cheevd(3F)

NAME
     CHEEVD - compute all eigenvalues and, optionally, eigenvectors 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( * )

PURPOSE
     CHEEVD computes all eigenvalues and, optionally, eigenvectors 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 contains 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 illegal value
             > 0:  if INFO = i, the algorithm failed to converge; i off-
             diagonal elements of an intermediate tridiagonal form did not
             converge to zero.