Hard infeasibility witnesses in power fitting

This notebook shows how the low-level inverse solver reports hard infeasibility when the requested equalities or bounds cannot all be satisfied at once.

import numpy as np

import pyvoro2.inverse as inverse
import pyvoro2.inverse.separator as separator

1) Build a contradictory hard system

For three collinear sites, forcing all pairwise separator positions to be at absolute position 0.0 is impossible.

points = np.array(
    [
        [0.0, 0.0, 0.0],
        [2.0, 0.0, 0.0],
        [4.0, 0.0, 0.0],
    ],
    dtype=float,
)
ids = np.array([10, 11, 12], dtype=int)
raw_observations = [
    (10, 11, 0.0),
    (11, 12, 0.0),
    (10, 12, 0.0),
]
observations = inverse.resolve_separator_observations(
    points,
    raw_observations,
    measurement="position",
    ids=ids,
    index_mode="id",
)

fit = inverse.fit_weights_from_separators(
    points,
    observations,
    model=separator.FitModel(feasible=separator.FixedValue(0.0)),
    solver="admm",
)
termination = fit.solver_termination

termination.status, termination.hard_feasible, fit.is_infeasible

Output

('infeasible_hard_constraints', False, True)

2) Inspect the contradiction witness

fit.conflicting_constraint_indices

Output

(0, 1, 2)

termination.conflict.message

Output

'inconsistent hard separator restrictions on connected component [0, 1, 2]; contradiction cycle uses constraint rows [0, 1, 2]'

termination.conflict.to_records(ids=ids)

Output

({'constraint_index': 0,
  'site_i': 10,
  'site_j': 11,
  'relation': '>=',
  'bound_value': -4.0},
 {'constraint_index': 1,
  'site_i': 11,
  'site_j': 12,
  'relation': '>=',
  'bound_value': -4.0},
 {'constraint_index': 2,
  'site_i': 10,
  'site_j': 12,
  'relation': '<=',
  'bound_value': -16.0})

3) Export the same information through the report helper

fit_report = fit.to_report(observations, use_ids=True)
fit_report["conflict"]

Output

{'message': 'inconsistent hard separator restrictions on connected component [0, 1, 2]; contradiction cycle uses constraint rows [0, 1, 2]',
 'component_nodes': [10, 11, 12],
 'cycle_nodes': [10, 11, 12],
 'constraint_indices': [0, 1, 2],
 'terms': [{'constraint_index': 0,
   'site_i': 10,
   'site_j': 11,
   'relation': '>=',
   'bound_value': -4.0},
  {'constraint_index': 1,
   'site_i': 11,
   'site_j': 12,
   'relation': '>=',
   'bound_value': -4.0},
  {'constraint_index': 2,
   'site_i': 10,
   'site_j': 12,
   'relation': '<=',
   'bound_value': -16.0}]}

The contradiction witness is intended to be compact and actionable rather than a full proof certificate.