SUBROUTINE HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI)
C***BEGIN PROLOGUE  HTRIBK
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 complex Hermitian matrix from
C            eigenvectors of real symmetric tridiagonal matrix output
C            from HTRIDI.
C***DESCRIPTION
C
C     This subroutine is a translation of a complex analogue of
C     the ALGOL procedure TRBAK1, NUM. MATH. 11, 181-195(1968)
C     by Martin, Reinsch, and Wilkinson.
C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971).
C
C     This subroutine forms the eigenvectors of a COMPLEX HERMITIAN
C     matrix by back transforming those of the corresponding
C     real symmetric tridiagonal matrix determined by  HTRIDI.
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.
C
C        AR and AI contain information about the unitary trans-
C          formations used in the reduction by  HTRIDI  in their
C          full lower triangles except for the diagonal of AR.
C
C        TAU contains further information about the transformations.
C
C        M is the number of eigenvectors to be back transformed.
C
C        ZR contains the eigenvectors to be back transformed
C          in its first M columns.
C
C     On OUTPUT
C
C        ZR and ZI contain the real and imaginary parts,
C          respectively, of the transformed eigenvectors
C          in their first M columns.
C
C     Note that the last component of each returned vector
C     is real and that vector Euclidean norms are preserved.
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  HTRIBK