 Balancing consists of applying an equivalence transformation
  to isolate eigenvalues and/or to make the 1-norms of the rows
  and columns ILO,...,IHI of A and B nearly equal. If THRESH &lt; 0,
  a search is performed to find those scaling factors giving the
  smallest norm ratio or product defined above (see the description
  of the parameter THRESH).

  Assuming JOB = 'S', let Dl and Dr be diagonal matrices containing
  the vectors LSCALE and RSCALE, respectively. The returned matrices
  are obtained usi