ZHBGV(3)       LAPACK routine of NEC Numeric Library Collection       ZHBGV(3)



NAME
       ZHBGV

SYNOPSIS
       SUBROUTINE ZHBGV (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ,
           WORK, RWORK, INFO)



PURPOSE
            ZHBGV 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.




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

           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangles of A and B are stored;
                     = 'L':  Lower triangles of A and B are stored.

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

           KA        (input)
                     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        (input)
                     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        (input/output)
                     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      (input)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KA+1.

           BB        (input/output)
                     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      (input)
                     LDBB is INTEGER
                     The leading dimension of the array BB.  LDBB >= KB+1.

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

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

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension (N)

           RWORK     (output)
                     RWORK is DOUBLE PRECISION array, dimension (3*N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                       ZHBGV(3)