Update discrete curves elastic metric for ratio equal to 1 #1992
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| from geomstats.vectorization import get_batch_shape | ||
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| def elastic_distance(space, point_a, point_b, a=1.0, b=0.5): |
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Should this overwrite elastic_metric.dist ? I guess this depends on the answer to the question: which one is faster 1) our current implementation of dist that uses our classes and the diffeo abstraction, or 2) this function?
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Spot on!
A quick test has shown elastic_distance to be faster (though both are fast).
Still, I have a refactoring in mind for NFoldMetric that is likely to put both on pair or even make the current one faster (it will take advantage of the fact most operations are vectorized for multiple batch dimensions).
I suggest to merge as is, and check this again after the refactoring I'm suggesting for the NFoldMetric.
(We can actually make elastic_distance even faster by computing the length directly from the velocity (since we use the point, we need to do finite differences again inside).)
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We'll check this again later @ninamiolane. I'm merging now as it is useful.
This PR updates discrete curves elastic metric to handle the case where
a / 2b = 1, for any ambient dimension, by using theorem 2.1 of (Bauer, 2022). It also uses the theorem 2.1 equation to improve testing (validates our diffeomorphism-based approach).Notice how easy this implementation is, suggesting our abstractions are not that bad! Here we use:
Diffeo,PullbackDiffeoMetric,ScalarProductMetric,NFoldManifold,NFoldMetric. Besides the specific implementation for the diffeos and the metric in the image space, we are simply reusing code without any specialization.Next steps: extend implementation for ratios other than 1. Only need to implement a different metric for the image space.