CSTEDC(l)								 )								 CSTEDC(l)

NAME

       CSTEDC - compute 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 symmetric 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 origi-
	       nal 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 contains 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 eigenvectors are desired, then LDZ >= max(1,N).

       WORK    (workspace/output) COMPLEX array, dimension (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.

	       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.

       RWORK   (workspace/output) REAL array,
	       dimension (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 .

	       If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the RWORK  array,  returns  this
	       value as the first entry of the RWORK array, and no error message related to LRWORK 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.  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 .

	       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
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       >  0:   The  algorithm  failed to compute an eigenvalue while working 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 version 3.0						   15 June 2000 							 CSTEDC(l)