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SUBROUTINE <a name="ZHBEVX.1"></a><a href="zhbevx.f.html#ZHBEVX.1">ZHBEVX</a>( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
$ VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
$ IWORK, IFAIL, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
DOUBLE PRECISION ABSTOL, VL, VU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IFAIL( * ), IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
$ Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZHBEVX.24"></a><a href="zhbevx.f.html#ZHBEVX.1">ZHBEVX</a> computes selected eigenvalues and, optionally, eigenvectors
</span><span class="comment">*</span><span class="comment"> of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
</span><span class="comment">*</span><span class="comment"> can be selected by specifying either a range of values or a range of
</span><span class="comment">*</span><span class="comment"> indices for the desired eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RANGE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'A': all eigenvalues will be found;
</span><span class="comment">*</span><span class="comment"> = 'V': all eigenvalues in the half-open interval (VL,VU]
</span><span class="comment">*</span><span class="comment"> will be found;
</span><span class="comment">*</span><span class="comment"> = 'I': the IL-th through IU-th eigenvalues will be found.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KD (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the Hermitian band
</span><span class="comment">*</span><span class="comment"> matrix A, stored in the first KD+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, AB is overwritten by values generated during the
</span><span class="comment">*</span><span class="comment"> reduction to tridiagonal form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KD + 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (output) COMPLEX*16 array, dimension (LDQ, N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', the N-by-N unitary matrix used in the
</span><span class="comment">*</span><span class="comment"> reduction to tridiagonal form.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', the array Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. If JOBZ = 'V', then
</span><span class="comment">*</span><span class="comment"> LDQ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VL (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> VU (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> If RANGE='V', the lower and upper bounds of the interval to
</span><span class="comment">*</span><span class="comment"> be searched for eigenvalues. VL < VU.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'I'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IL (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> If RANGE='I', the indices (in ascending order) of the
</span><span class="comment">*</span><span class="comment"> smallest and largest eigenvalues to be returned.
</span><span class="comment">*</span><span class="comment"> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'V'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The absolute error tolerance for the eigenvalues.
</span><span class="comment">*</span><span class="comment"> An approximate eigenvalue is accepted as converged
</span><span class="comment">*</span><span class="comment"> when it is determined to lie in an interval [a,b]
</span><span class="comment">*</span><span class="comment"> of width less than or equal to
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL + EPS * max( |a|,|b| ) ,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where EPS is the machine precision. If ABSTOL is less than
</span><span class="comment">*</span><span class="comment"> or equal to zero, then EPS*|T| will be used in its place,
</span><span class="comment">*</span><span class="comment"> where |T| is the 1-norm of the tridiagonal matrix obtained
</span><span class="comment">*</span><span class="comment"> by reducing AB to tridiagonal form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Eigenvalues will be computed most accurately when ABSTOL is
</span><span class="comment">*</span><span class="comment"> set to twice the underflow threshold 2*<a name="DLAMCH.103"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>('S'), not zero.
</span><span class="comment">*</span><span class="comment"> If this routine returns with INFO>0, indicating that some
</span><span class="comment">*</span><span class="comment"> eigenvectors did not converge, try setting ABSTOL to
</span><span class="comment">*</span><span class="comment"> 2*<a name="DLAMCH.106"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>('S').
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> See "Computing Small Singular Values of Bidiagonal Matrices
</span><span class="comment">*</span><span class="comment"> with Guaranteed High Relative Accuracy," by Demmel and
</span><span class="comment">*</span><span class="comment"> Kahan, LAPACK Working Note #3.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (output) INTEGER
</span><span class="comment">*</span><span class="comment"> The total number of eigenvalues found. 0 <= M <= N.
</span><span class="comment">*</span><span class="comment"> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The first M elements contain the selected eigenvalues in
</span><span class="comment">*</span><span class="comment"> ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
</span><span class="comment">*</span><span class="comment"> contain the orthonormal eigenvectors of the matrix A
</span><span class="comment">*</span><span class="comment"> corresponding to the selected eigenvalues, with the i-th
</span><span class="comment">*</span><span class="comment"> column of Z holding the eigenvector associated with W(i).
</span><span class="comment">*</span><span class="comment"> If an eigenvector fails to converge, then that column of Z
</span><span class="comment">*</span><span class="comment"> contains the latest approximation to the eigenvector, and the
</span><span class="comment">*</span><span class="comment"> index of the eigenvector is returned in IFAIL.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment"> Note: the user must ensure that at least max(1,M) columns are
</span><span class="comment">*</span><span class="comment"> supplied in the array Z; if RANGE = 'V', the exact value of M
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