DLAMSH - 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 DLAMSH
( S, LDS, NBULGE, JBLK, H, LDH, N, ULP )
INTEGER
LDS, NBULGE, JBLK, LDH, N
DOUBLE
PRECISION ULP
DOUBLE
PRECISION S(LDS,*), H(LDH,*)
PURPOSE
DLAMSH 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.
DLAMSH 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.