Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes 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 (MAX(1,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 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   (workspace/output) REAL 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 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   (workspace/output) INTEGER array, dimension (MAX(1,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.
                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) 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).

FURTHER DETAILS

        Based on contributions by
           Jeff Rutter, Computer Science Division, University of California
           at Berkeley, USA
        Modified description of INFO. Sven, 16 Feb 05.

 LAPACK driver routine (version 3.2)        April 2011                            CHEEVD(3lapack)