LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cchkhe()

 subroutine cchkhe ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

CCHKHE

Purpose:
` CCHKHE tests CHETRF, -TRI2, -TRS, -TRS2, -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 (NNB) 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 COMPLEX array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is COMPLEX array, dimension (NMAX*NMAX)` [out] AINV ` AINV is COMPLEX array, dimension (NMAX*NMAX)` [out] B ``` B is COMPLEX array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.``` [out] X ` X is COMPLEX array, dimension (NMAX*NSMAX)` [out] XACT ` XACT is COMPLEX array, dimension (NMAX*NSMAX)` [out] WORK ` WORK is COMPLEX 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.```

Definition at line 168 of file cchkhe.f.

171 *
172 * -- LAPACK test routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  LOGICAL TSTERR
178  INTEGER NMAX, NN, NNB, NNS, NOUT
179  REAL THRESH
180 * ..
181 * .. Array Arguments ..
182  LOGICAL DOTYPE( * )
183  INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
184  REAL RWORK( * )
185  COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
186  \$ WORK( * ), X( * ), XACT( * )
187 * ..
188 *
189 * =====================================================================
190 *
191 * .. Parameters ..
192  REAL ZERO
193  parameter( zero = 0.0e+0 )
194  COMPLEX CZERO
195  parameter( czero = ( 0.0e+0, 0.0e+0 ) )
196  INTEGER NTYPES
197  parameter( ntypes = 10 )
198  INTEGER NTESTS
199  parameter( ntests = 9 )
200 * ..
201 * .. Local Scalars ..
202  LOGICAL TRFCON, ZEROT
203  CHARACTER DIST, TYPE, UPLO, XTYPE
204  CHARACTER*3 PATH
205  INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
206  \$ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
207  \$ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
208  REAL ANORM, CNDNUM, RCOND, RCONDC
209 * ..
210 * .. Local Arrays ..
211  CHARACTER UPLOS( 2 )
212  INTEGER ISEED( 4 ), ISEEDY( 4 )
213  REAL RESULT( NTESTS )
214 * ..
215 * .. External Functions ..
216  REAL CLANHE, SGET06
217  EXTERNAL clanhe, sget06
218 * ..
219 * .. External Subroutines ..
220  EXTERNAL alaerh, alahd, alasum, cerrhe, cget04, checon,
223  \$ cpot03, cpot05, xlaenv
224 * ..
225 * .. Intrinsic Functions ..
226  INTRINSIC max, min
227 * ..
228 * .. Scalars in Common ..
229  LOGICAL LERR, OK
230  CHARACTER*32 SRNAMT
231  INTEGER INFOT, NUNIT
232 * ..
233 * .. Common blocks ..
234  COMMON / infoc / infot, nunit, ok, lerr
235  COMMON / srnamc / srnamt
236 * ..
237 * .. Data statements ..
238  DATA iseedy / 1988, 1989, 1990, 1991 /
239  DATA uplos / 'U', 'L' /
240 * ..
241 * .. Executable Statements ..
242 *
243 * Initialize constants and the random number seed.
244 *
245  path( 1: 1 ) = 'Complex precision'
246  path( 2: 3 ) = 'HE'
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 cerrhe( path, nout )
258  infot = 0
259 *
260 * Set the minimum block size for which the block routine should
261 * be used, which will be later returned by ILAENV
262 *
263  CALL xlaenv( 2, 2 )
264 *
265 * Do for each value of N in NVAL
266 *
267  DO 180 in = 1, nn
268  n = nval( in )
269  lda = max( n, 1 )
270  xtype = 'N'
271  nimat = ntypes
272  IF( n.LE.0 )
273  \$ nimat = 1
274 *
275  izero = 0
276 *
277 * Do for each value of matrix type IMAT
278 *
279  DO 170 imat = 1, nimat
280 *
281 * Do the tests only if DOTYPE( IMAT ) is true.
282 *
283  IF( .NOT.dotype( imat ) )
284  \$ GO TO 170
285 *
286 * Skip types 3, 4, 5, or 6 if the matrix size is too small.
287 *
288  zerot = imat.GE.3 .AND. imat.LE.6
289  IF( zerot .AND. n.LT.imat-2 )
290  \$ GO TO 170
291 *
292 * Do first for UPLO = 'U', then for UPLO = 'L'
293 *
294  DO 160 iuplo = 1, 2
295  uplo = uplos( iuplo )
296 *
297 * Begin generate test matrix A.
298 *
299 *
300 * Set up parameters with CLATB4 for the matrix generator
301 * based on the type of matrix to be generated.
302 *
303  CALL clatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
304  \$ CNDNUM, DIST )
305 *
306 * Generate a matrix with CLATMS.
