LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zchkhe ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, double precision THRESH, logical TSTERR, integer NMAX, complex*16, dimension( * ) A, complex*16, dimension( * ) AFAC, complex*16, dimension( * ) AINV, complex*16, dimension( * ) B, complex*16, dimension( * ) X, complex*16, dimension( * ) XACT, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

ZCHKHE

Purpose:
` ZCHKHE tests ZHETRF, -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 (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 DOUBLE PRECISION 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*16 array, dimension (NMAX*NMAX)` [out] AFAC ` AFAC is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] AINV ` AINV is COMPLEX*16 array, dimension (NMAX*NMAX)` [out] B ``` B is COMPLEX*16 array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL.``` [out] X ` X is COMPLEX*16 array, dimension (NMAX*NSMAX)` [out] XACT ` XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)` [out] WORK ` WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))` [out] RWORK ` RWORK is DOUBLE PRECISION 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 2013

Definition at line 173 of file zchkhe.f.

173 *
174 * -- LAPACK test routine (version 3.5.0) --
175 * -- LAPACK is a software package provided by Univ. of Tennessee, --
176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177 * November 2013
178 *
179 * .. Scalar Arguments ..
180  LOGICAL tsterr
181  INTEGER nmax, nn, nnb, nns, nout
182  DOUBLE PRECISION thresh
183 * ..
184 * .. Array Arguments ..
185  LOGICAL dotype( * )
186  INTEGER iwork( * ), nbval( * ), nsval( * ), nval( * )
187  DOUBLE PRECISION rwork( * )
188  COMPLEX*16 a( * ), afac( * ), ainv( * ), b( * ),
189  \$ work( * ), x( * ), xact( * )
190 * ..
191 *
192 * =====================================================================
193 *
194 * .. Parameters ..
195  DOUBLE PRECISION zero
196  parameter ( zero = 0.0d+0 )
197  COMPLEX*16 czero
198  parameter ( czero = ( 0.0d+0, 0.0d+0 ) )
199  INTEGER ntypes
200  parameter ( ntypes = 10 )
201  INTEGER ntests
202  parameter ( ntests = 9 )
203 * ..
204 * .. Local Scalars ..
205  LOGICAL trfcon, zerot
206  CHARACTER dist, TYPE, uplo, xtype
207  CHARACTER*3 path
208  INTEGER i, i1, i2, imat, in, inb, info, ioff, irhs,
209  \$ iuplo, izero, j, k, kl, ku, lda, lwork, mode,
210  \$ n, nb, nerrs, nfail, nimat, nrhs, nrun, nt
211  DOUBLE PRECISION anorm, cndnum, rcond, rcondc
212 * ..
213 * .. Local Arrays ..
214  CHARACTER uplos( 2 )
215  INTEGER iseed( 4 ), iseedy( 4 )
216  DOUBLE PRECISION result( ntests )
217 * ..
218 * .. External Functions ..
219  DOUBLE PRECISION dget06, zlanhe
220  EXTERNAL dget06, zlanhe
221 * ..
222 * .. External Subroutines ..
223  EXTERNAL alaerh, alahd, alasum, xlaenv, zerrhe, zget04,
226  \$ zpot02, zpot03, zpot05
227 * ..
228 * .. Intrinsic Functions ..
229  INTRINSIC max, min
230 * ..
231 * .. Scalars in Common ..
232  LOGICAL lerr, ok
233  CHARACTER*32 srnamt
234  INTEGER infot, nunit
235 * ..
236 * .. Common blocks ..
237  COMMON / infoc / infot, nunit, ok, lerr
238  COMMON / srnamc / srnamt
239 * ..
240 * .. Data statements ..
241  DATA iseedy / 1988, 1989, 1990, 1991 /
242  DATA uplos / 'U', 'L' /
243 * ..
244 * .. Executable Statements ..
245 *
246 * Initialize constants and the random number seed.
