LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
ccsdts.f File Reference

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Functions/Subroutines

subroutine ccsdts (M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK, RWORK, RESULT)
 CCSDTS More...
 

Function/Subroutine Documentation

subroutine ccsdts ( integer  M,
integer  P,
integer  Q,
complex, dimension( ldx, * )  X,
complex, dimension( ldx, * )  XF,
integer  LDX,
complex, dimension( ldu1, * )  U1,
integer  LDU1,
complex, dimension( ldu2, * )  U2,
integer  LDU2,
complex, dimension( ldv1t, * )  V1T,
integer  LDV1T,
complex, dimension( ldv2t, * )  V2T,
integer  LDV2T,
real, dimension( * )  THETA,
integer, dimension( * )  IWORK,
complex, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( * )  RWORK,
real, dimension( 15 )  RESULT 
)

CCSDTS

Purpose:
 CCSDTS tests CUNCSD, which, given an M-by-M partitioned unitary
 matrix X,
              Q  M-Q
       X = [ X11 X12 ] P   ,
           [ X21 X22 ] M-P

 computes the CSD

       [ U1    ]**T * [ X11 X12 ] * [ V1    ]
       [    U2 ]      [ X21 X22 ]   [    V2 ]

                             [  I  0  0 |  0  0  0 ]
                             [  0  C  0 |  0 -S  0 ]
                             [  0  0  0 |  0  0 -I ]
                           = [---------------------] = [ D11 D12 ] .
                             [  0  0  0 |  I  0  0 ]   [ D21 D22 ]
                             [  0  S  0 |  0  C  0 ]
                             [  0  0  I |  0  0  0 ]

 and also SORCSD2BY1, which, given
          Q
       [ X11 ] P   ,
       [ X21 ] M-P

 computes the 2-by-1 CSD

                                     [  I  0  0 ]
                                     [  0  C  0 ]
                                     [  0  0  0 ]
       [ U1    ]**T * [ X11 ] * V1 = [----------] = [ D11 ] ,
       [    U2 ]      [ X21 ]        [  0  0  0 ]   [ D21 ]
                                     [  0  S  0 ]
                                     [  0  0  I ]
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix X.  M >= 0.
[in]P
          P is INTEGER
          The number of rows of the matrix X11.  P >= 0.
[in]Q
          Q is INTEGER
          The number of columns of the matrix X11.  Q >= 0.
[in]X
          X is COMPLEX array, dimension (LDX,M)
          The M-by-M matrix X.
[out]XF
          XF is COMPLEX array, dimension (LDX,M)
          Details of the CSD of X, as returned by CUNCSD;
          see CUNCSD for further details.
[in]LDX
          LDX is INTEGER
          The leading dimension of the arrays X and XF.
          LDX >= max( 1,M ).
[out]U1
          U1 is COMPLEX array, dimension(LDU1,P)
          The P-by-P unitary matrix U1.
[in]LDU1
          LDU1 is INTEGER
          The leading dimension of the array U1. LDU >= max(1,P).
[out]U2
          U2 is COMPLEX array, dimension(LDU2,M-P)
          The (M-P)-by-(M-P) unitary matrix U2.
[in]LDU2
          LDU2 is INTEGER
          The leading dimension of the array U2. LDU >= max(1,M-P).
[out]V1T
          V1T is COMPLEX array, dimension(LDV1T,Q)
          The Q-by-Q unitary matrix V1T.
[in]LDV1T
          LDV1T is INTEGER
          The leading dimension of the array V1T. LDV1T >=
          max(1,Q).
[out]V2T
          V2T is COMPLEX array, dimension(LDV2T,M-Q)
          The (M-Q)-by-(M-Q) unitary matrix V2T.
[in]LDV2T
          LDV2T is INTEGER
          The leading dimension of the array V2T. LDV2T >=
          max(1,M-Q).
[out]THETA
          THETA is REAL array, dimension MIN(P,M-P,Q,M-Q)
          The CS values of X; the essentially diagonal matrices C and
          S are constructed from THETA; see subroutine CUNCSD for
          details.
[out]IWORK
          IWORK is INTEGER array, dimension (M)
[out]WORK
          WORK is COMPLEX array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK
[out]RWORK
          RWORK is REAL array
[out]RESULT
          RESULT is REAL array, dimension (15)
          The test ratios:
          First, the 2-by-2 CSD:
          RESULT(1) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
          RESULT(2) = norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 )
          RESULT(3) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
          RESULT(4) = norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 )
          RESULT(5) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
          RESULT(6) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
          RESULT(7) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
          RESULT(8) = norm( I - V2T'*V2T ) / ( MAX(1,M-Q)*ULP )
          RESULT(9) = 0        if THETA is in increasing order and
                               all angles are in [0,pi/2];
                    = ULPINV   otherwise.
          Then, the 2-by-1 CSD:
          RESULT(10) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
          RESULT(11) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
          RESULT(12) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
          RESULT(13) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
          RESULT(14) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
          RESULT(15) = 0        if THETA is in increasing order and
                                all angles are in [0,pi/2];
                     = ULPINV   otherwise.
          ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 231 of file ccsdts.f.

