chpevd(3F)

NAME
     CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A in packed storage

SYNOPSIS
     SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
                        LRWORK, IWORK, LIWORK, INFO )

         CHARACTER      JOBZ, UPLO

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

         INTEGER        IWORK( * )

         REAL           RWORK( * ), W( * )

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

PURPOSE
     CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A in packed storage.  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.

     AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
             On entry, the upper or lower triangle of the Hermitian matrix A,
             packed columnwise in a linear array.  The j-th column of A is
             stored in the array AP as follows:  if UPLO = 'U', AP(i + (j-
             1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-
             j)/2) = A(i,j) for j<=i<=n.

             On exit, AP is overwritten by values generated during the
             reduction to tridiagonal form.  If UPLO = 'U', the diagonal and
             first superdiagonal of the tridiagonal matrix T overwrite the
             corresponding elements of A, and if UPLO = 'L', the diagonal and
             first subdiagonal of T overwrite the corresponding elements of A.

     W       (output) REAL array, dimension (N)
             If INFO = 0, the eigenvalues in ascending order.

     Z       (output) COMPLEX array, dimension (LDZ, N)
             If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
             eigenvectors of the matrix A, with the i-th column of Z holding
             the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
             not referenced.

     LDZ     (input) INTEGER
             The leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
             'V', 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 array WORK.  If N <= 1,               LWORK must
             be at least 1.  If JOBZ = 'N' and N > 1, LWORK must be at least
             N.  If JOBZ = 'V' and N > 1, LWORK must be at least 2*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 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 array IWORK.  If JOBZ  = 'N' or 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.