dtgexc(3P) Sun Performance Library dtgexc(3P)NAMEdtgexc - reorder the generalized real Schur decomposition of a real
matrix pair (A,B) using an orthogonal equivalence transformation (A,
B) = Q * (A, B) * Z', so that the diagonal block of (A, B) with row
index IFST is moved to row ILST.
SYNOPSIS
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);
PURPOSEdtgexc 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
DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diago‐
nal blocks. B is upper triangular.
Optionally, the matrices Q and Z of generalized Schur vectors 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)'
ARGUMENTS
WANTQ (input) LOGICAL
.TRUE. : update the left transformation matrix Q;
.FALSE.: do not update Q.
WANTZ (input) LOGICAL
.TRUE. : update the right transformation matrix Z;
.FALSE.: do not update Z.
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 general‐
ized 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 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 dif‐
fer 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 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.
FURTHER DETAILS
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.
6 Mar 2009 dtgexc(3P)
