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NAME
     dstevd - compute all eigenvalues and, optionally,  eigenvec-
     tors of a real symmetric tridiagonal matrix

SYNOPSIS
     SUBROUTINE DSTEVD( JOBZ, N,  D,  E,  Z,  LDZ,  WORK,  LWORK,
               IWORK, LIWORK, INFO )

     CHARACTER JOBZ

     INTEGER INFO, LDZ, LIWORK, LWORK, N

     INTEGER IWORK( * )

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



     #include <sunperf.h>

     void dstevd(char jobz, int n, double *d, double  *e,  double
               *dz, int ldz, int *info) ;

PURPOSE
     DSTEVD computes all eigenvalues and,  optionally,  eigenvec-
     tors of a real symmetric tridiagonal matrix. 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.


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

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

     D         (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               On entry, the n diagonal elements of the tridiago-
               nal  matrix  A.   On exit, if INFO = 0, the eigen-
               values in ascending order.

     E         (input/output) DOUBLE PRECISION  array,  dimension
               (N)
               On entry, the (n-1) subdiagonal  elements  of  the
               tridiagonal  matrix A, stored in elements 1 to N-1
               of E; E(N) need not be set, but  is  used  by  the
               routine.   On  exit,  the  contents  of E are des-
               troyed.

     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  associ-
               ated  with  D(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 LWORK >  0,  WORK(1)
               returns the optimal LWORK.

     LWORK     (input) INTEGER
               The dimension of the array WORK.  If JOBZ   =  'N'
               or  N <= 1 then LWORK must be at least 1.  If JOBZ
               = 'V' and N > 1 then LWORK must be at least ( 1  +
               3*N  +  2*N*lg N + 2*N**2 ), where lg( N ) = smal-
               lest integer k such that 2**k >= N.

     IWORK     (workspace/output)   INTEGER   array,    dimension
               (LIWORK)
               On exit, if  LIWORK  >  0,  IWORK(1)  returns  the
               optimal LIWORK.

     LIWORK    (input) INTEGER
               The dimension of the array IWORK.  If JOBZ  =  'N'
               or N <= 1 then LIWORK must be at least 1.  If JOBZ
               = 'V' and N > 1  then  LIWORK  must  be  at  least
               2+5*N.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, the algorithm  failed  to  con-
               verge;  i  off-diagonal elements of E did not con-
               verge to zero.

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