fix(io): write LP bounds for tightened binary variables

[FBumann]

Note

The following content was generated by AI.

Summary

Closes #776.

Per-element bounds set below the implied [0, 1] on a binary variable (e.g. masking out a subset of entries with upper = 0) were silently dropped by LP file export. Such binaries appeared only in the binary section, which implies [0, 1]. The direct/matrix API honored the bounds (matrices._build_vars reads var.lower/var.upper unconditionally), so the same model had a different feasible set depending on io_api — a silent correctness trap where a model correct under io_api="direct" relaxed when solved through an LP file.

#773 had already added bound rows for fully-fixed binaries; this extends the same treatment to any binary whose bounds differ from (0, 1) anywhere.

Change

bounds_to_file now selects a binary for the bounds section when it has any non-default bound, via a small helper:

def _binary_has_nondefault_bounds(var):
    return bool((var.lower.values != 0).any() or (var.upper.values != 1).any())

• All-default binaries (the common case) still emit no bounds rows — one cheap vectorised .any() per binary, no change to output.
• Masked slots are tolerated: a false positive only routes the variable through the bounds loop, where masked labels (-1) are already dropped before writing.
• The matrix/direct path is intentionally left unchanged: it builds dense per-column bound arrays with no implicit [0, 1] default to skip, and it is already correct.

Before / after (repro from the issue)

m = linopy.Model()
x = m.add_variables(binary=True, coords=[pd.RangeIndex(4, name="t")], name="x")
x.upper = pd.Series([1, 1, 0, 0], index=pd.RangeIndex(4, name="t"))
m.add_constraints(x.sum() >= 2, name="atleast2")
m.add_objective(-1 * x.sum())

• Before: LP file had no bounds section → optimum -4; direct → -2.
• After: both paths → -2.

Tests

• test_to_file_lp_binary_default_bounds_omitted — default binary emits no bounds section.
• test_to_file_lp_binary_tightened_bounds — tightened entries reach the LP bounds section.
• test_lp_and_direct_agree_on_binary_bounds — the two paths agree on the optimum.

Follow-up

A separate PR will relax add_variables(binary=True, ...) to accept {0, 1} bounds at construction (currently raises), per the issue comment. Kept separate because that feature depends on this export fix being in place.