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Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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zgeev(l) |
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ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
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SUBROUTINE ZGEEV( |
JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) | ||
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CHARACTER |
JOBVL, JOBVR | ||
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INTEGER |
INFO, LDA, LDVL, LDVR, LWORK, N | ||
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DOUBLE |
PRECISION RWORK( * ) | ||
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COMPLEX*16 |
A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * ) |
ZGEEV computes
for an N-by-N complex nonsymmetric matrix A, the eigenvalues
and, optionally, the left and/or right eigenvectors. The
right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.
JOBVL (input) CHARACTER*1
= ’N’: left
eigenvectors of A are not computed;
= ’V’: left eigenvectors of are computed.
JOBVR (input) CHARACTER*1
= ’N’: right
eigenvectors of A are not computed;
= ’V’: right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A. On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = ’V’, the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = ’N’, VL is not referenced. u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if JOBVL = ’V’, LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = ’V’, the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = ’N’, VR is not referenced. v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if JOBVR = ’V’, LDVR >= N.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
RWORK (workspace) DOUBLE
PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value.
> 0: if INFO = i, the QR algorithm failed to compute all
the eigenvalues, and no eigenvectors have been computed;
elements and i+1:N of W contain eigenvalues which have
converged.
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zgeev(l) | |