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NAME
     dstedc - compute all eigenvalues and, optionally,  eigenvec-
     tors  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, * )



     #include <sunperf.h>

     void dstedc(char compz, int n, double *d, double *e,  double
               *dz, int ldz, int *info) ;

PURPOSE
     DSTEDC computes all eigenvalues and,  optionally,  eigenvec-
     tors  of a symmetric 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 tridiag-
               onal 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 tridi-
               agonal 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  contains  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 eigenvectors are desired, then 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 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 ) = smal-
               lest integer k such that 2**k >= N.   If  COMPZ  =
               'I'  and  N  > 1 then LWORK must be at least ( 1 +
               3*N + 2*N*lg N + 2*N**2 ).

     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 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 ( 2 + 5*N ).

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.
               > 0:  The algorithm failed to  compute  an  eigen-
               value while working on the submatrix lying in rows
               and columns INFO/(N+1) through mod(INFO,N+1).

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