# rebakb.f

          SUBROUTINE REBAKB (NM, N, B, DL, M, Z)
    C***BEGIN PROLOGUE  REBAKB
    C***PURPOSE  Form the eigenvectors of a generalized symmetric
    C            eigensystem from the eigenvectors of derived matrix output
    C            from REDUC2.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4C4
    C***TYPE      SINGLE PRECISION (REBAKB-S)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    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 the two-dimensional
    C          array parameters, B and Z, as declared in the calling
    C          program dimension statement.  NM is an INTEGER variable.
    C
    C        N is the order of the matrix system.  N is an INTEGER
    C          variable.  N must be less than or equal to NM.
    C
    C        B contains information about the similarity transformation
    C          (Cholesky decomposition) used in the reduction by  REDUC2
    C          in its strict lower triangle.  B is a two-dimensional
    C          REAL array, dimensioned B(NM,N).
    C
    C        DL contains further information about the transformation.
    C          DL is a one-dimensional REAL array, dimensioned DL(N).
    C
    C        M is the number of eigenvectors to be back transformed.
    C          M is an INTEGER variable.
    C
    C        Z contains the eigenvectors to be back transformed in its
    C          first M columns.  Z is a two-dimensional REAL array
    C          dimensioned Z(NM,M).
    C
    C     On Output
    C
    C        Z contains the transformed eigenvectors in its first
    C          M columns.
    C
    C     Questions and comments should be directed to B. S. Garbow,
    C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
    C     ------------------------------------------------------------------
    C
    C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
    C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
    C                 system Routines - EISPACK Guide, Springer-Verlag,
    C                 1976.
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   760101  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  REBAKB