 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dstebz()

 subroutine dstebz ( character RANGE, character ORDER, integer N, double precision VL, double precision VU, integer IL, integer IU, double precision ABSTOL, double precision, dimension( * ) D, double precision, dimension( * ) E, integer M, integer NSPLIT, double precision, dimension( * ) W, integer, dimension( * ) IBLOCK, integer, dimension( * ) ISPLIT, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DSTEBZ

Purpose:
``` DSTEBZ computes the eigenvalues of a symmetric tridiagonal
matrix T.  The user may ask for all eigenvalues, all eigenvalues
in the half-open interval (VL, VU], or the IL-th through IU-th
eigenvalues.

To avoid overflow, the matrix must be scaled so that its
largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
accuracy, it should not be much smaller than that.

See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford
University, July 21, 1966.```
Parameters
 [in] RANGE ``` RANGE is CHARACTER*1 = 'A': ("All") all eigenvalues will be found. = 'V': ("Value") all eigenvalues in the half-open interval (VL, VU] will be found. = 'I': ("Index") the IL-th through IU-th eigenvalues (of the entire matrix) will be found.``` [in] ORDER ``` ORDER is CHARACTER*1 = 'B': ("By Block") the eigenvalues will be grouped by split-off block (see IBLOCK, ISPLIT) and ordered from smallest to largest within the block. = 'E': ("Entire matrix") the eigenvalues for the entire matrix will be ordered from smallest to largest.``` [in] N ``` N is INTEGER The order of the tridiagonal matrix T. N >= 0.``` [in] VL ``` VL is DOUBLE PRECISION If RANGE='V', the lower bound of the interval to be searched for eigenvalues. Eigenvalues less than or equal to VL, or greater than VU, will not be returned. VL < VU. Not referenced if RANGE = 'A' or 'I'.``` [in] VU ``` VU is DOUBLE PRECISION If RANGE='V', the upper bound of the interval to be searched for eigenvalues. Eigenvalues less than or equal to VL, or greater than VU, will not be returned. VL < VU. Not referenced if RANGE = 'A' or 'I'.``` [in] IL ``` IL is INTEGER If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.``` [in] IU ``` IU is INTEGER If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.``` [in] ABSTOL ``` ABSTOL is DOUBLE PRECISION The absolute tolerance for the eigenvalues. An eigenvalue (or cluster) is considered to be located if it has been determined to lie in an interval whose width is ABSTOL or less. If ABSTOL is less than or equal to zero, then ULP*|T| will be used, where |T| means the 1-norm of T. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix T.``` [in] E ``` E is DOUBLE PRECISION array, dimension (N-1) The (n-1) off-diagonal elements of the tridiagonal matrix T.``` [out] M ``` M is INTEGER The actual number of eigenvalues found. 0 <= M <= N. (See also the description of INFO=2,3.)``` [out] NSPLIT ``` NSPLIT is INTEGER The number of diagonal blocks in the matrix T. 1 <= NSPLIT <= N.``` [out] W ``` W is DOUBLE PRECISION array, dimension (N) On exit, the first M elements of W will contain the eigenvalues. (DSTEBZ may use the remaining N-M elements as workspace.)``` [out] IBLOCK ``` IBLOCK is INTEGER array, dimension (N) At each row/column j where E(j) is zero or small, the matrix T is considered to split into a block diagonal matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which block (from 1 to the number of blocks) the eigenvalue W(i) belongs. (DSTEBZ may use the remaining N-M elements as workspace.)``` [out] ISPLIT ``` ISPLIT is INTEGER array, dimension (N) The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. (Only the first NSPLIT elements will actually be used, but since the user cannot know a priori what value NSPLIT will have, N words must be reserved for ISPLIT.)``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (4*N)` [out] IWORK ` IWORK is INTEGER array, dimension (3*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: some or all of the eigenvalues failed to converge or were not computed: =1 or 3: Bisection failed to converge for some eigenvalues; these eigenvalues are flagged by a negative block number. The effect is that the eigenvalues may not be as accurate as the absolute and relative tolerances. This is generally caused by unexpectedly inaccurate arithmetic. =2 or 3: RANGE='I' only: Not all of the eigenvalues IL:IU were found. Effect: M < IU+1-IL Cause: non-monotonic arithmetic, causing the Sturm sequence to be non-monotonic. Cure: recalculate, using RANGE='A', and pick out eigenvalues IL:IU. In some cases, increasing the PARAMETER "FUDGE" may make things work. = 4: RANGE='I', and the Gershgorin interval initially used was too small. No eigenvalues were computed. Probable cause: your machine has sloppy floating-point arithmetic. Cure: Increase the PARAMETER "FUDGE", recompile, and try again.```
Internal Parameters:
```  RELFAC  DOUBLE PRECISION, default = 2.0e0
The relative tolerance.  An interval (a,b] lies within
"relative tolerance" if  b-a < RELFAC*ulp*max(|a|,|b|),
where "ulp" is the machine precision (distance from 1 to
the next larger floating point number.)

