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SUBROUTINE <a name="ZHEGVD.1"></a><a href="zhegvd.f.html#ZHEGVD.1">ZHEGVD</a>( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, 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, ITYPE, LDA, LDB, 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 A( LDA, * ), B( LDB, * ), WORK( * )
<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="ZHEGVD.21"></a><a href="zhegvd.f.html#ZHEGVD.1">ZHEGVD</a> computes all the eigenvalues, and optionally, the eigenvectors
</span><span class="comment">*</span><span class="comment"> of a complex generalized Hermitian-definite eigenproblem, of the form
</span><span class="comment">*</span><span class="comment"> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
</span><span class="comment">*</span><span class="comment"> B are assumed to be Hermitian and B is also positive definite.
</span><span class="comment">*</span><span class="comment"> If eigenvectors are desired, it 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"> ITYPE (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies the problem type to be solved:
</span><span class="comment">*</span><span class="comment"> = 1: A*x = (lambda)*B*x
</span><span class="comment">*</span><span class="comment"> = 2: A*B*x = (lambda)*x
</span><span class="comment">*</span><span class="comment"> = 3: B*A*x = (lambda)*x
</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 triangles of A and B are stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangles of A and B are 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 matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) COMPLEX*16 array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment"> On entry, the Hermitian matrix A. If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment"> leading N-by-N upper triangular part of A contains the
</span><span class="comment">*</span><span class="comment"> upper triangular part of the matrix A. If UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> the leading N-by-N lower triangular part of A contains
</span><span class="comment">*</span><span class="comment"> the lower triangular part of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
</span><span class="comment">*</span><span class="comment"> matrix Z of eigenvectors. The eigenvectors are normalized
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if ITYPE = 1 or 2, Z**H*B*Z = I;
</span><span class="comment">*</span><span class="comment"> if ITYPE = 3, Z**H*inv(B)*Z = I.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
</span><span class="comment">*</span><span class="comment"> or the lower triangle (if UPLO='L') of A, including the
</span><span class="comment">*</span><span class="comment"> diagonal, is destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) COMPLEX*16 array, dimension (LDB, N)
</span><span class="comment">*</span><span class="comment"> On entry, the Hermitian matrix B. If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment"> leading N-by-N upper triangular part of B contains the
</span><span class="comment">*</span><span class="comment"> upper triangular part of the matrix B. If UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> the leading N-by-N lower triangular part of B contains
</span><span class="comment">*</span><span class="comment"> the lower triangular part of the matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO <= N, the part of B containing the matrix is
</span><span class="comment">*</span><span class="comment"> overwritten by the triangular factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment"> factorization B = U**H*U or B = L*L**H.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</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"> 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 length of the array WORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LWORK >= N + 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK >= 2*N + 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.103"></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, dimension (MAX(1,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 the array RWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LRWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LRWORK >= N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LRWORK >= 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.118"></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 the array IWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LIWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LIWORK >= 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LIWORK >= 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.133"></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: <a name="ZPOTRF.138"></a><a href="zpotrf.f.html#ZPOTRF.1">ZPOTRF</a> or <a name="ZHEEVD.138"></a><a href="zheevd.f.html#ZHEEVD.1">ZHEEVD</a> returned an error code:
</span><span class="comment">*</span><span class="comment"> <= N: if INFO = i and JOBZ = 'N', then the algorithm
</span><span class="comment">*</span><span class="comment"> failed to converge; i off-diagonal elements of an
</span><span class="comment">*</span><span class="comment"> intermediate tridiagonal form did not converge to
</span><span class="comment">*</span><span class="comment"> zero;
</span><span class="comment">*</span><span class="comment"> if INFO = i and JOBZ = 'V', then the algorithm
</span><span class="comment">*</span><span class="comment"> failed to compute an eigenvalue while working on
</span><span class="comment">*</span><span class="comment"> the submatrix lying in rows and columns INFO/(N+1)
</span><span class="comment">*</span><span class="comment"> through mod(INFO,N+1);
</span><span class="comment">*</span><span class="comment"> > N: if INFO = N + i, for 1 <= i <= N, then the leading
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