307 *
308  srnamt = 'CLATMS'
309  CALL clatms( n, n, dist, iseed, TYPE, RWORK, MODE,
310  \$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
311  \$ INFO )
312 *
313 * Check error code from CLATMS and handle error.
314 *
315  IF( info.NE.0 ) THEN
316  CALL alaerh( path, 'CLATMS', info, 0, uplo, n, n, -1,
317  \$ -1, -1, imat, nfail, nerrs, nout )
318 *
319 * Skip all tests for this generated matrix
320 *
321  GO TO 160
322  END IF
323 *
324 * For matrix types 3-6, zero one or more rows and
325 * columns of the matrix to test that INFO is returned
326 * correctly.
327 *
328  IF( zerot ) THEN
329  IF( imat.EQ.3 ) THEN
330  izero = 1
331  ELSE IF( imat.EQ.4 ) THEN
332  izero = n
333  ELSE
334  izero = n / 2 + 1
335  END IF
336 *
337  IF( imat.LT.6 ) THEN
338 *
339 * Set row and column IZERO to zero.
340 *
341  IF( iuplo.EQ.1 ) THEN
342  ioff = ( izero-1 )*lda
343  DO 20 i = 1, izero - 1
344  a( ioff+i ) = czero
345  20 CONTINUE
346  ioff = ioff + izero
347  DO 30 i = izero, n
348  a( ioff ) = czero
349  ioff = ioff + lda
350  30 CONTINUE
351  ELSE
352  ioff = izero
353  DO 40 i = 1, izero - 1
354  a( ioff ) = czero
355  ioff = ioff + lda
356  40 CONTINUE
357  ioff = ioff - izero
358  DO 50 i = izero, n
359  a( ioff+i ) = czero
360  50 CONTINUE
361  END IF
362  ELSE
363  IF( iuplo.EQ.1 ) THEN
364 *
365 * Set the first IZERO rows and columns to zero.
366 *
367  ioff = 0
368  DO 70 j = 1, n
369  i2 = min( j, izero )
370  DO 60 i = 1, i2
371  a( ioff+i ) = czero
372  60 CONTINUE
373  ioff = ioff + lda
374  70 CONTINUE
375  ELSE
376 *
377 * Set the last IZERO rows and columns to zero.
378 *
379  ioff = 0
380  DO 90 j = 1, n
381  i1 = max( j, izero )
382  DO 80 i = i1, n
383  a( ioff+i ) = czero
384  80 CONTINUE
385  ioff = ioff + lda
386  90 CONTINUE
387  END IF
388  END IF
389  ELSE
390  izero = 0
391  END IF
392 *
393 * Set the imaginary part of the diagonals.
394 *
395  CALL claipd( n, a, lda+1, 0 )
396 *
397 * End generate test matrix A.
398 *
399 *
400 * Do for each value of NB in NBVAL
401 *
402  DO 150 inb = 1, nnb
403 *
404 * Set the optimal blocksize, which will be later
405 * returned by ILAENV.
406 *
407  nb = nbval( inb )
408  CALL xlaenv( 1, nb )
409 *
410 * Copy the test matrix A into matrix AFAC which
411 * will be factorized in place. This is needed to
412 * preserve the test matrix A for subsequent tests.
413 *
414  CALL clacpy( uplo, n, n, a, lda, afac, lda )
415 *
416 * Compute the L*D*L**T or U*D*U**T factorization of the
417 * matrix. IWORK stores details of the interchanges and
418 * the block structure of D. AINV is a work array for
419 * block factorization, LWORK is the length of AINV.
420 *
421  lwork = max( 2, nb )*lda
422  srnamt = 'CHETRF'
423  CALL chetrf( uplo, n, afac, lda, iwork, ainv, lwork,
424  \$ info )
425 *
426 * Adjust the expected value of INFO to account for
427 * pivoting.
428 *
429  k = izero
430  IF( k.GT.0 ) THEN
431  100 CONTINUE
432  IF( iwork( k ).LT.0 ) THEN
433  IF( iwork( k ).NE.-k ) THEN
434  k = -iwork( k )
435  GO TO 100
436  END IF
437  ELSE IF( iwork( k ).NE.k ) THEN
438  k = iwork( k )
439  GO TO 100
440  END IF
441  END IF
442 *
443 * Check error code from CHETRF and handle error.
444 *
445  IF( info.NE.k )
446  \$ CALL alaerh( path, 'CHETRF', info, k, uplo, n, n,
447  \$ -1, -1, nb, imat, nfail, nerrs, nout )
448 *
449 * Set the condition estimate flag if the INFO is not 0.
