NAME

       zhbevd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhbevd (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
           IWORK, LIWORK, INFO)
            ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for OTHER matrices

Function/Subroutine Documentation

   subroutine zhbevd (characterJOBZ, characterUPLO, integerN, integerKD, complex*16, dimension(
       ldab, * )AB, integerLDAB, double precision, dimension( * )W, complex*16, dimension( ldz, *
       )Z, integerLDZ, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension(
       * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
        ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices

       Purpose:

            ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
            a complex Hermitian band 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.

       Parameters:
           JOBZ

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

           UPLO

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

           N

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

           KD

                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

           AB

                     AB is COMPLEX*16 array, dimension (LDAB, N)
                     On entry, the upper or lower triangle of the Hermitian band
                     matrix A, stored in the first KD+1 rows of the array.  The
                     j-th column of A is stored in the j-th column of the array AB
                     as follows:
                     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

                     On exit, AB is overwritten by values generated during the
                     reduction to tridiagonal form.  If UPLO = 'U', the first
                     superdiagonal and the diagonal of the tridiagonal matrix T
                     are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
                     the diagonal and first subdiagonal of T are returned in the
                     first two rows of AB.

           LDAB

                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD + 1.

           W

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

           Z

                     Z is 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

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', LDZ >= max(1,N).

           WORK

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

           LWORK

                     LWORK is INTEGER
                     The dimension 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.
                     If JOBZ = 'V' and N > 1, LWORK must be at least 2*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

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

           LRWORK

                     LRWORK is 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 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

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

           LIWORK

                     LIWORK is 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 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

                     INFO is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 215 of file zhbevd.f.

Author

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