on entry in upper
          Hessenberg form.  1 &lt;= H &lt;= K.

  ILO     (input)  INTEGER
  IHI     (input)  INTEGER
          It is assumed that each factor in A is already upper
          triangular in rows and columns 1:ILO-1 and IHI+1:N.
          1 &lt;= ILO &lt;= IHI &lt;= N, if N &gt; 0;
          ILO = 1 and IHI  = 0, if N = 0.

  S       (input)  INTEGER array, dimension (K)
          The leading K elements of this array must contain the
          signatures of the factors. Each entry in S must 