HQR(3F)

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


SYNOPSYS
          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
     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