perf: lp write speed

[FBumann]

Changes proposed in this Pull Request

Optimize the LP file writing pipeline, achieving ~40-60% speedup on m.to_file() across synthetic and realistic PyPSA models.

Benchmark results

Measured with dev-scripts/benchmark_lp_writer.py (10 iterations, warmup). Before/after run back-to-back on same machine.

basic_model (2 × N² vars, 2 × N² constraints):

N	Vars	Cons	Before	After	Speedup
50	5,000	5,000	24ms	10ms	56%
100	20,000	20,000	42ms	18ms	57%
200	80,000	80,000	138ms	51ms	63%
500	500,000	500,000	732ms	251ms	66%
1000	2,000,000	2,000,000	3091ms	1008ms	67%

knapsack_model (N binary vars, 1 constraint with N terms):

N	Vars	Before	After	Speedup
100	100	5.6ms	4.5ms	20%
1,000	1,000	7.8ms	5.5ms	29%
10,000	10,000	11.8ms	8.5ms	28%
50,000	50,000	36.6ms	23.6ms	36%
100,000	100,000	63.1ms	37.3ms	41%

PyPSA SciGrid-DE (realistic power system, 585 buses, 1423 generators, 852 lines):

Model	Vars	Cons	Before	After	Speedup
scigrid-de (24 snapshots)	59,640	142,968	294ms	262ms	11%

Per-commit impact (basic_model)

Cumulative impact measured on basic_model (N=100 → 20k vars, N=500 → 500k vars):

Commit	Description	N=100	N=500	Δ N=500
Baseline	Original code	44ms	722ms	—
ccb9cd2	Replace concat+sort with join in Constraint.to_polars(), remove group_by validation in constraints_to_file()	41ms	613ms	-15%
aab95f5	Skip group_terms when _term=1, build short DataFrame with numpy instead of xarray broadcast, fast sign column via pl.lit()	29ms	516ms	-16%
7762659	Skip group_terms in LinearExpression.to_polars() when no duplicate vars (objective speedup)	28ms	508ms	-2%
bdbb042	Pre-cast rhs to String in with_columns instead of inside concat_str	33ms	483ms	-5%
44b115f	Use Polars streaming engine for concat_str + write_csv with fallback to eager	36ms	390ms	-19%
Total		36ms	390ms	-46%

Per-commit impact (PyPSA SciGrid-DE 240h — 596,400 vars, 1,429,680 cons)

Measured with 2 warmup iterations + 8 timed iterations on the extended SciGrid-DE model (240 snapshots).

Commit	Description	Time	Δ cumulative	Δ vs previous
Baseline	Original code	2724ms ± 121ms	—	—
ccb9cd2	Replace concat+sort with join	1926ms ± 11ms	-29%	-29%
aab95f5	Skip group_terms, numpy short DF	1560ms ± 29ms	-43%	-19%
7762659	Skip group_terms in objective	1527ms ± 53ms	-44%	-2%
bdbb042	Pre-cast rhs to String	1576ms ± 21ms	-42%	+3% (regression)
44b115f	Polars streaming engine	1237ms ± 27ms	-55%	-21%

Note: bdbb042 shows a small +3% regression on the PyPSA model while helping the basic model. The streaming engine commit recovers and extends the gains.

Benchmark script

Run with python dev-scripts/benchmark_lp_writer.py. Tests basic_model, knapsack_model (up to 100k vars), and PyPSA SciGrid-DE.

Checklist

• Code changes are sufficiently documented; i.e. new functions contain docstrings and further explanations may be given in doc.
• Unit tests for new features were added (if applicable).
• A note for the release notes doc/release_notes.rst of the upcoming release is included.
• I consent to the release of this PR's code under the MIT license.

[FBumann]

Closed in favor of #564