ZHBEVX(3)
computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
SYNOPSIS
 SUBROUTINE ZHBEVX(

JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
IWORK, IFAIL, INFO )

CHARACTER
JOBZ, RANGE, UPLO

INTEGER
IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

DOUBLE
PRECISION ABSTOL, VL, VU

INTEGER
IFAIL( * ), IWORK( * )

DOUBLE
PRECISION RWORK( * ), W( * )

COMPLEX*16
AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
Z( LDZ, * )
PURPOSE
ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
can be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
ARGUMENTS
 JOBZ (input) CHARACTER*1

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

= 'A': all eigenvalues will be found;
= 'V': all eigenvalues in the halfopen interval (VL,VU]
will be found;
= 'I': the ILth through IUth eigenvalues will be found.
 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
jth column of A is stored in the jth column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+ij,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.
 Q (output) COMPLEX*16 array, dimension (LDQ, N)

If JOBZ = 'V', the NbyN unitary matrix used in the
reduction to tridiagonal form.
If JOBZ = 'N', the array Q is not referenced.
 LDQ (input) INTEGER

The leading dimension of the array Q. If JOBZ = 'V', then
LDQ >= max(1,N).
 VL (input) DOUBLE PRECISION

VU (input) DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
 IL (input) INTEGER

IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
 ABSTOL (input) DOUBLE PRECISION

The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( a,b ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*T will be used in its place,
where T is the 1norm of the tridiagonal matrix obtained
by reducing AB to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
 M (output) INTEGER

The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IUIL+1.
 W (output) DOUBLE PRECISION array, dimension (N)

The first M elements contain the selected eigenvalues in
ascending order.
 Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))

If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the ith
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
 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 (7*N)

 IWORK (workspace) INTEGER array, dimension (5*N)

 IFAIL (output) INTEGER array, dimension (N)

If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = 'N', then IFAIL is not referenced.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.