FUDGE   DOUBLE PRECISION, default = 2
A "fudge factor" to widen the Gershgorin intervals.  Ideally,
a value of 1 should work, but on machines with sloppy
arithmetic, this needs to be larger.  The default for
publicly released versions should be large enough to handle
the worst machine around.  Note that this has no effect
on accuracy of the solution.```
Date
June 2016

Definition at line 275 of file dstebz.f.

275 *
276 * -- LAPACK computational routine (version 3.7.0) --
277 * -- LAPACK is a software package provided by Univ. of Tennessee, --
278 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
279 * June 2016
280 *
281 * .. Scalar Arguments ..
282  CHARACTER order, range
283  INTEGER il, info, iu, m, n, nsplit
284  DOUBLE PRECISION abstol, vl, vu
285 * ..
286 * .. Array Arguments ..
287  INTEGER iblock( * ), isplit( * ), iwork( * )
288  DOUBLE PRECISION d( * ), e( * ), w( * ), work( * )
289 * ..
290 *
291 * =====================================================================
292 *
293 * .. Parameters ..
294  DOUBLE PRECISION zero, one, two, half
295  parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
296  \$ half = 1.0d0 / two )
297  DOUBLE PRECISION fudge, relfac
298  parameter( fudge = 2.1d0, relfac = 2.0d0 )
299 * ..
300 * .. Local Scalars ..
301  LOGICAL ncnvrg, toofew
302  INTEGER ib, ibegin, idiscl, idiscu, ie, iend, iinfo,
303  \$ im, in, ioff, iorder, iout, irange, itmax,
304  \$ itmp1, iw, iwoff, j, jb, jdisc, je, nb, nwl,
305  \$ nwu
306  DOUBLE PRECISION atoli, bnorm, gl, gu, pivmin, rtoli, safemn,
307  \$ tmp1, tmp2, tnorm, ulp, wkill, wl, wlu, wu, wul
308 * ..
309 * .. Local Arrays ..
310  INTEGER idumma( 1 )
311 * ..
312 * .. External Functions ..
313  LOGICAL lsame
314  INTEGER ilaenv
315  DOUBLE PRECISION dlamch
316  EXTERNAL lsame, ilaenv, dlamch
317 * ..
318 * .. External Subroutines ..
319  EXTERNAL dlaebz, xerbla
320 * ..
321 * .. Intrinsic Functions ..
322  INTRINSIC abs, int, log, max, min, sqrt
323 * ..
324 * .. Executable Statements ..
