Developer Reference

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

?larrb2

Provides limited bisection to locate eigenvalues for more accuracy.

Syntax

call slarrb2
(
n
,
d
,
lld
,
ifirst
,
ilast
,
rtol1
,
rtol2
,
offset
,
w
,
wgap
,
werr
,
work
,
iwork
,
pivmin
,
lgpvmn
,
lgspdm
,
twist
,
info
)
call dlarrb2
(
n
,
d
,
lld
,
ifirst
,
ilast
,
rtol1
,
rtol2
,
offset
,
w
,
wgap
,
werr
,
work
,
iwork
,
pivmin
,
lgpvmn
,
lgspdm
,
twist
,
info
)
Description
Given the relatively robust representation (RRR)
L
D
L
T
,
?larrb2
does "limited" bisection to refine the eigenvalues of
L
D
L
T
,
w
(
ifirst
-
offset
) through
w
(
ilast
-
offset
),
to more accuracy. Initial guesses for these eigenvalues are input in
w
, the corresponding estimate of the error in these guesses and their gaps are input in
werr
and
wgap
, respectively. During bisection, intervals [
left
,
right
] are maintained by storing their mid-points and semi-widths in the arrays
w
and
werr
respectively.
There are very few minor differences between larrb from LAPACK and this current
subroutine
?larrb2
. The most important reason for creating this nearly identical copy is profiling: in the ScaLAPACK MRRR algorithm, eigenvalue computation using
?larrb2
is used for refinement in the construction of the representation tree, as opposed to the initial computation of the eigenvalues for the root RRR which uses
?larrb
. When profiling, this allows an easy quantification of refinement work vs. computing eigenvalues of the root.
Input Parameters
n
INTEGER
The order of the matrix.
d
REAL
for
slarrb2
DOUBLE PRECISION
for
dlarrb2
Array of size
n.
The
n
diagonal elements of the diagonal matrix
D
.
lld
REAL
for
slarrb2
DOUBLE PRECISION
for
dlarrb2
Array of size
n
-1.
The (
n
-1) elements
l
i
*
l
i
*
d
(
i
)
.
ifirst
INTEGER
The index of the first eigenvalue to be computed.
ilast
INTEGER
The index of the last eigenvalue to be computed.
rtol1
,
rtol2
REAL
for
slarrb2
DOUBLE PRECISION
for
dlarrb2
Tolerance for the convergence of the bisection intervals.
An interval [
left
,
right
] has converged if
right
-
left
< max (
rtol1
*
gap
,
rtol2
* max(|
left
|, |
right
|)) where
gap
is the (estimated) distance to the nearest eigenvalue.
offset
INTEGER
Offset for the arrays
w
,
wgap
and