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NAME

       zhbgvd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhbgvd (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK,
           RWORK, LRWORK, IWORK, LIWORK, INFO)
           ZHBGST

Function/Subroutine Documentation

   subroutine zhbgvd (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, complex*16,
       dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB,
       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)
       ZHBGST

       Purpose:

            ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
            of a complex generalized Hermitian-definite banded eigenproblem, of
            the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
            and banded, and B is also positive definite.  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 triangles of A and B are stored;
                     = 'L':  Lower triangles of A and B are stored.

           N

                     N is INTEGER
                     The order of the matrices A and B.  N >= 0.

           KA

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

           KB

                     KB is INTEGER
                     The number of superdiagonals of the matrix B if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
                     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

                     On exit, the contents of AB are destroyed.

           LDAB

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

           BB

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

                     On exit, the factor S from the split Cholesky factorization
                     B = S**H*S, as returned by ZPBSTF.

           LDBB

                     LDBB is INTEGER
                     The leading dimension of the array BB.  LDBB >= KB+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 matrix Z of
                     eigenvectors, with the i-th column of Z holding the
                     eigenvector associated with W(i). The eigenvectors are
                     normalized so that Z**H*B*Z = 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 >= 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 >= 1.
                     If JOBZ = 'N' and N > 1, LWORK >= N.
                     If JOBZ = 'V' and N > 1, LWORK >= 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 (MAX(1,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 >= 1.
                     If JOBZ = 'N' and N > 1, LRWORK >= N.
                     If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
                     If JOBZ = 'V' and N > 1, LIWORK >= 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, and i is:
                        <= N:  the algorithm failed to converge:
                               i off-diagonal elements of an intermediate
                               tridiagonal form did not converge to zero;
                        > N:   if INFO = N + i, for 1 <= i <= N, then ZPBSTF
                               returned INFO = i: B is not positive definite.
                               The factorization of B could not be completed and
                               no eigenvalues or eigenvectors were computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Contributors:
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

       Definition at line 251 of file zhbgvd.f.

Author

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