Developer Reference

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

p?trord

Reorders the Schur factorization of a general matrix.

Syntax

call pstrord
(
compq
,
select
,
para
,
n
,
t
,
it
,
jt
,
desct
,
q
,
iq
,
jq
,
descq
,
wr
,
wi
,
m
,
work
,
lwork
,
iwork
,
liwork
,
info
)
call pdtrord
(
compq
,
select
,
para
,
n
,
t
,
it
,
jt
,
desct
,
q
,
iq
,
jq
,
descq
,
wr
,
wi
,
m
,
work
,
lwork
,
iwork
,
liwork
,
info
)
Description
p?trord
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.
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.
This
subroutine
uses a delay and accumulate procedure for performing the off-diagonal updates.
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
compq
(global)
CHARACTER*1
= 'V': update the matrix
q
of Schur vectors;
= 'N': do not update
q
.
select
(global)
INTEGER
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 1. 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 1; a complex conjugate pair of eigenvalues must be either both included in the cluster or both excluded.
para
(global)
INTEGER
*6
Block parameters:
para
(1)
maximum number of concurrent computational windows allowed in the algorithm; 0 <
para
(1)
min(
nprow
,
npcol
) must hold;
para
(2)
number of eigenvalues in each window; 0 <
para
(2)
<
para
(3)
must hold;
para
(3)
window size;
para
(2)
<
para
(3)
<
mb_t<