_COMQR2(3F)							   _COMQR2(3F)

NAME    [Toc]    [Back]

     COMQR2, SCOMQR2  -	 EISPACK routine.  This	subroutine finds the
     eigenvalues and eigenvectors of a COMPLEX UPPER Hessenberg	matrix by the
     QR	method.	 The eigenvectors of a COMPLEX GENERAL matrix can also be
     found if  CORTH  has been used to reduce this general matrix to
     Hessenberg	form.

SYNOPSYS    [Toc]    [Back]

	  subroutine  comqr2(nm,n,low,igh,ortr,orti,hr,hi,wr,wi,zr,zi,ierr)
	  integer	   nm, n, low, igh, ierr
	  double precision hr(nm,n), hi(nm,n), wr(n),	  wi(n)
	  double precision zr(nm,n), zi(nm,n), ortr(igh), orti(igh)

	  subroutine scomqr2(nm,n,low,igh,ortr,orti,hr,hi,wr,wi,zr,zi,ierr)
	  integer	   nm, n, low, igh, ierr
	  real		   hr(nm,n), hi(nm,n), wr(n),	  wi(n)
	  real		   zr(nm,n), zi(nm,n), ortr(igh), orti(igh)

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.

     ORTR and ORTI contain information about the unitary trans-	formations
     used in the reduction by  CORTH, if performed.  Only elements LOW through
     IGH are used.  If the eigenvectors	of the Hessenberg matrix are desired,
     set ORTR(J) and ORTI(J) to	0.0E0 for these	elements.

     HR	and HI contain the real	and imaginary parts, respectively, of the
     complex upper Hessenberg matrix.  Their lower triangles below the
     subdiagonal contain further information about the transformations which
     were used in the reduction	by  CORTH, if performed.  If the eigenvectors
     of	the Hessenberg matrix are desired, these elements may be arbitrary.
     On	OUTPUT

     ORTR , ORTI, and the upper	Hessenberg portions of HR and HI have been
     destroyed.

     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.

     ZR	and ZI contain the real	and imaginary parts, respectively, of the



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_COMQR2(3F)							   _COMQR2(3F)



     eigenvectors.  The	eigenvectors are unnormalized.	If an error exit is
     made, none	of the eigenvectors has	been found.

     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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