Implements zonal and mean methods in UxDataset; fixes weighted_mean() dims order assumption

[Sevans711]

Closes #1801 (sub-issue of #1734)
Closes #1800

Overview

Solves #1801 by implementing UxDataset.zonal_mean(), .zonal_average(), .zonal_anomaly(), .azimuthal_mean(), .azimuthal_average(), and .weighted_mean(). These use the new UxDataset._apply_across_data_vars helper function, which should be very useful when addressing other sub-issues of #1734.

Solves #1800 by updating weighted_mean code and docstring accordingly.

Corresponding readthedocs notebooks have been updated to include these new features, with simple examples for zonal_mean and azimuthal_mean, and a more detailed example for weighted_mean. Added relevant tests into test_dataset.py and test_weighted_mean.py.

Expansions of scope:

• Improved zonal_mean() docstring to be more honest and to clarify the different possible output shapes.
• (Design decision) used some keyword-only arguments in these new methods (see Utilize keyword-only arguments, at least in public API #1573) even though their UxDataArray counterparts do not require keyword-only arguments. Keyword-only restrictions are easy to lift later if needed (doesn't break backwards compatibility) but hard to introduce later (requires a deprecation cycle).
• Added support for xr.DataArray inputs to weighted_mean().
• Added clear DimensionError in weighted_mean() if user-provided weights have the wrong number of dimensions.
• Added missing link to "7. Zonal Anomalies" section, at top of zonal-average.ipynb.

Sidenote: I didn't make any edits to the bottom of the zonal-average.ipynb (lines 700+) myself, those are all from automatic ruff formatting.

Expected Usage

import uxarray as ux
uxds = ux.tutorial.open_dataset("outCSne30-timeseries")
uxds.zonal_mean()
uxds.zonal_anomaly()
uxds.azimuthal_mean(center_coord=(45, 0), outer_radius=50, radius_step=10)
uxds.weighted_mean()

PR Checklist

General

• An issue is created and linked
• Added appropriate labels (if your uxarray repo permissions allow it)
• Filled out Overview and Expected Usage (if applicable) sections

Testing & Benchmarking

• There is adequate test coverage of changes from this PR (add new tests if needed)
• [N/A] If this PR could affect performance, ran ASV benchmarks and confirmed they show expected behavior (add a new benchmark if necessary)

Documentation and Examples

• Docstrings updated with any function changes, and included in all new functions
• User (public) functions added to docs/api.rst; internal (private) function names start with an underscore (_)
• If touched any notebook files, cleared the output of all cells before committing
• [N/A] If added new notebook files, put into appropriate directories and referenced in appropriate files

AI Disclosure

AI Usage: Claude mostly just to settle on design for the new helper function; GitHub Copilot's inline code suggestions.

• I have tested and take responsibility for all AI-generated content in my PR.

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB