Compute a set of leading singular values or triplets.
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.
sig = bbsvds(bb,L)  
[U,S,V] = bbsvds(bb,L)  
[U,S,V] = bbsvds(bb,L,opt)  
[U,S,V,flag,h] = bbsvds(bb,L,opt) 
bbsvds
is designed to replace
in the case where the leading singular triplets are desired. It provides a simpler
interface than bbsvdf
, but is not as flexible
or efficient.
This function is capable of extracting singular values that exceeds the memory required to store the individual triplets. Unlike most other software, this does not come at a loss of accuracy of the small singular values.
Note: unlike
,
bbsvds
specifically exploits the case where only singular values are
required. If L
is large, it may be significantly more expensive to compute
singular triplets than singular values alone.
bb 
Blackbox operator or matrix 
L 
The number of singular values or triplets to compute 
opt
 Struct with options 
opt
is a structure with options that control the computation of
the SVD. The most useful options are described in
bbsvdopt
(the full list is given
in the reference documentation).
The parameter trip
can be used to suppress the output of the
singular vectors. This is only useful if you need flag
or h
.
In this case the matrices U
and V
will be empty.
In addition bbsvds
takes a few additional options.
Parameter:  sort [true  false ]


Determine if triplets will sorted. 
If sort=false
, the triplets appears in the order they converged.
This may be useful if you suspect that some triplets in a cluster was missed.
The default, sort=true
, is to sort the triplets in order of
decreasing singular values before returning the result.
Parameter:  tol [scalar]


Alternative tolerance setting (not recommended for general use). 
Specifies a tolerance level relative to a bound on the largest singular value of
bb
. This is different, but comparable, to svds
. This option
only works if bb
is a Matlab matrix, and its use is not
recommended. Please use atol
, which overrides tol
if present,
instead.
Setting tol
is equivalent to setting
atol=tol*sqrt(norm(bb,1)*norm(bb,inf))
.
Note: the default behaviour of bbsvds
is to compute the result as accurately
as possible. It is rarely necessary to specify the tolerance explicitly.
With a single output, sig
is a columnvector containing the
leading singular values of bb
.
With multiple outputs, the result in U
, S
, and
V
follows the same convention as
.
flag
is zero if all the requested triplets was computed, and nonzero
otherwise.
h
is a structure that contains internal information resulting from
the computation. It may be useful for debugging, and the contents is subject to change.
If bb
is a counting blackbox (created with
bbcount
), then the number of computed matrixvector
products is recorded after each triplet converges. When the computation has been completed,
the counts can be extracted using bbcountstat
:
stat=bbcountstat(bb,'bbsvds_count')

stat
is array of counter structs such that stat(k)
is the status
returned by bbcountstat
after k
triplets converged.
bbsvds
does not reset the operation count of the operator before
it starts. If you want to count only the operations used by bbsvds
,
you must run bbcountreset
before
bbsvds
:
stat=bbcountreset(bb)

The matrix west0479
is a 479by479 sparse matrix bundled with MATLAB. You may
compare the result of the following computations.
load west0479; 
svds
uses
bbsvdf
to compute the SVD. It allocates storage for
the singular triplets (if requested), and set up a callback function that copy the
SVD into these matrices as they are computed. After completing the computation, it
optionally sort the result in order of decreasing singular values.
If bb
is a counting blackbox (created with
bbcount
it also records the statistics as each
triplet converges.