NAME

       SLAMSH  -  send  multiple  shifts  through  a  small  (single  node) matrix to  see how consecutive small
       subdiagonal elements are modified by  subsequent shifts in an effort to maximize  the  number  of  bulges
       that can be sent through

SYNOPSIS

       SUBROUTINE SLAMSH ( S, LDS, NBULGE, JBLK, H, LDH, N, ULP )

           INTEGER       LDS, NBULGE, JBLK, LDH, N

           REAL          ULP

           REAL          S(LDS,*), H(LDH,*)

PURPOSE

       SLAMSH sends multiple shifts through a small (single node) matrix to
          see how consecutive small subdiagonal elements are modified by
          subsequent shifts in an effort to maximize the number of bulges
          that can be sent through.  SLAMSH should only be called when there are multiple shifts/bulges
          (NBULGE > 1) and the first shift is starting in the middle of an
          unreduced Hessenberg matrix because of two or more consecutive small
          subdiagonal elements.

ARGUMENTS

       S       (local input/output) REAL array, (LDS,*)
               On  entry, the matrix of shifts.  Only the 2x2 diagonal of S is referenced.  It is assumed that S
               has JBLK double shifts (size 2).  On exit, the data is rearranged in the best order for applying.

       LDS     (local input) INTEGER
               On entry, the leading dimension of S.  Unchanged on exit.  1 < NBULGE <= JBLK <= LDS/2

       NBULGE  (local input/output) INTEGER
               On entry, the number of bulges to send through H ( >1 ).  NBULGE should be less than the  maximum
               determined (JBLK).  1 < NBULGE <= JBLK <= LDS/2 On exit, the maximum number of bulges that can be
               sent through.

       JBLK    (local input) INTEGER
               On entry, the number of shifts determined for S.  Unchanged on exit.

       H       (local input/output) REAL array (LDH,N)
               On entry, the local matrix to apply the shifts on.  H should be aligned so that the starting  row
               is 2.  On exit, the data is destroyed.

       LDS     (local input) INTEGER
               On entry, the leading dimension of S.  Unchanged on exit.

       N       (local input) INTEGER
               On  entry,  the  size  of  H.  If all the bulges are expected to go through, N should be at least
               4*NBULGE+2.  Otherwise, NBULGE may be reduced by this routine.

       ULP     (local input) REAL
               On entry, machine precision Unchanged on exit.

               Implemented by:  G. Henry, May 1, 1997