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cstegr.f(3)				      LAPACK				      cstegr.f(3)

NAME
       cstegr.f -

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

Function/Subroutine Documentation
   subroutine cstegr (characterJOBZ, characterRANGE, integerN, real, dimension( * )D, real,
       dimension( * )E, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real,
       dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, integer, dimension( * )ISUPPZ,
       real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK,
       integerINFO)
       CSTEGR

       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 corresponding
	    real eigenvectors are pairwise orthogonal.

	    The spectrum may be computed either completely or partially by specifying
	    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.  Normal 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.

       Parameters:
	   JOBZ

		     JOBZ is CHARACTER*1
		     = 'N':  Compute eigenvalues only;
		     = 'V':  Compute eigenvalues and eigenvectors.

	   RANGE

		     RANGE is 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

		     N is INTEGER
		     The order of the matrix.  N >= 0.

	   D

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

	   E

		     E is 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

		     VL is REAL

	   VU

		     VU is 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

		     IL is INTEGER

	   IU

		     IU is 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

		     ABSTOL is REAL
		     Unused.  Was the absolute error tolerance for the
		     eigenvalues/eigenvectors in previous versions.

	   M

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

	   W

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

	   Z

		     Z is 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
		     corresponding 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

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

	   ISUPPZ

		     ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
		     The support of the eigenvectors in Z, i.e., the indices
		     indicating 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

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

	   LWORK

		     LWORK is 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

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

	   LIWORK

		     LIWORK is 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

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Inderjit Dhillon, IBM Almaden, USA
	    Osni Marques, LBNL/NERSC, USA
	    Christof Voemel, LBNL/NERSC, USA

       Definition at line 255 of file cstegr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      cstegr.f(3)
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