LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine schkpb ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, real, dimension( * ) A, real, dimension( * ) AFAC, real, dimension( * ) AINV, real, dimension( * ) B, real, dimension( * ) X, real, dimension( * ) XACT, real, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

SCHKPB

Purpose:
` SCHKPB tests SPBTRF, -TRS, -RFS, and -CON.`
Parameters
 [in] DOTYPE ``` DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.``` [in] NN ``` NN is INTEGER The number of values of N contained in the vector NVAL.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N.``` [in] NNB ``` NNB is INTEGER The number of values of NB contained in the vector NBVAL.``` [in] NBVAL ``` NBVAL is INTEGER array, dimension (NBVAL) The values of the blocksize NB.``` [in] NNS ``` NNS is INTEGER The number of values of NRHS contained in the vector NSVAL.``` [in] NSVAL ``` NSVAL is INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS.``` [in] THRESH ``` THRESH is REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0.``` [in] TSTERR ``` TSTERR is LOGICAL Flag that indicates whether error exits are to be tested.``` [in] NMAX ``` NMAX is INTEGER The maximum value permitted for N, used in dimensioning the work arrays.``` [out] A ` A is REAL array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is REAL array, dimension (NMAX*NMAX)` [out] AINV ` AINV is REAL array, dimension (NMAX*NMAX)` [out] B ``` B is REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.``` [out] X ` X is REAL array, dimension (NMAX*NSMAX)` [out] XACT ` XACT is REAL array, dimension (NMAX*NSMAX)` [out] WORK ``` WORK is REAL array, dimension (NMAX*max(3,NSMAX))``` [out] RWORK ``` RWORK is REAL array, dimension (max(NMAX,2*NSMAX))``` [out] IWORK ` IWORK is INTEGER array, dimension (NMAX)` [in] NOUT ``` NOUT is INTEGER The unit number for output.```
Date
November 2011

Definition at line 174 of file schkpb.f.

174 *
175 * -- LAPACK test routine (version 3.4.0) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * November 2011
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 one, zero
196  parameter ( one = 1.0e+0, zero = 0.0e+0 )
197  INTEGER ntypes, ntests
198  parameter ( ntypes = 8, ntests = 7 )
199  INTEGER nbw
200  parameter ( nbw = 4 )
201 * ..
202 * .. Local Scalars ..
203  LOGICAL zerot
204  CHARACTER dist, packit, TYPE, uplo, xtype
205  CHARACTER*3 path
206  INTEGER i, i1, i2, ikd, imat, in, inb, info, ioff,
207  \$ irhs, iuplo, iw, izero, k, kd, kl, koff, ku,
208  \$ lda, ldab, mode, n, nb, nerrs, nfail, nimat,
209  \$ nkd, nrhs, nrun
210  REAL ainvnm, anorm, cndnum, rcond, rcondc
211 * ..
212 * .. Local Arrays ..
213  INTEGER iseed( 4 ), iseedy( 4 ), kdval( nbw )
214  REAL result( ntests )
215 * ..
216 * .. External Functions ..
217  REAL sget06, slange, slansb
218  EXTERNAL sget06, slange, slansb
219 * ..
220 * .. External Subroutines ..
221  EXTERNAL alaerh, alahd, alasum, scopy, serrpo, sget04,
224  \$ sswap, xlaenv
225 * ..
226 * .. Intrinsic Functions ..
227  INTRINSIC max, min
228 * ..
229 * .. Scalars in Common ..
230  LOGICAL lerr, ok
231  CHARACTER*32 srnamt
232  INTEGER infot, nunit
233 * ..
234 * .. Common blocks ..
235  COMMON / infoc / infot, nunit, ok, lerr
236  COMMON / srnamc / srnamt
237 * ..
238 * .. Data statements ..
239  DATA iseedy / 1988, 1989, 1990, 1991 /
240 * ..
241 * .. Executable Statements ..
242 *
243 * Initialize constants and the random number seed.
244 *
245  path( 1: 1 ) = 'Single precision'
246  path( 2: 3 ) = 'PB'
247  nrun = 0
248  nfail = 0
249  nerrs = 0
250  DO 10 i = 1, 4
251  iseed( i ) = iseedy( i )
252  10 CONTINUE
253 *
254 * Test the error exits
255 *
256  IF( tsterr )
257  \$ CALL serrpo( path, nout )
258  infot = 0
259  CALL xlaenv( 2, 2 )
260  kdval( 1 ) = 0
261 *
262 * Do for each value of N in NVAL
263 *
264  DO 90 in = 1, nn
265  n = nval( in )
266  lda = max( n, 1 )
267  xtype = 'N'
268 *
269 * Set limits on the number of loop iterations.
