1CTGEVC(1) LAPACK routine (version 3.2) CTGEVC(1)
2
6 CTGEVC - computes some or all of the right and/or left eigenvectors of
7 a pair of complex matrices (S,P), where S and P are upper triangular
8
10 SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL,
11 VR, LDVR, MM, M, WORK, RWORK, INFO )
12 CHARACTER HOWMNY, SIDE
14 INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N
16 LOGICAL SELECT( * )
18 REAL RWORK( * )
20 COMPLEX P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, *
22 ), WORK( * )
23
25 CTGEVC computes some or all of the right and/or left eigenvectors of a
26 pair of complex matrices (S,P), where S and P are upper triangular.
27 Matrix pairs of this type are produced by the generalized Schur factor‐
28 ization of a complex matrix pair (A,B):
29 A = Q*S*Z**H, B = Q*P*Z**H
30 as computed by CGGHRD + CHGEQZ.
31 The right eigenvector x and the left eigenvector y of (S,P) correspond‐
32 ing to an eigenvalue w are defined by:
33 S*x = w*P*x, (y**H)*S = w*(y**H)*P,
34 where y**H denotes the conjugate tranpose of y.
35 The eigenvalues are not input to this routine, but are computed
36 directly from the diagonal elements of S and P.
37 This routine returns the matrices X and/or Y of right and left eigen‐
38 vectors of (S,P), or the products Z*X and/or Q*Y,
39 where Z and Q are input matrices.
40 If Q and Z are the unitary factors from the generalized Schur factor‐
41 ization of a matrix pair (A,B), then Z*X and Q*Y
42 are the matrices of right and left eigenvectors of (A,B).
43
45 SIDE (input) CHARACTER*1
46 = 'R': compute right eigenvectors only;
47 = 'L': compute left eigenvectors only;
48 = 'B': compute both right and left eigenvectors.
49 HOWMNY (input) CHARACTER*1
51 = 'A': compute all right and/or left eigenvectors;
52 = 'B': compute all right and/or left eigenvectors, backtrans‐
53 formed by the matrices in VR and/or VL; = 'S': compute selected
54 right and/or left eigenvectors, specified by the logical array
55 SELECT.
56 SELECT (input) LOGICAL array, dimension (N)
58 If HOWMNY='S', SELECT specifies the eigenvectors to be com‐
59 puted. The eigenvector corresponding to the j-th eigenvalue is
60 computed if SELECT(j) = .TRUE.. Not referenced if HOWMNY = 'A'
61 or 'B'.
62 N (input) INTEGER
64 The order of the matrices S and P. N >= 0.
65 S (input) COMPLEX array, dimension (LDS,N)
67 The upper triangular matrix S from a generalized Schur factor‐
68 ization, as computed by CHGEQZ.
69 LDS (input) INTEGER
71 The leading dimension of array S. LDS >= max(1,N).
72 P (input) COMPLEX array, dimension (LDP,N)
74 The upper triangular matrix P from a generalized Schur factor‐
75 ization, as computed by CHGEQZ. P must have real diagonal ele‐
76 ments.
77 LDP (input) INTEGER
79 The leading dimension of array P. LDP >= max(1,N).
80 VL (input/output) COMPLEX array, dimension (LDVL,MM)
82 On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must con‐
83 tain an N-by-N matrix Q (usually the unitary matrix Q of left
84 Schur vectors returned by CHGEQZ). On exit, if SIDE = 'L' or
85 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigen‐
86 vectors of (S,P); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY =
87 'S', the left eigenvectors of (S,P) specified by SELECT, stored
88 consecutively in the columns of VL, in the same order as their
89 eigenvalues. Not referenced if SIDE = 'R'.
90 LDVL (input) INTEGER
92 The leading dimension of array VL. LDVL >= 1, and if SIDE =
93 'L' or 'l' or 'B' or 'b', LDVL >= N.
94 VR (input/output) COMPLEX array, dimension (LDVR,MM)
96 On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con‐
97 tain an N-by-N matrix Q (usually the unitary matrix Z of right
98 Schur vectors returned by CHGEQZ). On exit, if SIDE = 'R' or
99 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigen‐
100 vectors of (S,P); if HOWMNY = 'B', the matrix Z*X; if HOWMNY =
101 'S', the right eigenvectors of (S,P) specified by SELECT,
102 stored consecutively in the columns of VR, in the same order as
103 their eigenvalues. Not referenced if SIDE = 'L'.
104 LDVR (input) INTEGER
106 The leading dimension of the array VR. LDVR >= 1, and if SIDE
107 = 'R' or 'B', LDVR >= N.
108 MM (input) INTEGER
110 The number of columns in the arrays VL and/or VR. MM >= M.
111 M (output) INTEGER
113 The number of columns in the arrays VL and/or VR actually used
114 to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to
115 N. Each selected eigenvector occupies one column.
116 WORK (workspace) COMPLEX array, dimension (2*N)
118 RWORK (workspace) REAL array, dimension (2*N)
120 INFO (output) INTEGER
122 = 0: successful exit.
123 < 0: if INFO = -i, the i-th argument had an illegal value.
124 LAPACK routine (version 3.2) November 2008 CTGEVC(1)