1ZTGEVC(1) LAPACK routine (version 3.1) ZTGEVC(1)
2
6 ZTGEVC - some or all of the right and/or left eigenvectors of a pair of
7 complex matrices (S,P), where S and P are upper triangular
8
10 SUBROUTINE ZTGEVC( 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 DOUBLE PRECISION RWORK( * )
20 COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), VR( LDVR, *
22 ), WORK( * )
23
25 ZTGEVC 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
31 as computed by ZGGHRD + ZHGEQZ.
33 The right eigenvector x and the left eigenvector y of (S,P) correspond‐
35 ing to an eigenvalue w are defined by:
36 S*x = w*P*x, (y**H)*S = w*(y**H)*P,
38 where y**H denotes the conjugate tranpose of y.
40 The eigenvalues are not input to this routine, but are computed
41 directly from the diagonal elements of S and P.
42 This routine returns the matrices X and/or Y of right and left eigen‐
44 vectors of (S,P), or the products Z*X and/or Q*Y,
45 where Z and Q are input matrices.
46 If Q and Z are the unitary factors from the generalized Schur factor‐
47 ization of a matrix pair (A,B), then Z*X and Q*Y
48 are the matrices of right and left eigenvectors of (A,B).
49
52 SIDE (input) CHARACTER*1
53 = 'R': compute right eigenvectors only;
54 = 'L': compute left eigenvectors only;
55 = 'B': compute both right and left eigenvectors.
56 HOWMNY (input) CHARACTER*1
58 = 'A': compute all right and/or left eigenvectors;
59 = 'B': compute all right and/or left eigenvectors, backtrans‐
60 formed by the matrices in VR and/or VL; = 'S': compute selected
61 right and/or left eigenvectors, specified by the logical array
62 SELECT.
63 SELECT (input) LOGICAL array, dimension (N)
65 If HOWMNY='S', SELECT specifies the eigenvectors to be com‐
66 puted. The eigenvector corresponding to the j-th eigenvalue is
67 computed if SELECT(j) = .TRUE.. Not referenced if HOWMNY = 'A'
68 or 'B'.
69 N (input) INTEGER
71 The order of the matrices S and P. N >= 0.
72 S (input) COMPLEX*16 array, dimension (LDS,N)
74 The upper triangular matrix S from a generalized Schur factor‐
75 ization, as computed by ZHGEQZ.
76 LDS (input) INTEGER
78 The leading dimension of array S. LDS >= max(1,N).
79 P (input) COMPLEX*16 array, dimension (LDP,N)
81 The upper triangular matrix P from a generalized Schur factor‐
82 ization, as computed by ZHGEQZ. P must have real diagonal ele‐
83 ments.
84 LDP (input) INTEGER
86 The leading dimension of array P. LDP >= max(1,N).
87 VL (input/output) COMPLEX*16 array, dimension (LDVL,MM)
89 On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must con‐
90 tain an N-by-N matrix Q (usually the unitary matrix Q of left
91 Schur vectors returned by ZHGEQZ). On exit, if SIDE = 'L' or
92 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigen‐
93 vectors of (S,P); if HOWMNY = 'B', the matrix Q*Y; if HOWMNY =
94 'S', the left eigenvectors of (S,P) specified by SELECT, stored
95 consecutively in the columns of VL, in the same order as their
96 eigenvalues. Not referenced if SIDE = 'R'.
97 LDVL (input) INTEGER
99 The leading dimension of array VL. LDVL >= 1, and if SIDE =
100 'L' or 'l' or 'B' or 'b', LDVL >= N.
101 VR (input/output) COMPLEX*16 array, dimension (LDVR,MM)
103 On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con‐
104 tain an N-by-N matrix Q (usually the unitary matrix Z of right
105 Schur vectors returned by ZHGEQZ). On exit, if SIDE = 'R' or
106 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigen‐
107 vectors of (S,P); if HOWMNY = 'B', the matrix Z*X; if HOWMNY =
108 'S', the right eigenvectors of (S,P) specified by SELECT,
109 stored consecutively in the columns of VR, in the same order as
110 their eigenvalues. Not referenced if SIDE = 'L'.
111 LDVR (input) INTEGER
113 The leading dimension of the array VR. LDVR >= 1, and if SIDE
114 = 'R' or 'B', LDVR >= N.
115 MM (input) INTEGER
117 The number of columns in the arrays VL and/or VR. MM >= M.
118 M (output) INTEGER
120 The number of columns in the arrays VL and/or VR actually used
121 to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to
122 N. Each selected eigenvector occupies one column.
123 WORK (workspace) COMPLEX*16 array, dimension (2*N)
125 RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
127 INFO (output) INTEGER
129 = 0: successful exit.
130 < 0: if INFO = -i, the i-th argument had an illegal value.
131 LAPACK routine (version 3.1) November 2006 ZTGEVC(1)