  INTEGER ISEED( 4 ), ISEEDY( 4 )
205  REAL RESULT( NTESTS )
206 * ..
207 * .. External Functions ..
208  LOGICAL LSAME
209  REAL SGET06, SLANSP
210  EXTERNAL lsame, sget06, slansp
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL alaerh, alahd, alasum, scopy, serrsy, sget04,
214  $ slacpy, slarhs, slatb4, slatms, sppt02, sppt03,
215  $ sppt05, sspcon, ssprfs, sspt01, ssptrf, ssptri,
216  $ ssptrs
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  path( 1: 1 ) = 'Single precision'
239  path( 2: 3 ) = 'SP'
240  nrun = 0
241  nfail = 0
242  nerrs = 0
243  DO 10 i = 1, 4
244  iseed( i ) = iseedy( i )
245  10 CONTINUE
246 *
247 * Test the error exits
248 *
249  IF( tsterr )
250  $ CALL serrsy( path, nout )
251  infot = 0
252 *
253 * Do for each value of N in NVAL
254 *
255  DO 170 in = 1, nn
256  n = nval( in )
257  lda = max( n, 1 )
258  xtype = 'N'
259  nimat = ntypes
260  IF( n.LE.0 )
261  $ nimat = 1
262 *
263  izero = 0
264  DO 160 imat = 1, nimat
265 *
266 * Do the tests only if DOTYPE( IMAT ) is true.
267 *
268  IF( .NOT.dotype( imat ) )
269  $ GO TO 160
270 *
271 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
272 *
273  zerot = imat.GE.3 .AND. imat.LE.6
274  IF( zerot .AND. n.LT.imat-2 )
275  $ GO TO 160
276 *
277 * Do first for UPLO = 'U', then for UPLO = 'L'
278 *
279  DO 150 iuplo = 1, 2
280  uplo = uplos( iuplo )
281  IF( lsame( uplo, 'U' ) ) THEN
282  packit = 'C'
283  ELSE
284  packit = 'R'
285  END IF
286 *
287 * Set up parameters with SLATB4 and generate a test matrix
288 * with SLATMS.
289 *
290  CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
291  $ cndnum, dist )
292 *
293  srnamt = 'SLATMS'
294  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
295  $ cndnum, anorm, kl, ku, packit, a, lda, work,
296  $ info )
297 *
298 * Check error code from SLATMS.
299 *
300  IF( info.NE.0 ) THEN
301  CALL alaerh( path, 'SLATMS', info, 0, uplo, n, n, -1,
302  $ -1, -1, imat, nfail, nerrs, nout )
303  GO TO 150
304  END IF
305 *
306 * For types 3-6, zero one or more rows and columns of
307 * the matrix to test that INFO is returned correctly.
308 *
309  IF( zerot ) THEN
310  IF( imat.EQ.3 ) THEN
311  izero = 1
312  ELSE IF( imat.EQ.4 ) THEN
313  izero = n
314  ELSE
315  izero = n / 2 + 1
316  END IF
317 *
318  IF( imat.LT.6 ) THEN
319 *
320 * Set row and column IZERO to zero.
321 *
322  IF( iuplo.EQ.1 ) THEN
323  ioff = ( izero-1 )*izero / 2
324  DO 20 i = 1, izero - 1
325  a( ioff+i ) = zero
326  20 CONTINUE
327  ioff = ioff + izero
328  DO 30 i = izero, n
329  a( ioff ) = zero
330  ioff = ioff + i
331  30 CONTINUE
332  ELSE
333  ioff = izero
334  DO 40 i = 1, izero - 1
335  a( ioff ) = zero
336  ioff = ioff + n - i
337  40 CONTINUE
338  ioff = ioff - izero
339  DO 50 i = izero, n
340  a( ioff+i ) = zero
341  50 CONTINUE
342  END IF
343  ELSE
344  ioff = 0
345  IF( iuplo.EQ.1 ) THEN
346 *
347 * Set the first IZERO rows and columns to zero.
