LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dchksp.f
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1 *> \brief \b DCHKSP
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 DCHKSP( 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 * DOUBLE PRECISION THRESH
19 * ..
20 * .. Array Arguments ..
21 * LOGICAL DOTYPE( * )
22 * INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
23 * DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
24 * $ RWORK( * ), WORK( * ), X( * ), XACT( * )
25 * ..
26 *
27 *
28 *> \par Purpose:
29 * =============
30 *>
31 *> \verbatim
32 *>
33 *> DCHKSP tests DSPTRF, -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 DOUBLE PRECISION
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 DOUBLE PRECISION array, dimension
95 *> (NMAX*(NMAX+1)/2)
96 *> \endverbatim
97 *>
98 *> \param[out] AFAC
99 *> \verbatim
100 *> AFAC is DOUBLE PRECISION array, dimension
101 *> (NMAX*(NMAX+1)/2)
102 *> \endverbatim
103 *>
104 *> \param[out] AINV
105 *> \verbatim
106 *> AINV is DOUBLE PRECISION array, dimension
107 *> (NMAX*(NMAX+1)/2)
108 *> \endverbatim
109 *>
110 *> \param[out] B
111 *> \verbatim
112 *> B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (NMAX*NSMAX)
119 *> \endverbatim
120 *>
121 *> \param[out] XACT
122 *> \verbatim
123 *> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
124 *> \endverbatim
125 *>
126 *> \param[out] WORK
127 *> \verbatim
128 *> WORK is DOUBLE PRECISION array, dimension
129 *> (NMAX*max(2,NSMAX))
130 *> \endverbatim
131 *>
132 *> \param[out] RWORK
133 *> \verbatim
134 *> RWORK is DOUBLE PRECISION 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 *> \ingroup double_lin
158 *
159 * =====================================================================
160  SUBROUTINE dchksp( 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  DOUBLE PRECISION THRESH
172 * ..
173 * .. Array Arguments ..
174  LOGICAL DOTYPE( * )
175  INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
176  DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
177  $ rwork( * ), work( * ), x( * ), xact( * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  DOUBLE PRECISION ZERO
184  PARAMETER ( ZERO = 0.0d+0 )
185  INTEGER NTYPES
186  parameter( ntypes = 10 )
187  INTEGER NTESTS
188  parameter( ntests = 8 )
189 * ..
190 * .. Local Scalars ..
191  LOGICAL TRFCON, ZEROT
192  CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
193  CHARACTER*3 PATH
194  INTEGER I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
195  $ izero, j, k, kl, ku, lda, mode, n, nerrs,
196  $ nfail, nimat, npp, nrhs, nrun, nt
197  DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
198 * ..
199 * .. Local Arrays ..
200  CHARACTER UPLOS( 2 )
201  INTEGER ISEED( 4 ), ISEEDY( 4 )
202  DOUBLE PRECISION RESULT( NTESTS )
203 * ..
204 * .. External Functions ..
205  LOGICAL LSAME
206  DOUBLE PRECISION DGET06, DLANSP
207  EXTERNAL lsame, dget06, dlansp
208 * ..
209 * .. External Subroutines ..
210  EXTERNAL alaerh, alahd, alasum, dcopy, derrsy, dget04,
213  $ dsptrs
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max, min
217 * ..
218 * .. Scalars in Common ..
219  LOGICAL LERR, OK
220  CHARACTER*32 SRNAMT
221  INTEGER INFOT, NUNIT
222 * ..
223 * .. Common blocks ..
224  COMMON / infoc / infot, nunit, ok, lerr
225  COMMON / srnamc / srnamt
226 * ..
227 * .. Data statements ..
228  DATA iseedy / 1988, 1989, 1990, 1991 /
229  DATA uplos / 'U', 'L' /
230 * ..
231 * .. Executable Statements ..
232 *
233 * Initialize constants and the random number seed.
