LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cchksp.f
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1 *> \brief \b CCHKSP
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 CCHKSP( 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 RWORK( * )
24 * COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
25 * $ WORK( * ), X( * ), XACT( * )
26 * ..
27 *
28 *
29 *> \par Purpose:
30 * =============
31 *>
32 *> \verbatim
33 *>
34 *> CCHKSP tests CSPTRF, -TRI, -TRS, -RFS, and -CON
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] DOTYPE
41 *> \verbatim
42 *> DOTYPE is LOGICAL array, dimension (NTYPES)
43 *> The matrix types to be used for testing. Matrices of type j
44 *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
45 *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
46 *> \endverbatim
47 *>
48 *> \param[in] NN
49 *> \verbatim
50 *> NN is INTEGER
51 *> The number of values of N contained in the vector NVAL.
52 *> \endverbatim
53 *>
54 *> \param[in] NVAL
55 *> \verbatim
56 *> NVAL is INTEGER array, dimension (NN)
57 *> The values of the matrix dimension N.
58 *> \endverbatim
59 *>
60 *> \param[in] NNS
61 *> \verbatim
62 *> NNS is INTEGER
63 *> The number of values of NRHS contained in the vector NSVAL.
64 *> \endverbatim
65 *>
66 *> \param[in] NSVAL
67 *> \verbatim
68 *> NSVAL is INTEGER array, dimension (NNS)
69 *> The values of the number of right hand sides NRHS.
70 *> \endverbatim
71 *>
72 *> \param[in] THRESH
73 *> \verbatim
74 *> THRESH is REAL
75 *> The threshold value for the test ratios. A result is
76 *> included in the output file if RESULT >= THRESH. To have
77 *> every test ratio printed, use THRESH = 0.
78 *> \endverbatim
79 *>
80 *> \param[in] TSTERR
81 *> \verbatim
82 *> TSTERR is LOGICAL
83 *> Flag that indicates whether error exits are to be tested.
84 *> \endverbatim
85 *>
86 *> \param[in] NMAX
87 *> \verbatim
88 *> NMAX is INTEGER
89 *> The maximum value permitted for N, used in dimensioning the
90 *> work arrays.
91 *> \endverbatim
92 *>
93 *> \param[out] A
94 *> \verbatim
95 *> A is COMPLEX array, dimension
96 *> (NMAX*(NMAX+1)/2)
97 *> \endverbatim
98 *>
99 *> \param[out] AFAC
100 *> \verbatim
101 *> AFAC is COMPLEX array, dimension
102 *> (NMAX*(NMAX+1)/2)
103 *> \endverbatim
104 *>
105 *> \param[out] AINV
106 *> \verbatim
107 *> AINV is COMPLEX array, dimension
108 *> (NMAX*(NMAX+1)/2)
109 *> \endverbatim
110 *>
111 *> \param[out] B
112 *> \verbatim
113 *> B is COMPLEX array, dimension (NMAX*NSMAX)
114 *> where NSMAX is the largest entry in NSVAL.
115 *> \endverbatim
116 *>
117 *> \param[out] X
118 *> \verbatim
119 *> X is COMPLEX array, dimension (NMAX*NSMAX)
120 *> \endverbatim
121 *>
122 *> \param[out] XACT
123 *> \verbatim
124 *> XACT is COMPLEX array, dimension (NMAX*NSMAX)
125 *> \endverbatim
126 *>
127 *> \param[out] WORK
128 *> \verbatim
129 *> WORK is COMPLEX array, dimension
130 *> (NMAX*max(2,NSMAX))
131 *> \endverbatim
132 *>
133 *> \param[out] RWORK
134 *> \verbatim
135 *> RWORK is REAL array,
136 *> dimension (NMAX+2*NSMAX)
137 *> \endverbatim
138 *>
139 *> \param[out] IWORK
140 *> \verbatim
141 *> IWORK is INTEGER array, dimension (NMAX)
142 *> \endverbatim
143 *>
144 *> \param[in] NOUT
145 *> \verbatim
146 *> NOUT is INTEGER
147 *> The unit number for output.
148 *> \endverbatim
149 *
150 * Authors:
151 * ========
152 *
153 *> \author Univ. of Tennessee
154 *> \author Univ. of California Berkeley
155 *> \author Univ. of Colorado Denver
156 *> \author NAG Ltd.
157 *
158 *> \ingroup complex_lin
159 *
160 * =====================================================================
161  SUBROUTINE cchksp( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
162  $ NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK,
163  $ IWORK, NOUT )
164 *
165 * -- LAPACK test routine --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 *
169 * .. Scalar Arguments ..
170  LOGICAL TSTERR
171  INTEGER NMAX, NN, NNS, NOUT
172  REAL THRESH
173 * ..
174 * .. Array Arguments ..
175  LOGICAL DOTYPE( * )
176  INTEGER IWORK( * ), NSVAL( * ), NVAL( * )
177  REAL RWORK( * )
178  COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
179  $ work( * ), x( * ), xact( * )
180 * ..
181 *
182 * =====================================================================
183 *
184 * .. Parameters ..
185  REAL ZERO
186  PARAMETER ( ZERO = 0.0e+0 )
187  INTEGER NTYPES
188  parameter( ntypes = 11 )
189  INTEGER NTESTS
190  parameter( ntests = 8 )
191 * ..
192 * .. Local Scalars ..
193  LOGICAL TRFCON, ZEROT
194  CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
195  CHARACTER*3 PATH
196  INTEGER I, I1, I2, IMAT, IN, INFO, IOFF, IRHS, IUPLO,
197  $ izero, j, k, kl, ku, lda, mode, n, nerrs,
198  $ nfail, nimat, npp, nrhs, nrun, nt
199  REAL ANORM, CNDNUM, RCOND, RCONDC
200 * ..
201 * .. Local Arrays ..
202  CHARACTER UPLOS( 2 )
203  INTEGER ISEED( 4 ), ISEEDY( 4 )
204  REAL RESULT( NTESTS )
205 * ..
206 * .. External Functions ..
207  LOGICAL LSAME
208  REAL CLANSP, SGET06
209  EXTERNAL lsame, clansp, sget06
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL alaerh, alahd, alasum, ccopy, cerrsy, cget04,
215  $ csptri, csptrs
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC max, min
219 * ..
220 * .. Scalars in Common ..
221  LOGICAL LERR, OK
222  CHARACTER*32 SRNAMT
223  INTEGER INFOT, NUNIT
224 * ..
225 * .. Common blocks ..
226  COMMON / infoc / infot, nunit, ok, lerr
227  COMMON / srnamc / srnamt
228 * ..
229 * .. Data statements ..
230  DATA iseedy / 1988, 1989, 1990, 1991 /
231  DATA uplos / 'U', 'L' /
232 * ..
233 * .. Executable Statements ..
234 *
235 * Initialize constants and the random number seed.
236 *
237  path( 1: 1 ) = 'Complex precision'
238  path( 2: 3 ) = 'SP'
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 cerrsy( path, nout )
250  infot = 0
251 *
252 * Do for each value of N in NVAL
253 *
254  DO 170 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 160 imat = 1, nimat
263 *
264 * Do the tests only if DOTYPE( IMAT ) is true.
265 *
266  IF( .NOT.dotype( imat ) )
267  $ GO TO 160
268 *
269 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
270 *
271  zerot = imat.GE.3 .AND. imat.LE.6
272  IF( zerot .AND. n.LT.imat-2 )
273  $ GO TO 160
274 *
275 * Do first for UPLO = 'U', then for UPLO = 'L'
276 *
277  DO 150 iuplo = 1, 2
278  uplo = uplos( iuplo )
279  IF( lsame( uplo, 'U' ) ) THEN
280  packit = 'C'
281  ELSE
282  packit = 'R'
283  END IF
284 *
285  IF( imat.NE.ntypes ) THEN
286 *
287 * Set up parameters with CLATB4 and generate a test
288 * matrix with CLATMS.
289 *
290  CALL clatb4( path, imat, n, n, TYPE, kl, ku, anorm,
291  $ mode, cndnum, dist )
292 *
293  srnamt = 'CLATMS'
294  CALL clatms( n, n, dist, iseed, TYPE, rwork, mode,
295  $ cndnum, anorm, kl, ku, packit, a, lda,
296  $ work, info )
297 *
298 * Check error code from CLATMS.
299 *
300  IF( info.NE.0 ) THEN
301  CALL alaerh( path, 'CLATMS', info, 0, uplo, n, n,
302  $ -1, -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  IF( iuplo.EQ.1 ) THEN
345 *
346 * Set the first IZERO rows and columns to zero.
