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REBAKB(NM,N,B,DL,M,Z)

       SUBROUTINE REBAKB(NM,N,B,DL,M,Z)
 C
       INTEGER I,J,K,M,N,I1,II,NM
       REAL B(NM,N),DL(N),Z(NM,M)
       REAL X
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE REBAKB,
 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 FORMS THE EIGENVECTORS OF A GENERALIZED
 C     SYMMETRIC EIGENSYSTEM BY BACK TRANSFORMING THOSE OF THE
 C     DERIVED SYMMETRIC MATRIX DETERMINED BY  REDUC2.
 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 MATRIX SYSTEM.
 C
 C        B CONTAINS INFORMATION ABOUT THE SIMILARITY TRANSFORMATION
 C          (CHOLESKY DECOMPOSITION) USED IN THE REDUCTION BY  REDUC2
 C          IN ITS STRICT LOWER TRIANGLE.
 C
 C        DL CONTAINS FURTHER INFORMATION ABOUT THE TRANSFORMATION.
 C
 C        M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
 C
 C        Z CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED
 C          IN ITS FIRST M COLUMNS.
 C
 C     ON OUTPUT
 C
 C        Z CONTAINS THE TRANSFORMED EIGENVECTORS
 C          IN ITS FIRST M COLUMNS.
 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