325 *
326  info = 0
327 *
328 * Decode RANGE
329 *
330  IF( lsame( range, 'A' ) ) THEN
331  irange = 1
332  ELSE IF( lsame( range, 'V' ) ) THEN
333  irange = 2
334  ELSE IF( lsame( range, 'I' ) ) THEN
335  irange = 3
336  ELSE
337  irange = 0
338  END IF
339 *
340 * Decode ORDER
341 *
342  IF( lsame( order, 'B' ) ) THEN
343  iorder = 2
344  ELSE IF( lsame( order, 'E' ) ) THEN
345  iorder = 1
346  ELSE
347  iorder = 0
348  END IF
349 *
350 * Check for Errors
351 *
352  IF( irange.LE.0 ) THEN
353  info = -1
354  ELSE IF( iorder.LE.0 ) THEN
355  info = -2
356  ELSE IF( n.LT.0 ) THEN
357  info = -3
358  ELSE IF( irange.EQ.2 ) THEN
359  IF( vl.GE.vu )
360  \$ info = -5
361  ELSE IF( irange.EQ.3 .AND. ( il.LT.1 .OR. il.GT.max( 1, n ) ) )
362  \$ THEN
363  info = -6
364  ELSE IF( irange.EQ.3 .AND. ( iu.LT.min( n, il ) .OR. iu.GT.n ) )
365  \$ THEN
366  info = -7
367  END IF
368 *
369  IF( info.NE.0 ) THEN
370  CALL xerbla( 'DSTEBZ', -info )
371  RETURN
372  END IF
373 *
374 * Initialize error flags
375 *
376  info = 0
377  ncnvrg = .false.
378  toofew = .false.
379 *
380 * Quick return if possible
381 *
382  m = 0
383  IF( n.EQ.0 )
384  \$ RETURN
385 *
386 * Simplifications:
387 *
388  IF( irange.EQ.3 .AND. il.EQ.1 .AND. iu.EQ.n )
389  \$ irange = 1
390 *
391 * Get machine constants
392 * NB is the minimum vector length for vector bisection, or 0
393 * if only scalar is to be done.
394 *
395  safemn = dlamch( 'S' )
396  ulp = dlamch( 'P' )
397  rtoli = ulp*relfac
398  nb = ilaenv( 1, 'DSTEBZ', ' ', n, -1, -1, -1 )
399  IF( nb.LE.1 )
400  \$ nb = 0
401 *
402 * Special Case when N=1
403 *
404  IF( n.EQ.1 ) THEN
405  nsplit = 1
406  isplit( 1 ) = 1
407  IF( irange.EQ.2 .AND. ( vl.GE.d( 1 ) .OR. vu.LT.d( 1 ) ) ) THEN
408  m = 0
409  ELSE
410  w( 1 ) = d( 1 )
411  iblock( 1 ) = 1
412  m = 1
413  END IF
414  RETURN
415  END IF
416 *
417 * Compute Splitting Points
418 *
419  nsplit = 1
420  work( n ) = zero
421  pivmin = one
422 *
423  DO 10 j = 2, n
424  tmp1 = e( j-1 )**2
425  IF( abs( d( j )*d( j-1 ) )*ulp**2+safemn.GT.tmp1 ) THEN
426  isplit( nsplit ) = j - 1
427  nsplit = nsplit + 1
428  work( j-1 ) = zero
429  ELSE
430  work( j-1 ) = tmp1
431  pivmin = max( pivmin, tmp1 )
432  END IF
433  10 CONTINUE
434  isplit( nsplit ) = n
435  pivmin = pivmin*safemn
436 *
437 * Compute Interval and ATOLI
438 *
439  IF( irange.EQ.3 ) THEN
440 *
441 * RANGE='I': Compute the interval containing eigenvalues
442 * IL through IU.
