GNU/Linux man pages
Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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sgeev(l) |
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SGEEV - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
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SUBROUTINE SGEEV( |
JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO ) | ||
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CHARACTER |
JOBVL, JOBVR | ||
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INTEGER |
INFO, LDA, LDVL, LDVR, LWORK, N | ||
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REAL |
A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), WI( * ), WORK( * ), WR( * ) |
SGEEV computes
for an N-by-N real 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 A 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) REAL 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).
WR (output) REAL array, dimension (N)
WI (output) REAL array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
VL (output) REAL 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. If the j-th
eigenvalue is real, then u(j) = VL(:,j), the j-th column of
VL. If the j-th and (j+1)-st eigenvalues form a complex
conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
u(j+1) = VL(:,j) - i*VL(:,j+1).
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if JOBVL = ’V’, LDVL >= N.
VR (output) REAL 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. If the j-th
eigenvalue is real, then v(j) = VR(:,j), the j-th column of
VR. If the j-th and (j+1)-st eigenvalues form a complex
conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
v(j+1) = VR(:,j) - i*VR(:,j+1).
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if JOBVR = ’V’, LDVR >= N.
WORK (workspace/output) REAL 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(1,3*N), and if JOBVL = ’V’ or JOBVR = ’V’, LWORK >= 4*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.
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 i+1:N of WR and WI contain eigenvalues which have
converged.
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sgeev(l) | |