247 *
248  path( 1: 1 ) = 'Zomplex precision'
249  path( 2: 3 ) = 'HE'
250  nrun = 0
251  nfail = 0
252  nerrs = 0
253  DO 10 i = 1, 4
254  iseed( i ) = iseedy( i )
255  10 CONTINUE
256 *
257 * Test the error exits
258 *
259  IF( tsterr )
260  \$ CALL zerrhe( path, nout )
261  infot = 0
262 *
263 * Set the minimum block size for which the block routine should
264 * be used, which will be later returned by ILAENV
265 *
266  CALL xlaenv( 2, 2 )
267 *
268 * Do for each value of N in NVAL
269 *
270  DO 180 in = 1, nn
271  n = nval( in )
272  lda = max( n, 1 )
273  xtype = 'N'
274  nimat = ntypes
275  IF( n.LE.0 )
276  \$ nimat = 1
277 *
278  izero = 0
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 * Set up parameters with ZLATB4 for the matrix generator
298 * based on the type of matrix to be generated.
299 *
300  CALL zlatb4( path, imat, n, n, TYPE, kl, ku, anorm, mode,
301  \$ cndnum, dist )
302 *
303 * Generate a matrix with ZLATMS.
304 *
305  srnamt = 'ZLATMS'
306  CALL zlatms( n, n, dist, iseed, TYPE, rwork, mode,
307  \$ cndnum, anorm, kl, ku, uplo, a, lda, work,
308  \$ info )
309 *
310 * Check error code from ZLATMS and handle error.
311 *
312  IF( info.NE.0 ) THEN
313  CALL alaerh( path, 'ZLATMS', info, 0, uplo, n, n, -1,
314  \$ -1, -1, imat, nfail, nerrs, nout )
315 *
316 * Skip all tests for this generated matrix
317 *
318  GO TO 160
319  END IF
320 *
321 * For types 3-6, zero one or more rows and columns of
322 * the matrix to test that INFO is returned correctly.
323 *
324  IF( zerot ) THEN
325  IF( imat.EQ.3 ) THEN
326  izero = 1
327  ELSE IF( imat.EQ.4 ) THEN
328  izero = n
329  ELSE
330  izero = n / 2 + 1
331  END IF
332 *
333  IF( imat.LT.6 ) THEN
334 *
335 * Set row and column IZERO to zero.
336 *
337  IF( iuplo.EQ.1 ) THEN
338  ioff = ( izero-1 )*lda
339  DO 20 i = 1, izero - 1
340  a( ioff+i ) = czero
341  20 CONTINUE
342  ioff = ioff + izero
343  DO 30 i = izero, n
344  a( ioff ) = czero
345  ioff = ioff + lda
346  30 CONTINUE
347  ELSE
348  ioff = izero
349  DO 40 i = 1, izero - 1
350  a( ioff ) = czero
351  ioff = ioff + lda
352  40 CONTINUE
353  ioff = ioff - izero
354  DO 50 i = izero, n
355  a( ioff+i ) = czero
356  50 CONTINUE
357  END IF
358  ELSE
359  IF( iuplo.EQ.1 ) THEN
360 *
361 * Set the first IZERO rows and columns to zero.
362 *
363  ioff = 0
364  DO 70 j = 1, n
365  i2 = min( j, izero )
366  DO 60 i = 1, i2
367  a( ioff+i ) = czero
368  60 CONTINUE
369  ioff = ioff + lda
370  70 CONTINUE
371  ELSE
372 *
373 * Set the last IZERO rows and columns to zero.
374 *
375  ioff = 0
376  DO 90 j = 1, n
377  i1 = max( j, izero )
378  DO 80 i = i1, n
379  a( ioff+i ) = czero
380  80 CONTINUE
381  ioff = ioff + lda
382  90 CONTINUE
383  END IF
384  END IF
385  ELSE
386  izero = 0
387  END IF
388 *
389 * End generate test matrix A.
