REDUC(3F)

NAME
     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
          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
     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