443 *
444 * Compute Gershgorin interval for entire (split) matrix
445 * and use it as the initial interval
446 *
447  gu = d( 1 )
448  gl = d( 1 )
449  tmp1 = zero
450 *
451  DO 20 j = 1, n - 1
452  tmp2 = sqrt( work( j ) )
453  gu = max( gu, d( j )+tmp1+tmp2 )
454  gl = min( gl, d( j )-tmp1-tmp2 )
455  tmp1 = tmp2
456  20 CONTINUE
457 *
458  gu = max( gu, d( n )+tmp1 )
459  gl = min( gl, d( n )-tmp1 )
460  tnorm = max( abs( gl ), abs( gu ) )
461  gl = gl - fudge*tnorm*ulp*n - fudge*two*pivmin
462  gu = gu + fudge*tnorm*ulp*n + fudge*pivmin
463 *
464 * Compute Iteration parameters
465 *
466  itmax = int( ( log( tnorm+pivmin )-log( pivmin ) ) /
467  \$ log( two ) ) + 2
468  IF( abstol.LE.zero ) THEN
469  atoli = ulp*tnorm
470  ELSE
471  atoli = abstol
472  END IF
473 *
474  work( n+1 ) = gl
475  work( n+2 ) = gl
476  work( n+3 ) = gu
477  work( n+4 ) = gu
478  work( n+5 ) = gl
479  work( n+6 ) = gu
480  iwork( 1 ) = -1
481  iwork( 2 ) = -1
482  iwork( 3 ) = n + 1
483  iwork( 4 ) = n + 1
484  iwork( 5 ) = il - 1
485  iwork( 6 ) = iu
486 *
487  CALL dlaebz( 3, itmax, n, 2, 2, nb, atoli, rtoli, pivmin, d, e,
488  \$ work, iwork( 5 ), work( n+1 ), work( n+5 ), iout,
489  \$ iwork, w, iblock, iinfo )
490 *
491  IF( iwork( 6 ).EQ.iu ) THEN
492  wl = work( n+1 )
493  wlu = work( n+3 )
494  nwl = iwork( 1 )
495  wu = work( n+4 )
496  wul = work( n+2 )
497  nwu = iwork( 4 )
498  ELSE
499  wl = work( n+2 )
500  wlu = work( n+4 )
501  nwl = iwork( 2 )
502  wu = work( n+3 )
503  wul = work( n+1 )
504  nwu = iwork( 3 )
505  END IF
506 *
507  IF( nwl.LT.0 .OR. nwl.GE.n .OR. nwu.LT.1 .OR. nwu.GT.n ) THEN
508  info = 4
509  RETURN
510  END IF
511  ELSE
512 *
513 * RANGE='A' or 'V' -- Set ATOLI
514 *
515  tnorm = max( abs( d( 1 ) )+abs( e( 1 ) ),
516  \$ abs( d( n ) )+abs( e( n-1 ) ) )
517 *
518  DO 30 j = 2, n - 1
519  tnorm = max( tnorm, abs( d( j ) )+abs( e( j-1 ) )+
520  \$ abs( e( j ) ) )
521  30 CONTINUE
522 *
523  IF( abstol.LE.zero ) THEN
524  atoli = ulp*tnorm
525  ELSE
526  atoli = abstol
527  END IF
528 *
529  IF( irange.EQ.2 ) THEN
530  wl = vl
531  wu = vu
532  ELSE
533  wl = zero
534  wu = zero
535  END IF
536  END IF
537 *
538 * Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
539 * NWL accumulates the number of eigenvalues .le. WL,
540 * NWU accumulates the number of eigenvalues .le. WU
541 *
542  m = 0
543  iend = 0
544  info = 0
545  nwl = 0
546  nwu = 0
547 *
548  DO 70 jb = 1, nsplit
549  ioff = iend
550  ibegin = ioff + 1
551  iend = isplit( jb )
