CXML
        	    
LAPACK version 3.0
dsyevd(3)

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

SYNTAX
  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( * )

DESCRIPTION
  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 digits,
  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 triangle (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.