BBTools
Compute a set of leading singular triplets of a black-box operator.
NOTE: triplets are not guaranteed to convergence in any particular order. If you need a predetermined number of the dominating triplets of the operator, please compute a few extra triplets and discard any unwanted triplets.
h=bbsvdf(bb,f,...) | |
h=bbsvdf(bb,opt,f,...) |
This is a medium-level routine for computing some leading singular triplets of a black-box matrix. For a high-level alternative see bbsvds.
As a result of design decisions meant to minimize memory consumption, the function
bbsvdf may seem complicated to use. It is best used as a subroutine for
functions at a higher level. You should evaluate the package using
bbsvds to determine whether bbsvdf is
worthwhile.
bb |
Black-box operator or matrix |
f |
to callback function. |
opt
| Struct with options |
The call-back function, f, is called with the following syntax:
done = f(u,v,sig,...) |
The trailing arguments are the same as those given to bbsvdf.
The return-value done should be true if bbsvdf
should stop further processing and false otherwise.
The idea of returning triplets to a user-defined function may be unfamiliar. However, many applications can use the triplets one at a time and then dispose of them (e.g. solving equations). This scheme allows one to use more triplets than will fit in memory.
opt, if given, is a structure that allows one to tune the computation.
This should not normally be necessary unless memory consumption is an issue.
See bbsvdopt for a description of the most useful
options (the full list is given in the
reference documentation).
The SVD resulting from the computation is returned using the call-back function
f. This is the main result of the computation.
h is a structure with internal data used by bbsvdf.
It is highly unlikely that a normal user would ever use the result, which contains data such
as unconverged subspaces. The exact format of this result is subject to change and should
not be relied upon.
In short, only highly adventurous people who thinks they know what they are doing, and people trying to debug the package should use this output.
In exact arithmetics the algorithm would be equivalent to Lanczos Bidiagonalization [15] with implicit restarting [17]. To battle rounding errors it also uses reorthogonalization, using a scheme that falls somewhere in between full reorthogonalization and selective reorthogonalization, depending on the deflation strategy.
[15] Christopher Conway Paige and Michael A. Saunders. LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Transactions on Mathematical Software (TOMS), 8(1):43-71, 1982. ACM Press. ISSN: 0098-3500. (Paper)
[17] Danny C. Sorensen. Implicitly restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations. Published in 1996. Reference number: TR-96-40. (Technical report: )
bbsolveoptbbsvdmem