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