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DSYGVD(l)			       )			     DSYGVD(l)

NAME
       DSYGVD  - 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

SYNOPSIS
       SUBROUTINE DSYGVD( ITYPE,  JOBZ,	 UPLO,	N,  A,	LDA,  B, LDB, W, WORK,
			  LWORK, IWORK, LIWORK, INFO )

	   CHARACTER	  JOBZ, UPLO

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

	   INTEGER	  IWORK( * )

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

PURPOSE
       DSYGVD  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.  If eigen‐
       vectors are desired, it uses a divide and conquer algorithm.

       The  divide  and	 conquer  algorithm  makes very mild assumptions about
       floating point arithmetic. It will work on machines with a guard	 digit
       in add/subtract, or on those binary machines without guard digits which
       subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It	 could
       conceivably  fail on hexadecimal or decimal machines without guard dig‐
       its, but we know of none.

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 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    dimension	  of   the   array   WORK.    If   N   <=   1,
	       LWORK >= 1.  If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.  If  JOBZ
	       = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

	       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.

       IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	       On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

       LIWORK  (input) INTEGER
	       The   dimension	 of   the   array   IWORK.    If   N   <=   1,
	       LIWORK  >=  1.  If JOBZ	= 'N' and N > 1, LIWORK >= 1.  If JOBZ
	       = 'V' and N > 1, LIWORK >= 3 + 5*N.

	       If LIWORK = -1, then a workspace query is assumed; the  routine
	       only  calculates	 the  optimal size of the IWORK array, returns
	       this value as the first entry of the IWORK array, and no	 error
	       message related to LIWORK 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 DSYEVD returned an error code:
	       <=  N:	if INFO = i, DSYEVD 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.

FURTHER DETAILS
       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK version 3.0		 15 June 2000			     DSYGVD(l)
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