270 *
271  nkd = max( 1, min( n, 4 ) )
272  nimat = ntypes
273  IF( n.EQ.0 )
274  \$ nimat = 1
275 *
276  kdval( 2 ) = n + ( n+1 ) / 4
277  kdval( 3 ) = ( 3*n-1 ) / 4
278  kdval( 4 ) = ( n+1 ) / 4
279 *
280  DO 80 ikd = 1, nkd
281 *
282 * Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
283 * makes it easier to skip redundant values for small values
284 * of N.
285 *
286  kd = kdval( ikd )
287  ldab = kd + 1
288 *
289 * Do first for UPLO = 'U', then for UPLO = 'L'
290 *
291  DO 70 iuplo = 1, 2
292  koff = 1
293  IF( iuplo.EQ.1 ) THEN
294  uplo = 'U'
295  koff = max( 1, kd+2-n )
296  packit = 'Q'
297  ELSE
298  uplo = 'L'
299  packit = 'B'
300  END IF
301 *
302  DO 60 imat = 1, nimat
303 *
304 * Do the tests only if DOTYPE( IMAT ) is true.
305 *
306  IF( .NOT.dotype( imat ) )
307  \$ GO TO 60
308 *
309 * Skip types 2, 3, or 4 if the matrix size is too small.
310 *
311  zerot = imat.GE.2 .AND. imat.LE.4
312  IF( zerot .AND. n.LT.imat-1 )
313  \$ GO TO 60
314 *
315  IF( .NOT.zerot .OR. .NOT.dotype( 1 ) ) THEN
316 *
317 * Set up parameters with SLATB4 and generate a test
318 * matrix with SLATMS.
319 *
320  CALL slatb4( path, imat, n, n, TYPE, kl, ku, anorm,
321  \$ mode, cndnum, dist )
322 *
323  srnamt = 'SLATMS'
324  CALL slatms( n, n, dist, iseed, TYPE, rwork, mode,
325  \$ cndnum, anorm, kd, kd, packit,
326  \$ a( koff ), ldab, work, info )
327 *
328 * Check error code from SLATMS.
329 *
330  IF( info.NE.0 ) THEN
331  CALL alaerh( path, 'SLATMS', info, 0, uplo, n,
332  \$ n, kd, kd, -1, imat, nfail, nerrs,
333  \$ nout )
334  GO TO 60
335  END IF
336  ELSE IF( izero.GT.0 ) THEN
337 *
338 * Use the same matrix for types 3 and 4 as for type
339 * 2 by copying back the zeroed out column,
340 *
341  iw = 2*lda + 1
342  IF( iuplo.EQ.1 ) THEN
343  ioff = ( izero-1 )*ldab + kd + 1
344  CALL scopy( izero-i1, work( iw ), 1,
345  \$ a( ioff-izero+i1 ), 1 )
346  iw = iw + izero - i1
347  CALL scopy( i2-izero+1, work( iw ), 1,
348  \$ a( ioff ), max( ldab-1, 1 ) )
349  ELSE
350  ioff = ( i1-1 )*ldab + 1
351  CALL scopy( izero-i1, work( iw ), 1,
352  \$ a( ioff+izero-i1 ),
353  \$ max( ldab-1, 1 ) )
354  ioff = ( izero-1 )*ldab + 1
355  iw = iw + izero - i1
356  CALL scopy( i2-izero+1, work( iw ), 1,
357  \$ a( ioff ), 1 )
358  END IF
359  END IF
360 *
361 * For types 2-4, zero one row and column of the matrix
362 * to test that INFO is returned correctly.