450 *
451  IF( info.NE.0 ) THEN
452  trfcon = .true.
453  ELSE
454  trfcon = .false.
455  END IF
456 *
457 *+ TEST 1
458 * Reconstruct matrix from factors and compute residual.
459 *
460  CALL chet01( uplo, n, a, lda, afac, lda, iwork, ainv,
461  \$ lda, rwork, result( 1 ) )
462  nt = 1
463 *
464 *+ TEST 2
465 * Form the inverse and compute the residual,
466 * if the factorization was competed without INFO > 0
467 * (i.e. there is no zero rows and columns).
468 * Do it only for the first block size.
469 *
470  IF( inb.EQ.1 .AND. .NOT.trfcon ) THEN
471  CALL clacpy( uplo, n, n, afac, lda, ainv, lda )
472  srnamt = 'CHETRI2'
473  lwork = (n+nb+1)*(nb+3)
474  CALL chetri2( uplo, n, ainv, lda, iwork, work,
475  \$ lwork, info )
476 *
477 * Check error code from CHETRI2 and handle error.
478 *
479  IF( info.NE.0 )
480  \$ CALL alaerh( path, 'CHETRI2', info, -1, uplo, n,
481  \$ n, -1, -1, -1, imat, nfail, nerrs,
482  \$ nout )
483 *
484 * Compute the residual for a symmetric matrix times
485 * its inverse.
486 *
487  CALL cpot03( uplo, n, a, lda, ainv, lda, work, lda,
488  \$ rwork, rcondc, result( 2 ) )
489  nt = 2
490  END IF
491 *
492 * Print information about the tests that did not pass
493 * the threshold.
494 *
495  DO 110 k = 1, nt
496  IF( result( k ).GE.thresh ) THEN
497  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
498  \$ CALL alahd( nout, path )
499  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
500  \$ result( k )
501  nfail = nfail + 1
502  END IF
503  110 CONTINUE
504  nrun = nrun + nt
505 *
506 * Skip the other tests if this is not the first block
507 * size.
508 *
509  IF( inb.GT.1 )
510  \$ GO TO 150
511 *
512 * Do only the condition estimate if INFO is not 0.
513 *
514  IF( trfcon ) THEN
515  rcondc = zero
516  GO TO 140
517  END IF
518 *
519 * Do for each value of NRHS in NSVAL.
520 *
521  DO 130 irhs = 1, nns
522  nrhs = nsval( irhs )
523 *
524 *+ TEST 3 (Using TRS)
525 * Solve and compute residual for A * X = B.
526 *
527 * Choose a set of NRHS random solution vectors
528 * stored in XACT and set up the right hand side B
529 *
530  srnamt = 'CLARHS'
531  CALL clarhs( path, xtype, uplo, ' ', n, n, kl, ku,
532  \$ nrhs, a, lda, xact, lda, b, lda,
533  \$ iseed, info )
534  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
535 *
536  srnamt = 'CHETRS'
537  CALL chetrs( uplo, n, nrhs, afac, lda, iwork, x,
538  \$ lda, info )
539 *
540 * Check error code from CHETRS and handle error.
541 *
542  IF( info.NE.0 )
543  \$ CALL alaerh( path, 'CHETRS', info, 0, uplo, n,
544  \$ n, -1, -1, nrhs, imat, nfail,
545  \$ nerrs, nout )
546 *
547  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
548 *
549 * Compute the residual for the solution
550 *
551  CALL cpot02( uplo, n, nrhs, a, lda, x, lda, work,
552  \$ lda, rwork, result( 3 ) )
553 *
554 *+ TEST 4 (Using TRS2)
555 * Solve and compute residual for A * X = B.
556 *
557 * Choose a set of NRHS random solution vectors
558 * stored in XACT and set up the right hand side B
559 *
560  srnamt = 'CLARHS'
561  CALL clarhs( path, xtype, uplo, ' ', n, n, kl, ku,
562  \$ nrhs, a, lda, xact, lda, b, lda,
563  \$ iseed, info )
564  CALL clacpy( 'Full', n, nrhs, b, lda, x, lda )
565 *
566  srnamt = 'CHETRS2'
567  CALL chetrs2( uplo, n, nrhs, afac, lda, iwork, x,
568  \$ lda, work, info )
569 *
570 * Check error code from CHETRS2 and handle error.
571 *
572  IF( info.NE.0 )
573  \$ CALL alaerh( path, 'CHETRS2', info, 0, uplo, n,
574  \$ n, -1, -1, nrhs, imat, nfail,
575  \$ nerrs, nout )
576 *
577  CALL clacpy( 'Full', n, nrhs, b, lda, work, lda )
578 *
579 * Compute the residual for the solution
580 *
581  CALL cpot02( uplo, n, nrhs, a, lda, x, lda, work,
582  \$ lda, rwork, result( 4 ) )
583 *
584 *+ TEST 5
585 * Check solution from generated exact solution.
