Added L1Potts class

[mstorath]

Summary

Adds L1Potts, an exact O(KN) solver for the (weighted) L1 Potts model —
penalized piecewise-constant estimation under L1 data fidelity, robust to
heavy-tailed noise and outliers:

min_u  γ · #{i : u_i ≠ u_{i+1}}  +  Σ_i w_i · |f_i - u_i|

This complements Pelt(model="l1") with a far faster algorithm specialized
for this functional. On a 5000-sample noisy 1D signal: ~20× faster than
Pelt(model="l1", min_size=1, jump=1), with identical functional value
to machine precision.

Algorithm

Implements Algorithm 1 of Storath, Weinmann & Unser (2017):

• Theorem 2 of the paper: the optimum lies in V = unique(signal),
  because the weighted L1 median is always a data value. So the search
  space is reduced from ℝ^N to V^N.
• Viterbi-style DP over (level, sample) pairs, with the
  Felzenszwalb-Huttenlocher trick for the Potts penalty (O(K) per
  column instead of O(K²)).
• Time complexity O(K·N), where K is the number of distinct values in the
  signal.

Forward pass matches the paper exactly. Backtracking uses explicit parent
pointers (uint8 matrix + prev-argmin vector) instead of the paper's
in-place float64 subtraction trick — mathematically equivalent, ~8× less
memory.

Currently 1D-only and penalty-only mode (no n_bkps / epsilon); the
algorithm is exact, so min_size/jump are fixed at 1.

What's included

• src/ruptures/detection/l1potts.py — solver + input validation
• tests/test_l1potts.py — 71 tests covering correctness, weights,
  hardening, edge cases:
  • functional-value parity with Pelt+CostL1 over multiple seeds
  • replication-equivalence for integer weights, weight ratios up to
    10000:1
  • positive homogeneity (scaling weights and γ by the same α) over 7
    orders of magnitude
  • reversal symmetry of the functional
  • rejection of NaN/Inf, non-numeric dtypes, empty signals,
    predict-before-fit
  • SyntaxWarning regression net (subprocess + compile())
• docs/user-guide/detection/l1potts.md — user guide page
• docs/code-reference/detection/l1potts-reference.md — autodoc stub
• mkdocs.yml — nav entries
• Top-level export rpt.L1Potts

Disclosure

Implementation prepared with assistance from Claude (Anthropic) acting as a
coding agent. The algorithm is the cited authors' (SWU2017); the agent's
contributions were the parent-pointer backtracking variant (memory
optimization), input hardening, and the test suite.

[edelweiss611428]

Hi could you submit a feature request to https://github.com/edelweiss611428/rupturesRcpp @mstorath

I may implement this later.

[deepcharles]

This looks good! Thanks Martin!

Before I merge, can you add the changes on the main branch (git rebase)?

[codecov]

Codecov Report

❌ Patch coverage is 98.00000% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.70%. Comparing base (6e3bb72) to head (0b81e9b).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/ruptures/detection/l1potts.py	97.95%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #344      +/-   ##
==========================================
- Coverage   98.77%   98.70%   -0.08%     
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  Files          40       41       +1     
  Lines         982     1081      +99     
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+ Hits          970     1067      +97     
- Misses         12       14       +2     

Flag	Coverage Δ
unittests	98.70% <98.00%> (-0.08%)	⬇️

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