feat(ga): Implement Cauchy's bound for automatic root range detection #18

jono · 2025-10-27T18:35:03Z

jono commented

2025-10-27 18:35:03 +00:00

The previous benchmark results showed that the GA was failing to find accurate roots (high MAE) for many polynomials. This was because the fixed default search range ([-100, 100]) was often incorrect, and the GA was searching in the wrong place.

This commit introduces a significantly more robust solution:

Adds a _get_cauchy_bound helper function to mathematically calculate a search radius that is guaranteed to contain all real roots.
Updates _solve_x_numpy and _solve_x_cuda with new logic:
- If the user provides a custom min_range or max_range, we treat them as an expert and use their specified range.
- If the user is using the default range, we silently discard it and use the smarter, automatically-calculated Cauchy bound instead.

This provides the best of both worlds: a powerful, smart default for most users and an "expert override" for those who need to fine-tune the search area.

The previous benchmark results showed that the GA was failing to find accurate roots (high MAE) for many polynomials. This was because the fixed default search range ([-100, 100]) was often incorrect, and the GA was searching in the wrong place. This commit introduces a significantly more robust solution: 1. Adds a `_get_cauchy_bound` helper function to mathematically calculate a search radius that is guaranteed to contain all real roots. 2. Updates `_solve_x_numpy` and `_solve_x_cuda` with new logic: * If the user provides a *custom* `min_range` or `max_range`, we treat them as an expert and use their specified range. * If the user is using the *default* range, we silently discard it and use the smarter, automatically-calculated Cauchy bound instead. This provides the best of both worlds: a powerful, smart default for most users and an "expert override" for those who need to fine-tune the search area.

jono added 1 commit 2025-10-27 18:35:04 +00:00

feat(ga): Implement Cauchy's bound for automatic root range detection

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962eab5af7

The previous benchmark results showed that the GA was failing to find accurate roots (high MAE) for many polynomials. This was because the fixed default search range ([-100, 100]) was often incorrect, and the GA was searching in the wrong place.

This commit introduces a significantly more robust solution:

1.  Adds a `_get_cauchy_bound` helper function to mathematically calculate a search radius that is guaranteed to contain all real roots.

2.  Updates `_solve_x_numpy` and `_solve_x_cuda` with new logic:
    * If the user provides a *custom* `min_range` or `max_range`, we treat them as an expert and use their specified range.
    * If the user is using the *default* range, we silently discard it and use the smarter, automatically-calculated Cauchy bound instead.

This provides the best of both worlds: a powerful, smart default for most users and an "expert override" for those who need to fine-tune the search area.

jono merged commit 962eab5af7 into main

2025-10-27 18:36:41 +00:00

jono deleted branch v0.4.2-dev

2025-10-27 18:36:42 +00:00

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Reference: jono/PolySolve#18