Developer Reference

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

p?laqr2

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

call pslaqr2
(
wantt
,
wantz
,
n
,
ktop
,
kbot
,
nw
,
a
,
desca
,
iloz
,
ihiz
,
z
,
descz
,
ns
,
nd
,
sr
,
si
,
t
,
ldt
,
v
,
ldv
,
wr
,
wi
,
work
,
lwork
)
call pdlaqr2
(
wantt
,
wantz
,
n
,
ktop
,
kbot
,
nw
,
a
,
desca
,
iloz
,
ihiz
,
z
,
descz
,
ns
,
nd
,
sr
,
si
,
t
,
ldt
,
v
,
ldv
,
wr
,
wi
,
work
,
lwork
)
Description
p?laqr2
accepts as input an upper Hessenberg matrix
A
and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output
A
is overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of
A
. It is to be hoped that the final version of
A
has many zero subdiagonal entries.
This
routine
handles small deflation windows which is affordable by one processor. Normally, it is called by
p?laqr1
. All the inputs are assumed to be valid without checking.
Optimization Notice
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
Input Parameters
wantt
(global )
LOGICAL
If
.TRUE.
, then the Hessenberg matrix
A
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
A
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
A
and (if
wantz
is
.TRUE.
) the order of the orthogonal matrix
Z
.
ktop
,
kbot
(global )
INTEGER
It is assumed without a check that either
kbot
=
n
or
A
(
kbot
+1,
kbot
)=0.
kbot
and
ktop
together determine an isolated block along the diagonal of the Hessenberg matrix. However,
A
(
ktop
,
ktop
-1)=0 is not essentially necessary if
wantt
is
.TRUE.
.
nw
(global )
INTEGER
Deflation window size. 1
nw
(
kbot
-
ktop
+1). Normally
nw
3 if
p?laqr2
is called by
p?laqr1
.
a
REAL
for
pslaqr2
DOUBLE PRECISION
for
pdlaqr2
(local ) array of size
(
lld_a
,
LOC
c
(
n
))
The initial
n
-by-
n
section of
a