231 *
232 * -- LAPACK test routine (version 3.4.0) --
233 * -- LAPACK is a software package provided by Univ. of Tennessee, --
234 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
235 * November 2011
236 *
237 * .. Scalar Arguments ..
238  INTEGER ldx, ldu1, ldu2, ldv1t, ldv2t, lwork, m, p, q
239 * ..
240 * .. Array Arguments ..
241  INTEGER iwork( * )
242  REAL result( 15 ), rwork( * ), theta( * )
243  COMPLEX u1( ldu1, * ), u2( ldu2, * ), v1t( ldv1t, * ),
244  $ v2t( ldv2t, * ), work( lwork ), x( ldx, * ),
245  $ xf( ldx, * )
246 * ..
247 *
248 * =====================================================================
249 *
250 * .. Parameters ..
251  REAL piover2, realone, realzero
252  parameter( piover2 = 1.57079632679489662e0,
253  $ realone = 1.0e0, realzero = 0.0e0 )
254  COMPLEX zero, one
255  parameter( zero = (0.0e0,0.0e0), one = (1.0e0,0.0e0) )
256 * ..
257 * .. Local Scalars ..
258  INTEGER i, info, r
259  REAL eps2, resid, ulp, ulpinv
260 * ..
261 * .. External Functions ..
262  REAL slamch, clange, clanhe
263  EXTERNAL slamch, clange, clanhe
264 * ..
265 * .. External Subroutines ..
266  EXTERNAL cgemm, cherk, clacpy, claset, cuncsd, cuncsd2by1
267 * ..
268 * .. Intrinsic Functions ..
269  INTRINSIC cmplx, cos, max, min, REAL, sin
270 * ..
271 * .. Executable Statements ..
272 *
273  ulp = slamch( 'Precision' )
274  ulpinv = realone / ulp
275 *
276 * The first half of the routine checks the 2-by-2 CSD
277 *
278  CALL claset( 'Full', m, m, zero, one, work, ldx )
279  CALL cherk( 'Upper', 'Conjugate transpose', m, m, -realone,
280  $ x, ldx, realone, work, ldx )
281  IF (m.GT.0) THEN
282  eps2 = max( ulp,
283  $ clange( '1', m, m, work, ldx, rwork ) / REAL( M ) )
284  ELSE
285  eps2 = ulp
286  END IF
287  r = min( p, m-p, q, m-q )
288 *
289 * Copy the matrix X to the array XF.
290 *
291  CALL clacpy( 'Full', m, m, x, ldx, xf, ldx )
292 *
293 * Compute the CSD
294 *
295  CALL cuncsd( 'Y', 'Y', 'Y', 'Y', 'N', 'D', m, p, q, xf(1,1), ldx,
296  $ xf(1,q+1), ldx, xf(p+1,1), ldx, xf(p+1,q+1), ldx,
297  $ theta, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t,
298  $ work, lwork, rwork, 17*(r+2), iwork, info )
299 *
300 * Compute XF := diag(U1,U2)'*X*diag(V1,V2) - [D11 D12; D21 D22]
301 *
302  CALL clacpy( 'Full', m, m, x, ldx, xf, ldx )
303 *
304  CALL cgemm( 'No transpose', 'Conjugate transpose', p, q, q, one,
305  $ xf, ldx, v1t, ldv1t, zero, work, ldx )
306 *
307  CALL cgemm( 'Conjugate transpose', 'No transpose', p, q, p, one,
308  $ u1, ldu1, work, ldx, zero, xf, ldx )
309 *
310  DO i = 1, min(p,q)-r
311  xf(i,i) = xf(i,i) - one
312  END DO
313  DO i = 1, r
314  xf(min(p,q)-r+i,min(p,q)-r+i) =
315  $ xf(min(p,q)-r+i,min(p,q)-r+i) - cmplx( cos(theta(i)),
316  $ 0.0e0 )
317  END DO
318 *
319  CALL cgemm( 'No transpose', 'Conjugate transpose', p, m-q, m-q,
