numeric or complex square Matrix inheriting from class "Matrix".
Missing values (NAs) are not allowed.
OPTIONAL ARGUMENTS:
vectors:
either a logical value telling whether or not to compute eigenvectors, or
else a logical vector of length 2 telling whether or not to compute the
left and right eigenvectors, respectively. The default is to compute both
sets of eigenvectors.
balance:
either a logical value or a logical vector of length 2 telling whether or not
to perform permutations on the matrix to make it more nearly upper triangular
and to perform diagonal scaling to make the rows and columns more equal in
norm, respectively, prior to computing the eigenvalue decomposition.
Column permutation will not change the condition numbers
(in exact arithmetic), but diagonal scaling will.
Both may affect the performance of the algorithm.
By default, no balancing is performed.
rcond:
either a logical value or a logical vector of length 2 telling whether or
not to compute reciprocal condition numbers for the eigenvalues and right
eigenvectors, respectively, and return them as attributes.
By default, neither is computed.
schur:
tells whether or not to return a matrix whose upper portion contains the
Schur form (of the balanced matrix if balancing is requested) as an
attribute. By default, the Schur form is not returned.
tune:
a integer vector or list of named tuning parameters that may affect
computational efficiency. The relevant parameters are
NB, NBMIN, NX, NS, and MAXB, as described in .laenv.
The default is to use the settings in .laenv, which are initialized in
S-Plus but may be changed by the user.
workspace:
workspace provided to the underlying software.
The default is to use the minimum allowed value.
The optimal workspace for the problem (for the given tune specifications) is
included as part of the output attributes.
VALUE:
The result is an object of class c("eigen.Matrix", "decomp").
When the matrix is real, and there are complex eigenvalues, the
corresponding eigenvectors will be represented by their real and imaginary
parts, respectively, rather than by complex conjugate pairs.
They can be transformed into matrices of eigenvectors via the function
expand.
Attributes include the one-norm of the balanced matrix, balancing information
(if balancing is requested via balance), condition numbers (if requested via
rcond), a matrix containing the Schur form (if requested via schur),
workspace information, and a copy of the call to eigen.Matrix.
DETAILS:
Based on the functions dgeevx and zgeevx from Lapack (Anderson et al. 1994).
Parameters in tune may affect performance and workspace requirements,
but the optimal settings are both machine and problem dependent.
Users may want to experiment with tune (see Anderson et al., p. 72-74) to
obtain improved performance.
REFERENCES:
Anderson, E., et al. (1994).
LAPACK User's Guide,
2nd edition, SIAM, Philadelphia.