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

NAME

       LAPACK-3  -  computes  all  the  eigenvalues  and,  optionally,  eigenvectors of a complex
       Hermitian matrix A in packed storage

SYNOPSIS

       SUBROUTINE ZHPEVD( 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( * )

           DOUBLE         PRECISION RWORK( * ), W( * )

           COMPLEX*16     AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE

       ZHPEVD  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*16 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) DOUBLE PRECISION array, dimension (N)
                If INFO = 0, the eigenvalues in ascending order.

        Z       (output) COMPLEX*16 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*16 array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the required 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.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the required 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) DOUBLE PRECISION array,
                dimension (LRWORK)
                On exit, if INFO = 0, RWORK(1) returns the required 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 + 5*N + 2*N**2.
                If LRWORK = -1, then a workspace query is assumed; the
                routine only calculates the required 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 required 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 3 + 5*N.
                If LIWORK = -1, then a workspace query is assumed; the
                routine only calculates the required 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, the algorithm failed to converge; i
                off-diagonal elements of an intermediate tridiagonal
                form did not converge to zero.

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