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DSTEDC(l)			       )			     DSTEDC(l)

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

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

	   CHARACTER	  COMPZ

	   INTEGER	  INFO, LDZ, LIWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       DSTEDC 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 real symmetric matrix can also be found
       if DSYTRD or DSPTRD or DSBTRD 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 DLAED3 for details.

ARGUMENTS
       COMPZ   (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only.
	       = 'I':  Compute eigenvectors of tridiagonal matrix also.
	       = 'V':  Compute eigenvectors of original dense symmetric matrix
	       also.   On  entry,  Z  contains	the  orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N-1)
	       On  entry,  the subdiagonal elements of the tridiagonal matrix.
	       On exit, E has been destroyed.

       Z       (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
	       On entry, if COMPZ = 'V', then Z contains the orthogonal 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  symmetric 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) DOUBLE PRECISION 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 N <= 1 then
	       LWORK must be at least 1.  If COMPZ = 'V' and N > 1 then	 LWORK
	       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 then LWORK must be at least ( 1 + 4*N + N**2 ).

	       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.  If COMPZ = 'N'  or  N	 <=  1
	       then  LIWORK must be at least 1.	 If COMPZ = 'V' and N > 1 then
	       LIWORK must be at least ( 6 + 6*N + 5*N*lg N ).	If COMPZ = 'I'
	       and N > 1 then 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 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
       Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0		 15 June 2000			     DSTEDC(l)
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