the matrix to be decomposed. This can be either normal matrix
or 'external matrix' object (e.g. one, created via 'extmat' function).
neig
number of desired eigentriples
opts
different options for eigensolver. See 'Details' section
for more information
lambda
set of already computed singular values (used for
continuation of the decomposition).
U
matrix of already computed eigenvectors (used for
continuation of the decomposition).
Details
These routines provides an interface to state-of-art
implementation of eigensolver. In particular, nu-TRLAN does the
thick-restart Lanczos eigendecomposition of a matrix.
'opts' is a list of different options which can be passed to the
routines. Note that by default more or less suitable values for these
options are set by the routines automatically.
The options for nu-TRLAN are:
kmax
integer, maximum number of iterations.
maxiter
integer. maximum number of matrix-vector products.
tol
numeric, tolerance level.
verbose
integer, verboseness level.
Value
The returned value is a list with components
d
a vector containing the eigenvalues of 'X'
u
a matrix whose columns contain the eigenvectors of
'X'
References
Wu, K. and Simon, H. (2000). Thick-restart Lanczos method for
large symmetric eigenvalue problems. SIAM J. Matrix Anal. Appl. 22, 2, 602-616.
Yamazaki, I., Bai, Z., Simon, H., Wang, L.-W., and Wu,
K. (2008). Adaptive projection subspace dimension for the thick
restart Lanczos method. Tech. rep., Lawrence Berkeley National
Laboratory, University of California, One Cyclotron road, Berkeley, California 94720.
Korobeynikov, A. (2010) Computation- and space-efficient implementation of
SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268