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REDUC2(NM,N,A,B,DL,IERR)

       SUBROUTINE REDUC2(NM,N,A,B,DL,IERR)
 C
       INTEGER I,J,K,N,I1,J1,NM,NN,IERR
       DOUBLE PRECISION A(NM,N),B(NM,N),DL(N)
       DOUBLE PRECISION X,Y
 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 BURTON S. GARBOW,
 C     MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
 C
 C     THIS VERSION DATED AUGUST 1983.
 C
 C     ------------------------------------------------------------------
 C