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CSTEGR(1)	  LAPACK computational routine (version 3.2)	     CSTEGR(1)

NAME
       CSTEGR - computes selected eigenvalues and, optionally, eigenvectors of
       a real symmetric tridiagonal matrix T

SYNOPSIS
       SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M,  W,
			  Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO )

	   IMPLICIT	  NONE

	   CHARACTER	  JOBZ, RANGE

	   INTEGER	  IL, INFO, IU, LDZ, LIWORK, LWORK, M, N

	   REAL		  ABSTOL, VL, VU

	   INTEGER	  ISUPPZ( * ), IWORK( * )

	   REAL		  D( * ), E( * ), W( * ), WORK( * )

	   COMPLEX	  Z( LDZ, * )

PURPOSE
       CSTEGR computes selected eigenvalues and, optionally, eigenvectors of a
       real symmetric tridiagonal matrix T. Any such unreduced	matrix	has  a
       well  defined  set  of  pairwise different real eigenvalues, the corre‐
       sponding real eigenvectors are pairwise orthogonal.
       The spectrum may be computed either completely or partially by specify‐
       ing  either  an	interval  (VL,VU]  or a range of indices IL:IU for the
       desired eigenvalues.
       CSTEGR is a compatability wrapper around the improved  CSTEMR  routine.
       See SSTEMR for further details.
       One  important  change  is that the ABSTOL parameter no longer provides
       any benefit and hence is no longer used.
       Note : CSTEGR and CSTEMR work only on machines  which  follow  IEEE-754
       floating-point standard in their handling of infinities and NaNs.  Nor‐
       mal execution may create these exceptiona values and  hence  may	 abort
       due  to a floating point exception in environments which do not conform
       to the IEEE-754 standard.

ARGUMENTS
       JOBZ    (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only;
	       = 'V':  Compute eigenvalues and eigenvectors.

       RANGE   (input) CHARACTER*1
	       = 'A': all eigenvalues will be found.
	       = 'V': all eigenvalues in the half-open interval	 (VL,VU]  will
	       be  found.   = 'I': the IL-th through IU-th eigenvalues will be
	       found.

       N       (input) INTEGER
	       The order of the matrix.	 N >= 0.

       D       (input/output) REAL array, dimension (N)
	       On entry, the N diagonal elements of the tridiagonal matrix  T.
	       On exit, D is overwritten.

       E       (input/output) REAL array, dimension (N)
	       On  entry,  the	(N-1)  subdiagonal elements of the tridiagonal
	       matrix T in elements 1 to N-1 of E. E(N) need  not  be  set  on
	       input,  but  is	used  internally  as workspace.	 On exit, E is
	       overwritten.

       VL      (input) REAL
	       VU      (input) REAL If RANGE='V', the lower and	 upper	bounds
	       of  the	interval to be searched for eigenvalues. VL < VU.  Not
	       referenced if RANGE = 'A' or 'I'.

       IL      (input) INTEGER
	       IU      (input) INTEGER If RANGE='I', the indices (in ascending
	       order)  of the smallest and largest eigenvalues to be returned.
	       1 <= IL <= IU <= N, if N > 0.  Not referenced if RANGE = 'A' or
	       'V'.

       ABSTOL  (input) REAL
	       Unused.	 Was  the  absolute  error tolerance for the eigenval‐
	       ues/eigenvectors in previous versions.

       M       (output) INTEGER
	       The total number of eigenvalues found.  0 <= M <= N.  If	 RANGE
	       = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

       W       (output) REAL array, dimension (N)
	       The  first  M  elements	contain	 the  selected	eigenvalues in
	       ascending order.

       Z       (output) COMPLEX array, dimension (LDZ, max(1,M) )
	       If JOBZ = 'V', and if INFO = 0, then the first M columns	 of  Z
	       contain	the  orthonormal  eigenvectors	of the matrix T corre‐
	       sponding to the selected eigenvalues, with the i-th column of Z
	       holding	the  eigenvector associated with W(i).	If JOBZ = 'N',
	       then Z is not referenced.  Note: the user must ensure  that  at
	       least  max(1,M) columns are supplied in the array Z; if RANGE =
	       'V', the exact value of M is not known in advance and an	 upper
	       bound must be used.  Supplying N columns is always safe.

       LDZ     (input) INTEGER
	       The  leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	       'V', then LDZ >= max(1,N).

       ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
	       The support of the eigenvectors in Z, i.e., the	indices	 indi‐
	       cating the nonzero elements in Z. The i-th computed eigenvector
	       is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i
	       ).  This	 is  relevant  in  the	case when the matrix is split.
	       ISUPPZ is only accessed when JOBZ is 'V' and N > 0.

       WORK    (workspace/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal (and minimal)
	       LWORK.

       LWORK   (input) INTEGER
	       The dimension of the array WORK. LWORK >= max(1,18*N) if JOBZ =
	       'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.  If	 LWORK	=  -1,
	       then  a workspace query is assumed; the routine only calculates
	       the optimal size of the WORK array, returns this value  as  the
	       first  entry of the WORK array, and no error message related to
	       LWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	       On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

       LIWORK  (input) INTEGER
	       The dimension of the array IWORK.  LIWORK >= max(1,10*N) if the
	       eigenvectors  are desired, and LIWORK >= max(1,8*N) if only the
	       eigenvalues are to  be  computed.   If  LIWORK  =  -1,  then  a
	       workspace  query	 is  assumed;  the routine only calculates the
	       optimal size of the IWORK array,	 returns  this	value  as  the
	       first entry of the IWORK array, and no error message related to
	       LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       On exit, INFO = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = 1X, internal error in SLARRE,  if  INFO	=  2X,
	       internal	 error	in CLARRV.  Here, the digit X = ABS( IINFO ) <
	       10, where IINFO is the nonzero error code returned by SLARRE or
	       CLARRV, respectively.

FURTHER DETAILS
       Based on contributions by
	  Inderjit Dhillon, IBM Almaden, USA
	  Osni Marques, LBNL/NERSC, USA
	  Christof Voemel, LBNL/NERSC, USA

 LAPACK computational routine (veNovember22008			     CSTEGR(1)
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