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NAME

       zhbevx.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhbevx (JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M,
           W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
            ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for OTHER matrices

Function/Subroutine Documentation

   subroutine zhbevx (character JOBZ, character RANGE, character UPLO, integer N, integer KD,
       complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldq, * ) Q,
       integer LDQ, double precision VL, double precision VU, integer IL, integer IU, double
       precision ABSTOL, integer M, double precision, dimension( * ) W, complex*16, dimension(
       ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, double precision, dimension( * )
       RWORK, integer, dimension( * ) IWORK, integer, dimension( * ) IFAIL, integer INFO)
        ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices

       Purpose:

            ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
            of a complex Hermitian band matrix A.  Eigenvalues and eigenvectors
            can be selected by specifying either a range of values or a range of
            indices for the desired eigenvalues.

       Parameters:
           JOBZ

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

           RANGE

                     RANGE is CHARACTER*1
                     = 'A': all eigenvalues will be found;
                     = 'V': all eigenvalues in the half-open interval (VL,VU]
                            will be found;
                     = 'I': the IL-th through IU-th eigenvalues will be found.

           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.

           LDAB

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

           Q

                     Q is COMPLEX*16 array, dimension (LDQ, N)
                     If JOBZ = 'V', the N-by-N unitary matrix used in the
                                     reduction to tridiagonal form.
                     If JOBZ = 'N', the array Q is not referenced.

           LDQ

                     LDQ is INTEGER
                     The leading dimension of the array Q.  If JOBZ = 'V', then
                     LDQ >= max(1,N).

           VL

                     VL is DOUBLE PRECISION

           VU

                     VU is DOUBLE PRECISION
                     If RANGE='V', the lower and upper bounds of the interval to
                     be searched for eigenvalues. VL < VU.
                     Not referenced if RANGE = 'A' or 'I'.

           IL

                     IL is INTEGER

           IU

                     IU is INTEGER
                     If RANGE='I', the indices (in ascending order) of the
                     smallest and largest eigenvalues to be returned.
                     1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
                     Not referenced if RANGE = 'A' or 'V'.

           ABSTOL

                     ABSTOL is DOUBLE PRECISION
                     The absolute error tolerance for the eigenvalues.
                     An approximate eigenvalue is accepted as converged
                     when it is determined to lie in an interval [a,b]
                     of width less than or equal to

                             ABSTOL + EPS *   max( |a|,|b| ) ,

                     where EPS is the machine precision.  If ABSTOL is less than
                     or equal to zero, then  EPS*|T|  will be used in its place,
                     where |T| is the 1-norm of the tridiagonal matrix obtained
                     by reducing AB to tridiagonal form.

                     Eigenvalues will be computed most accurately when ABSTOL is
                     set to twice the underflow threshold 2*DLAMCH('S'), not zero.
                     If this routine returns with INFO>0, indicating that some
                     eigenvectors did not converge, try setting ABSTOL to
                     2*DLAMCH('S').

                     See "Computing Small Singular Values of Bidiagonal Matrices
                     with Guaranteed High Relative Accuracy," by Demmel and
                     Kahan, LAPACK Working Note #3.

           M

                     M is INTEGER
                     The total number of eigenvalues found.  0 <= M <= N.
                     If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

           W

                     W is DOUBLE PRECISION array, dimension (N)
                     The first M elements contain the selected eigenvalues in
                     ascending order.

           Z

                     Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
                     If JOBZ = 'V', then if INFO = 0, the first M columns of Z
                     contain the orthonormal eigenvectors of the matrix A
                     corresponding to the selected eigenvalues, with the i-th
                     column of Z holding the eigenvector associated with W(i).
                     If an eigenvector fails to converge, then that column of Z
                     contains the latest approximation to the eigenvector, and the
                     index of the eigenvector is returned in IFAIL.
                     If JOBZ = 'N', then Z is not referenced.
                     Note: the user must ensure that at least max(1,M) columns are
                     supplied in the array Z; if RANGE = 'V', the exact value of M
                     is not known in advance and an upper bound must be used.

           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 (N)

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (7*N)

           IWORK

                     IWORK is INTEGER array, dimension (5*N)

           IFAIL

                     IFAIL is INTEGER array, dimension (N)
                     If JOBZ = 'V', then if INFO = 0, the first M elements of
                     IFAIL are zero.  If INFO > 0, then IFAIL contains the
                     indices of the eigenvectors that failed to converge.
                     If JOBZ = 'N', then IFAIL is not referenced.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, then i eigenvectors failed to converge.
                           Their indices are stored in array IFAIL.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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