586 *
587  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
588  \$ result( 5 ) )
589 *
590 *+ TESTS 6, 7, and 8
591 * Use iterative refinement to improve the solution.
592 *
593  srnamt = 'CHERFS'
594  CALL cherfs( uplo, n, nrhs, a, lda, afac, lda,
595  \$ iwork, b, lda, x, lda, rwork,
596  \$ rwork( nrhs+1 ), work,
597  \$ rwork( 2*nrhs+1 ), info )
598 *
599 * Check error code from CHERFS and handle error.
600 *
601  IF( info.NE.0 )
602  \$ CALL alaerh( path, 'CHERFS', info, 0, uplo, n,
603  \$ n, -1, -1, nrhs, imat, nfail,
604  \$ nerrs, nout )
605 *
606  CALL cget04( n, nrhs, x, lda, xact, lda, rcondc,
607  \$ result( 6 ) )
608  CALL cpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
609  \$ xact, lda, rwork, rwork( nrhs+1 ),
610  \$ result( 7 ) )
611 *
612 * Print information about the tests that did not pass
613 * the threshold.
614 *
615  DO 120 k = 3, 8
616  IF( result( k ).GE.thresh ) THEN
617  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
618  \$ CALL alahd( nout, path )
619  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
620  \$ imat, k, result( k )
621  nfail = nfail + 1
622  END IF
623  120 CONTINUE
624  nrun = nrun + 6
625 *
626 * End do for each value of NRHS in NSVAL.
627 *
628  130 CONTINUE
629 *
630 *+ TEST 9
631 * Get an estimate of RCOND = 1/CNDNUM.
632 *
633  140 CONTINUE
634  anorm = clanhe( '1', uplo, n, a, lda, rwork )
635  srnamt = 'CHECON'
636  CALL checon( uplo, n, afac, lda, iwork, anorm, rcond,
637  \$ work, info )
638 *
639 * Check error code from CHECON and handle error.
640 *
641  IF( info.NE.0 )
642  \$ CALL alaerh( path, 'CHECON', info, 0, uplo, n, n,
643  \$ -1, -1, -1, imat, nfail, nerrs, nout )
644 *
645 * Compute the test ratio to compare values of RCOND
646 *
647  result( 9 ) = sget06( rcond, rcondc )
648 *
649 * Print information about the tests that did not pass
650 * the threshold.
651 *
652  IF( result( 9 ).GE.thresh ) THEN
653  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
654  \$ CALL alahd( nout, path )
655  WRITE( nout, fmt = 9997 )uplo, n, imat, 8,
656  \$ result( 9 )
657  nfail = nfail + 1
658  END IF
659  nrun = nrun + 1
660  150 CONTINUE
661  160 CONTINUE
662  170 CONTINUE
663  180 CONTINUE
664 *
665 * Print a summary of the results.
666 *
667  CALL alasum( path, nout, nfail, nrun, nerrs )
668 *
669  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
670  \$ i2, ', test ', i2, ', ratio =', g12.5 )
671  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
672  \$ i2, ', test(', i2, ') =', g12.5 )
673  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
674  \$ ', test(', i2, ') =', g12.5 )
675  RETURN
676 *
677 * End of CCHKHE
678 *
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:81
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 clarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
CLARHS
Definition: clarhs.f:208
subroutine cpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPOT05
Definition: cpot05.f:165
subroutine clatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
Definition: clatb4.f:121
subroutine cget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
Definition: cget04.f:102
subroutine cerrhe(PATH, NUNIT)
CERRHE
Definition: cerrhe.f:55
subroutine cpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
CPOT03
Definition: cpot03.f:126
subroutine chet01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CHET01
Definition: chet01.f:126
subroutine claipd(N, A, INDA, VINDA)
CLAIPD
Definition: claipd.f:83
subroutine cpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CPOT02
Definition: cpot02.f:127
subroutine clatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
CLATMS
Definition: clatms.f:332
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
subroutine chetrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHETRF
Definition: chetrf.f:177
subroutine cherfs(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CHERFS
Definition: cherfs.f:192
subroutine chetri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHETRI2
Definition: chetri2.f:127
subroutine checon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
CHECON
Definition: checon.f:125
subroutine chetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CHETRS
Definition: chetrs.f:120
subroutine chetrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
CHETRS2
Definition: chetrs2.f:127
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
real function sget06(RCOND, RCONDC)
SGET06
Definition: sget06.f:55
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