Developer Reference

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

p?trsen

Reorders the Schur factorization of a matrix and (optionally) computes the reciprocal condition numbers and invariant subspace for the selected cluster of eigenvalues.

Syntax

call pstrsen
(
job
,
compq
,
select
,
para
,
n
,
t
,
it
,
jt
,
desct
,
q
,
iq
,
jq
,
descq
,
wr
,
wi
,
m
,
s
,
sep
,
work
,
lwork
,
iwork
,
liwork
,
info
)
call pdtrsen
(
job
,
compq
,
select
,
para
,
n
,
t
,
it
,
jt
,
desct
,
q
,
iq
,
jq
,
descq
,
wr
,
wi
,
m
,
s
,
sep
,
work
,
lwork
,
iwork
,
liwork
,
info
)
Description
p?trsen
reorders the real Schur factorization of a real matrix
A
=
Q
*
T
*
Q
T
, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix
T
, and the leading columns of
Q
form an orthonormal basis of the corresponding right invariant subspace. The reordering is performed by
p?trord
.
Optionally the
routine
computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.
T
must be in Schur form (as returned by
p?lahqr
), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks.
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
job
(global )
CHARACTER
*1
Specifies whether condition numbers are required for the cluster of eigenvalues (
s
) or the invariant subspace (
sep
):
= 'N': no condition numbers are required;
= 'E': only the condition number for the cluster of eigenvalues is computed (
s
);
= 'V': only the condition number for the invariant subspace is computed (
sep
);
= 'B': condition numbers for both the cluster and the invariant subspace are computed (
s
and
sep
).
compq
(global )
CHARACTER
*1
= 'V': update the matrix
q
of Schur vectors;
= 'N': do not update
q
.
select
(global )
LOGICAL
array of size
n
select
specifies the eigenvalues in the selected cluster. To select a real eigenvalue
w
(
j
),
select
(
j
)
must be set to
.TRUE.
. To select a complex conjugate pair of eigenvalues
w
(
j
) and
w
(
j
+1), corresponding to a 2-by-2 diagonal block, either
select
(
j
)
or
select
(
j
+1)
or both must be set to