390 *
391 *
392 * Set the imaginary part of the diagonals.
393 *
394  CALL zlaipd( n, a, lda+1, 0 )
395 *
396 * Do for each value of NB in NBVAL
397 *
398  DO 150 inb = 1, nnb
399 *
400 * Set the optimal blocksize, which will be later
401 * returned by ILAENV.
402 *
403  nb = nbval( inb )
404  CALL xlaenv( 1, nb )
405 *
406 * Copy the test matrix A into matrix AFAC which
407 * will be factorized in place. This is needed to
408 * preserve the test matrix A for subsequent tests.
409 *
410  CALL zlacpy( uplo, n, n, a, lda, afac, lda )
411 *
412 * Compute the L*D*L**T or U*D*U**T factorization of the
413 * matrix. IWORK stores details of the interchanges and
414 * the block structure of D. AINV is a work array for
415 * block factorization, LWORK is the length of AINV.
416 *
417  lwork = max( 2, nb )*lda
418  srnamt = 'ZHETRF'
419  CALL zhetrf( uplo, n, afac, lda, iwork, ainv, lwork,
420  \$ info )
421 *
422 * Adjust the expected value of INFO to account for
423 * pivoting.
424 *
425  k = izero
426  IF( k.GT.0 ) THEN
427  100 CONTINUE
428  IF( iwork( k ).LT.0 ) THEN
429  IF( iwork( k ).NE.-k ) THEN
430  k = -iwork( k )
431  GO TO 100
432  END IF
433  ELSE IF( iwork( k ).NE.k ) THEN
434  k = iwork( k )
435  GO TO 100
436  END IF
437  END IF
438 *
439 * Check error code from ZHETRF and handle error.
440 *
441  IF( info.NE.k )
442  \$ CALL alaerh( path, 'ZHETRF', info, k, uplo, n, n,
443  \$ -1, -1, nb, imat, nfail, nerrs, nout )
444 *
445 * Set the condition estimate flag if the INFO is not 0.
446 *
447  IF( info.NE.0 ) THEN
448  trfcon = .true.
449  ELSE
450  trfcon = .false.
451  END IF
452 *
453 *+ TEST 1
454 * Reconstruct matrix from factors and compute residual.
455 *
456  CALL zhet01( uplo, n, a, lda, afac, lda, iwork, ainv,
457  \$ lda, rwork, result( 1 ) )
458  nt = 1
459 *
460 *+ TEST 2
461 * Form the inverse and compute the residual.
462 *
463  IF( inb.EQ.1 .AND. .NOT.trfcon ) THEN
464  CALL zlacpy( uplo, n, n, afac, lda, ainv, lda )
465  srnamt = 'ZHETRI2'
466  lwork = (n+nb+1)*(nb+3)
467  CALL zhetri2( uplo, n, ainv, lda, iwork, work,
468  \$ lwork, info )
469 *
470 * Check error code from ZHETRI and handle error.
471 *
472  IF( info.NE.0 )
473  \$ CALL alaerh( path, 'ZHETRI', info, -1, uplo, n,
474  \$ n, -1, -1, -1, imat, nfail, nerrs,
475  \$ nout )
476 *
477 * Compute the residual for a symmetric matrix times
478 * its inverse.
479 *
480  CALL zpot03( uplo, n, a, lda, ainv, lda, work, lda,
481  \$ rwork, rcondc, result( 2 ) )
482  nt = 2
483  END IF
484 *
485 * Print information about the tests that did not pass
486 * the threshold.
487 *
488  DO 110 k = 1, nt
489  IF( result( k ).GE.thresh ) THEN
490  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
491  \$ CALL alahd( nout, path )
492  WRITE( nout, fmt = 9999 )uplo, n, nb, imat, k,
493  \$ result( k )
494  nfail = nfail + 1
495  END IF
496  110 CONTINUE
497  nrun = nrun + nt
498 *
499 * Skip the other tests if this is not the first block
500 * size.