320  $ one, xf(1,q+1), ldx, v2t, ldv2t, zero, work, ldx )
321 *
322  CALL cgemm( 'Conjugate transpose', 'No transpose', p, m-q, p,
323  $ one, u1, ldu1, work, ldx, zero, xf(1,q+1), ldx )
324 *
325  DO i = 1, min(p,m-q)-r
326  xf(p-i+1,m-i+1) = xf(p-i+1,m-i+1) + one
327  END DO
328  DO i = 1, r
329  xf(p-(min(p,m-q)-r)+1-i,m-(min(p,m-q)-r)+1-i) =
330  $ xf(p-(min(p,m-q)-r)+1-i,m-(min(p,m-q)-r)+1-i) +
331  $ cmplx( sin(theta(r-i+1)), 0.0e0 )
332  END DO
333 *
334  CALL cgemm( 'No transpose', 'Conjugate transpose', m-p, q, q, one,
335  $ xf(p+1,1), ldx, v1t, ldv1t, zero, work, ldx )
336 *
337  CALL cgemm( 'Conjugate transpose', 'No transpose', m-p, q, m-p,
338  $ one, u2, ldu2, work, ldx, zero, xf(p+1,1), ldx )
339 *
340  DO i = 1, min(m-p,q)-r
341  xf(m-i+1,q-i+1) = xf(m-i+1,q-i+1) - one
342  END DO
343  DO i = 1, r
344  xf(m-(min(m-p,q)-r)+1-i,q-(min(m-p,q)-r)+1-i) =
345  $ xf(m-(min(m-p,q)-r)+1-i,q-(min(m-p,q)-r)+1-i) -
346  $ cmplx( sin(theta(r-i+1)), 0.0e0 )
347  END DO
348 *
349  CALL cgemm( 'No transpose', 'Conjugate transpose', m-p, m-q, m-q,
350  $ one, xf(p+1,q+1), ldx, v2t, ldv2t, zero, work, ldx )
351 *
352  CALL cgemm( 'Conjugate transpose', 'No transpose', m-p, m-q, m-p,
353  $ one, u2, ldu2, work, ldx, zero, xf(p+1,q+1), ldx )
354 *
355  DO i = 1, min(m-p,m-q)-r
356  xf(p+i,q+i) = xf(p+i,q+i) - one
357  END DO
358  DO i = 1, r
359  xf(p+(min(m-p,m-q)-r)+i,q+(min(m-p,m-q)-r)+i) =
360  $ xf(p+(min(m-p,m-q)-r)+i,q+(min(m-p,m-q)-r)+i) -
361  $ cmplx( cos(theta(i)), 0.0e0 )
362  END DO
363 *
364 * Compute norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 ) .
365 *
366  resid = clange( '1', p, q, xf, ldx, rwork )
367  result( 1 ) = ( resid / REAL(MAX(1,P,Q)) ) / eps2
368 *
369 * Compute norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 ) .
370 *
371  resid = clange( '1', p, m-q, xf(1,q+1), ldx, rwork )
372  result( 2 ) = ( resid / REAL(MAX(1,P,M-Q)) ) / eps2
373 *
374 * Compute norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 ) .
375 *
376  resid = clange( '1', m-p, q, xf(p+1,1), ldx, rwork )
377  result( 3 ) = ( resid / REAL(MAX(1,M-P,Q)) ) / eps2
378 *
379 * Compute norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 ) .
380 *
381  resid = clange( '1', m-p, m-q, xf(p+1,q+1), ldx, rwork )
382  result( 4 ) = ( resid / REAL(MAX(1,M-P,M-Q)) ) / eps2
383 *
384 * Compute I - U1'*U1
385 *
386  CALL claset( 'Full', p, p, zero, one, work, ldu1 )
387  CALL cherk( 'Upper', 'Conjugate transpose', p, p, -realone,
388  $ u1, ldu1, realone, work, ldu1 )
389 *
390 * Compute norm( I - U'*U ) / ( MAX(1,P) * ULP ) .
391 *
392  resid = clanhe( '1', 'Upper', p, work, ldu1, rwork )
393  result( 5 ) = ( resid / REAL(MAX(1,P)) ) / ulp
394 *
395 * Compute I - U2'*U2
396 *
397  CALL claset( 'Full', m-p, m-p, zero, one, work, ldu2 )
398  CALL cherk( 'Upper', 'Conjugate transpose', m-p, m-p, -realone,
