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DSYEVD(l)			       )			     DSYEVD(l)

NAME
       DSYEVD  -  compute  all	eigenvalues and, optionally, eigenvectors of a
       real symmetric matrix A

SYNOPSIS
       SUBROUTINE DSYEVD( JOBZ, UPLO,  N,  A,  LDA,  W,	 WORK,	LWORK,	IWORK,
			  LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, LDA, LIWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION A( LDA, * ), W( * ), WORK( * )

PURPOSE
       DSYEVD computes all eigenvalues and, optionally, eigenvectors of a real
       symmetric matrix A. If eigenvectors are desired, it uses a  divide  and
       conquer algorithm.

       The  divide  and	 conquer  algorithm  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 dig‐
       its, but we know of none.

       Because of large use of	BLAS  of  level	 3,  DSYEVD  needs  N**2  more
       workspace than DSYEVX.

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

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

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

       A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
	       On  entry,  the symmetric matrix A.  If UPLO = 'U', the leading
	       N-by-N upper triangular part of A contains the upper triangular
	       part  of the matrix A.  If UPLO = 'L', the leading N-by-N lower
	       triangular part of A contains the lower triangular part of  the
	       matrix A.  On exit, if JOBZ = 'V', then if INFO = 0, A contains
	       the orthonormal eigenvectors of the matrix A.  If JOBZ  =  'N',
	       then on exit the lower triangle (if UPLO='L') or the upper tri‐
	       angle (if UPLO='U') of A, including the diagonal, is destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       W       (output) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, the eigenvalues in ascending order.

       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   N   <=   1,
	       LWORK must be at least 1.  If JOBZ = 'N' and N > 1, LWORK  must
	       be  at  least 2*N+1.  If JOBZ = 'V' and N > 1, LWORK must be at
	       least 1 + 6*N + 2*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   N   <=   1,
	       LIWORK must be at least 1.  If JOBZ  = 'N' and N	 >  1,	LIWORK
	       must  be	 at least 1.  If JOBZ  = 'V' and 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:   if  INFO	 = i, the algorithm failed to converge; i off-
	       diagonal elements of an intermediate tridiagonal form  did  not
	       converge to zero.

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			     DSYEVD(l)
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