501 *
502  IF( inb.GT.1 )
503  \$ GO TO 150
504 *
505 * Do only the condition estimate if INFO is not 0.
506 *
507  IF( trfcon ) THEN
508  rcondc = zero
509  GO TO 140
510  END IF
511 *
512 * Do for each value of NRHS in NSVAL.
513 *
514  DO 130 irhs = 1, nns
515  nrhs = nsval( irhs )
516 *
517 *+ TEST 3 (Using TRS)
518 * Solve and compute residual for A * X = B.
519 *
520 * Choose a set of NRHS random solution vectors
521 * stored in XACT and set up the right hand side B
522 *
523  srnamt = 'ZLARHS'
524  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
525  \$ nrhs, a, lda, xact, lda, b, lda,
526  \$ iseed, info )
527  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
528 *
529  srnamt = 'ZHETRS'
530  CALL zhetrs( uplo, n, nrhs, afac, lda, iwork, x,
531  \$ lda, info )
532 *
533 * Check error code from ZHETRS and handle error.
534 *
535  IF( info.NE.0 )
536  \$ CALL alaerh( path, 'ZHETRS', info, 0, uplo, n,
537  \$ n, -1, -1, nrhs, imat, nfail,
538  \$ nerrs, nout )
539 *
540  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
541 *
542 * Compute the residual for the solution
543 *
544  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
545  \$ lda, rwork, result( 3 ) )
546 *
547 *+ TEST 4 (Using TRS2)
548 * Solve and compute residual for A * X = B.
549 *
550 * Choose a set of NRHS random solution vectors
551 * stored in XACT and set up the right hand side B
552 *
553  srnamt = 'ZLARHS'
554  CALL zlarhs( path, xtype, uplo, ' ', n, n, kl, ku,
555  \$ nrhs, a, lda, xact, lda, b, lda,
556  \$ iseed, info )
557  CALL zlacpy( 'Full', n, nrhs, b, lda, x, lda )
558 *
559  srnamt = 'ZHETRS2'
560  CALL zhetrs2( uplo, n, nrhs, afac, lda, iwork, x,
561  \$ lda, work, info )
562 *
563 * Check error code from ZHETRS2 and handle error.
564 *
565  IF( info.NE.0 )
566  \$ CALL alaerh( path, 'ZHETRS2', info, 0, uplo, n,
567  \$ n, -1, -1, nrhs, imat, nfail,
568  \$ nerrs, nout )
569 *
570  CALL zlacpy( 'Full', n, nrhs, b, lda, work, lda )
571 *
572 * Compute the residual for the solution
573 *
574  CALL zpot02( uplo, n, nrhs, a, lda, x, lda, work,
575  \$ lda, rwork, result( 4 ) )
576 *
577 *+ TEST 5
578 * Check solution from generated exact solution.
579 *
580  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
581  \$ result( 5 ) )
582 *
583 *+ TESTS 6, 7, and 8
584 * Use iterative refinement to improve the solution.
585 *
586  srnamt = 'ZHERFS'
587  CALL zherfs( uplo, n, nrhs, a, lda, afac, lda,
588  \$ iwork, b, lda, x, lda, rwork,
589  \$ rwork( nrhs+1 ), work,
590  \$ rwork( 2*nrhs+1 ), info )
591 *
592 * Check error code from ZHERFS.
593 *
594  IF( info.NE.0 )
595  \$ CALL alaerh( path, 'ZHERFS', info, 0, uplo, n,
596  \$ n, -1, -1, nrhs, imat, nfail,
597  \$ nerrs, nout )
598 *
599  CALL zget04( n, nrhs, x, lda, xact, lda, rcondc,
600  \$ result( 6 ) )
601  CALL zpot05( uplo, n, nrhs, a, lda, b, lda, x, lda,
602  \$ xact, lda, rwork, rwork( nrhs+1 ),
603  \$ result( 7 ) )
604 *
605 * Print information about the tests that did not pass
606 * the threshold.
