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SUBROUTINE REDUC2(NM,N,A,B,DL,IERR)
C
INTEGER I,J,K,N,I1,J1,NM,NN,IERR
REAL A(NM,N),B(NM,N),DL(N)
REAL 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
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C