363 *
364  izero = 0
365  IF( zerot ) THEN
366  IF( imat.EQ.2 ) THEN
367  izero = 1
368  ELSE IF( imat.EQ.3 ) THEN
369  izero = n
370  ELSE
371  izero = n / 2 + 1
372  END IF
373 *
374 * Save the zeroed out row and column in WORK(*,3)
375 *
376  iw = 2*lda
377  DO 20 i = 1, min( 2*kd+1, n )
378  work( iw+i ) = zero
379  20 CONTINUE
380  iw = iw + 1
381  i1 = max( izero-kd, 1 )
382  i2 = min( izero+kd, n )
383 *
384  IF( iuplo.EQ.1 ) THEN
385  ioff = ( izero-1 )*ldab + kd + 1
386  CALL sswap( izero-i1, a( ioff-izero+i1 ), 1,
387  \$ work( iw ), 1 )
388  iw = iw + izero - i1
389  CALL sswap( i2-izero+1, a( ioff ),
390  \$ max( ldab-1, 1 ), work( iw ), 1 )
391  ELSE
392  ioff = ( i1-1 )*ldab + 1
393  CALL sswap( izero-i1, a( ioff+izero-i1 ),
394  \$ max( ldab-1, 1 ), work( iw ), 1 )
395  ioff = ( izero-1 )*ldab + 1
396  iw = iw + izero - i1
397  CALL sswap( i2-izero+1, a( ioff ), 1,
398  \$ work( iw ), 1 )
399  END IF
400  END IF
401 *
402 * Do for each value of NB in NBVAL
403 *
404  DO 50 inb = 1, nnb
405  nb = nbval( inb )
406  CALL xlaenv( 1, nb )
407 *
408 * Compute the L*L' or U'*U factorization of the band
409 * matrix.
410 *
411  CALL slacpy( 'Full', kd+1, n, a, ldab, afac, ldab )
412  srnamt = 'SPBTRF'
413  CALL spbtrf( uplo, n, kd, afac, ldab, info )
414 *
415 * Check error code from SPBTRF.
416 *
417  IF( info.NE.izero ) THEN
418  CALL alaerh( path, 'SPBTRF', info, izero, uplo,
419  \$ n, n, kd, kd, nb, imat, nfail,
420  \$ nerrs, nout )
421  GO TO 50
422  END IF
423 *
424 * Skip the tests if INFO is not 0.
425 *
426  IF( info.NE.0 )
427  \$ GO TO 50
428 *
429 *+ TEST 1
430 * Reconstruct matrix from factors and compute
431 * residual.
432 *
433  CALL slacpy( 'Full', kd+1, n, afac, ldab, ainv,
434  \$ ldab )
435  CALL spbt01( uplo, n, kd, a, ldab, ainv, ldab,
436  \$ rwork, result( 1 ) )
437 *
438 * Print the test ratio if it is .GE. THRESH.
439 *
440  IF( result( 1 ).GE.thresh ) THEN
441  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
442  \$ CALL alahd( nout, path )
443  WRITE( nout, fmt = 9999 )uplo, n, kd, nb, imat,
444  \$ 1, result( 1 )
445  nfail = nfail + 1
446  END IF
447  nrun = nrun + 1
448 *
449 * Only do other tests if this is the first blocksize.
450 *
451  IF( inb.GT.1 )
452  \$ GO TO 50
453 *
454 * Form the inverse of A so we can get a good estimate
455 * of RCONDC = 1/(norm(A) * norm(inv(A))).
456 *
457  CALL slaset( 'Full', n, n, zero, one, ainv, lda )
458  srnamt = 'SPBTRS'
459  CALL spbtrs( uplo, n, kd, n, afac, ldab, ainv, lda,
460  \$ info )
461 *
462 * Compute RCONDC = 1/(norm(A) * norm(inv(A))).
463 *
464  anorm = slansb( '1', uplo, n, kd, a, ldab, rwork )
465  ainvnm = slange( '1', n, n, ainv, lda, rwork )
466  IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
467  rcondc = one
468  ELSE
469  rcondc = ( one / anorm ) / ainvnm
470  END IF
471 *
472  DO 40 irhs = 1, nns
473  nrhs = nsval( irhs )
474 *
475 *+ TEST 2
476 * Solve and compute residual for A * X = B.
477 *
478  srnamt = 'SLARHS'
479  CALL slarhs( path, xtype, uplo, ' ', n, n, kd,
480  \$ kd, nrhs, a, ldab, xact, lda, b,
481  \$ lda, iseed, info )
482  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
483 *
484  srnamt = 'SPBTRS'
485  CALL spbtrs( uplo, n, kd, nrhs, afac, ldab, x,
486  \$ lda, info )
487 *
488 * Check error code from SPBTRS.
489 *
490  IF( info.NE.0 )
491  \$ CALL alaerh( path, 'SPBTRS', info, 0, uplo,
492  \$ n, n, kd, kd, nrhs, imat, nfail,
493  \$ nerrs, nout )
494 *
495  CALL slacpy( 'Full', n, nrhs, b, lda, work,
496  \$ lda )
497  CALL spbt02( uplo, n, kd, nrhs, a, ldab, x, lda,
498  \$ work, lda, rwork, result( 2 ) )
499 *
500 *+ TEST 3
501 * Check solution from generated exact solution.
