Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?lamsh

Sends multiple shifts through a small (single node) matrix to maximize the number of bulges that can be sent through.

Syntax

call slamsh
(
s
,
lds
,
nbulge
,
jblk
,
h
,
ldh
,
n
,
ulp
)
call dlamsh
(
s
,
lds
,
nbulge
,
jblk
,
h
,
ldh
,
n
,
ulp
)
call clamsh
(
s
,
lds
,
nbulge
,
jblk
,
h
,
ldh
,
n
,
ulp
)
call zlamsh
(
s
,
lds
,
nbulge
,
jblk
,
h
,
ldh
,
n
,
ulp
)
Description
The
?lamsh
routine
sends multiple shifts through a small (single node) matrix to see how small consecutive subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. The
subroutine
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 small consecutive subdiagonal elements.
Input Parameters
s
(local)
REAL
for
slamsh
DOUBLE PRECISION
for
dlamsh
COMPLEX
for
clamsh
DOUBLE COMPLEX
for
zlamsh
Array of size
(
lds
, 2*
jblk
)
.
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).
lds
(local)
INTEGER
.
On entry, the leading dimension of
S
; unchanged on exit.
1<
nbulge
jblk
lds
/2
.
nbulge
(local)
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
.
jblk
(local)
INTEGER
.
On entry, the number of double shifts determined for
S
; unchanged on exit.
h
(local)
REAL
for
slamsh
DOUBLE PRECISION
for
dlamsh
COMPLEX
for
clamsh
DOUBLE COMPLEX
for
zlamsh
Array of size
(
ldh
,
n
)
.
On entry, the local matrix to apply the shifts on.
h
should be aligned so that the starting row is 2.
ldh
(local)
INTEGER
.
On entry, the leading dimension of
H
; unchanged on exit.
n
(local)
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)
REAL
for
slamsh
DOUBLE PRECISION
for
dlamsh
REAL
for
clamsh
DOUBLE PRECISION
for
zlamsh
On entry, machine precision. Unchanged on exit.
Output Parameters
s
On exit, the data is rearranged in the best order for applying.
nbulge
On exit, the maximum number of bulges that can be sent through.
h
On exit, the data is destroyed.