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

NAME

       LAPACK-3  -  computes  all  the eigenvalues, and optionally, the eigenvectors of a complex
       generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

SYNOPSIS

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

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N

           DOUBLE        PRECISION RWORK( * ), W( * )

           COMPLEX*16    AB( LDAB, * ), BB( LDBB, * ), WORK( * ), Z( LDZ, * )

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

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

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

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

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

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

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

        WORK    (workspace) COMPLEX*16 array, dimension (N)

        RWORK   (workspace) DOUBLE PRECISION array, dimension (3*N)

        INFO    (output) 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 driver routine (version 3.2)        April 2011                             ZHBGV(3lapack)