1CGEEV(1) LAPACK driver routine (version 3.2) CGEEV(1)
2
6 CGEEV - computes for an N-by-N complex nonsymmetric matrix A, the ei‐
7 genvalues and, optionally, the left and/or right eigenvectors
8
10 SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK,
11 LWORK, RWORK, INFO )
12 CHARACTER JOBVL, JOBVR
14 INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
16 REAL RWORK( * )
18 COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ),
20 WORK( * )
21
23 CGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigen‐
24 values and, optionally, the left and/or right eigenvectors. The right
25 eigenvector v(j) of A satisfies
26 A * v(j) = lambda(j) * v(j)
27 where lambda(j) is its eigenvalue.
28 The left eigenvector u(j) of A satisfies
29 u(j)**H * A = lambda(j) * u(j)**H
30 where u(j)**H denotes the conjugate transpose of u(j).
31 The computed eigenvectors are normalized to have Euclidean norm equal
32 to 1 and largest component real.
33
35 JOBVL (input) CHARACTER*1
36 = 'N': left eigenvectors of A are not computed;
37 = 'V': left eigenvectors of are computed.
38 JOBVR (input) CHARACTER*1
40 = 'N': right eigenvectors of A are not computed;
41 = 'V': right eigenvectors of A are computed.
42 N (input) INTEGER
44 The order of the matrix A. N >= 0.
45 A (input/output) COMPLEX array, dimension (LDA,N)
47 On entry, the N-by-N matrix A. On exit, A has been overwrit‐
48 ten.
49 LDA (input) INTEGER
51 The leading dimension of the array A. LDA >= max(1,N).
52 W (output) COMPLEX array, dimension (N)
54 W contains the computed eigenvalues.
55 VL (output) COMPLEX array, dimension (LDVL,N)
57 If JOBVL = 'V', the left eigenvectors u(j) are stored one after
58 another in the columns of VL, in the same order as their eigen‐
59 values. If JOBVL = 'N', VL is not referenced. u(j) = VL(:,j),
60 the j-th column of VL.
61 LDVL (input) INTEGER
63 The leading dimension of the array VL. LDVL >= 1; if JOBVL =
64 'V', LDVL >= N.
65 VR (output) COMPLEX array, dimension (LDVR,N)
67 If JOBVR = 'V', the right eigenvectors v(j) are stored one
68 after another in the columns of VR, in the same order as their
69 eigenvalues. If JOBVR = 'N', VR is not referenced. v(j) =
70 VR(:,j), the j-th column of VR.
71 LDVR (input) INTEGER
73 The leading dimension of the array VR. LDVR >= 1; if JOBVR =
74 'V', LDVR >= N.
75 WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
77 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
78 LWORK (input) INTEGER
80 The dimension of the array WORK. LWORK >= max(1,2*N). For
81 good performance, LWORK must generally be larger. If LWORK =
82 -1, then a workspace query is assumed; the routine only calcu‐
83 lates the optimal size of the WORK array, returns this value as
84 the first entry of the WORK array, and no error message related
85 to LWORK is issued by XERBLA.
86 RWORK (workspace) REAL array, dimension (2*N)
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value.
92 > 0: if INFO = i, the QR algorithm failed to compute all the
93 eigenvalues, and no eigenvectors have been computed; elements
94 and i+1:N of W contain eigenvalues which have converged.
95 LAPACK driver routine (version 3.N2o)vember 2008 CGEEV(1)