Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

void pslaqr3
(
MKL_INT*
wantt
,
MKL_INT*
wantz
,
MKL_INT*
n
,
MKL_INT*
ktop
,
MKL_INT*
kbot
,
MKL_INT*
nw
,
float*
h
,
MKL_INT*
desch
,
MKL_INT*
iloz
,
MKL_INT*
ihiz
,
float*
z
,
MKL_INT*
descz
,
MKL_INT*
ns
,
MKL_INT*
nd
,
float*
sr
,
float*
si
,
float*
v
,
MKL_INT*
descv
,
MKL_INT*
nh
,
float*
t
,
MKL_INT*
desct
,
MKL_INT*
nv
,
float*
wv
,
MKL_INT*
descw
,
float*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
,
MKL_INT*
reclevel
);
void pdlaqr3
(
MKL_INT*
wantt
,
MKL_INT*
wantz
,
MKL_INT*
n
,
MKL_INT*
ktop
,
MKL_INT*
kbot
,
MKL_INT*
nw
,
double*
h
,
MKL_INT*
desch
,
MKL_INT*
iloz
,
MKL_INT*
ihiz
,
double*
z
,
MKL_INT*
descz
,
MKL_INT*
ns
,
MKL_INT*
nd
,
double*
sr
,
double*
si
,
double*
v
,
MKL_INT*
descv
,
MKL_INT*
nh
,
double*
t
,
MKL_INT*
desct
,
MKL_INT*
nv
,
double*
wv
,
MKL_INT*
descw
,
double*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
,
MKL_INT*
reclevel
);
Include Files
  • mkl_scalapack.h
Description
This
function
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 )
If
wantt
 is non-zero
, then the Hessenberg matrix
H
 is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling
function
).
If
wantt
 equals zero
, then only enough of
H
 is updated to preserve the eigenvalues.
wantz
(global )
If
wantz
 is non-zero
, then the orthogonal matrix
Z
 is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling
function
).
If
wantz
 equals zero
, then
z
 is not referenced.
n
(global )
The order of the matrix
H
 and (if
wantz
 is
non-zero
), the order of the orthogonal matrix
Z
.
ktop
(global )
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 )
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 )
Deflation window size. 1
≤
nw
≤
 (
kbot
-
ktop
+1).
h
(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) 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
Array of size
lld_
z *
LOC
c
(
n
)
If
wantz
 is
non-zero
, then on output, the orthogonal similarity transformation mentioned above has been accumulated into
the matrix
Z
(
iloz
:
ihiz
,
kbot
:
ktop
) from the right.
If
wantz
 is
zero
, then
z
 is unreferenced.
descz
(global and local) array of size
dlen_
.
The array descriptor for the distributed matrix
Z
.
v
(global workspace) array of size
lld_v
 *
LOC
c
nw
)
An
nw
-by-
nw
 distributed work array.
descv
(global and local) array of size
dlen_
.
The array descriptor for the distributed matrix
V
.
nh
The number of columns of
t
.
nh
≥
nw
.
t
(global workspace) array of size
lld_t
 *
LOC
c
(
nh
)
desct
(global and local) array of size
dlen_
.
The array descriptor for the distributed matrix
T
.
nv
(global )
The number of rows of work array
wv
 available for workspace.
nv
≥
nw
.
wv
(global workspace) array of size
lld_w
 *
LOC
c
(
nw
)
descw
(global and local) array of size
dlen_
.
The array descriptor for the distributed matrix
wv
.
work
(local workspace) array of size
lwork
.
lwork
(local )
The size of the work array
work
 (
lwork
≥
1).
lwork
 = 2*
nw
 suffices, but greater efficiency may result from larger values of
lwork
.
If
lwork
 = -1, then a workspace query is assumed;
p?laqr3
 only estimates the optimal workspace size for the given values of
n
,
nw
,
ktop
 and
kbot
. The estimate is returned in
work
[0]
. No error message related to
lwork
 is issued by
xerbla
. Neither
h
 nor
z
 are accessed.
iwork
(local workspace) array of size
liwork
liwork
(local )
The length of the workspace array
iwork
 (
liwork
≥
1).
If
liwork
=-1, then a workspace query is assumed.
OUTPUT Parameters
h
On output
h
 has been transformed by an orthogonal similarity transformation, perturbed, and the returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.
z
IF
wantz
 is
non-zero
, then on output, the orthogonal similarity transformation mentioned above has been accumulated into
the matrix
Z
(
iloz
:
ihiz
,
kbot
:
ktop
) from the right.
If
wantz
 is
zero
, then
z
 is unreferenced.
ns
(global )
The number of unconverged (that is, approximate) eigenvalues returned in
sr
 and
si
 that may be used as shifts by the calling
function
.
nd
(global )
The number of converged eigenvalues uncovered by this
function
.
sr
,
si
(global ) array of size
kbot
. The real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in
sr
[
kbot
-
nd
-
ns
] through
sr
[
kbot
-
nd
-1] and
si
[
kbot
-
nd
-
ns
] through
si
[
kbot
-
nd
-1]
, respectively. The real and imaginary parts of converged eigenvalues are stored in
sr
[
kbot
-
nd
] through
sr
[
kbot
-1] and
si
[
kbot
-
nd
] through
si
[
kbot
-1]
, respectively.
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.