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SUBROUTINE <a name="ZHBEVD.1"></a><a href="zhbevd.f.html#ZHBEVD.1">ZHBEVD</a>( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
$ LWORK, RWORK, LRWORK, IWORK, LIWORK, 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, UPLO
INTEGER INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), 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="ZHBEVD.21"></a><a href="zhbevd.f.html#ZHBEVD.1">ZHBEVD</a> computes all the eigenvalues and, optionally, eigenvectors of
</span><span class="comment">*</span><span class="comment"> a complex Hermitian band matrix A. If eigenvectors are desired, it
</span><span class="comment">*</span><span class="comment"> uses a divide and conquer algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The divide and conquer algorithm makes very mild assumptions about
</span><span class="comment">*</span><span class="comment"> floating point arithmetic. It will work on machines with a guard
</span><span class="comment">*</span><span class="comment"> digit in add/subtract, or on those binary machines without guard
</span><span class="comment">*</span><span class="comment"> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
</span><span class="comment">*</span><span class="comment"> Cray-2. It could conceivably fail on hexadecimal or decimal machines
</span><span class="comment">*</span><span class="comment"> without guard digits, but we know of none.
</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"> 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. If UPLO = 'U', the first
</span><span class="comment">*</span><span class="comment"> superdiagonal and the diagonal of the tridiagonal matrix T
</span><span class="comment">*</span><span class="comment"> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> the diagonal and first subdiagonal of T are returned in the
</span><span class="comment">*</span><span class="comment"> first two rows of AB.
</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"> W (output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, the eigenvalues in 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, N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
</span><span class="comment">*</span><span class="comment"> eigenvectors of the matrix A, with the i-th column of Z
</span><span class="comment">*</span><span class="comment"> holding the eigenvector associated with W(i).
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= 1, and if
</span><span class="comment">*</span><span class="comment"> JOBZ = 'V', LDZ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LWORK must be at least N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal sizes of the WORK, RWORK and
</span><span class="comment">*</span><span class="comment"> IWORK arrays, returns these values as the first entries of
</span><span class="comment">*</span><span class="comment"> the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.94"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RWORK (workspace/output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension (LRWORK)
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LRWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of array RWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LRWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LRWORK must be at least
</span><span class="comment">*</span><span class="comment"> 1 + 5*N + 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LRWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the optimal sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.111"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LIWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of array IWORK.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the optimal sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.125"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit.
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, the algorithm failed to converge; i
</span><span class="comment">*</span><span class="comment"> off-diagonal elements of an intermediate tridiagonal
</span><span class="comment">*</span><span class="comment"> form did not converge to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
$ CONE = ( 1.0D0, 0.0D0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LOWER, LQUERY, WANTZ
INTEGER IINFO, IMAX, INDE, INDWK2, INDWRK, ISCALE,
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