Refactor simplex and Lazy simplex improvement

[nathanneike]

Types of changes

Refactor
Performance improvement
Tests

Motivation and context / Related issue

This refactors the network simplex storage used by lazy EMD so that lazy mode avoids materializing dense per-arc storage where possible.

The lazy path now uses explicit storage/accessor modes for costs, flows, endpoints, and arc states. Real transport arc costs are computed on demand from sample coordinates, while artificial simplex root arc costs are still stored explicitly. Lazy EMD also returns sparse transport output instead of allocating a dense transport matrix internally. Dense and sparse EMD behavior are unchanged.

This substantially reduces memory usage for lazy EMD. For larger problems, it can also improve runtime: although lazy mode recomputes real arc costs, it avoids materializing and repeatedly accessing a multi-GiB dense cost matrix, reducing memory-bandwidth pressure.

n	method	time (s)	peak memory (MiB)	extra memory during solve (MiB)
100	dense	0.002	699.2	0.0
100	lazy	0.002	698.7	0.0
300	dense	0.007	698.5	0.0
300	lazy	0.014	698.4	0.0
1000	dense	0.102	734.7	35.8
1000	lazy	0.205	698.0	0.0
3000	dense	1.077	1048.4	349.3
3000	lazy	2.197	698.8	0.0
10000	dense	15.682	4502.4	3803.7
10000	lazy	30.598	722.9	23.8
15000	dense	39.547	6695.0	5996.3
15000	lazy	72.819	754.5	55.7
20000	dense	175.729	6945.5	6245.9
20000	lazy	134.256	797.3	99.5
25000	dense	370.609	7098.5	6400.4
25000	lazy	241.820	853.9	155.4

Peak memory includes the Python/import baseline. The “extra memory during solve” column better isolates solver-side growth. These timings use the default squared Euclidean distance in 2D. The runtime crossover depends on the distance metric and feature dimension: lazy mode recomputes costs on demand, so it benefits most when avoiding dense memory traffic is more expensive than recomputing the distance. In this local benchmark, the crossover happens between n=15000 and n=20000.

How has this been tested (if it applies)

Rebuilt the C++/Cython extension and ran the whole test suite

PR checklist

• I have read the CONTRIBUTING document.
• The documentation is up-to-date with the changes I made (check build artifacts).
• All tests passed, and additional code has been covered with new tests.
• I have added the PR and Issue fix to the RELEASES.md file.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.85%. Comparing base (19db3ee) to head (523a0d6).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #813   +/-   ##
=======================================
  Coverage   96.85%   96.85%           
=======================================
  Files         115      115           
  Lines       23344    23373   +29     
=======================================
+ Hits        22610    22639   +29     
  Misses        734      734           

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