1CTGEXC(1) LAPACK routine (version 3.1) CTGEXC(1)
2
6 CTGEXC - the generalized Schur decomposition of a complex matrix pair
7 (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B)
8 * Z', so that the diagonal block of (A, B) with row index IFST is moved
9 to row ILST
10
12 SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
13 IFST, ILST, INFO )
14 LOGICAL WANTQ, WANTZ
16 INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
18 COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), Z( LDZ, * )
20
22 CTGEXC reorders the generalized Schur decomposition of a complex matrix
23 pair (A,B), using an unitary equivalence transformation (A, B) := Q *
24 (A, B) * Z', so that the diagonal block of (A, B) with row index IFST
25 is moved to row ILST.
26 (A, B) must be in generalized Schur canonical form, that is, A and B
28 are both upper triangular.
29 Optionally, the matrices Q and Z of generalized Schur vectors are
31 updated.
32 Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
34 Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
35
38 WANTQ (input) LOGICAL
39 WANTZ (input) LOGICAL
41 N (input) INTEGER
43 The order of the matrices A and B. N >= 0.
44 A (input/output) COMPLEX array, dimension (LDA,N)
46 On entry, the upper triangular matrix A in the pair (A, B). On
47 exit, the updated matrix A.
48 LDA (input) INTEGER
50 The leading dimension of the array A. LDA >= max(1,N).
51 B (input/output) COMPLEX array, dimension (LDB,N)
53 On entry, the upper triangular matrix B in the pair (A, B). On
54 exit, the updated matrix B.
55 LDB (input) INTEGER
57 The leading dimension of the array B. LDB >= max(1,N).
58 Q (input/output) COMPLEX array, dimension (LDZ,N)
60 On entry, if WANTQ = .TRUE., the unitary 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) COMPLEX array, dimension (LDZ,N)
68 On entry, if WANTZ = .TRUE., the unitary 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) 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.
80 INFO (output) INTEGER
82 =0: Successful exit.
83 <0: if INFO = -i, the i-th argument had an illegal value.
84 =1: The transformed matrix pair (A, B) would be too far from
85 generalized Schur form; the problem is ill- conditioned. (A, B)
86 may have been partially reordered, and ILST points to the first
87 row of the current position of the block being moved.
88
90 Based on contributions by
91 Bo Kagstrom and Peter Poromaa, Department of Computing Science,
92 Umea University, S-901 87 Umea, Sweden.
93 [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
95 Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
96 M.S. Moonen et al (eds), Linear Algebra for Large Scale and
97 Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
98 [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
100 Eigenvalues of a Regular Matrix Pair (A, B) and Condition
101 Estimation: Theory, Algorithms and Software, Report
102 UMINF - 94.04, Department of Computing Science, Umea University,
103 S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
104 To appear in Numerical Algorithms, 1996.
105 [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
107 for Solving the Generalized Sylvester Equation and Estimating the
108 Separation between Regular Matrix Pairs, Report UMINF - 93.23,
109 Department of Computing Science, Umea University, S-901 87 Umea,
110 Sweden, December 1993, Revised April 1994, Also as LAPACK working
111 Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
112 1996.
113 LAPACK routine (version 3.1) November 2006 CTGEXC(1)