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NAME
     cheevd - compute all eigenvalues and, optionally,  eigenvec-
     tors of a complex Hermitian matrix A

SYNOPSIS
     SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA,  W,  WORK,  LWORK,
               RWORK, LRWORK, IWORK, LIWORK, INFO )

     CHARACTER JOBZ, UPLO

     INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N

     INTEGER IWORK( * )

     REAL RWORK( * ), W( * )

     COMPLEX A( LDA, * ), WORK( * )



     #include <sunperf.h>

     void cheevd(char jobz, char uplo, int n,  complex  *ca,  int
               lda, float *w, int *info) ;

PURPOSE
     CHEEVD computes all eigenvalues and,  optionally,  eigenvec-
     tors  of  a complex Hermitian 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.


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) COMPLEX array, dimension (LDA, N)
               On entry, the Hermitian matrix A.  If UPLO =  'U',
               the leading N-by-N upper triangular part of A con-
               tains 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) REAL array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

     WORK      (workspace/output)   COMPLEX   array,    dimension
               (LWORK)
               On exit, if LWORK > 0, WORK(1) returns the optimal
               LWORK.

     LWORK     (input) INTEGER
               The  length  of  the  array  WORK.   If  N  <=  1,
               LWORK  must be at least 1.  If JOBZ  = 'N' and N >
               1, LWORK must be at least N + 1.  If JOBZ   =  'V'
               and N > 1, LWORK must be at least 2*N + N**2.

     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  N  <=  1,
               LRWORK must be at least 1.  If JOBZ  = 'N' and N >
               1, LRWORK must be at least N.  If JOBZ  = 'V'  and
               N  > 1, LRWORK must be at least 1 + 4*N + 2*N*lg N
               + 3*N**2 , where lg( N ) = smallest 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  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 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 an intermediate
               tridiagonal form did not converge to zero.

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