ctgexc(3P) Sun Performance Library ctgexc(3P)NAMEctgexc - reorder the generalized Schur decomposition of a complex
matrix pair (A,B), using an unitary 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 CTGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, INFO)
COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
LOGICAL WANTQ, WANTZ
SUBROUTINE CTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, INFO)
COMPLEX A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
LOGICAL*8 WANTQ, WANTZ
F95 INTERFACE
SUBROUTINE TGEXC(WANTQ, WANTZ, [N], A, [LDA], B, [LDB], Q, [LDQ], Z,
[LDZ], IFST, ILST, [INFO])
COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
INTEGER :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
LOGICAL :: WANTQ, WANTZ
SUBROUTINE TGEXC_64(WANTQ, WANTZ, [N], A, [LDA], B, [LDB], Q, [LDQ],
Z, [LDZ], IFST, ILST, [INFO])
COMPLEX, DIMENSION(:,:) :: A, B, Q, Z
INTEGER(8) :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, INFO
LOGICAL(8) :: WANTQ, WANTZ
C INTERFACE
#include <sunperf.h>
void ctgexc(int wantq, int wantz, int n, complex *a, int lda, complex
*b, int ldb, complex *q, int ldq, complex *z, int ldz, int
*ifst, int *ilst, int *info);
void ctgexc_64(long wantq, long wantz, long n, complex *a, long lda,
complex *b, long ldb, complex *q, long ldq, complex *z, long
ldz, long *ifst, long *ilst, long *info);
PURPOSEctgexc reorders the generalized Schur decomposition of a complex matrix
pair (A,B), using an unitary 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.
(A, B) must be in generalized Schur canonical form, that is, A and B
are both 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 upper triangular matrix A in the pair (A, B).
On exit, the updated matrix A.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
B (input/output)
On entry, the upper triangular matrix B in the pair (A, B).
On exit, the updated matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
Q (input/output)
On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit,
the updated matrix Q. If WANTQ = .FALSE., Q is not refer‐
enced.
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 unitary matrix Z. On exit,
the updated matrix Z. If WANTZ = .FALSE., Z is not refer‐
enced.
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.
ILST (input/output)
See the description of IFST.
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.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
Eigenvalues of a Regular Matrix Pair (A, B) and Condition
Estimation: Theory, Algorithms and Software, Report
UMINF - 94.04, Department of Computing Science, Umea University,
S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
To appear in Numerical Algorithms, 1996.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
for Solving the Generalized Sylvester Equation and Estimating the
Separation between Regular Matrix Pairs, Report UMINF - 93.23,
Department of Computing Science, Umea University, S-901 87 Umea,
Sweden, December 1993, Revised April 1994, Also as LAPACK working
Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
1996.
6 Mar 2009 ctgexc(3P)
