ZHBEV(l) LAPACK driver routine (version 1.1) ZHBEV(l)
NAME
ZHBEV - compute all the eigenvalues and, optionally, eigenvectors of a com-
plex 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, eigenvectors of a com-
plex 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 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 (input) INTEGER
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 eigen-
vectors 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*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 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.
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