Weighted lp metric

[luisheb]

Describe the proposed changes

In some applications, it is useful to emphasize certain time points more than others when measuring the distance between functional observations. This can be achieved by introducing a weight function $w(t)$ inside the integral. The weight function assigns varying importance to different regions of the domain $\mathcal{T}$, resulting in a weighted $L^p$ norm.

These classes generalize the standard Lp norm and distance by supporting such weighting. This is useful in domains where relevance is time- or region-specific—such as emphasizing peak hours in energy data or symptom windows in medical signals.

Classes

• skfda.misc.metrics.WeightedLpNorm
• skfda.misc.metrics.WeightedLpDistance

Functional Wrappers

The following functional wrappers are provided for convenience, allowing direct evaluation of the norm or distance without explicitly creating a class instance:

• skfda.misc.metrics.weighted_lp_norm
• skfda.misc.metrics.weighted_lp_distance

These norms and distances are compatible with the same functionality that uses standard Lp norms, including classification pipelines, clustering algorithms, and pairwise distance computations.

Checklist before requesting a review

• I have performed a self-review of my code
• The code conforms to the style used in this package
• The code is fully documented and typed (type-checked with Mypy)
• I have added thorough tests for the new/changed functionality

[codecov]

Codecov Report

Attention: Patch coverage is 92.85714% with 12 lines in your changes missing coverage. Please review.

Project coverage is 87.11%. Comparing base (e44d8e5) to head (5785403).
Report is 1 commits behind head on develop.

Files with missing lines	Patch %	Lines
skfda/misc/metrics/_weighted_lp_norm.py	85.13%	11 Missing ⚠️
skfda/misc/metrics/_weighted_lp_distances.py	95.00%	1 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #690      +/-   ##
===========================================
+ Coverage    87.04%   87.11%   +0.07%     
===========================================
  Files          199      202       +3     
  Lines        14639    14759     +120     
===========================================
+ Hits         12742    12858     +116     
- Misses        1897     1901       +4     

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