1STGEXC(1) LAPACK routine (version 3.2) STGEXC(1)
2
6 STGEXC - reorders the generalized real Schur decomposition of a real
7 matrix pair (A,B) using an orthogonal equivalence transformation (A,
8 B) = Q * (A, B) * Z',
9
11 SUBROUTINE STGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
12 IFST, ILST, WORK, LWORK, INFO )
13 LOGICAL WANTQ, WANTZ
15 INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
17 REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK( * ), Z(
19 LDZ, * )
20
22 STGEXC reorders the generalized real Schur decomposition of a real
23 matrix pair (A,B) using an orthogonal equivalence transformation so
24 that the diagonal block of (A, B) with row index IFST is moved to row
25 ILST.
26 (A, B) must be in generalized real Schur canonical form (as returned by
27 SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diago‐
28 nal blocks. B is upper triangular.
29 Optionally, the matrices Q and Z of generalized Schur vectors are
30 updated.
31 Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
32 Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
33
35 WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix
36 Q;
37 WANTZ (input) LOGICAL
39 N (input) INTEGER
41 The order of the matrices A and B. N >= 0.
42 A (input/output) REAL array, dimension (LDA,N)
44 On entry, the matrix A in generalized real Schur canonical
45 form. On exit, the updated matrix A, again in generalized real
46 Schur canonical form.
47 LDA (input) INTEGER
49 The leading dimension of the array A. LDA >= max(1,N).
50 B (input/output) REAL array, dimension (LDB,N)
52 On entry, the matrix B in generalized real Schur canonical form
53 (A,B). On exit, the updated matrix B, again in generalized
54 real Schur canonical form (A,B).
55 LDB (input) INTEGER
57 The leading dimension of the array B. LDB >= max(1,N).
58 Q (input/output) REAL array, dimension (LDZ,N)
60 On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit,
61 the updated matrix Q. If WANTQ = .FALSE., Q is not referenced.
62 LDQ (input) INTEGER
64 The leading dimension of the array Q. LDQ >= 1. If WANTQ =
65 .TRUE., LDQ >= N.
66 Z (input/output) REAL array, dimension (LDZ,N)
68 On entry, if WANTZ = .TRUE., the orthogonal matrix Z. On exit,
69 the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.
70 LDZ (input) INTEGER
72 The leading dimension of the array Z. LDZ >= 1. If WANTZ =
73 .TRUE., LDZ >= N.
74 IFST (input/output) INTEGER
76 ILST (input/output) INTEGER Specify the reordering of the
77 diagonal blocks of (A, B). The block with row index IFST is
78 moved to row ILST, by a sequence of swapping between adjacent
79 blocks. On exit, if IFST pointed on entry to the second row of
80 a 2-by-2 block, it is changed to point to the first row; ILST
81 always points to the first row of the block in its final posi‐
82 tion (which may differ from its input value by +1 or -1). 1 <=
83 IFST, ILST <= N.
84 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
86 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
87 LWORK (input) INTEGER
89 The dimension of the array WORK. LWORK >= 1 when N <= 1, oth‐
90 erwise LWORK >= 4*N + 16. If LWORK = -1, then a workspace
91 query is assumed; the routine only calculates the optimal size
92 of the WORK array, returns this value as the first entry of the
93 WORK array, and no error message related to LWORK is issued by
94 XERBLA.
95 INFO (output) INTEGER
97 =0: successful exit.
98 <0: if INFO = -i, the i-th argument had an illegal value.
99 =1: The transformed matrix pair (A, B) would be too far from
100 generalized Schur form; the problem is ill- conditioned. (A, B)
101 may have been partially reordered, and ILST points to the first
102 row of the current position of the block being moved.
103
105 Based on contributions by
106 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
107 Umea University, S-901 87 Umea, Sweden.
108 [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
109 Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
110 M.S. Moonen et al (eds), Linear Algebra for Large Scale and
111 Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
112 LAPACK routine (version 3.2) November 2008 STGEXC(1)