Developer Reference

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

?laqr5

Performs a single small-bulge multi-shift QR sweep.

Syntax

call slaqr5
(
wantt
,
wantz
,
kacc22
,
n
,
ktop
,
kbot
,
nshfts
,
sr, si,
h
,
ldh
,
iloz
,
ihiz
,
z
,
ldz
,
v, ldv, u, ldu, nv, wv,
ldwv, nh, wh, ldwh
)
call dlaqr5
(
wantt
,
wantz
,
kacc22
,
n
,
ktop
,
kbot
,
nshfts
,
sr, si,
h
,
ldh
,
iloz
,
ihiz
,
z
,
ldz
,
v, ldv, u, ldu, nv, wv,
ldwv, nh, wh, ldwh
)
call claqr5
(
wantt
,
wantz
,
kacc22
,
n
,
ktop
,
kbot
,
nshfts
,
s,
h
,
ldh
,
iloz
,
ihiz
,
z
,
ldz
,
v, ldv, u, ldu, nv, wv,
ldwv, nh, wh, ldwh
)
call zlaqr5
(
wantt
,
wantz
,
kacc22
,
n
,
ktop
,
kbot
,
nshfts
,
s,
h
,
ldh
,
iloz
,
ihiz
,
z
,
ldz
,
v, ldv, u, ldu, nv, wv,
ldwv, nh, wh, ldwh
)
Include Files
  • mkl.fi
Description
This auxiliary routine called by
?laqr0
performs a single small-bulge multi-shift QR sweep.
Input Parameters
wantt
LOGICAL
.
wantt
=
.TRUE.
if the quasi-triangular/triangular Schur factor is computed.
wantt
is set to
.FALSE.
otherwise.
wantz
LOGICAL
.
wantz
=
.TRUE.
if the orthogonal/unitary Schur factor is computed.
wantz
is set to
.FALSE.
otherwise.
kacc22
INTEGER
. Possible values are 0, 1, or 2.
Specifies the computation mode of far-from-diagonal orthogonal updates.
= 0
: the routine does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.
= 1
: the routine accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries.
= 2
: the routine accumulates reflections, uses matrix-matrix multiply to update the far-from-diagonal matrix entries, and takes advantage of 2-by-2 block structure during matrix multiplies.
n
INTEGER
. The order of the Hessenberg matrix
H
upon which the routine operates.
ktop
,
kbot
INTEGER
.
It is assumed without a check that either
ktop
=1
or
h
(
ktop
,
ktop-1
)=0
, and either
kbot
=
n
or
h
(
kbot
+1,
kbot
)=0
.
nshfts
INTEGER
.
Number of simultaneous shifts, must be positive and even.
sr
,
si
REAL
for
slaqr5
DOUBLE PRECISION
for
dlaqr5
Arrays,
DIMENSION
(
nshfts
) each.
sr
contains the real parts and
si
contains the imaginary parts of the
nshfts
shifts of origin that define the multi-shift QR sweep.
s
COMPLEX
for
claqr5
DOUBLE COMPLEX
for
zlaqr5
.
Arrays,
DIMENSION
(
nshfts
).
s
contains the shifts of origin that define the multi-shift QR sweep.
h
REAL
for
slaqr5