Support additional LinearSystem normalizers

arvoelke / nengolib

Nengo library of additional extensions

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Support additional LinearSystem normalizers #42

Open arvoelke opened 8 years ago

arvoelke commented 8 years ago

[x] L1-Norm (#43)
[x] H2-Norm (#103)
[x] Balanced Realization (#85)
[x] Identity realization (#103)
[ ] ~~Controllable~~
[ ] ~~Observable~~
[ ] Mechanism for pretending the input is something + arbitrary filter
[x] Document in LinearNetwork notebook

arvoelke commented 8 years ago

Also implemenet/document sphere versus cube, and relationship to correlation between states and shared worst-case inputs.

arvoelke commented 8 years ago

Also see #50.

arvoelke commented 7 years ago

Really, all of the normalizers should be wrappers that invoke some method that returns a similarity transformation. This would be the most general way of giving the user an understanding of how things have changed (i.e., the change of the basis) which they should know in order to understand the encoding. Scaling by a radii vector is a diagonal transform. Scaling each dimension by the same radius can (and should?) be abstracted away and done separately.

arvoelke commented 7 years ago

The above could also be used in the following way: apply the similarity transform T to F obtained by normalizing F*H for some input filter H that corresponds to a transfer function from full-spectrum white noise to a typical input signal for example.

arvoelke commented 7 years ago

After #103 it is harder to do controllable/observable as a realizer (formerly as a normalizer), but this is a nonissue because you can just pass sys.controllable to the LinearNetwork for example. Documentation in the notebook is the main thing that is lacking.