svd: Generic Singular Value Decomposition of a Matrix
In svd: Interfaces to Various State-of-Art SVD and Eigensolvers
svd R Documentation
Generic Singular Value Decomposition of a Matrix
Description
Compute the singular-value decomposition of a real or complex
rectangular matrix.
Usage
propack.svd(X, neig = min(m, n), opts = list())
trlan.svd(X, neig = min(m, n), opts = list(), lambda = NULL, U = NULL)
ztrlan.svd(X, neig = min(m, n), opts = list(), lambda = NULL, U = NULL)
Arguments
X
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 two state-of-art
implementations of truncated SVD.
PROPACK does this via the implicitly restarted Lanczos
bidiagonalization with partial reorthogonalization. nu-TRLAN does the
thick-restart Lanczos eigendecomposition of cross-product 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 PROPACK are:
- kmax
integer, maximum number of iterations.
- dim
integer, dimension of Krylov subspace.
- p
integer, number of shifts per restart.
- maxiter
integer. maximum number of restarts.
- tol
numeric, tolerance level.
- verbose
logical, if 'TRUE', provide verbose output.
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 singular values of 'x'
u
a matrix whose columns contain the left singular vectors of
'X'
v
a matrix whose columns contain the right singular vectors of
'X' (only for 'propack.svd')
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.
Larsen, R. M. (1998). Efficient algorithms for helioseismic inversion.
Ph.D. thesis, University of Aarhus, Denmark.
Korobeynikov, A. (2010) Computation- and space-efficient implementation of
SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268
svd documentation built on July 26, 2023, 5:36 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| svd | R Documentation |
Generic Singular Value Decomposition of a Matrix
Description
Compute the singular-value decomposition of a real or complex rectangular matrix.
Usage
propack.svd(X, neig = min(m, n), opts = list())
trlan.svd(X, neig = min(m, n), opts = list(), lambda = NULL, U = NULL)
ztrlan.svd(X, neig = min(m, n), opts = list(), lambda = NULL, U = NULL)
Arguments
X |
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 two state-of-art implementations of truncated SVD.
PROPACK does this via the implicitly restarted Lanczos bidiagonalization with partial reorthogonalization. nu-TRLAN does the thick-restart Lanczos eigendecomposition of cross-product 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 PROPACK are:
- kmax
integer, maximum number of iterations.
- dim
integer, dimension of Krylov subspace.
- p
integer, number of shifts per restart.
- maxiter
integer. maximum number of restarts.
- tol
numeric, tolerance level.
- verbose
logical, if 'TRUE', provide verbose output.
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 singular values of 'x' |
u |
a matrix whose columns contain the left singular vectors of 'X' |
v |
a matrix whose columns contain the right singular vectors of 'X' (only for 'propack.svd') |
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.
Larsen, R. M. (1998). Efficient algorithms for helioseismic inversion. Ph.D. thesis, University of Aarhus, Denmark.
Korobeynikov, A. (2010) Computation- and space-efficient implementation of SSA. Statistics and Its Interface, Vol. 3, No. 3, Pp. 257-268
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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