_COMQR(3F)							    _COMQR(3F)

NAME    [Toc]    [Back]

     COMQR, SCOMQR   -	EISPACK	routine.  This subroutine finds	the
     eigenvalues of a COMPLEX upper Hessenberg matrix by the QR	method.

SYNOPSYS    [Toc]    [Back]

	  subroutine  comqr(nm,	n, low,	igh, hr, hi, wr, wi, ierr)
	  integer	   nm, n, low, igh, ierr
	  double precision hr(nm,n), hi(nm,n), wr(n), wi(n)

	  subroutine scomqr(nm,	n, low,	igh, hr, hi, wr, wi, ierr)
	  integer	   nm, n, low, igh, ierr
	  real		   hr(nm,n), hi(nm,n), wr(n), wi(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.

     LOW and IGH are integers determined by the	balancing subroutine  CBAL.
     If	 CBAL  has not been used, set LOW=1, IGH=N.

     HR	and HI contain the real	and imaginary parts, respectively, of the
     complex upper Hessenberg matrix.  Their lower triangles below the
     subdiagonal contain information about the unitary transformations used in
     the reduction by  CORTH, if performed.  On	OUTPUT The upper Hessenberg
     portions of HR and	HI have	been destroyed.	 Therefore, they must be saved
     before calling  COMQR  if subsequent calculation of eigenvectors is to be
     performed.

     WR	and WI contain the real	and imaginary parts, respectively, of the
     eigenvalues.  If an error exit is made, the eigenvalues should be correct
     for indices IERR+1,...,N.

     IERR is set to ZERO       for normal return, J	     if	the J-th
     eigenvalue	has not	been
	determined after a total of 30*N iterations.  Calls CSROOT for complex
     square root.  Calls PYTHAG(A,B) for sqrt(A**2 + B**2).  Calls CDIV	for
     complex division.	Questions and comments should be directed to B.	S.
     Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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