_HQR(3F)							      _HQR(3F)

NAME    [Toc]    [Back]

     HQR, SHQR	-  EISPACK routine.  This subroutine finds the eigenvalues of
     a REAL UPPER Hessenberg matrix by the QR method.

SYNOPSYS    [Toc]    [Back]

	  subroutine  hqr(nm, n, low, igh, h, wr, wi, ierr)
	  integer	   nm, n, low, igh, ierr
	  double precision h(nm,n), wr(n), wi(n)

	  subroutine shqr(nm, n, low, igh, h, wr, wi, ierr)
	  integer	   nm, n, low, igh, ierr
	  real		   h(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  BALANC.
     If	 BALANC	 has not been used, set	LOW=1, IGH=N.

     H contains	the upper Hessenberg matrix.  Information about	the
     transformations used in the reduction to Hessenberg form by  ELMHES  or
     ORTHES, if	performed, is stored in	the remaining triangle under the
     Hessenberg	matrix.	 On OUTPUT

     H has been	destroyed.  Therefore, it must be saved	before calling	HQR
     if	subsequent calculation and back	transformation of eigenvectors is to
     be	performed.

     WR	and WI contain the real	and imaginary parts, respectively, of the
     eigenvalues.  The eigenvalues are unordered except	that complex conjugate
     pairs of values appear consecutively with the eigenvalue having the
     positive imaginary	part first.  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.  Questions	and comments
     should be directed	to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
     NATIONAL LABORATORY


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