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NAME
     cstedc - compute all eigenvalues and, optionally,  eigenvec-
     tors  of a symmetric tridiagonal matrix using the divide and
     conquer method

SYNOPSIS
     SUBROUTINE CSTEDC( COMPZ, N, D,  E,  Z,  LDZ,  WORK,  LWORK,
               RWORK, LRWORK, IWORK, LIWORK, INFO )

     CHARACTER COMPZ

     INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N

     INTEGER IWORK( * )

     REAL D( * ), E( * ), RWORK( * )

     COMPLEX WORK( * ), Z( LDZ, * )



     #include <sunperf.h>

     void cstedc(char compz, int n, float *d, float  *e,  complex
               *cz, int ldz, int *info) ;

PURPOSE
     CSTEDC 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  complex
     Hermitian  matrix  can  also be found if CHETRD or CHPTRD or
     CHBTRD 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 SLAED3 for details.


ARGUMENTS
     COMPZ     (input) CHARACTER*1
               = 'N':  Compute eigenvalues only.
               = 'I':  Compute eigenvectors of tridiagonal matrix
               also.
               = 'V':  Compute eigenvectors of original Hermitian
               matrix  also.   On  entry,  Z contains the unitary
               matrix used to reduce the original matrix to  tri-
               diagonal form.

     N         (input) INTEGER
               The dimension of the symmetric tridiagonal matrix.
               N >= 0.

     D         (input/output) REAL 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) REAL array, dimension (N-1)
               On entry, the subdiagonal elements of the tridiag-
               onal matrix.  On exit, E has been destroyed.

     Z         (input/output) COMPLEX array, dimension (LDZ,N)
               On entry, if COMPZ = 'V', then Z contains the uni-
               tary  matrix  used in the reduction to tridiagonal
               form.  On exit, if INFO = 0, then if COMPZ =  'V',
               Z  contains  the  orthonormal  eigenvectors of the
               original Hermitian matrix, and if COMPZ =  'I',  Z
               contains  the orthonormal eigenvectors of the sym-
               metric 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)   COMPLEX   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  'I',  or N <= 1, LWORK must be at least 1.  If
               COMPZ = 'V' and N > 1, LWORK must be at least N*N.

     RWORK     (workspace/output) REAL array,
               dimension  (LRWORK)  On  exit,  if  LRWORK  >   0,
               RWORK(1) returns the optimal LRWORK.

     LRWORK    (input) INTEGER
               The dimension of the array RWORK.  If COMPZ =  'N'
               or  N <= 1, LRWORK must be at least 1.  If COMPZ =
               'V' and N > 1, LRWORK must be at least 1 +  3*N  +
               2*N*lg  N  +  3*N**2  ,  where  lg( N ) = smallest
               integer k such that 2**k >= N.  If COMPZ = 'I' and
               N  > 1, LRWORK must be at least 1 + 3*N + 2*N*lg N
               + 3*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, LIWORK must be at least 1.  If COMPZ =
               'V' or N > 1,  LIWORK must be at least 6 +  6*N  +
               5*N*lg  N.   If COMPZ = 'I' or N > 1,  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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