Contents
dtgexc - reorder the generalized real Schur decomposition of
a real matrix pair (A,B) using an orthogonal equivalence
transformation (A, B) = Q * (A, B) * Z',
SUBROUTINE DTGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, WORK, LWORK, INFO)
INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL WANTQ, WANTZ
DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*),
WORK(*)
SUBROUTINE DTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, WORK, LWORK, INFO)
INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL*8 WANTQ, WANTZ
DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*),
WORK(*)
F95 INTERFACE
SUBROUTINE TGEXC(WANTQ, WANTZ, N, A, [LDA], B, [LDB], Q, [LDQ], Z,
[LDZ], IFST, ILST, [WORK], [LWORK], [INFO])
INTEGER :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL :: WANTQ, WANTZ
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B, Q, Z
SUBROUTINE TGEXC_64(WANTQ, WANTZ, N, A, [LDA], B, [LDB], Q, [LDQ], Z,
[LDZ], IFST, ILST, [WORK], [LWORK], [INFO])
INTEGER(8) :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL(8) :: WANTQ, WANTZ
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B, Q, Z
C INTERFACE
#include <sunperf.h>
void dtgexc(int wantq, int wantz, int n, double *a, int lda,
double *b, int ldb, double *q, int ldq, double *z,
int ldz, int *ifst, int *ilst, int *info);
void dtgexc_64(long wantq, long wantz, long n, double *a,
long lda, double *b, long ldb, double *q, long
ldq, double *z, long ldz, long *ifst, long *ilst,
long *info);
dtgexc reorders the generalized real Schur decomposition of
a real matrix pair (A,B) using an orthogonal equivalence
transformation
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 vec-
tors are updated.
Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
WANTQ (input)
WANTZ (input)
N (input) The order of the matrices A and B. N >= 0.
A (input/output)
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 (input)
The leading dimension of the array A. LDA >=
max(1,N).
B (input/output)
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 (input)
The leading dimension of the array B. LDB >=
max(1,N).
Q (input/output)
On entry, if WANTQ = .TRUE., the orthogonal matrix
Q. On exit, the updated matrix Q. If WANTQ =
.FALSE., Q is not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >= 1.
If WANTQ = .TRUE., LDQ >= N.
Z (input/output)
On entry, if WANTZ = .TRUE., the orthogonal matrix
Z. On exit, the updated matrix Z. If WANTZ =
.FALSE., Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1.
If WANTZ = .TRUE., LDZ >= N.
IFST (input/output)
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 adja-
cent 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.
ILST (input/output)
See the description of IFST.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of the array WORK. 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 (output)
=0: successful exit.
<0: if INFO = -i, the i-th argument had an ille-
gal 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 par-
tially reordered, and ILST points to the first row
of the current position of the block being moved.
Based on contributions by
Bo Kagstrom and Peter Poromaa, Department of Computing
Science,
Umea University, S-901 87 Umea, Sweden.
[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.