348 *
349  DO 70 j = 1, n
350  i2 = min( j, izero )
351  DO 60 i = 1, i2
352  a( ioff+i ) = zero
353  60 CONTINUE
354  ioff = ioff + j
355  70 CONTINUE
356  ELSE
357 *
358 * Set the last IZERO rows and columns to zero.
359 *
360  DO 90 j = 1, n
361  i1 = max( j, izero )
362  DO 80 i = i1, n
363  a( ioff+i ) = zero
364  80 CONTINUE
365  ioff = ioff + n - j
366  90 CONTINUE
367  END IF
368  END IF
369  ELSE
370  izero = 0
371  END IF
372 *
373 * Compute the L*D*L' or U*D*U' factorization of the matrix.
374 *
375  npp = n*( n+1 ) / 2
376  CALL scopy( npp, a, 1, afac, 1 )
377  srnamt = 'SSPTRF'
378  CALL ssptrf( uplo, n, afac, iwork, info )
379 *
380 * Adjust the expected value of INFO to account for
381 * pivoting.
382 *
383  k = izero
384  IF( k.GT.0 ) THEN
385  100 CONTINUE
386  IF( iwork( k ).LT.0 ) THEN
387  IF( iwork( k ).NE.-k ) THEN
388  k = -iwork( k )
389  GO TO 100
390  END IF
391  ELSE IF( iwork( k ).NE.k ) THEN
392  k = iwork( k )
393  GO TO 100
394  END IF
395  END IF
396 *
397 * Check error code from SSPTRF.
398 *
399  IF( info.NE.k )
400  $ CALL alaerh( path, 'SSPTRF', info, k, uplo, n, n, -1,
401  $ -1, -1, imat, nfail, nerrs, nout )
402  IF( info.NE.0 ) THEN
403  trfcon = .true.
404  ELSE
405  trfcon = .false.
406  END IF
407 *
408 *+ TEST 1
409 * Reconstruct matrix from factors and compute residual.
410 *
411  CALL sspt01( uplo, n, a, afac, iwork, ainv, lda, rwork,
412  $ result( 1 ) )
413  nt = 1
414 *
415 *+ TEST 2
416 * Form the inverse and compute the residual.
417 *
418  IF( .NOT.trfcon ) THEN
419  CALL scopy( npp, afac, 1, ainv, 1 )
420  srnamt = 'SSPTRI'
421  CALL ssptri( uplo, n, ainv, iwork, work, info )
422 *
423 * Check error code from SSPTRI.
424 *
425  IF( info.NE.0 )
426  $ CALL alaerh( path, 'SSPTRI', info, 0, uplo, n, n,
427  $ -1, -1, -1, imat, nfail, nerrs, nout )
428 *
429  CALL sppt03( uplo, n, a, ainv, work, lda, rwork,
430  $ rcondc, result( 2 ) )
431  nt = 2
432  END IF
433 *
434 * Print information about the tests that did not pass
435 * the threshold.
436 *
437  DO 110 k = 1, nt
438  IF( result( k ).GE.thresh ) THEN
439  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
440  $ CALL alahd( nout, path )
441  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
442  $ result( k )
443  nfail = nfail + 1
444  END IF
445  110 CONTINUE
446  nrun = nrun + nt
447 *
448 * Do only the condition estimate if INFO is not 0.
449 *
450  IF( trfcon ) THEN
451  rcondc = zero
452  GO TO 140
453  END IF
454 *
455  DO 130 irhs = 1, nns
456  nrhs = nsval( irhs )
457 *
458 *+ TEST 3
459 * Solve and compute residual for A * X = B.
460 *
461  srnamt = 'SLARHS'
462  CALL slarhs( path, xtype, uplo, ' ', n, n, kl, ku,
463  $ nrhs, a, lda, xact, lda, b, lda, iseed,
464  $ info )
465  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
466 *
467  srnamt = 'SSPTRS'
468  CALL ssptrs( uplo, n, nrhs, afac, iwork, x, lda,
469  $ info )
470 *
471 * Check error code from SSPTRS.
