1CTGEX2(1) LAPACK auxiliary routine (version 3.2) CTGEX2(1)
2
6 CTGEX2 - swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
7
9 SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
10 INFO )
11 LOGICAL WANTQ, WANTZ
13 INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, N
15 COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
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19 CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) in
20 an upper triangular matrix pair (A, B) by an unitary equivalence trans‐
21 formation.
22 (A, B) must be in generalized Schur canonical form, that is, A and B
23 are both upper triangular.
24 Optionally, the matrices Q and Z of generalized Schur vectors are
25 updated.
26 Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
27 Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
28
30 WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix
31 Q;
32 WANTZ (input) LOGICAL
34 N (input) INTEGER
36 The order of the matrices A and B. N >= 0.
37 A (input/output) COMPLEX arrays, dimensions (LDA,N)
39 On entry, the matrix A in the pair (A, B). On exit, the
40 updated matrix A.
41 LDA (input) INTEGER
43 The leading dimension of the array A. LDA >= max(1,N).
44 B (input/output) COMPLEX arrays, dimensions (LDB,N)
46 On entry, the matrix B in the pair (A, B). On exit, the
47 updated matrix B.
48 LDB (input) INTEGER
50 The leading dimension of the array B. LDB >= max(1,N).
51 Q (input/output) COMPLEX array, dimension (LDZ,N)
53 If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, the
54 updated matrix Q. Not referenced if WANTQ = .FALSE..
55 LDQ (input) INTEGER
57 The leading dimension of the array Q. LDQ >= 1; If WANTQ =
58 .TRUE., LDQ >= N.
59 Z (input/output) COMPLEX array, dimension (LDZ,N)
61 If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, the
62 updated matrix Z. Not referenced if WANTZ = .FALSE..
63 LDZ (input) INTEGER
65 The leading dimension of the array Z. LDZ >= 1; If WANTZ =
66 .TRUE., LDZ >= N.
67 J1 (input) INTEGER
69 The index to the first block (A11, B11).
70 INFO (output) INTEGER
72 =0: Successful exit.
73 =1: The transformed matrix pair (A, B) would be too far from
74 generalized Schur form; the problem is ill- conditioned.
75
77 Based on contributions by
78 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
79 Umea University, S-901 87 Umea, Sweden.
80 In the current code both weak and strong stability tests are performed.
81 The user can omit the strong stability test by changing the internal
82 logical parameter WANDS to .FALSE.. See ref. [2] for details.
83 [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
84 Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
85 M.S. Moonen et al (eds), Linear Algebra for Large Scale and
86 Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
87 [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
88 Eigenvalues of a Regular Matrix Pair (A, B) and Condition
89 Estimation: Theory, Algorithms and Software, Report UMINF-94.04,
90 Department of Computing Science, Umea University, S-901 87 Umea,
91 Sweden, 1994. Also as LAPACK Working Note 87. To appear in
92 Numerical Algorithms, 1996.
93 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 CTGEX2(1)