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Improve numerical stability and robustness of enumpoly - #1057
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The branch-and-bound subdivision in `enumpoly` is bounded by a minimum rectangle size. However, given that the number of rectangles that can be searched goes up exponentially as the size is refined, this is not a very good bound on the total amount of work allowed - and means pathological cases can run more or less forever. This introduces a `max_rectangles` parameter, which limits the total amount of searching on a given support. It's set provisionally to 20000 as a first guess at a reasonable value. If this budget is exhausted, a new event type (different from "singular" supports) is generated; this is emitted in the command-line tool if the `-V` switch is specified.
This adds an LU factorisation class internally to the branch-and-bound equation solver internal to `enumpoly_solve`. The revised approach has much better numerical stability on less-well-conditioned systems. This addresses the root cause of very long (and ultimately futile) searches on some supports, where equations would not solve due to numerical inaccuracy. Closes #1055.
rahulsavani
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Aug 20, 2026
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Very happy with this.
I added the tests I had in mind for enumpoly. It runs too slow under behavior strategies to do too many equilibria, so only 2 there, and 10 for the original strategic form version.
One thing I recalled by accidentally setting stop_after to 0 is that it is equivalent to stop_after being None. I think that None corresponding to "all" equilibria is natural, but for 0 much less so, so I wonder if that should be mentioned in the docs for any methods that have stop_after as a param? If you agree I can create a separate issue and do that shortly.
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stop_after = 0 working is accidental leakage from the convention in the C++ code. Please make an issue and we can discuss fixing it. |
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This makes two improvements:
max_rectanglesargument to the branch-and-bound equation solver, to prevent it from futilely subdividing down to rectangles of size 1e-8 everywhere;Closes #1055.