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Use interval arithmetic #6

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denisrosset opened this issue Jan 26, 2021 · 0 comments
Open

Use interval arithmetic #6

denisrosset opened this issue Jan 26, 2021 · 0 comments

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@denisrosset
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The idea is to add support for interval arithmetic in representations, so that computations can be verified.

Preliminary work was done in the past in the https://github.com/replab/replab/tree/topic/intlab branch.

Compared to the past, RepLAB has a good implementation of exact arithmetic nowadays. Thus, compared with the previous attempt, we could use INTLAB to certify results in targeted places.

This project could proceed as follows.

  1. Use interval arithmetic in targeted places

Add a strict mode to RepLAB. In that mode, all parent representations have an exact representation of their images available. One starts by computing and caching the corresponding interval matrices, which can then be used to certify the error bounds returned by the various equivariant projections.

Then, one can use the returned error bound to validate the decomposition into irreducible representations, and the various places when generic sampling is used in RepLAB to implement primitives.

  1. Generalize the use of interval arithmetic

As a second step, one could have intval as an additional valid argument alongside exact and double / double_sparse . This would require a more clever caching strategy for the internal data of Rep / SubRep etc.

@denisrosset denisrosset changed the title Add support for interval arithmetic in all representations Use interval arithmetic Dec 7, 2021
@denisrosset denisrosset transferred this issue from replab/replab Dec 7, 2021
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