Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?laqr5

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

Syntax

void pslaqr5
(
MKL_INT*
wantt
,
MKL_INT*
wantz
,
MKL_INT*
kacc22
,
MKL_INT*
n
,
MKL_INT*
ktop
,
MKL_INT*
kbot
,
MKL_INT*
nshfts
,
float*
sr
,
float*
si
,
float*
h
,
MKL_INT*
desch
,
MKL_INT*
iloz
,
MKL_INT*
ihiz
,
float*
z
,
MKL_INT*
descz
,
float*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
);
void pdlaqr5
(
MKL_INT*
wantt
,
MKL_INT*
wantz
,
MKL_INT*
kacc22
,
MKL_INT*
n
,
MKL_INT*
ktop
,
MKL_INT*
kbot
,
MKL_INT*
nshfts
,
double*
sr
,
double*
si
,
double*
h
,
MKL_INT*
desch
,
MKL_INT*
iloz
,
MKL_INT*
ihiz
,
double*
z
,
MKL_INT*
descz
,
double*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
);
Include Files
  • mkl_scalapack.h
Description
This auxiliary
function
called by
p?laqr0
 performs a single small-bulge multi-shift QR sweep by chasing separated groups of bulges along the main block diagonal of a Hessenberg matrix
H
.
Input Parameters
wantt
(global) scalar
wantt
is non-zero
 if the quasi-triangular Schur factor is being computed.
wantt
 is set to
zero
 otherwise.
wantz
(global) scalar
wantz
is non-zero
 if the orthogonal Schur factor is being computed.
wantz
 is set to
zero
 otherwise.
kacc22
(global)
Value 0, 1, or 2. Specifies the computation mode of far-from-diagonal orthogonal updates.
= 0:
p?laqr5
 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries.
= 1:
p?laqr5
 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries.
= 2:
p?laqr5
 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
(global) scalar
The order of the Hessenberg matrix
H
 and, if
wantz
is non-zero
, the order of the orthogonal matrix
Z
.
ktop
,
kbot
(global) scalar
These are the first and last rows and columns of an isolated diagonal block upon which the QR sweep is to be applied. 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
(global) scalar
nshfts
 gives the number of simultaneous shifts.
nshfts
 must be positive and even.
sr
,
si
(global) Array of size
nshfts
sr
 contains the real parts and
si
 contains the imaginary parts of the
nshfts
 shifts of origin that define the multi-shift QR sweep.
h
(local) Array of size
lld_h
 *
LOC
c
(
n
)
On input
h
 contains a Hessenberg matrix
H
.
desch
(global and local)
array of size
dlen_
.
The array descriptor for the distributed matrix
H
 .
iloz
,
ihiz
(global)
Specify the rows of the matrix
Z
 to which transformations must be applied if
wantz
is non-zero
. 1
≤
iloz
≤
ihiz
≤
n
z
(local) array of size
lld_z
 *
LOC
c
(
n
)
If
wantz
is non-zero
, then the QR Sweep orthogonal similarity transformation is accumulated into the matrix
Z
(
iloz
:
ihiz
,
kbot
:
ktop
) from the right. If
wantz
equals zero
, then
z
 is unreferenced.
descz
(global and local) array of size
dlen_
.
The array descriptor for the distributed matrix
Z
.
work
(local workspace) array of size
lwork
lwork
(local)
The size of the
work
 array (
lwork
≥
1).
If
lwork
=-1, then a workspace query is assumed.
iwork
(local workspace) array of size
liwork
liwork
(local)
The size of the
iwork
 array (
liwork
≥
1).
If
liwork
=-1, then a workspace query is assumed.
Output Parameters
h
A multi-shift QR sweep with shifts
sr
(
j
)+
i
*
si
(
j
) is applied to the isolated diagonal block in rows and columns
ktop
 through
kbot
 of the matrix
H
.
z
If
wantz
is non-zero
,
z
 is updated with transformations applied only to the submatrix
Z
(
iloz
:
ihiz
,
kbot
:
ktop
).
work
[0]
On exit, if
info
 = 0,
work
[0]
 returns the optimal
lwork
.
iwork
[0]
On exit, if
info
 = 0,
iwork
[0]
 returns the optimal
liwork
.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.