CHBEV(3f)

NAME
CHBEV - all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

SYNOPSIS

SUBROUTINE CHBEV(
    JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO )

CHARACTER
    JOBZ, UPLO

INTEGER
    INFO, KD, LDAB, LDZ, N

REAL
    RWORK( * ), W( * )

COMPLEX
    AB( LDAB, * ), WORK( * ), Z( LDZ, * )

PURPOSE
CHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

ARGUMENTS

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

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

N       (input) INTEGER
    The order of the matrix A. N >= 0.

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

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

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

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

WORK    (workspace) COMPLEX array, dimension (N)

RWORK   (workspace) REAL array, dimension (max(1,3*N-2))

INFO    (output) 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.