SUBROUTINE HTRID3(NM,N,A,D,E,E2,TAU)
C***BEGIN PROLOGUE  HTRID3
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C1B1
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Reduces complex Hermitian (packed) matrix to real
C            symmetric tridiagonal matrix by unitary similarity
C            transformations.
C***DESCRIPTION
C
C     This subroutine is a translation of a complex analogue of
C     the ALGOL procedure TRED3, 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 reduces a COMPLEX HERMITIAN matrix, stored as
C     a single square array, to a real symmetric tridiagonal matrix
C     using unitary similarity transformations.
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        A contains the lower triangle of the complex hermitian input
C          matrix.  The real parts of the matrix elements are stored
C          in the full lower triangle of A, and the imaginary parts
C          are stored in the transposed positions of the strict upper
C          triangle of A.  No storage is required for the zero
C          imaginary parts of the diagonal elements.
C
C     On OUTPUT
C
C        A contains information about the unitary transformations
C          used in the reduction.
C
C        D contains the diagonal elements of the the tridiagonal matrix.
C
C        E contains the subdiagonal elements of the tridiagonal
C          matrix in its last N-1 positions.  E(1) is set to zero.
C
C        E2 contains the squares of the corresponding elements of E.
C          E2 may coincide with E if the squares are not needed.
C
C        TAU contains further information about the transformations.
C
C     Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
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  PYTHAG
C***END PROLOGUE  HTRID3