Piecewise-affine schedules

piecewise_affine declares that one output is affine in a named variable between known breakpoints. It is the preferred representation for tax brackets, transfer phase-outs, floors, and schedules with several kinks or jumps.

import lcm


@lcm.piecewise_affine(
    output="resources",
    variable="liquid",
    breakpoints=(
        lcm.affine_breakpoint(
            threshold="first_threshold",
            kind="continuous_kink",
        ),
        lcm.affine_breakpoint(
            threshold="asset_test",
            kind="jump",
        ),
    ),
)
def resources(*, liquid, first_threshold, asset_test, transfer):
    # The function remains the executable economic schedule.
    ...

affine_breakpoint¶

affine_breakpoint(threshold, kind="continuous_kink", indexed_by=None, static_index=None, threshold_subkey=None) identifies one boundary.

• threshold names the flat parameter or parameter table.

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

• indexed_by names a categorical state when the threshold varies across categories.

• static_index selects a fixed table position.

• threshold_subkey selects a nested parameter leaf.

Use only the indexing fields required by the parameter shape. Invalid or contradictory combinations are rejected when the declaration is built.

Solver contract¶

The decorated function remains ordinary Python and is valid under GridSearch. NBEGM uses the metadata to partition the liquid axis into smooth affine runs, create one-sided boundary candidates, and choose the appropriate envelope route.

The declaration asserts affinity between breakpoints. Solver validation probes the assembled economic DAG and rejects hidden non-affinity or current-state dependence that would invalidate the per-run inversion. NBEGM(probe_failure="assume_declared") is an explicit author assertion for a probe that cannot execute; it should be paired with independent grid-search comparisons and is not the default.

Use case pieces for one supported binary formula split. Feasibility comparisons belong to structured Conditions.