472 *
473  IF( info.NE.0 )
474  $ CALL alaerh( path, 'SSPTRS', info, 0, uplo, n, n,
475  $ -1, -1, nrhs, imat, nfail, nerrs,
476  $ nout )
477 *
478  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
479  CALL sppt02( uplo, n, nrhs, a, x, lda, work, lda,
480  $ rwork, result( 3 ) )
481 *
482 *+ TEST 4
483 * Check solution from generated exact solution.
484 *
485  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
486  $ result( 4 ) )
487 *
488 *+ TESTS 5, 6, and 7
489 * Use iterative refinement to improve the solution.
490 *
491  srnamt = 'SSPRFS'
492  CALL ssprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
493  $ lda, rwork, rwork( nrhs+1 ), work,
494  $ iwork( n+1 ), info )
495 *
496 * Check error code from SSPRFS.
497 *
498  IF( info.NE.0 )
499  $ CALL alaerh( path, 'SSPRFS', info, 0, uplo, n, n,
500  $ -1, -1, nrhs, imat, nfail, nerrs,
501  $ nout )
502 *
503  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
504  $ result( 5 ) )
505  CALL sppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
506  $ lda, rwork, rwork( nrhs+1 ),
507  $ result( 6 ) )
508 *
509 * Print information about the tests that did not pass
510 * the threshold.
511 *
512  DO 120 k = 3, 7
513  IF( result( k ).GE.thresh ) THEN
514  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
515  $ CALL alahd( nout, path )
516  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
517  $ k, result( k )
518  nfail = nfail + 1
519  END IF
520  120 CONTINUE
521  nrun = nrun + 5
522  130 CONTINUE
523 *
524 *+ TEST 8
525 * Get an estimate of RCOND = 1/CNDNUM.
526 *
527  140 CONTINUE
528  anorm = slansp( '1', uplo, n, a, rwork )
529  srnamt = 'SSPCON'
530  CALL sspcon( uplo, n, afac, iwork, anorm, rcond, work,
531  $ iwork( n+1 ), info )
532 *
533 * Check error code from SSPCON.
534 *
535  IF( info.NE.0 )
536  $ CALL alaerh( path, 'SSPCON', info, 0, uplo, n, n, -1,
537  $ -1, -1, imat, nfail, nerrs, nout )
538 *
539  result( 8 ) = sget06( rcond, rcondc )
540 *
541 * Print the test ratio if it is .GE. THRESH.
542 *
543  IF( result( 8 ).GE.thresh ) THEN
544  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
545  $ CALL alahd( nout, path )
546  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
547  $ result( 8 )
548  nfail = nfail + 1
549  END IF
550  nrun = nrun + 1
551  150 CONTINUE
552  160 CONTINUE
553  170 CONTINUE
554 *
555 * Print a summary of the results.
556 *
557  CALL alasum( path, nout, nfail, nrun, nerrs )
558 *
559  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
560  $ i2, ', ratio =', g12.5 )
561  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
562  $ i2, ', test(', i2, ') =', g12.5 )
563  RETURN
564 *
565 * End of SCHKSP
566 *
567  END
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
schksp
subroutine schksp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
SCHKSP
Definition: schksp.f:165
alahd
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:109
sspcon
subroutine sspcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSPCON
Definition: sspcon.f:127
sppt02
subroutine sppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
SPPT02
Definition: sppt02.f:124
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
ssptrs
subroutine ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
Definition: ssptrs.f:117
scopy
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
serrsy
subroutine serrsy(PATH, NUNIT)
SERRSY
Definition: serrsy.f:57
ssprfs
subroutine ssprfs(UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SSPRFS
Definition: ssprfs.f:181
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
sspt01
subroutine sspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
SSPT01
Definition: sspt01.f:112
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
ssptrf
subroutine ssptrf(UPLO, N, AP, IPIV, INFO)
SSPTRF
Definition: ssptrf.f:159
ssptri
subroutine ssptri(UPLO, N, AP, IPIV, WORK, INFO)
SSPTRI
Definition: ssptri.f:111
sppt05
subroutine sppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPPT05
Definition: sppt05.f:158