552  in = iend - ioff
553 *
554  IF( in.EQ.1 ) THEN
555 *
556 * Special Case -- IN=1
557 *
558  IF( irange.EQ.1 .OR. wl.GE.d( ibegin )-pivmin )
559  \$ nwl = nwl + 1
560  IF( irange.EQ.1 .OR. wu.GE.d( ibegin )-pivmin )
561  \$ nwu = nwu + 1
562  IF( irange.EQ.1 .OR. ( wl.LT.d( ibegin )-pivmin .AND. wu.GE.
563  \$ d( ibegin )-pivmin ) ) THEN
564  m = m + 1
565  w( m ) = d( ibegin )
566  iblock( m ) = jb
567  END IF
568  ELSE
569 *
570 * General Case -- IN > 1
571 *
572 * Compute Gershgorin Interval
573 * and use it as the initial interval
574 *
575  gu = d( ibegin )
576  gl = d( ibegin )
577  tmp1 = zero
578 *
579  DO 40 j = ibegin, iend - 1
580  tmp2 = abs( e( j ) )
581  gu = max( gu, d( j )+tmp1+tmp2 )
582  gl = min( gl, d( j )-tmp1-tmp2 )
583  tmp1 = tmp2
584  40 CONTINUE
585 *
586  gu = max( gu, d( iend )+tmp1 )
587  gl = min( gl, d( iend )-tmp1 )
588  bnorm = max( abs( gl ), abs( gu ) )
589  gl = gl - fudge*bnorm*ulp*in - fudge*pivmin
590  gu = gu + fudge*bnorm*ulp*in + fudge*pivmin
591 *
592 * Compute ATOLI for the current submatrix
593 *
594  IF( abstol.LE.zero ) THEN
595  atoli = ulp*max( abs( gl ), abs( gu ) )
596  ELSE
597  atoli = abstol
598  END IF
599 *
600  IF( irange.GT.1 ) THEN
601  IF( gu.LT.wl ) THEN
602  nwl = nwl + in
603  nwu = nwu + in
604  GO TO 70
605  END IF
606  gl = max( gl, wl )
607  gu = min( gu, wu )
608  IF( gl.GE.gu )
609  \$ GO TO 70
610  END IF
611 *
612 * Set Up Initial Interval
613 *
614  work( n+1 ) = gl
615  work( n+in+1 ) = gu
616  CALL dlaebz( 1, 0, in, in, 1, nb, atoli, rtoli, pivmin,
617  \$ d( ibegin ), e( ibegin ), work( ibegin ),
618  \$ idumma, work( n+1 ), work( n+2*in+1 ), im,
619  \$ iwork, w( m+1 ), iblock( m+1 ), iinfo )
620 *
621  nwl = nwl + iwork( 1 )
622  nwu = nwu + iwork( in+1 )
623  iwoff = m - iwork( 1 )
624 *
625 * Compute Eigenvalues
626 *
627  itmax = int( ( log( gu-gl+pivmin )-log( pivmin ) ) /
628  \$ log( two ) ) + 2
629  CALL dlaebz( 2, itmax, in, in, 1, nb, atoli, rtoli, pivmin,
630  \$ d( ibegin ), e( ibegin ), work( ibegin ),
631  \$ idumma, work( n+1 ), work( n+2*in+1 ), iout,
632  \$ iwork, w( m+1 ), iblock( m+1 ), iinfo )
633 *
634 * Copy Eigenvalues Into W and IBLOCK
635 * Use -JB for block number for unconverged eigenvalues.
636 *
637  DO 60 j = 1, iout
638  tmp1 = half*( work( j+n )+work( j+in+n ) )
639 *
640 * Flag non-convergence.
641 *
642  IF( j.GT.iout-iinfo ) THEN
643  ncnvrg = .true.
644  ib = -jb
645  ELSE
646  ib = jb
647  END IF
648  DO 50 je = iwork( j ) + 1 + iwoff,
649  \$ iwork( j+in ) + iwoff
650  w( je ) = tmp1
651  iblock( je ) = ib
652  50 CONTINUE
653  60 CONTINUE
654 *
655  m = m + im
656  END IF
657  70 CONTINUE
658 *
659 * If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
660 * If NWL+1 < IL or NWU > IU, discard extra eigenvalues.