347 *
348  ioff = 0
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  ioff = 0
361  DO 90 j = 1, n
362  i1 = max( j, izero )
363  DO 80 i = i1, n
364  a( ioff+i ) = zero
365  80 CONTINUE
366  ioff = ioff + n - j
367  90 CONTINUE
368  END IF
369  END IF
370  ELSE
371  izero = 0
372  END IF
373  ELSE
374 *
375 * Use a special block diagonal matrix to test alternate
376 * code for the 2 x 2 blocks.
377 *
378  CALL clatsp( uplo, n, a, iseed )
379  END IF
380 *
381 * Compute the L*D*L' or U*D*U' factorization of the matrix.
382 *
383  npp = n*( n+1 ) / 2
384  CALL ccopy( npp, a, 1, afac, 1 )
385  srnamt = 'CSPTRF'
386  CALL csptrf( uplo, n, afac, iwork, info )
387 *
388 * Adjust the expected value of INFO to account for
389 * pivoting.
390 *
391  k = izero
392  IF( k.GT.0 ) THEN
393  100 CONTINUE
394  IF( iwork( k ).LT.0 ) THEN
395  IF( iwork( k ).NE.-k ) THEN
396  k = -iwork( k )
397  GO TO 100
398  END IF
399  ELSE IF( iwork( k ).NE.k ) THEN
400  k = iwork( k )
401  GO TO 100
402  END IF
403  END IF
404 *
405 * Check error code from CSPTRF.
406 *
407  IF( info.NE.k )
408  $ CALL alaerh( path, 'CSPTRF', info, k, uplo, n, n, -1,
409  $ -1, -1, imat, nfail, nerrs, nout )
410  IF( info.NE.0 ) THEN
411  trfcon = .true.
412  ELSE
413  trfcon = .false.
414  END IF
415 *
416 *+ TEST 1
417 * Reconstruct matrix from factors and compute residual.
418 *
419  CALL cspt01( uplo, n, a, afac, iwork, ainv, lda, rwork,
420  $ result( 1 ) )
421  nt = 1
422 *
423 *+ TEST 2
424 * Form the inverse and compute the residual.
425 *
426  IF( .NOT.trfcon ) THEN
427  CALL ccopy( npp, afac, 1, ainv, 1 )
428  srnamt = 'CSPTRI'
429  CALL csptri( uplo, n, ainv, iwork, work, info )
430 *
431 * Check error code from CSPTRI.
432 *
433  IF( info.NE.0 )
434  $ CALL alaerh( path, 'CSPTRI', info, 0, uplo, n, n,
435  $ -1, -1, -1, imat, nfail, nerrs, nout )
436 *
437  CALL cspt03( uplo, n, a, ainv, work, lda, rwork,
438  $ rcondc, result( 2 ) )
439  nt = 2
440  END IF
441 *
442 * Print information about the tests that did not pass
443 * the threshold.
444 *
445  DO 110 k = 1, nt
446  IF( result( k ).GE.thresh ) THEN
447  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
448  $ CALL alahd( nout, path )
449  WRITE( nout, fmt = 9999 )uplo, n, imat, k,
450  $ result( k )
451  nfail = nfail + 1
452  END IF
453  110 CONTINUE
454  nrun = nrun + nt
455 *
456 * Do only the condition estimate if INFO is not 0.
457 *
458  IF( trfcon ) THEN
459  rcondc = zero
460  GO TO 140
461  END IF
462 *
463  DO 130 irhs = 1, nns
464  nrhs = nsval( irhs )
465 *
466 *+ TEST 3
467 * Solve and compute residual for A * X = B.
468 *
469  srnamt = 'CLARHS'
470  CALL clarhs( path, xtype, uplo, ' ', n, n, kl, ku,
471  $ nrhs, a, lda, xact, lda, b, lda, iseed,
472  $ info )
473  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
474 *
475  srnamt = 'CSPTRS'
476  CALL csptrs( uplo, n, nrhs, afac, iwork, x, lda,
477  $ info )
478 *
479 * Check error code from CSPTRS.
480 *
481  IF( info.NE.0 )
482  $ CALL alaerh( path, 'CSPTRS', info, 0, uplo, n, n,
483  $ -1, -1, nrhs, imat, nfail, nerrs,
484  $ nout )
485 *
486  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
487  CALL cspt02( uplo, n, nrhs, a, x, lda, work, lda,
488  $ rwork, result( 3 ) )
489 *
490 *+ TEST 4
491 * Check solution from generated exact solution.
