CXML
        	    
LAPACK version 3.0
zhegv(3)

PURPOSE
  ZHEGV - compute all the eigenvalues, and optionally, the eigenvectors of a
  complex generalized Hermitian-definite eigenproblem, of the form
  A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

SYNTAX
  SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK,
		    RWORK, INFO )

      CHARACTER	    JOBZ, UPLO

      INTEGER	    INFO, ITYPE, LDA, LDB, LWORK, N

      DOUBLE	    PRECISION RWORK( * ), W( * )

      COMPLEX*16    A( LDA, * ), B( LDB, * ), WORK( * )

DESCRIPTION
  ZHEGV computes all the eigenvalues, and optionally, the eigenvectors of a
  complex generalized Hermitian-definite eigenproblem, of the form
  A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are
  assumed to be Hermitian and B is also
  positive definite.

ARGUMENTS
  ITYPE	  (input) INTEGER
	  Specifies the problem type to be solved:
	  = 1:	A*x = (lambda)*B*x
	  = 2:	A*B*x = (lambda)*x
	  = 3:	B*A*x = (lambda)*x

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

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangles of A and B are stored;
	  = 'L':  Lower triangles of A and B are stored.

  N	  (input) INTEGER
	  The order of the matrices A and B.  N >= 0.

  A	  (input/output) COMPLEX*16 array, dimension (LDA, N)
	  On entry, the Hermitian matrix A.  If UPLO = 'U', the leading N-
	  by-N upper triangular part of A contains the upper triangular part
	  of the matrix A.  If UPLO = 'L', the leading N-by-N lower
	  triangular part of A contains the lower triangular part of the
	  matrix A.

	  On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z
	  of eigenvectors.  The eigenvectors are normalized as follows: if
	  ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.  If
	  JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the
	  lower triangle (if UPLO='L') of A, including the diagonal, is
	  destroyed.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,N).

  B	  (input/output) COMPLEX*16 array, dimension (LDB, N)
	  On entry, the Hermitian positive definite matrix B.  If UPLO = 'U',
	  the leading N-by-N upper triangular part of B contains the upper
	  triangular part of the matrix B.  If UPLO = 'L', the leading N-by-N
	  lower triangular part of B contains the lower triangular part of
	  the matrix B.

	  On exit, if INFO <= N, the part of B containing the matrix is
	  overwritten by the triangular factor U or L from the Cholesky
	  factorization B = U**H*U or B = L*L**H.

  LDB	  (input) INTEGER
	  The leading dimension of the array B.	 LDB >= max(1,N).

  W	  (output) DOUBLE PRECISION array, dimension (N)
	  If INFO = 0, the eigenvalues in ascending order.

  WORK	  (workspace/output) COMPLEX*16 array, dimension (LWORK)
	  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK	  (input) INTEGER
	  The length of the array WORK.	 LWORK >= max(1,2*N-1).	 For optimal
	  efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD
	  returned by ILAENV.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

  RWORK	  (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value
	  > 0:	ZPOTRF or ZHEEV returned an error code:
	  <= N:	 if INFO = i, ZHEEV failed to converge; i off-diagonal
	  elements of an intermediate tridiagonal form did not converge to
	  zero; > N:   if INFO = N + i, for 1 <= i <= N, then the leading
	  minor of order i of B is not positive definite.  The factorization
	  of B could not be completed and no eigenvalues or eigenvectors were
	  computed.