SUBROUTINE REDUC2(NM,N,A,B,DL,IERR)
C***BEGIN PROLOGUE  REDUC2
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C1C
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Reduces certain generalized symmetric eigenproblems
C            standard symmetric eigenproblem, using Cholesky
C            factorization.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure REDUC2,
C     NUM. MATH. 11, 99-110(1968) by Martin and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 303-314(1971).
C
C     This subroutine reduces the generalized SYMMETRIC eigenproblems
C     ABx=(LAMBDA)x OR BAy=(LAMBDA)y, where B is POSITIVE DEFINITE,
C     to the standard symmetric eigenproblem using the Cholesky
C     factorization of B.
C
C     On Input
C
C        NM must be set to the row dimension of two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.
C
C        N is the order of the matrices A and B.  If the Cholesky
C          factor L of B is already available, N should be prefixed
C          with a minus sign.
C
C        A AND B contain the real symmetric input matrices.  Only the
C          full upper triangles of the matrices need be supplied.  If
C          N is negative, the strict lower triangle of B contains,
C          instead, the strict lower triangle of its Cholesky factor L.
C
C        DL contains, if N is negative, the diagonal elements of L.
C
C     On Output
C
C        A contains in its full lower triangle the full lower triangle
C          of the symmetric matrix derived from the reduction to the
C          standard form.  The strict upper triangle of A is unaltered.
C
C        B contains in its strict lower triangle the strict lower
C          triangle of its Cholesky factor L.  The full upper
C          triangle of B is unaltered.
C
C        DL contains the diagonal elements of L.
C
C        IERR is set to
C          Zero       for normal return,
C          7*N+1      if B is not positive definite.
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  REDUC2