ZHEEVD(3)      LAPACK routine of NEC Numeric Library Collection      ZHEEVD(3)



NAME
       ZHEEVD

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



PURPOSE
            ZHEEVD 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)
                     JOBZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only;
                     = 'V':  Compute eigenvalues and eigenvectors.

           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           A         (input/output)
                     A is 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 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

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

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is 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 sizes of the WORK, RWORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

           RWORK     (output)
                     RWORK is DOUBLE PRECISION array,
                                                    dimension (LRWORK)
                     On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

           LRWORK    (input)
                     LRWORK is 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 sizes of the WORK, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

           IWORK     (output)
                     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                     On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

           LIWORK    (input)
                     LIWORK is 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.

                     If LIWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal sizes of the WORK, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
                           to converge; i off-diagonal elements of an intermediate
                           tridiagonal form did not converge to zero;
                           if INFO = i and JOBZ = 'V', then the algorithm failed
                           to compute an eigenvalue while working on the submatrix
                           lying in rows and columns INFO/(N+1) through
                           mod(INFO,N+1).



LAPACK routine                  31 October 2017                      ZHEEVD(3)