1DTGEX2(1) LAPACK auxiliary routine (version 3.2) DTGEX2(1)
2
6 DTGEX2 - swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of
7 size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B)
8 by an orthogonal equivalence transformation
9
11 SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
12 N1, N2, WORK, LWORK, INFO )
13 LOGICAL WANTQ, WANTZ
15 INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
17 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
19 WORK( * ), Z( LDZ, * )
20
22 DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size
23 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by
24 an orthogonal equivalence transformation. (A, B) must be in general‐
25 ized real Schur canonical form (as returned by DGGES), i.e. A is block
26 upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper
27 triangular.
28 Optionally, the matrices Q and Z of generalized Schur vectors are
29 updated.
30 Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
31 Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
32
34 WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix
35 Q;
36 WANTZ (input) LOGICAL
38 N (input) INTEGER
40 The order of the matrices A and B. N >= 0.
41 A (input/output) DOUBLE PRECISION arrays, dimensions (LDA,N)
43 On entry, the matrix A in the pair (A, B). On exit, the updated
44 matrix A.
45 LDA (input) INTEGER
47 The leading dimension of the array A. LDA >= max(1,N).
48 B (input/output) DOUBLE PRECISION arrays, dimensions (LDB,N)
50 On entry, the matrix B in the pair (A, B). On exit, the updated
51 matrix B.
52 LDB (input) INTEGER
54 The leading dimension of the array B. LDB >= max(1,N).
55 Q (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
57 On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit,
58 the updated matrix Q. Not referenced if WANTQ = .FALSE..
59 LDQ (input) INTEGER
61 The leading dimension of the array Q. LDQ >= 1. If WANTQ =
62 .TRUE., LDQ >= N.
63 Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
65 On entry, if WANTZ =.TRUE., the orthogonal matrix Z. On exit,
66 the updated matrix Z. Not referenced if WANTZ = .FALSE..
67 LDZ (input) INTEGER
69 The leading dimension of the array Z. LDZ >= 1. If WANTZ =
70 .TRUE., LDZ >= N.
71 J1 (input) INTEGER
73 The index to the first block (A11, B11). 1 <= J1 <= N.
74 N1 (input) INTEGER
76 The order of the first block (A11, B11). N1 = 0, 1 or 2.
77 N2 (input) INTEGER
79 The order of the second block (A22, B22). N2 = 0, 1 or 2.
80 WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
82 LWORK (input) INTEGER
84 The dimension of the array WORK. LWORK >= MAX( 1, N*(N2+N1),
85 (N2+N1)*(N2+N1)*2 )
86 INFO (output) INTEGER
88 =0: Successful exit
89 >0: If INFO = 1, the transformed matrix (A, B) would be too far
90 from generalized Schur form; the blocks are not swapped and (A,
91 B) and (Q, Z) are unchanged. The problem of swapping is too
92 ill-conditioned. <0: If INFO = -16: LWORK is too small. Appro‐
93 priate value for LWORK is returned in WORK(1).
94
96 Based on contributions by
97 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
98 Umea University, S-901 87 Umea, Sweden.
99 In the current code both weak and strong stability tests are performed.
100 The user can omit the strong stability test by changing the internal
101 logical parameter WANDS to .FALSE.. See ref. [2] for details.
102 [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
103 Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
104 M.S. Moonen et al (eds), Linear Algebra for Large Scale and
105 Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
106 [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
107 Eigenvalues of a Regular Matrix Pair (A, B) and Condition
108 Estimation: Theory, Algorithms and Software,
109 Report UMINF - 94.04, Department of Computing Science, Umea
110 University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working
111 Note 87. To appear in Numerical Algorithms, 1996.
112 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 DTGEX2(1)