502 *
503  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
504  \$ result( 3 ) )
505 *
506 *+ TESTS 4, 5, and 6
507 * Use iterative refinement to improve the solution.
508 *
509  srnamt = 'SPBRFS'
510  CALL spbrfs( uplo, n, kd, nrhs, a, ldab, afac,
511  \$ ldab, b, lda, x, lda, rwork,
512  \$ rwork( nrhs+1 ), work, iwork,
513  \$ info )
514 *
515 * Check error code from SPBRFS.
516 *
517  IF( info.NE.0 )
518  \$ CALL alaerh( path, 'SPBRFS', info, 0, uplo,
519  \$ n, n, kd, kd, nrhs, imat, nfail,
520  \$ nerrs, nout )
521 *
522  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
523  \$ result( 4 ) )
524  CALL spbt05( uplo, n, kd, nrhs, a, ldab, b, lda,
525  \$ x, lda, xact, lda, rwork,
526  \$ rwork( nrhs+1 ), result( 5 ) )
527 *
528 * Print information about the tests that did not
529 * pass the threshold.
530 *
531  DO 30 k = 2, 6
532  IF( result( k ).GE.thresh ) THEN
533  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
534  \$ CALL alahd( nout, path )
535  WRITE( nout, fmt = 9998 )uplo, n, kd,
536  \$ nrhs, imat, k, result( k )
537  nfail = nfail + 1
538  END IF
539  30 CONTINUE
540  nrun = nrun + 5
541  40 CONTINUE
542 *
543 *+ TEST 7
544 * Get an estimate of RCOND = 1/CNDNUM.
545 *
546  srnamt = 'SPBCON'
547  CALL spbcon( uplo, n, kd, afac, ldab, anorm, rcond,
548  \$ work, iwork, info )
549 *
550 * Check error code from SPBCON.
551 *
552  IF( info.NE.0 )
553  \$ CALL alaerh( path, 'SPBCON', info, 0, uplo, n,
554  \$ n, kd, kd, -1, imat, nfail, nerrs,
555  \$ nout )
556 *
557  result( 7 ) = sget06( rcond, rcondc )
558 *
559 * Print the test ratio if it is .GE. THRESH.
560 *
561  IF( result( 7 ).GE.thresh ) THEN
562  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
563  \$ CALL alahd( nout, path )
564  WRITE( nout, fmt = 9997 )uplo, n, kd, imat, 7,
565  \$ result( 7 )
566  nfail = nfail + 1
567  END IF
568  nrun = nrun + 1
569  50 CONTINUE
570  60 CONTINUE
571  70 CONTINUE
572  80 CONTINUE
573  90 CONTINUE
574 *
575 * Print a summary of the results.
576 *
577  CALL alasum( path, nout, nfail, nrun, nerrs )
578 *
579  9999 FORMAT( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NB=', i4,
580  \$ ', type ', i2, ', test ', i2, ', ratio= ', g12.5 )
581  9998 FORMAT( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ', NRHS=', i3,
582  \$ ', type ', i2, ', test(', i2, ') = ', g12.5 )
583  9997 FORMAT( ' UPLO=''', a1, ''', N=', i5, ', KD=', i5, ',', 10x,
584  \$ ' type ', i2, ', test(', i2, ') = ', g12.5 )
585  RETURN
586 *
587 * End of SCHKPB
588 *
subroutine alahd(IOUNIT, PATH)
ALAHD
Definition: alahd.f:95
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 spbt02(UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
SPBT02
Definition: spbt02.f:138
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 spbcon(UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO)
SPBCON
Definition: spbcon.f:134
real function sget06(RCOND, RCONDC)
SGET06
Definition: sget06.f:57
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine spbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
SPBTRS
Definition: spbtrs.f:123
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 slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:323
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: slaset.f:112
subroutine spbrfs(UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SPBRFS
Definition: spbrfs.f:191
real function slansb(NORM, UPLO, N, K, AB, LDAB, WORK)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
Definition: slansb.f:131
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:116
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104
subroutine spbtrf(UPLO, N, KD, AB, LDAB, INFO)
SPBTRF
Definition: spbtrf.f:144
subroutine spbt05(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SPBT05
Definition: spbt05.f:173
subroutine spbt01(UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
SPBT01
Definition: spbt01.f:121
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:53
subroutine serrpo(PATH, NUNIT)
SERRPO
Definition: serrpo.f:57
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:53
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75

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