## Developer Reference

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

# p?laqr3

Performs the orthogonal/unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).

## Syntax

Description
This
subroutine
accepts as input an upper Hessenberg matrix
H
and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output
H
is overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of
H
. It is to be hoped that the final version of
H
has many zero subdiagonal entries.
Input Parameters
wantt
(global )
LOGICAL
If
.TRUE.
, then the Hessenberg matrix
H
is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling
subroutine
).
If
.FALSE.
, then only enough of
H
is updated to preserve the eigenvalues.
wantz
(global )
LOGICAL
If
.TRUE.
, then the orthogonal matrix
Z
is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling
subroutine
).
If
.FALSE.
, then
z
is not referenced.
n
(global )
INTEGER
The order of the matrix
H
and (if
wantz
is
.TRUE.
), the order of the orthogonal matrix
Z
.
ktop
(global )
INTEGER
It is assumed that either
ktop
= 1 or
H
(
ktop
,
ktop
-1)=0.
kbot
and
ktop
together determine an isolated block along the diagonal of the Hessenberg matrix.
kbot
(global )
INTEGER
It is assumed without a check that either
kbot
=
n
or
H
(
kbot
+1,
kbot
)=0.
kbot
and
ktop
together determine an isolated block along the diagonal of the Hessenberg matrix.
nw
(global )
INTEGER
Deflation window size. 1
nw
(
kbot
-
ktop
+1).
h
REAL
for
pslaqr3
DOUBLE PRECISION
for
pdlaqr3
(local ) array of size
(
lld_h
,
LOC
c
(
n
))
The initial
n
-by-
n
section of
H
stores the Hessenberg matrix undergoing aggressive early deflation.
desch
(global and local)
INTEGER
array of size
dlen_
.
The array descriptor for the distributed matrix
H
.
iloz
,
ihiz
(global )
INTEGER
Specify the rows of the matrix
Z
to which transformations must be applied if