WIP: Interpolator class to cache interpolation matrix

[christianbrodbeck]

Addressing #4651

This should be the bare bones of the refactoring.

@larsoner is this enough to make it savable?

And what additional information should we store? The list of bad channels might be good, to make sure it's the same as inst before applying?

[codecov-io]

Codecov Report

Merging #4658 into master will decrease coverage by 0.02%.
The diff coverage is 72.5%.

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[jasmainak]

practically speaking, how much speed gain do you observe for EEG and for MEG by caching these matrices?

[christianbrodbeck]

computing one interpolation matrix takes in the order of seconds for me

[jasmainak]

also for EEG?

[christianbrodbeck]

I haven't looked at EEG, only MEG.

[larsoner]

And what additional information should we store? The list of bad channels might be good, to make sure it's the same as inst before applying?

I think the things we'd need to check would be:

1. The set (and order) of good and bad channel names should need to match exactly for it to operate.
2. The sensor coordinates in the head coordinate frame must match to numerical precision.
3. The origin (for MEG, maybe also EEG?) of the approximation must match to numerical precision.

I think this is enough to guarantee that the same interpolator can be used.

[jasmainak]

okay. IMO, it makes sense only to cache self_dots and cross_dots as EEG interpolation is rather fast

[christianbrodbeck]

@jasmainak If we already go through the trouble of managing a cached object, is there an advantage to not caching the rest? I'm also thinking of epoch-wise interpolation, where you might want to apply an interpolator hundreds of times, so it might be preferable to store the highest level possible.

[jasmainak]

@christianbrodbeck from what I understood, you only store the mapping_matrix but not self_dots and cross_dots in the Interpolator object. The problem with this approach is that it won't help in epoch-wise interpolation if different epochs have different bad channels ... (if you all epochs have the same bad channel, you might as well do the interpolation on the raw object once before epoching)

My first thought had been to compute an n_channels x n_channels mapping matrix and slice it, but it cannot be sliced to give you a mapping matrix of n_channels x n_bads. The math doesn't work out. You can only slice the self_dots and cross_dots and then you have to assemble the mapping_matrix again, but that already saves you significant computation

[larsoner]

You can only slice the self_dots and cross_dots and then you have to assemble the mapping_matrix again, but that already saves you significant computation

If this is indeed the bottleneck, then for you would only ever need one of these for each MEG system, since the electrodes do not move. That would be nice. However, for EEG I doubt it's this simple since it uses some other interpolation mode.

@christianbrodbeck this one is pretty old, perhaps we should close and reconsider the best way to cache the interpolation next time someone hits a need for it?

[larsoner]

I'll close since it seems unlikely that this will be implemented soon, and rebases are needed anyway