Stgexc.f -
subroutine stgexc (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, WORK, LWORK, INFO)
STGEXC
STGEXC
Purpose:
STGEXC reorders the generalized real Schur decomposition of a real
matrix pair (A,B) using an orthogonal equivalence transformation
(A, B) = Q * (A, B) * Z**T,
so that the diagonal block of (A, B) with row index IFST is moved
to row ILST.
(A, B) must be in generalized real Schur canonical form (as returned
by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
diagonal blocks. 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
Parameters:
WANTQ
WANTQ is LOGICAL
.TRUE. : update the left transformation matrix Q;
.FALSE.: do not update Q.
WANTZ
WANTZ is LOGICAL
.TRUE. : update the right transformation matrix Z;
.FALSE.: do not update Z.
N
N is INTEGER
The order of the matrices A and B. N >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the matrix A in generalized real Schur canonical
form.
On exit, the updated matrix A, again in generalized
real Schur canonical form.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B
B is REAL array, dimension (LDB,N)
On entry, the matrix B in generalized real Schur canonical
form (A,B).
On exit, the updated matrix B, again in generalized
real Schur canonical form (A,B).
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
Q
Q is REAL array, dimension (LDZ,N)
On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
On exit, the updated matrix Q.
If WANTQ = .FALSE., Q is not referenced.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1.
If WANTQ = .TRUE., LDQ >= N.
Z
Z is REAL array, dimension (LDZ,N)
On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
On exit, the updated matrix Z.
If WANTZ = .FALSE., Z is not referenced.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1.
If WANTZ = .TRUE., LDZ >= N.
IFST
IFST is INTEGER
ILST
ILST is INTEGER
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.
On exit, if IFST pointed on entry to the second row of
a 2-by-2 block, 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 or -1). 1 <= IFST, ILST <= N.
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO
INFO is INTEGER
=0: successful exit.
<0: if INFO = -i, the i-th argument had an illegal value.
=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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.
References:
[1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
M.S. Moonen et al (eds), Linear Algebra for Large Scale and
Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
Definition at line 220 of file stgexc.f.
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