492 *
493  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
494  $ result( 4 ) )
495 *
496 *+ TESTS 5, 6, and 7
497 * Use iterative refinement to improve the solution.
498 *
499  srnamt = 'CSPRFS'
500  CALL csprfs( uplo, n, nrhs, a, afac, iwork, b, lda, x,
501  $ lda, rwork, rwork( nrhs+1 ), work,
502  $ rwork( 2*nrhs+1 ), info )
503 *
504 * Check error code from CSPRFS.
505 *
506  IF( info.NE.0 )
507  $ CALL alaerh( path, 'CSPRFS', info, 0, uplo, n, n,
508  $ -1, -1, nrhs, imat, nfail, nerrs,
509  $ nout )
510 *
511  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
512  $ result( 5 ) )
513  CALL cppt05( uplo, n, nrhs, a, b, lda, x, lda, xact,
514  $ lda, rwork, rwork( nrhs+1 ),
515  $ result( 6 ) )
516 *
517 * Print information about the tests that did not pass
518 * the threshold.
519 *
520  DO 120 k = 3, 7
521  IF( result( k ).GE.thresh ) THEN
522  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
523  $ CALL alahd( nout, path )
524  WRITE( nout, fmt = 9998 )uplo, n, nrhs, imat,
525  $ k, result( k )
526  nfail = nfail + 1
527  END IF
528  120 CONTINUE
529  nrun = nrun + 5
530  130 CONTINUE
531 *
532 *+ TEST 8
533 * Get an estimate of RCOND = 1/CNDNUM.
534 *
535  140 CONTINUE
536  anorm = clansp( '1', uplo, n, a, rwork )
537  srnamt = 'CSPCON'
538  CALL cspcon( uplo, n, afac, iwork, anorm, rcond, work,
539  $ info )
540 *
541 * Check error code from CSPCON.
542 *
543  IF( info.NE.0 )
544  $ CALL alaerh( path, 'CSPCON', info, 0, uplo, n, n, -1,
545  $ -1, -1, imat, nfail, nerrs, nout )
546 *
547  result( 8 ) = sget06( rcond, rcondc )
548 *
549 * Print the test ratio if it is .GE. THRESH.
550 *
551  IF( result( 8 ).GE.thresh ) THEN
552  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
553  $ CALL alahd( nout, path )
554  WRITE( nout, fmt = 9999 )uplo, n, imat, 8,
555  $ result( 8 )
556  nfail = nfail + 1
557  END IF
558  nrun = nrun + 1
559  150 CONTINUE
560  160 CONTINUE
561  170 CONTINUE
562 *
563 * Print a summary of the results.
564 *
565  CALL alasum( path, nout, nfail, nrun, nerrs )
566 *
567  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', type ', i2, ', test ',
568  $ i2, ', ratio =', g12.5 )
569  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
570  $ i2, ', test(', i2, ') =', g12.5 )
571  RETURN
572 *
573 * End of CCHKSP
574 *
575  END
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 ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine clarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
CLARHS
Definition: clarhs.f:208
subroutine clatsp(UPLO, N, X, ISEED)
CLATSP
Definition: clatsp.f:84
subroutine clatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
Definition: clatb4.f:121
subroutine cspt02(UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CSPT02
Definition: cspt02.f:123
subroutine cget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
Definition: cget04.f:102
subroutine cerrsy(PATH, NUNIT)
CERRSY
Definition: cerrsy.f:55
subroutine cspt03(UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND, RESID)
CSPT03
Definition: cspt03.f:110
subroutine cspt01(UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CSPT01
Definition: cspt01.f:112
subroutine cppt05(UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPPT05
Definition: cppt05.f:157
subroutine cchksp(DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKSP
Definition: cchksp.f:164
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:332
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine csprfs(UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CSPRFS
Definition: csprfs.f:180
subroutine csptri(UPLO, N, AP, IPIV, WORK, INFO)
CSPTRI
Definition: csptri.f:109
subroutine csptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CSPTRS
Definition: csptrs.f:115
subroutine csptrf(UPLO, N, AP, IPIV, INFO)
CSPTRF
Definition: csptrf.f:158
subroutine cspcon(UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO)
CSPCON
Definition: cspcon.f:118