234 *
235  path( 1: 1 ) = 'Double precision'
236  path( 2: 3 ) = 'SP'
237  nrun = 0
238  nfail = 0
239  nerrs = 0
240  DO 10 i = 1, 4
241  iseed( i ) = iseedy( i )
242  10 CONTINUE
243 *
244 * Test the error exits
245 *
246  IF( tsterr )
247  $ CALL derrsy( path, nout )
248  infot = 0
249 *
250 * Do for each value of N in NVAL
251 *
252  DO 170 in = 1, nn
253  n = nval( in )
254  lda = max( n, 1 )
255  xtype = 'N'
256  nimat = ntypes
257  IF( n.LE.0 )
258  $ nimat = 1
259 *
260  izero = 0
261  DO 160 imat = 1, nimat
262 *
263 * Do the tests only if DOTYPE( IMAT ) is true.
264 *
265  IF( .NOT.dotype( imat ) )
266  $ GO TO 160
267 *
268 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
269 *
270  zerot = imat.GE.3 .AND. imat.LE.6
271  IF( zerot .AND. n.LT.imat-2 )
272  $ GO TO 160
273 *
274 * Do first for UPLO = 'U', then for UPLO = 'L'
275 *
276  DO 150 iuplo = 1, 2
277  uplo = uplos( iuplo )
278  IF( lsame( uplo, 'U' ) ) THEN
279  packit = 'C'
280  ELSE
281  packit = 'R'
282  END IF
283 *
284 * Set up parameters with DLATB4 and generate a test matrix
285 * with DLATMS.
286 *
287  CALL dlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
288  $ cndnum, dist )
289 *
290  srnamt = 'DLATMS'
291  CALL dlatms( n, n, dist, iseed, TYPE, rwork, mode,
292  $ cndnum, anorm, kl, ku, packit, a, lda, work,
293  $ info )
294 *
295 * Check error code from DLATMS.
296 *
297  IF( info.NE.0 ) THEN
298  CALL alaerh( path, 'DLATMS', info, 0, uplo, n, n, -1,
299  $ -1, -1, imat, nfail, nerrs, nout )
300  GO TO 150
301  END IF
302 *
303 * For types 3-6, zero one or more rows and columns of
304 * the matrix to test that INFO is returned correctly.
305 *
306  IF( zerot ) THEN
307  IF( imat.EQ.3 ) THEN
308  izero = 1
309  ELSE IF( imat.EQ.4 ) THEN
310  izero = n
311  ELSE
312  izero = n / 2 + 1
313  END IF
314 *
315  IF( imat.LT.6 ) THEN
316 *
317 * Set row and column IZERO to zero.
318 *
319  IF( iuplo.EQ.1 ) THEN
320  ioff = ( izero-1 )*izero / 2
321  DO 20 i = 1, izero - 1
322  a( ioff+i ) = zero
323  20 CONTINUE
324  ioff = ioff + izero
325  DO 30 i = izero, n
326  a( ioff ) = zero
327  ioff = ioff + i
328  30 CONTINUE
329  ELSE
330  ioff = izero
331  DO 40 i = 1, izero - 1
332  a( ioff ) = zero
333  ioff = ioff + n - i
334  40 CONTINUE
335  ioff = ioff - izero
336  DO 50 i = izero, n
337  a( ioff+i ) = zero
338  50 CONTINUE
339  END IF
340  ELSE
341  ioff = 0
342  IF( iuplo.EQ.1 ) THEN
343 *
344 * Set the first IZERO rows and columns to zero.
345 *
346  DO 70 j = 1, n
347  i2 = min( j, izero )
348  DO 60 i = 1, i2
349  a( ioff+i ) = zero
350  60 CONTINUE
351  ioff = ioff + j
352  70 CONTINUE
353  ELSE
354 *
355 * Set the last IZERO rows and columns to zero.
356 *
357  DO 90 j = 1, n
358  i1 = max( j, izero )
359  DO 80 i = i1, n
360  a( ioff+i ) = zero
361  80 CONTINUE
362  ioff = ioff + n - j
363  90 CONTINUE
364  END IF
365  END IF
366  ELSE
367  izero = 0
368  END IF
369 *
370 * Compute the L*D*L' or U*D*U' factorization of the matrix.
