## Developer Reference

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

# ?larrv2

Computes the eigenvectors of the tridiagonal matrix
T
=
L
*
D
*
L
T
given
L
,
D
and the eigenvalues of
L
*
D
*
L
T
.

## Syntax

Description
?larrv2
computes the eigenvectors of the tridiagonal matrix
T
=
L
D
L
T
given
L
,
D
and approximations to the eigenvalues of
L
D
L
T
. The input eigenvalues should have been computed by larre2a or by previous calls to
?larrv2
.
The major difference between the parallel and the sequential construction of the representation tree is that in the parallel case, not all eigenvalues of a given cluster might be computed locally. Other processors might "own" and refine part of an eigenvalue cluster. This is crucial for scalability. Thus there might be communication necessary before the current level of the representation tree can be parsed.
• The calling sequence has two additional integer parameters,
dol
and
dou
, that should satisfy
m
dou
dol
1. These parameters are only relevant when both eigenvalues and eigenvectors are computed (
stegr2b
parameter
jobz
= 'V').
?larrv2
only computes the eigenvectors corresponding to eigenvalues
dol
through
dou
in
w
. (That is, instead of computing the eigenvectors belonging to
w
(1) through
w
(
m
)
, only the eigenvectors belonging to eigenvalues
w
(
dol
) through
w
(
dou
)
are computed. In this case, only the eigenvalues
dol
:
dou
are guaranteed to be accurately refined to all figures by Rayleigh-Quotient iteration.
vstart
,
finish
,
ndepth
,
parity
,
zoffset
are included as a thread-safe implementation equivalent to save variables. These variables store details about the local representation tree which is computed layerwise. For scalability reasons, eigenvalues belonging to the locally relevant representation tree might be computed on other processors. These need to be communicated before the inspection of the RRRs can proceed on any given layer. Note that only when the variable
finish
is
true
, the computation has ended. All eigenpairs between
dol
and
dou
have been computed.
m
is set to
dou
-
dol
+ 1.
• ?larrv2
needs more workspace in
z
than the sequential
slarrv
. It is used to store the conformal embedding of the local representation tree.
Optimization Notice
Intel's compilers may or may not optimize to the same de