HTRIDI(3F)

NAME
     HTRIDI, SHTRIDI  -  EISPACK routine.  This subroutine reduces a COMPLEX
     HERMITIAN matrix to a real symmetric tridiagonal matrix using unitary
     similarity transformations.


SYNOPSYS
          subroutine  htridi(nm, n, ar, ai, d, e, e2, tau)
          integer          nm, n
          double precision ar(nm,n),ai(nm,n),d(n),e(n),e2(n),tau(2,n)

          subroutine shtridi(nm, n, ar, ai, d, e, e2, tau)
          integer          nm, n
          real             ar(nm,n),ai(nm,n),d(n),e(n),e2(n),tau(2,n)



DESCRIPTION
     On INPUT

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     N is the order of the matrix.

     AR and AI contain the real and imaginary parts, respectively, of the
     complex hermitian input matrix.  Only the lower triangle of the matrix
     need be supplied.  On OUTPUT

     AR and AI contain information about the unitary trans- formations used in
     the reduction in their full lower triangles.  Their strict upper
     triangles and the diagonal of AR are unaltered.

     D contains the diagonal elements of the tridiagonal matrix.

     E contains the subdiagonal elements of the tridiagonal matrix in its last
     N-1 positions.  E(1) is set to zero.

     E2 contains the squares of the corresponding elements of E. E2 may
     coincide with E if the squares are not needed.

     TAU contains further information about the transformations. Calls
     PYTHAG(A,B) for sqrt(A**2 + B**2).  Questions and comments should be
     directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL
     LABORATORY