SUBROUTINE REBAKB(NM,N,B,DL,M,Z)
C***BEGIN PROLOGUE  REBAKB
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C4
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Forms eigenvectors of generalized symmetric eigensystem
C            from eigenvectors of derived matrix output from REDUC2
C***DESCRIPTION
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 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  REBAKB