371 *
372  npp = n*( n+1 ) / 2
373  CALL dcopy( npp, a, 1, afac, 1 )
374  srnamt = 'DSPTRF'
375  CALL dsptrf( uplo, n, afac, iwork, info )
376 *
377 * Adjust the expected value of INFO to account for
378 * pivoting.
379 *
380  k = izero
381  IF( k.GT.0 ) THEN
382  100 CONTINUE
383  IF( iwork( k ).LT.0 ) THEN
384  IF( iwork( k ).NE.-k ) THEN
385  k = -iwork( k )
386  GO TO 100
387  END IF
388  ELSE IF( iwork( k ).NE.k ) THEN
389  k = iwork( k )
390  GO TO 100
391  END IF
392  END IF
393 *
394 * Check error code from DSPTRF.
395 *
396  IF( info.NE.k )
397  $ CALL alaerh( path, 'DSPTRF', info, k, uplo, n, n, -1,
398  $ -1, -1, imat, nfail, nerrs, nout )
399  IF( info.NE.0 ) THEN
400  trfcon = .true.
401  ELSE
402  trfcon = .false.
403  END IF
404 *
405 *+ TEST 1
406 * Reconstruct matrix from factors and compute residual.
407 *
408  CALL dspt01( uplo, n, a, afac, iwork, ainv, lda, rwork,
409  $ result( 1 ) )
410  nt = 1
411 *
412 *+ TEST 2
413 * Form the inverse and compute the residual.
414 *
415  IF( .NOT.trfcon ) THEN
416  CALL dcopy( npp, afac, 1, ainv, 1 )
417  srnamt = 'DSPTRI'
418  CALL dsptri( uplo, n, ainv, iwork, work, info )
419 *
420 * Check error code from DSPTRI.
421 *
422  IF( info.NE.0 )
423  $ CALL alaerh( path, 'DSPTRI', info, 0, uplo, n, n,
424  $ -1, -1, -1, imat, nfail, nerrs, nout )
425 *
426  CALL dppt03( uplo, n, a, ainv, work, lda, rwork,
427  $ rcondc, result( 2 ) )
428  nt = 2
429  END IF
430 *
431 * Print information about the tests that did not pass
432 * the threshold.
433 *
434  DO 110 k = 1, nt
435  IF( result( k ).GE.thresh ) THEN
436  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
437  $ CALL alahd( nout, path )
438  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
439  $ result( k )
440  nfail = nfail + 1
441  END IF
442  110 CONTINUE
443  nrun = nrun + nt
444 *
445 * Do only the condition estimate if INFO is not 0.
446 *
447  IF( trfcon ) THEN
448  rcondc = zero
449  GO TO 140
450  END IF
451 *
452  DO 130 irhs = 1, nns
453  nrhs = nsval( irhs )
454 *
455 *+ TEST 3
456 * Solve and compute residual for A * X = B.
457 *
458  srnamt = 'DLARHS'
459  CALL dlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
460  $ nrhs, a, lda, xact, lda, b, lda, iseed,
461  $ info )
462  CALL dlacpy( 'Full', n, nrhs, b, lda, x, lda )
463 *
464  srnamt = 'DSPTRS'
465  CALL dsptrs( uplo, n, nrhs, afac, iwork, x, lda,
466  $ info )
467 *
468 * Check error code from DSPTRS.
469 *
470  IF( info.NE.0 )
471  $ CALL alaerh( path, 'DSPTRS', info, 0, uplo, n, n,
472  $ -1, -1, nrhs, imat, nfail, nerrs,
473  $ nout )
474 *
475  CALL dlacpy( 'Full', n, nrhs, b, lda, work, lda )
476  CALL dppt02( uplo, n, nrhs, a, x, lda, work, lda,
477  $ rwork, result( 3 ) )
478 *
479 *+ TEST 4
480 * Check solution from generated exact solution.
