Case pieces

Case pieces declare a supported binary split of one economic output into two smooth formulas. The decorators attach metadata and return the original functions unchanged, so the same regime remains executable under GridSearch.

Boundary predicate¶

import lcm

eligible = lcm.case_boundary(
    condition=lcm.ref("liquid") < lcm.ref("asset_limit"),
    kind="jump",
)

The declaration records:

• both named operands from the lcm.ref(...) comparison;

• exact-boundary ownership from the comparison operator (< above leaves equality to the otherwise side, while <= gives it to when);

• kind: "continuous_kink", "jump", or "hard_constraint".

The condition must be one <, <=, >, or >= comparison. Compound conditions and bare callable predicates cannot declare a case-piece boundary because they do not identify one ordered split with unambiguous ownership.

Piece formulas¶

@lcm.piece(output="subsidy", when=eligible)
def subsidy_when_eligible(subsidy_high):
    return subsidy_high


@lcm.piece(output="subsidy", otherwise=eligible)
def subsidy_otherwise(subsidy_low):
    return subsidy_low

Exactly one when and one otherwise formula define the split output. A piece should be smooth within its declared side. @lcm.smooth_helper can attest a reviewed numerical helper whose implementation contains a benign clip, maximum, or abs that the automatic smoothness gate would otherwise reject.

The current NBEGM case-piece route is deliberately narrow: one supported binary split of the additive subsidy/cash-on-hand structure on the declared liquid state, with flat piece parameters and no taste shocks. Model construction refuses declarations outside that route instead of silently applying a heuristic.

Use piecewise-affine schedules for several brackets, floors, or mixed breakpoint kinds. Read Declared non-convex budgets for the numerical reason the metadata exists.