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DSPEVD(l)			       )			     DSPEVD(l)

NAME
       DSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
       real symmetric matrix A in packed storage

SYNOPSIS
       SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ,	 WORK,	LWORK,	IWORK,
			  LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

	   INTEGER	  INFO, LDZ, LIWORK, LWORK, N

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       DSPEVD  computes all the eigenvalues and, optionally, eigenvectors of a
       real symmetric matrix A in packed storage. 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.

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.

       AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	       On entry, the upper or lower triangle of the  symmetric	matrix
	       A,  packed  columnwise in a linear array.  The j-th column of A
	       is stored in the array AP as follows: if UPLO  =	 'U',  AP(i  +
	       (j-1)*j/2)  =  A(i,j)  for  1<=i<=j;  if	 UPLO  =  'L',	AP(i +
	       (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

	       On exit, AP is  overwritten  by	values	generated  during  the
	       reduction to tridiagonal form.  If UPLO = 'U', the diagonal and
	       first superdiagonal of the tridiagonal matrix T	overwrite  the
	       corresponding  elements	of  A, and if UPLO = 'L', the diagonal
	       and first subdiagonal of T overwrite the corresponding elements
	       of A.

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

       Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
	       If  JOBZ	 =  'V',  then if INFO = 0, Z contains the orthonormal
	       eigenvectors of the matrix A, with the i-th column of Z holding
	       the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
	       not referenced.

       LDZ     (input) INTEGER
	       The leading dimension of the array Z.  LDZ >= 1, and if JOBZ  =
	       'V', 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	  N   <=    1,
	       LWORK  must be at least 1.  If JOBZ = 'N' and N > 1, LWORK must
	       be at least 2*N.	 If JOBZ = 'V' and N > 1,  LWORK  must	be  at
	       least 1 + 6*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 JOBZ  = 'N' or  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.

LAPACK version 3.0		 15 June 2000			     DSPEVD(l)
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