481 *
482  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
483  $ result( 4 ) )
484 *
485 *+ TESTS 5, 6, and 7
486 * Use iterative refinement to improve the solution.
487 *
488  srnamt = 'DSPRFS'
489  CALL dsprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
490  $ lda, rwork, rwork( nrhs+1 ), work,
491  $ iwork( n+1 ), info )
492 *
493 * Check error code from DSPRFS.
494 *
495  IF( info.NE.0 )
496  $ CALL alaerh( path, 'DSPRFS', info, 0, uplo, n, n,
497  $ -1, -1, nrhs, imat, nfail, nerrs,
498  $ nout )
499 *
500  CALL dget04( n, nrhs, x, lda, xact, lda, rcondc,
501  $ result( 5 ) )
502  CALL dppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
503  $ lda, rwork, rwork( nrhs+1 ),
504  $ result( 6 ) )
505 *
506 * Print information about the tests that did not pass
507 * the threshold.
508 *
509  DO 120 k = 3, 7
510  IF( result( k ).GE.thresh ) THEN
511  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
512  $ CALL alahd( nout, path )
513  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
514  $ k, result( k )
515  nfail = nfail + 1
516  END IF
517  120 CONTINUE
518  nrun = nrun + 5
519  130 CONTINUE
520 *
521 *+ TEST 8
522 * Get an estimate of RCOND = 1/CNDNUM.
523 *
524  140 CONTINUE
525  anorm = dlansp( '1', uplo, n, a, rwork )
526  srnamt = 'DSPCON'
527  CALL dspcon( uplo, n, afac, iwork, anorm, rcond, work,
528  $ iwork( n+1 ), info )
529 *
530 * Check error code from DSPCON.
531 *
532  IF( info.NE.0 )
533  $ CALL alaerh( path, 'DSPCON', info, 0, uplo, n, n, -1,
534  $ -1, -1, imat, nfail, nerrs, nout )
535 *
536  result( 8 ) = dget06( rcond, rcondc )
537 *
538 * Print the test ratio if it is .GE. THRESH.
539 *
540  IF( result( 8 ).GE.thresh ) THEN
541  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
542  $ CALL alahd( nout, path )
543  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
544  $ result( 8 )
545  nfail = nfail + 1
546  END IF
547  nrun = nrun + 1
548  150 CONTINUE
549  160 CONTINUE
550  170 CONTINUE
551 *
552 * Print a summary of the results.
553 *
554  CALL alasum( path, nout, nfail, nrun, nerrs )
555 *
556  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
557  $ i2, ', ratio =', g12.5 )
558  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
559  $ i2, ', test(', i2, ') =', g12.5 )
560  RETURN
561 *
562 * End of DCHKSP
563 *
564  END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.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 dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
DLARHS
Definition: dlarhs.f:205
subroutine dppt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
DPPT02
Definition: dppt02.f:122
subroutine dget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
DGET04
Definition: dget04.f:102
subroutine dspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
DSPT01
Definition: dspt01.f:110
subroutine derrsy(PATH, NUNIT)
DERRSY
Definition: derrsy.f:55
subroutine dppt03(UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
DPPT03
Definition: dppt03.f:110
subroutine dchksp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
DCHKSP
Definition: dchksp.f:163
subroutine dlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
DLATB4
Definition: dlatb4.f:120
subroutine dppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
DPPT05
Definition: dppt05.f:156
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dsptri(UPLO, N, AP, IPIV, WORK, INFO)
DSPTRI
Definition: dsptri.f:109
subroutine dsptrf(UPLO, N, AP, IPIV, INFO)
DSPTRF
Definition: dsptrf.f:159
subroutine dsprfs(UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DSPRFS
Definition: dsprfs.f:179
subroutine dsptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
DSPTRS
Definition: dsptrs.f:115
subroutine dspcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DSPCON
Definition: dspcon.f:125