607 *
608  DO 120 k = 3, 8
609  IF( result( k ).GE.thresh ) THEN
610  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
611  \$ CALL alahd( nout, path )
612  WRITE( nout, fmt = 9998 )uplo, n, nrhs,
613  \$ imat, k, result( k )
614  nfail = nfail + 1
615  END IF
616  120 CONTINUE
617  nrun = nrun + 6
618 *
619 * End do for each value of NRHS in NSVAL.
620 *
621  130 CONTINUE
622 *
623 *+ TEST 9
624 * Get an estimate of RCOND = 1/CNDNUM.
625 *
626  140 CONTINUE
627  anorm = zlanhe( '1', uplo, n, a, lda, rwork )
628  srnamt = 'ZHECON'
629  CALL zhecon( uplo, n, afac, lda, iwork, anorm, rcond,
630  \$ work, info )
631 *
632 * Check error code from ZHECON and handle error.
633 *
634  IF( info.NE.0 )
635  \$ CALL alaerh( path, 'ZHECON', info, 0, uplo, n, n,
636  \$ -1, -1, -1, imat, nfail, nerrs, nout )
637 *
638  result( 9 ) = dget06( rcond, rcondc )
639 *
640 * Print information about the tests that did not pass
641 * the threshold.
642 *
643  IF( result( 9 ).GE.thresh ) THEN
644  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
645  \$ CALL alahd( nout, path )
646  WRITE( nout, fmt = 9997 )uplo, n, imat, 9,
647  \$ result( 9 )
648  nfail = nfail + 1
649  END IF
650  nrun = nrun + 1
651  150 CONTINUE
652  160 CONTINUE
653  170 CONTINUE
654  180 CONTINUE
655 *
656 * Print a summary of the results.
657 *
658  CALL alasum( path, nout, nfail, nrun, nerrs )
659 *
660  9999 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NB =', i4, ', type ',
661  \$ i2, ', test ', i2, ', ratio =', g12.5 )
662  9998 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ', NRHS=', i3, ', type ',
663  \$ i2, ', test(', i2, ') =', g12.5 )
664  9997 FORMAT( ' UPLO = ''', a1, ''', N =', i5, ',', 10x, ' type ', i2,
665  \$ ', test(', i2, ') =', g12.5 )
666  RETURN
667 *
668 * End of ZCHKHE
669 *
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 zhetri2(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRI2
Definition: zhetri2.f:129
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zherfs(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZHERFS
Definition: zherfs.f:194
subroutine zget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
ZGET04
Definition: zget04.f:104
subroutine zerrhe(PATH, NUNIT)
ZERRHE
Definition: zerrhe.f:57
subroutine zpot02(UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZPOT02
Definition: zpot02.f:129
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: zlanhe.f:126
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
subroutine zhet01(UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
ZHET01
Definition: zhet01.f:128
subroutine zhetrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
ZHETRS2
Definition: zhetrs2.f:129
subroutine xlaenv(ISPEC, NVALUE)
XLAENV
Definition: xlaenv.f:83
subroutine zpot03(UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
ZPOT03
Definition: zpot03.f:128
subroutine zlatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
ZLATB4
Definition: zlatb4.f:123
subroutine zlaipd(N, A, INDA, VINDA)
ZLAIPD
Definition: zlaipd.f:85
subroutine zhetrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF
Definition: zhetrf.f:179
double precision function dget06(RCOND, RCONDC)
DGET06
Definition: dget06.f:57
subroutine zlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
ZLATMS
Definition: zlatms.f:334
subroutine zpot05(UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
ZPOT05
Definition: zpot05.f:167
subroutine zhetrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZHETRS
Definition: zhetrs.f:122
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:75
subroutine zhecon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
ZHECON
Definition: zhecon.f:127

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