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CSTEDC(1)		 LAPACK routine (version 3.2)		     CSTEDC(1)

NAME
       CSTEDC  -  computes  all eigenvalues and, optionally, eigenvectors of a
       symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS
       SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK,  LRWORK,
			  IWORK, LIWORK, INFO )

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, LIWORK, LRWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   REAL		  D( * ), E( * ), RWORK( * )

	   COMPLEX	  WORK( * ), Z( LDZ, * )

PURPOSE
       CSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
       metric tridiagonal matrix using the divide  and	conquer	 method.   The
       eigenvectors  of	 a  full  or band complex Hermitian matrix can also be
       found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix
       to tridiagonal form.
       This  code makes very mild assumptions about floating point arithmetic.
       It will work on machines with a guard  digit  in	 add/subtract,	or  on
       those binary machines without guard digits which subtract like the Cray
       X-MP, Cray Y-MP, Cray C-90, or Cray-2.  It could	 conceivably  fail  on
       hexadecimal  or	decimal	 machines without guard digits, but we know of
       none.  See SLAED3 for details.

ARGUMENTS
       COMPZ   (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only.
	       = 'I':  Compute eigenvectors of tridiagonal matrix also.
	       = 'V':  Compute eigenvectors of original Hermitian matrix also.
	       On  entry,  Z  contains	the  unitary matrix used to reduce the
	       original matrix to tridiagonal form.

       N       (input) INTEGER
	       The dimension of the symmetric tridiagonal matrix.  N >= 0.

       D       (input/output) REAL array, dimension (N)
	       On entry, the diagonal elements of the tridiagonal matrix.   On
	       exit, if INFO = 0, the eigenvalues in ascending order.

       E       (input/output) REAL array, dimension (N-1)
	       On  entry,  the subdiagonal elements of the tridiagonal matrix.
	       On exit, E has been destroyed.

       Z       (input/output) COMPLEX array, dimension (LDZ,N)
	       On entry, if COMPZ = 'V', then Z contains  the  unitary	matrix
	       used  in the reduction to tridiagonal form.  On exit, if INFO =
	       0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors
	       of  the	original  Hermitian matrix, and if COMPZ = 'I', Z con‐
	       tains the orthonormal eigenvectors of the symmetric tridiagonal
	       matrix.	If  COMPZ = 'N', then Z is not referenced.

       LDZ     (input) INTEGER
	       The  leading dimension of the array Z.  LDZ >= 1.  If eigenvec‐
	       tors are desired, then LDZ >= max(1,N).

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

       LWORK   (input) INTEGER
	       The dimension of the array WORK.	 If COMPZ = 'N' or 'I',	 or  N
	       <=  1,  LWORK  must  be	at least 1.  If COMPZ = 'V' and N > 1,
	       LWORK must be at least N*N.  Note that for COMPZ = 'V', then if
	       N is less than or equal to the minimum divide size, usually 25,
	       then LWORK need only be 1.  If LWORK =  -1,  then  a  workspace
	       query is assumed; the routine only calculates the optimal sizes
	       of the WORK, RWORK and IWORK arrays, returns  these  values  as
	       the  first  entries of the WORK, RWORK and IWORK arrays, and no
	       error message related to LWORK or LRWORK or LIWORK is issued by
	       XERBLA.

       RWORK   (workspace/output) REAL array, dimension (MAX(1,LRWORK))
	       On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

       LRWORK  (input) INTEGER
	       The  dimension  of  the array RWORK.  If COMPZ = 'N' or N <= 1,
	       LRWORK must be at least 1.  If COMPZ = 'V' and N	 >  1,	LRWORK
	       must  be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
	       smallest integer k such that 2**k >= N.	If COMPZ = 'I' and N >
	       1,  LRWORK  must	 be at least 1 + 4*N + 2*N**2 .	 Note that for
	       COMPZ = 'I' or 'V', then if N is less than or equal to the min‐
	       imum  divide  size,  usually  25,  then	LRWORK	need  only  be
	       max(1,2*(N-1)).	If LRWORK = -1,	 then  a  workspace  query  is
	       assumed;	 the  routine only calculates the optimal sizes of the
	       WORK, RWORK and IWORK arrays, returns these values as the first
	       entries	of the WORK, RWORK and IWORK arrays, and no error mes‐
	       sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.

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

       LIWORK  (input) INTEGER
	       The dimension of the array IWORK.  If COMPZ = 'N' or  N	<=  1,
	       LIWORK  must  be	 at least 1.  If COMPZ = 'V' or N > 1,	LIWORK
	       must be at least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or N >  1,
	       LIWORK must be at least 3 + 5*N .  Note that for COMPZ = 'I' or
	       'V', then if N is less than or  equal  to  the  minimum	divide
	       size,  usually 25, then LIWORK need only be 1.  If LIWORK = -1,
	       then a workspace query is assumed; the routine only  calculates
	       the  optimal sizes of the WORK, RWORK and IWORK arrays, returns
	       these values as the first entries of the WORK, RWORK and	 IWORK
	       arrays,	and  no	 error	message	 related to LWORK or LRWORK or
	       LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  The algorithm failed to compute an eigenvalue while work‐
	       ing  on	the  submatrix	lying  in  rows and columns INFO/(N+1)
	       through mod(INFO,N+1).

FURTHER DETAILS
       Based on contributions by
	  Jeff Rutter, Computer Science Division, University of California
	  at Berkeley, USA

 LAPACK routine (version 3.2)	 November 2008			     CSTEDC(1)
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