SUBROUTINE HTRID3 (NM, N, A, D, E, E2, TAU)
C***BEGIN PROLOGUE HTRID3
C***PURPOSE Reduce a complex Hermitian (packed) matrix to a real
C symmetric tridiagonal matrix by unitary similarity
C***LIBRARY SLATEC (EISPACK)
C***TYPE SINGLE PRECISION (HTRID3-S)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
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 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 On INPUT
C NM must be set to the row dimension of the two-dimensional
C array parameter, A, as declared in the calling program
C dimension statement. NM is an INTEGER variable.
C N is the order of the matrix. N is an INTEGER variable.
C N must be less than or equal to NM.
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. A is a two-
C dimensional REAL array, dimensioned A(NM,N).
C On OUTPUT
C A contains some information about the unitary transformations
C used in the reduction.
C D contains the diagonal elements of the real symmetric
C tridiagonal matrix. D is a one-dimensional REAL array,
C dimensioned D(N).
C E contains the subdiagonal elements of the real tridiagonal
C matrix in its last N-1 positions. E(1) is set to zero.
C E is a one-dimensional REAL array, dimensioned E(N).
C E2 contains the squares of the corresponding elements of E.
C E2(1) is set to zero. E2 may coincide with E if the squares
C are not needed. E2 is a one-dimensional REAL array,
C dimensioned E2(N).
C TAU contains further information about the transformations.
C TAU is a one-dimensional REAL array, dimensioned TAU(2,N).
C Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
C Questions and comments should be directed to B. S. Garbow,
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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***ROUTINES CALLED PYTHAG
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 HTRID3