CXML
        	    
LAPACK version 3.0
dsygv(3)

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

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

      CHARACTER	    JOBZ, UPLO

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

      DOUBLE	    PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )

DESCRIPTION
  DSYGV computes all the eigenvalues, and optionally, the eigenvectors of a
  real generalized symmetric-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 symmetric 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) DOUBLE PRECISION array, dimension (LDA, N)
	  On entry, the symmetric 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**T*B*Z = I; if ITYPE = 3, Z**T*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) DOUBLE PRECISION array, dimension (LDB, N)
	  On entry, the symmetric 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**T*U or B = L*L**T.

  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) DOUBLE PRECISION 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(1,3*N-1).	 For optimal
	  efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for DSYTRD
	  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.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value
	  > 0:	DPOTRF or DSYEV returned an error code:
	  <= N:	 if INFO = i, DSYEV 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.