661 *
662  IF( irange.EQ.3 ) THEN
663  im = 0
664  idiscl = il - 1 - nwl
665  idiscu = nwu - iu
666 *
667  IF( idiscl.GT.0 .OR. idiscu.GT.0 ) THEN
668  DO 80 je = 1, m
669  IF( w( je ).LE.wlu .AND. idiscl.GT.0 ) THEN
670  idiscl = idiscl - 1
671  ELSE IF( w( je ).GE.wul .AND. idiscu.GT.0 ) THEN
672  idiscu = idiscu - 1
673  ELSE
674  im = im + 1
675  w( im ) = w( je )
676  iblock( im ) = iblock( je )
677  END IF
678  80 CONTINUE
679  m = im
680  END IF
681  IF( idiscl.GT.0 .OR. idiscu.GT.0 ) THEN
682 *
683 * Code to deal with effects of bad arithmetic:
684 * Some low eigenvalues to be discarded are not in (WL,WLU],
685 * or high eigenvalues to be discarded are not in (WUL,WU]
686 * so just kill off the smallest IDISCL/largest IDISCU
687 * eigenvalues, by simply finding the smallest/largest
688 * eigenvalue(s).
689 *
690 * (If N(w) is monotone non-decreasing, this should never
691 * happen.)
692 *
693  IF( idiscl.GT.0 ) THEN
694  wkill = wu
695  DO 100 jdisc = 1, idiscl
696  iw = 0
697  DO 90 je = 1, m
698  IF( iblock( je ).NE.0 .AND.
699  \$ ( w( je ).LT.wkill .OR. iw.EQ.0 ) ) THEN
700  iw = je
701  wkill = w( je )
702  END IF
703  90 CONTINUE
704  iblock( iw ) = 0
705  100 CONTINUE
706  END IF
707  IF( idiscu.GT.0 ) THEN
708 *
709  wkill = wl
710  DO 120 jdisc = 1, idiscu
711  iw = 0
712  DO 110 je = 1, m
713  IF( iblock( je ).NE.0 .AND.
714  \$ ( w( je ).GT.wkill .OR. iw.EQ.0 ) ) THEN
715  iw = je
716  wkill = w( je )
717  END IF
718  110 CONTINUE
719  iblock( iw ) = 0
720  120 CONTINUE
721  END IF
722  im = 0
723  DO 130 je = 1, m
724  IF( iblock( je ).NE.0 ) THEN
725  im = im + 1
726  w( im ) = w( je )
727  iblock( im ) = iblock( je )
728  END IF
729  130 CONTINUE
730  m = im
731  END IF
732  IF( idiscl.LT.0 .OR. idiscu.LT.0 ) THEN
733  toofew = .true.
734  END IF
735  END IF
736 *
737 * If ORDER='B', do nothing -- the eigenvalues are already sorted
738 * by block.
739 * If ORDER='E', sort the eigenvalues from smallest to largest
740 *
741  IF( iorder.EQ.1 .AND. nsplit.GT.1 ) THEN
742  DO 150 je = 1, m - 1
743  ie = 0
744  tmp1 = w( je )
745  DO 140 j = je + 1, m
746  IF( w( j ).LT.tmp1 ) THEN
747  ie = j
748  tmp1 = w( j )
749  END IF
750  140 CONTINUE
751 *
752  IF( ie.NE.0 ) THEN
753  itmp1 = iblock( ie )
754  w( ie ) = w( je )
755  iblock( ie ) = iblock( je )
756  w( je ) = tmp1
757  iblock( je ) = itmp1
758  END IF
759  150 CONTINUE
760  END IF
761 *
762  info = 0
763  IF( ncnvrg )
764  \$ info = info + 1
765  IF( toofew )
766  \$ info = info + 2
767  RETURN
768 *
769 * End of DSTEBZ
770 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dlaebz(IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, NAB, WORK, IWORK, INFO)
DLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than ...
Definition: dlaebz.f:321
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
Here is the call graph for this function:
Here is the caller graph for this function: