BBTools

bbsvdopt

Create parameters for computing an SVD.

Syntax

Description

bbsvdopt creates a set of parameters that can be passed to bbsvds and bbsvdf. It tries to determine a good default strategy that suits the computation on hand.

bbsvdopt fill in default values for the parameters that are not set explicitly in opt, but does not not change any fields found in the input-structure. The argument trip may also be given as a field in opt.

Although it is unnecessary to use bbsvdopt explicitly, it is provided as a separate function for the cases where it is necessary to tune the computation. This most common situation is that a computation takes up more memory than is available.

In this case, it is much easier to construct a set of options by building on the defaults rather than starting from scratch. It can also be used to investigate exactly how bbsvds and bbsvdf plan to cope with the given problem.

Input Arguments

Output Arguments

The output is a structure suitable to be passed to bbsvds, bbsvdf, and bbsvdmem.

Parameters

This will only discuss the most important parameters to understand. The full list of parameters are given in the reference documentation.

It is important to set trip correctly. If singular vectors are wanted, and trip is false, then the singular vectors may not be mutually orthogonal. Conversely, if trip is true and the singular vectors are not required, then the computation may use a massive amount of resources (time and memory) without any benefits.

bbsvds returns empty singular matrices if trip=false. This protect a user from getting inaccurate results inadvertently. Note that the actual algorithm can be overruled, irrespective of trip.

Caveat: if singular vectors are computed, and trip is set correctly -- to be precise if dsides=2 -- then the singular triplets are numerically mutually orthogonal. However, due to rounding errors, triplets with very small singular values may be less orthogonal to each other than what can be achieved for most of the triplets. See the reference documentation for an elaboration of this.

By default, disp=1, the routines regularly shows how far they are in the computation. Instead, disp=-1 should quench almost any output, while disp=0 only shows the most important information.

In the other end, disp=2 shows more details more often. It is intended for parameter tuning and debugging.

Normally, BBTools expects that a sufficient amount of memory is present to complete a computation reasonably efficiently. For large-scale problems, it may be necessary to use a strategy that use a reduced amount of memory.

mem is only suggestive, and is the last priority that will be honored. Use bbsvdmem to estimate the actual requirement.

atol specifies the absolute accuracy of the singular values before a triplets is deemed to converge. That is, if the computation returns a singular value, σ, then it satisfies |σ-σ₀|≤atol, where σ₀ is an exact singular value. (This only holds if rounding errors are negligible.)

It is rarely necessary to set this parameter manually, provided bb is correctly implemented. Although it is possible to gain some speed by relaxing the tolerance, the speedup is rarely significant if more than a few singular values are requested. (BBTools must find the vectors to the attainable accuracy in order to extract the remaining triplets).

However, one may decrease atol to a level that is lower than the guaranteed level of accuracy (the default). Although nothing is guaranteed, it is often possible to get surprisingly accurate results. This, however, comes at a somewhat high cost.

Examples

The following code creates a 25000×50000 black-box operator and determine a set of parameters for extracting either 200 singular values or full triplets:

	bb=bbkron(randn(100),randn(250,500));
	opt1=bbsvdopt(bb,200,false);
	opt2=bbsvdopt(bb,200,true)

See Also

bbsvds, bbsvdf, bbsvdmem.

bbsvdmembbsvds