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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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ctrevc(l) |
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CTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
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SUBROUTINE CTREVC( |
SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) | ||
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CHARACTER |
HOWMNY, SIDE | ||
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INTEGER |
INFO, LDT, LDVL, LDVR, M, MM, N | ||
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LOGICAL |
SELECT( * ) | ||
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REAL |
RWORK( * ) | ||
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COMPLEX |
T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * ) |
CTREVC computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by:
T*x = w*x, y’*T = w*y’
where y’ denotes the conjugate transpose of the vector y.
If all
eigenvectors are requested, the routine may either return
the matrices X and/or Y of right or left eigenvectors of T,
or the products Q*X and/or Q*Y, where Q is an input unitary
matrix. If T was obtained from the Schur factorization of an
original matrix A = Q*T*Q’, then Q*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 matrix T. N >= 0.
T (input/output) COMPLEX array, dimension (LDT,N)
The upper triangular matrix T. T is modified, but restored on exit.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= 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 Schur vectors returned by CHSEQR). On exit, if SIDE = ’L’ or ’B’, VL contains: if HOWMNY = ’A’, the matrix Y of left eigenvectors of T; VL is lower triangular. The i-th column VL(i) of VL is the eigenvector corresponding to T(i,i). if HOWMNY = ’B’, the matrix Q*Y; if HOWMNY = ’S’, the left eigenvectors of T 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 the 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 Q of Schur vectors returned by CHSEQR). On exit, if SIDE = ’R’ or ’B’, VR contains: if HOWMNY = ’A’, the matrix X of right eigenvectors of T; VR is upper triangular. The i-th column VR(i) of VR is the eigenvector corresponding to T(i,i). if HOWMNY = ’B’, the matrix Q*X; if HOWMNY = ’S’, the right eigenvectors of T 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 (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
The algorithm used in this program is basically backward (forward) substitution, with scaling to make the the code robust against possible overflow.
Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|.
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ctrevc(l) | |