_REDUC(3F)							    _REDUC(3F)

NAME    [Toc]    [Back]

     REDUC, SREDUC   -	EISPACK	routine.  This subroutine reduces the
     generalized SYMMETRIC eigenproblem	Ax=(LAMBDA)Bx, where B is POSITIVE
     DEFINITE, to the standard symmetric eigenproblem using the	Cholesky
     factorization of B.

SYNOPSYS    [Toc]    [Back]

	  subroutine  reduc(nm,	n, a, b, dl, ierr)
	  integer	   nm, n, ierr
	  double precision a(nm,n), b(nm,n), dl(n)

	  subroutine sreduc(nm,	n, a, b, dl, ierr)
	  integer	   nm, n, ierr
	  real		   a(nm,n), b(nm,n), dl(n)

DESCRIPTION    [Toc]    [Back]

     On	Input

     NM	must be	set to the row dimension of two-dimensional array parameters
     as	declared in the	calling	program	dimension statement.

     N is the order of the matrices A and B.  If the Cholesky factor L of B is
     already available,	N should be prefixed with a minus sign.

     A and B contain the real symmetric	input matrices.	 Only the full upper
     triangles of the matrices need be supplied.  If N is negative, the	strict
     lower triangle of B contains, instead, the	strict lower triangle of its
     Cholesky factor L.

     DL	contains, if N is negative, the	diagonal elements of L.	On Output

     A contains	in its full lower triangle the full lower triangle of the
     symmetric matrix derived from the reduction to the	standard form.	The
     strict upper triangle of A	is unaltered.

     B contains	in its strict lower triangle the strict	lower triangle of its
     Cholesky factor L.	 The full upper	triangle of B is unaltered.

     DL	contains the diagonal elements of L.

     IERR is set to Zero       for normal return, 7*N+1	     if	B is not
     positive definite.	 Questions and comments	should be directed to B. S.
     Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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