1ZTGEX2(1)           LAPACK auxiliary routine (version 3.1)           ZTGEX2(1)
2
3
4

NAME

6       ZTGEX2 - adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
7

SYNOPSIS

9       SUBROUTINE ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1,
10                          INFO )
11
12           LOGICAL        WANTQ, WANTZ
13
14           INTEGER        INFO, J1, LDA, LDB, LDQ, LDZ, N
15
16           COMPLEX*16     A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
17

PURPOSE

19       ZTGEX2 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
23       (A, B) must be in generalized Schur canonical form, that is,  A  and  B
24       are both upper triangular.
25
26       Optionally,  the  matrices  Q  and  Z  of generalized Schur vectors are
27       updated.
28
29              Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
30              Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
31
32
33

ARGUMENTS

35       WANTQ   (input) LOGICAL
36
37       WANTZ   (input) LOGICAL
38
39       N       (input) INTEGER
40               The order of the matrices A and B. N >= 0.
41
42       A       (input/output) COMPLEX*16 arrays, dimensions (LDA,N)
43               On entry, the matrix A in  the  pair  (A,  B).   On  exit,  the
44               updated matrix A.
45
46       LDA     (input)  INTEGER
47               The leading dimension of the array A. LDA >= max(1,N).
48
49       B       (input/output) COMPLEX*16 arrays, dimensions (LDB,N)
50               On  entry,  the  matrix  B  in  the  pair (A, B).  On exit, the
51               updated matrix B.
52
53       LDB     (input)  INTEGER
54               The leading dimension of the array B. LDB >= max(1,N).
55
56       Q       (input/output) COMPLEX*16 array, dimension (LDZ,N)
57               If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,  the
58               updated matrix Q.  Not referenced if WANTQ = .FALSE..
59
60       LDQ     (input) INTEGER
61               The  leading  dimension  of  the  array Q. LDQ >= 1; If WANTQ =
62               .TRUE., LDQ >= N.
63
64       Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
65               If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,  the
66               updated matrix Z.  Not referenced if WANTZ = .FALSE..
67
68       LDZ     (input) INTEGER
69               The  leading  dimension  of  the  array Z. LDZ >= 1; If WANTZ =
70               .TRUE., LDZ >= N.
71
72       J1      (input) INTEGER
73               The index to the first block (A11, B11).
74
75       INFO    (output) INTEGER
76               =0:  Successful exit.
77               =1:  The transformed matrix pair (A, B) would be too  far  from
78               generalized Schur form; the problem is ill- conditioned.
79

FURTHER DETAILS

81       Based on contributions by
82          Bo Kagstrom and Peter Poromaa, Department of Computing Science,
83          Umea University, S-901 87 Umea, Sweden.
84
85       In the current code both weak and strong stability tests are performed.
86       The user can omit the strong stability test by  changing  the  internal
87       logical parameter WANDS to .FALSE.. See ref. [2] for details.
88
89       [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
90           Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
91           M.S. Moonen et al (eds), Linear Algebra for Large Scale and
92           Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
93
94       [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
95           Eigenvalues of a Regular Matrix Pair (A, B) and Condition
96           Estimation: Theory, Algorithms and Software, Report UMINF-94.04,
97           Department of Computing Science, Umea University, S-901 87 Umea,
98           Sweden, 1994. Also as LAPACK Working Note 87. To appear in
99           Numerical Algorithms, 1996.
100
101
102
103
104 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZTGEX2(1)