399  $ u2, ldu2, realone, work, ldu2 )
400 *
401 * Compute norm( I - U2'*U2 ) / ( MAX(1,M-P) * ULP ) .
402 *
403  resid = clanhe( '1', 'Upper', m-p, work, ldu2, rwork )
404  result( 6 ) = ( resid / REAL(MAX(1,M-P)) ) / ulp
405 *
406 * Compute I - V1T*V1T'
407 *
408  CALL claset( 'Full', q, q, zero, one, work, ldv1t )
409  CALL cherk( 'Upper', 'No transpose', q, q, -realone,
410  $ v1t, ldv1t, realone, work, ldv1t )
411 *
412 * Compute norm( I - V1T*V1T' ) / ( MAX(1,Q) * ULP ) .
413 *
414  resid = clanhe( '1', 'Upper', q, work, ldv1t, rwork )
415  result( 7 ) = ( resid / REAL(MAX(1,Q)) ) / ulp
416 *
417 * Compute I - V2T*V2T'
418 *
419  CALL claset( 'Full', m-q, m-q, zero, one, work, ldv2t )
420  CALL cherk( 'Upper', 'No transpose', m-q, m-q, -realone,
421  $ v2t, ldv2t, realone, work, ldv2t )
422 *
423 * Compute norm( I - V2T*V2T' ) / ( MAX(1,M-Q) * ULP ) .
424 *
425  resid = clanhe( '1', 'Upper', m-q, work, ldv2t, rwork )
426  result( 8 ) = ( resid / REAL(MAX(1,M-Q)) ) / ulp
427 *
428 * Check sorting
429 *
430  result( 9 ) = realzero
431  DO i = 1, r
432  IF( theta(i).LT.realzero .OR. theta(i).GT.piover2 ) THEN
433  result( 9 ) = ulpinv
434  END IF
435  IF( i.GT.1) THEN
436  IF ( theta(i).LT.theta(i-1) ) THEN
437  result( 9 ) = ulpinv
438  END IF
439  END IF
440  END DO
441 *
442 * The second half of the routine checks the 2-by-1 CSD
443 *
444  CALL claset( 'Full', q, q, zero, one, work, ldx )
445  CALL cherk( 'Upper', 'Conjugate transpose', q, m, -realone,
446  $ x, ldx, realone, work, ldx )
447  IF (m.GT.0) THEN
448  eps2 = max( ulp,
449  $ clange( '1', q, q, work, ldx, rwork ) / REAL( M ) )
450  ELSE
451  eps2 = ulp
452  END IF
453  r = min( p, m-p, q, m-q )
454 *
455 * Copy the matrix X to the array XF.
456 *
457  CALL clacpy( 'Full', m, q, x, ldx, xf, ldx )
458 *
459 * Compute the CSD
460 *
461  CALL cuncsd2by1( 'Y', 'Y', 'Y', m, p, q, xf(1,1), ldx, xf(p+1,1),
462  $ ldx, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work,
463  $ lwork, rwork, 17*(r+2), iwork, info )
464 *
465 * Compute [X11;X21] := diag(U1,U2)'*[X11;X21]*V1 - [D11;D21]
466 *
467  CALL cgemm( 'No transpose', 'Conjugate transpose', p, q, q, one,
468  $ x, ldx, v1t, ldv1t, zero, work, ldx )
469 *
470  CALL cgemm( 'Conjugate transpose', 'No transpose', p, q, p, one,
471  $ u1, ldu1, work, ldx, zero, x, ldx )
472 *
473  DO i = 1, min(p,q)-r
474  x(i,i) = x(i,i) - one
475  END DO
476  DO i = 1, r
477  x(min(p,q)-r+i,min(p,q)-r+i) =
478  $ x(min(p,q)-r+i,min(p,q)-r+i) - cmplx( cos(theta(i)),
479  $ 0.0e0 )
480  END DO
481 *
482  CALL cgemm( 'No transpose', 'Conjugate transpose', m-p, q, q, one,
483  $ x(p+1,1), ldx, v1t, ldv1t, zero, work, ldx )
484 *
485  CALL cgemm( 'Conjugate transpose', 'No transpose', m-p, q, m-p,
486  $ one, u2, ldu2, work, ldx, zero, x(p+1,1), ldx )
