_COMLR2(3F)							   _COMLR2(3F)

NAME    [Toc]    [Back]

     COMLR2, SCOMLR2  -	 EISPACK routine.  This	subroutine finds the
     eigenvalues and eigenvectors of a COMPLEX UPPER Hessenberg	matrix by the
     modified LR method.  The eigenvectors of a	COMPLEX	GENERAL	matrix can
     also be found if  COMHES  has been	used to	reduce this general matrix to
     Hessenberg	form.

SYNOPSYS    [Toc]    [Back]

	  subroutine  comlr2(nm, n, low, igh, int, hr, hi, wr, wi, zr, zi,
     ierr)
	  integer	    nm,	n, low,	igh, ierr
	  integer	    int(igh)
	  double precision  hr(nm,n),hi(nm,n),wr(n),wi(n),zr(nm,n),zi(nm,n)

	  subroutine scomlr2(nm, n, low, igh, int, hr, hi, wr, wi, zr, zi,
     ierr)
	  integer	    nm,	n, low,	igh, ierr
	  integer	    int(igh)
	  real		    hr(nm,n),hi(nm,n),wr(n),wi(n),zr(nm,n),zi(nm,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.

     INT contains information on the rows and columns interchanged in the
     reduction by  COMHES, if performed.  Only elements	LOW through IGH	are
     used.  If the eigenvectors	of the HESSEN- BERG matrix are desired,	set
     INT(J)=J 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 the multipliers which were used in the	reduction by
     COMHES, if	performed.  If the eigenvectors	of the Hessenberg matrix are
     desired, these elements must be set to zero.  On OUTPUT The upper
     Hessenberg	portions of HR and HI have been	destroyed, but the location
     HR(1,1) contains the norm of the triangularized matrix.

     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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_COMLR2(3F)							   _COMLR2(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 CDIV for complex division.  Questions and comments
     should be directed	to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
     NATIONAL LABORATORY


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