Duals and bases

polar-high exposes the full HiGHS post-solve surface, not just the primal solution.

Constraint duals

sol = p.solve()
duals = sol.constraint_dual("balance")
# polars frame: (key, dual) — key is a comma-joined string of dim values

The frame's index columns mirror the over= frame you supplied to add_cstr, so you can join duals against parameters or other solution frames directly.

Reduced costs (column duals)

sol.col_dual              # numpy array sized to the LP's column count

To map this back to a specific variable's cells, join via var.frame["col_id"]:

import polars as pl
v_red = (v.frame
         .with_columns(reduced_cost=pl.Series(sol.col_dual[v.frame["col_id"]])))

The live HiGHS handle

sol.highs                  # highspy.Highs — kept alive across solves
sol.highs.getInfo()
sol.highs.getModelStatus()
sol.highs.getBasis()
sol.highs.writeModel("debug.mps")

Whatever highspy exposes is yours. This is also how WarmProblem re-uses the basis between solves: it holds onto the same Highs instance and feeds it changeRowBound / changeCoeff / changeObjectiveCoef calls between solves.

When you need duals during build

Duals are only available after solve(). If you need them inside an iterative scheme (e.g. column generation, Benders), look at LagrangianProblem — it provides a generic dual-subgradient driver wired to WarmProblem.