_HTRID3(3F)							   _HTRID3(3F)

NAME    [Toc]    [Back]

     HTRID3, SHTRID3  -	 EISPACK routine.  This	subroutine reduces a COMPLEX
     HERMITIAN matrix, stored as a single square array,	to a real symmetric
     tridiagonal matrix	using unitary similarity transformations.

SYNOPSYS    [Toc]    [Back]

	  subroutine  htrid3(nm, n, a, d, e, e2, tau)
	  integer	   nm, n
	  double precision a(nm,n), d(n), e(n),	e2(n), tau(2,n)

	  subroutine shtrid3(nm, n, a, d, e, e2, tau)
	  integer	   nm, n
	  real		   a(nm,n), d(n), e(n),	e2(n), tau(2,n)

DESCRIPTION    [Toc]    [Back]

     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.

     A contains	the lower triangle of the complex hermitian input matrix.  The
     real parts	of the matrix elements are stored in the full lower triangle
     of	A, and the imaginary parts are stored in the transposed	positions of
     the strict	upper triangle of A.  No storage is required for the zero
     imaginary parts of	the diagonal elements.	On OUTPUT

     A contains	information about the unitary transformations used in the
     reduction.

     D contains	the diagonal elements of the 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


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