ZHEEVD  -  compute all eigenvalues and, optionally, eigen­
       vectors of a complex Hermitian matrix A


SYNOPSIS

       SUBROUTINE ZHEEVD( 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( * )

           DOUBLE         PRECISION RWORK( * ), W( * )

           COMPLEX*16     A( LDA, * ), WORK( * )


PURPOSE

       ZHEEVD 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 assump­
       tions 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  with­
       out 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*16 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

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

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO = 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.

               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.

       RWORK   (workspace/output) DOUBLE PRECISION array,
               dimension (LRWORK) On exit, if INFO = 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 + 5*N + 2*N**2.

               If LRWORK = -1, then a workspace query is assumed;
               the  routine  only  calculates the optimal size of
               the RWORK array, returns this value as  the  first
               entry  of  the  RWORK  array, and no error message
               related to LRWORK 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  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 3 + 5*N.

               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 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.


FURTHER DETAILS

       Based on contributions by
          Jeff Rutter, Computer Science Division,  University  of
       California
          at Berkeley, USA


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