Contents

?tgexc

Reorders the generalized Schur decomposition of a pair of matrices (A,B) so that one diagonal block of (A,B) moves to another row index.

Syntax

Include Files
• mkl.h
Description
The routine reorders the generalized real-Schur/Schur decomposition of a real/complex matrix pair (
A
,
B
) using an orthogonal/unitary equivalence transformation
(
A
,
B
) =
Q
*(
A
,
B
)*
Z
H
,
so that the diagonal block of (
A
,
B
) with row index
ifst
is moved to row
ilst
. Matrix pair (
A
,
B
) must be in a generalized real-Schur/Schur canonical form (as returned by gges), that is,
A
is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks and
B
is upper triangular. Optionally, the matrices
Q
and
Z
of generalized Schur vectors are updated.
Q
in
*
A
in
*
Z
in
T
=
Q
out
*
A
out
*
Z
out
T
Q
in
*
B
in
*
Z
in
T
=
Q
out
*
B
out
*
Z
out
T
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
wantq
,
wantz
If
wantq
=
1
, update the left transformation matrix
Q
;
If
wantq
=
0
, do not update
Q
;
If
wantz
=
1
, update the right transformation matrix
Z
;
If
wantz
=
0
, do not update
Z
.
n
The order of the matrices
A
and
B
(
n
0).
a
,
b
,
q
,
z
Arrays:
a
(size max(1,
lda
*
n
))
contains the matrix
A
.
b
(size max(1,
ldb
*
n
))
contains the matrix
B
.
q
(size at least 1 if
wantq
= 0 and at least max(1,
ldq
*
n
) if
wantq
= 1)
If
wantq
=
0
, then
q
is not referenced.
If
wantq
=
1
, then
q
must contain the orthogonal/unitary matrix
Q
.
z
(size at least 1 if
wantz
= 0 and at least max(1,
ldz
*
n
) if
wantz
= 1)
If
wantz
=
0
, then
z
is not referenced.
If
wantz
=
1
, then
z
must contain the orthogonal/unitary matrix
Z
.
lda
a
; at least max(1,
n
).
ldb
b
; at least max(1,
n
).
ldq
q
;
If
wantq
=
0
, then
ldq
1.
If
wantq
=
1
, then
ldq
max(1,
n
).
ldz
z
;
If
wantz
=
0
, then
ldz
1.
If
wantz
=
1
, then
ldz
max(1,
n
).
ifst
,
ilst
Specify the reordering of the diagonal blocks of (
A
,
B
). The block with row index
ifst
is moved to row
ilst
, by a sequence of swapping between adjacent blocks. Constraint:
1
ifst
,
ilst
n
.
Output Parameters
a
,
b
,
q
,
z
Overwritten by the updated matrices
A
,
B
,
Q
, and
Z
respectively.
ifst
,
ilst
Overwritten for real flavors only.
If
ifst
pointed to the second row of a 2 by 2 block on entry, it is changed to point to the first row;
ilst
always points to the first row of the block in its final position (which may differ from its input value by
±
1).
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
If
info
= 1
, the transformed matrix pair (
A
,
B
) would be too far from generalized Schur form; the problem is ill-conditioned. (
A
,
B
) may have been partially reordered, and
ilst
points to the first row of the current position of the block being moved.

Product and Performance Information

1

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