487 *
488  DO i = 1, min(m-p,q)-r
489  x(m-i+1,q-i+1) = x(m-i+1,q-i+1) - one
490  END DO
491  DO i = 1, r
492  x(m-(min(m-p,q)-r)+1-i,q-(min(m-p,q)-r)+1-i) =
493  $ x(m-(min(m-p,q)-r)+1-i,q-(min(m-p,q)-r)+1-i) -
494  $ cmplx( sin(theta(r-i+1)), 0.0e0 )
495  END DO
496 *
497 * Compute norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 ) .
498 *
499  resid = clange( '1', p, q, x, ldx, rwork )
500  result( 10 ) = ( resid / REAL(MAX(1,P,Q)) ) / eps2
501 *
502 * Compute norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 ) .
503 *
504  resid = clange( '1', m-p, q, x(p+1,1), ldx, rwork )
505  result( 11 ) = ( resid / REAL(MAX(1,M-P,Q)) ) / eps2
506 *
507 * Compute I - U1'*U1
508 *
509  CALL claset( 'Full', p, p, zero, one, work, ldu1 )
510  CALL cherk( 'Upper', 'Conjugate transpose', p, p, -realone,
511  $ u1, ldu1, realone, work, ldu1 )
512 *
513 * Compute norm( I - U1'*U1 ) / ( MAX(1,P) * ULP ) .
514 *
515  resid = clanhe( '1', 'Upper', p, work, ldu1, rwork )
516  result( 12 ) = ( resid / REAL(MAX(1,P)) ) / ulp
517 *
518 * Compute I - U2'*U2
519 *
520  CALL claset( 'Full', m-p, m-p, zero, one, work, ldu2 )
521  CALL cherk( 'Upper', 'Conjugate transpose', m-p, m-p, -realone,
522  $ u2, ldu2, realone, work, ldu2 )
523 *
524 * Compute norm( I - U2'*U2 ) / ( MAX(1,M-P) * ULP ) .
525 *
526  resid = clanhe( '1', 'Upper', m-p, work, ldu2, rwork )
527  result( 13 ) = ( resid / REAL(MAX(1,M-P)) ) / ulp
528 *
529 * Compute I - V1T*V1T'
530 *
531  CALL claset( 'Full', q, q, zero, one, work, ldv1t )
532  CALL cherk( 'Upper', 'No transpose', q, q, -realone,
533  $ v1t, ldv1t, realone, work, ldv1t )
534 *
535 * Compute norm( I - V1T*V1T' ) / ( MAX(1,Q) * ULP ) .
536 *
537  resid = clanhe( '1', 'Upper', q, work, ldv1t, rwork )
538  result( 14 ) = ( resid / REAL(MAX(1,Q)) ) / ulp
539 *
540 * Check sorting
541 *
542  result( 15 ) = realzero
543  DO i = 1, r
544  IF( theta(i).LT.realzero .OR. theta(i).GT.piover2 ) THEN
545  result( 15 ) = ulpinv
546  END IF
547  IF( i.GT.1) THEN
548  IF ( theta(i).LT.theta(i-1) ) THEN
549  result( 15 ) = ulpinv
550  END IF
551  END IF
552  END DO
553 *
554  RETURN
555 *
556 * End of CCSDTS
557 *
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: claset.f:108
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:117
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, or the element of largest absolute value of a complex Hermitian matrix.
Definition: clanhe.f:126
recursive subroutine cuncsd(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD
Definition: cuncsd.f:322
subroutine cuncsd2by1(JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD2BY1
Definition: cuncsd2by1.f:264
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:105
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175

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