Add Weighted Quantile and Percentile Support to jax.numpy

[Aniketsy]

#32647

This PR adds support for weighted quantile and percentile computations to jax.numpy.quantile, jax.numpy.nanquantile, jax.numpy.percentile, and jax.numpy.nanpercentile .

Please let me know if my approach or fix needs any improvements . I’m open to feedback and happy to make changes based on suggestions.
Thankyou !

[gemini-code-assist]

Summary of Changes

Hello @Aniketsy, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request significantly enhances the jax.numpy module by introducing support for weighted quantile and percentile calculations. By integrating an optional weights argument into the existing quantile, nanquantile, percentile, and nanpercentile functions, users can now perform more sophisticated statistical analyses where individual data points contribute differently to the overall distribution. The change involves modifying function signatures and implementing the core weighted logic within the internal _quantile function, ensuring accurate results across various interpolation methods and proper handling of NaN values.

Highlights

• Weighted Quantile/Percentile Support: The jax.numpy.quantile, jax.numpy.nanquantile, jax.numpy.percentile, and jax.numpy.nanpercentile functions now accept an optional weights parameter, enabling weighted computations.
• Core Weighted Logic Implementation: The internal _quantile function has been extended to handle weighted inputs, including sorting data and weights, calculating cumulative normalized weights, and determining quantile values based on various interpolation methods.
• NaN Handling with Weights: The weighted quantile logic correctly handles NaN values by masking them and adjusting weights accordingly when squash_nans is enabled.
• New Test Case: A new unit test, test_weighted_quantile_linear, has been added to tests/lax_numpy_reducers_test.py to validate the correctness of the weighted quantile calculation.

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[gemini-code-assist]

Code Review

This pull request introduces support for weighted quantiles and percentiles, which is a valuable addition. The overall approach is sound, but there are a couple of significant issues in the implementation within _quantile. Firstly, there's a structural issue where the new logic for weighted quantiles is added after the axis variable has been processed, leading to dead code and incorrect behavior for NaN handling when axis is None. Secondly, the implementation for the weighted case appears to be incorrect when q (the quantiles) is a vector. I've provided detailed comments and suggestions for fixes. I also recommend expanding the test suite to cover these edge cases to ensure the feature is robust.

[Aniketsy]

@jakevdp please review these changes, when you get a chance. I'm not sure if i correctly placed -handle weights also all tests are not covered yet, should i add. Thanks!