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SUBROUTINE <a name="CHEGV.1"></a><a href="chegv.f.html#CHEGV.1">CHEGV</a>( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
$ LWORK, RWORK, 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, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL RWORK( * ), W( * )
COMPLEX 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="CHEGV.20"></a><a href="chegv.f.html#CHEGV.1">CHEGV</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.
</span><span class="comment">*</span><span class="comment"> Here A and B are assumed to be Hermitian and B is also
</span><span class="comment">*</span><span class="comment"> positive definite.
</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 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 array, dimension (LDB, N)
</span><span class="comment">*</span><span class="comment"> On entry, the Hermitian positive definite matrix B.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U', the leading N-by-N upper triangular part of B
</span><span class="comment">*</span><span class="comment"> contains the upper triangular part of the matrix B.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', the leading N-by-N lower triangular part of B
</span><span class="comment">*</span><span class="comment"> contains 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) REAL 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 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. LWORK >= max(1,2*N-1).
</span><span class="comment">*</span><span class="comment"> For optimal efficiency, LWORK >= (NB+1)*N,
</span><span class="comment">*</span><span class="comment"> where NB is the blocksize for <a name="CHETRD.88"></a><a href="chetrd.f.html#CHETRD.1">CHETRD</a> returned by <a name="ILAENV.88"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.
</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 size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.93"></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) REAL array, dimension (max(1, 3*N-2))
</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="CPOTRF.100"></a><a href="cpotrf.f.html#CPOTRF.1">CPOTRF</a> or <a name="CHEEV.100"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a> returned an error code:
</span><span class="comment">*</span><span class="comment"> <= N: if INFO = i, <a name="CHEEV.101"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a> failed to converge;
</span><span class="comment">*</span><span class="comment"> i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment"> tridiagonal form did not converge to zero;
</span><span class="comment">*</span><span class="comment"> > N: if INFO = N + i, for 1 <= i <= N, then the leading
</span><span class="comment">*</span><span class="comment"> minor of order i of B is not positive definite.
</span><span class="comment">*</span><span class="comment"> The factorization of B could not be completed and
</span><span class="comment">*</span><span class="comment"> no eigenvalues or eigenvectors were computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
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