ZHBEV - compute all the eigenvalues and, optionally,
eigenvectors of a complex Hermitian band matrix A
SYNOPSIS
SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
WORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KD, LDAB, LDZ, N
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
PURPOSE
ZHBEV computes all the eigenvalues and, optionally, eigen
vectors 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*16 array, dimension (LDAB,
N)
On entry, the upper or lower triangle of the Her
mitian 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.
The leading dimension of the array AB. LDAB >= KD
+ 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
orthonormal eigenvectors of the matrix A, with the
i-th column of Z holding the eigenvector associ
ated with W(i). If JOBZ = 'N', then Z is not ref
erenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace) COMPLEX*16 array, dimension (N)
RWORK (workspace) DOUBLE PRECISION array,
dimension (max(1,3*N-2))
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: if INFO = i, the algorithm failed to con
verge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero.
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