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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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ctgevc(l) |
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CTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
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SUBROUTINE CTGEVC( |
SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) | ||
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CHARACTER |
HOWMNY, SIDE | ||
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INTEGER |
INFO, LDA, LDB, LDVL, LDVR, M, MM, N | ||
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LOGICAL |
SELECT( * ) | ||
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REAL |
RWORK( * ) | ||
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COMPLEX |
A( LDA, * ), B( LDB, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * ) |
CTGEVC computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B). The right generalized eigenvector x and the left generalized eigenvector y of (A,B) corresponding to a generalized eigenvalue w are defined by:
(A - wB) * x = 0 and y**H * (A - wB) = 0
where y**H denotes the conjugate tranpose of y.
If an eigenvalue w is determined by zero diagonal elements of both A and B, a unit vector is returned as the corresponding eigenvector.
If all
eigenvectors are requested, the routine may either return
the matrices X and/or Y of right or left eigenvectors of
(A,B), or the products Z*X and/or Q*Y, where Z and Q are
input unitary matrices. If (A,B) was obtained from the
generalized Schur factorization of an original pair of
matrices
(A0,B0) = (Q*A*Z**H,Q*B*Z**H),
then Z*X and Q*Y are the matrices of right or left
eigenvectors of A.
SIDE (input) CHARACTER*1
= ’R’: compute
right eigenvectors only;
= ’L’: compute left eigenvectors only;
= ’B’: compute both right and left
eigenvectors.
HOWMNY (input) CHARACTER*1
= ’A’: compute all
right and/or left eigenvectors;
= ’B’: compute all right and/or left
eigenvectors, and backtransform them using the input
matrices supplied in VR and/or VL; = ’S’:
compute selected right and/or left eigenvectors, specified
by the logical array SELECT.
SELECT (input) LOGICAL array, dimension (N)
If HOWMNY=’S’, SELECT specifies the eigenvectors to be computed. If HOWMNY=’A’ or ’B’, SELECT is not referenced. To select the eigenvector corresponding to the j-th eigenvalue, SELECT(j) must be set to .TRUE..
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The upper triangular matrix A.
LDA (input) INTEGER
The leading dimension of array A. LDA >= max(1,N).
B (input) COMPLEX array, dimension (LDB,N)
The upper triangular matrix B. B must have real diagonal elements.
LDB (input) INTEGER
The leading dimension of array B. LDB >= max(1,N).
VL (input/output) COMPLEX array, dimension (LDVL,MM)
On entry, if SIDE = ’L’ or ’B’ and HOWMNY = ’B’, VL must contain an N-by-N matrix Q (usually the unitary matrix Q of left Schur vectors returned by CHGEQZ). On exit, if SIDE = ’L’ or ’B’, VL contains: if HOWMNY = ’A’, the matrix Y of left eigenvectors of (A,B); if HOWMNY = ’B’, the matrix Q*Y; if HOWMNY = ’S’, the left eigenvectors of (A,B) specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. If SIDE = ’R’, VL is not referenced.
LDVL (input) INTEGER
The leading dimension of array VL. LDVL >= max(1,N) if SIDE = ’L’ or ’B’; LDVL >= 1 otherwise.
VR (input/output) COMPLEX array, dimension (LDVR,MM)
On entry, if SIDE = ’R’ or ’B’ and HOWMNY = ’B’, VR must contain an N-by-N matrix Q (usually the unitary matrix Z of right Schur vectors returned by CHGEQZ). On exit, if SIDE = ’R’ or ’B’, VR contains: if HOWMNY = ’A’, the matrix X of right eigenvectors of (A,B); if HOWMNY = ’B’, the matrix Z*X; if HOWMNY = ’S’, the right eigenvectors of (A,B) specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. If SIDE = ’L’, VR is not referenced.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = ’R’ or ’B’; LDVR >= 1 otherwise.
MM (input) INTEGER
The number of columns in the arrays VL and/or VR. MM >= M.
M (output) INTEGER
The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = ’A’ or ’B’, M is set to N. Each selected eigenvector occupies one column.
WORK (workspace) COMPLEX array,
dimension (2*N)
RWORK (workspace) REAL array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal
value.
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ctgevc(l) | |