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json
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mathematics
nonlinear-systems
model-reduction
state-representation
exterior-algebra
exact-arithmetic
File size: 1,546 Bytes
33e9f46 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | """Check exported rational certificates without invoking the compiler."""
import json
from pathlib import Path
import sympy as sp
from src.continuation import ExteriorCertificate, Ratio
ROOT = Path(__file__).resolve().parent
def matrix(rows):
return sp.Matrix([[sp.Rational(value) for value in row] for row in rows])
def ratio(record):
return Ratio(matrix(record['beta']), matrix(record['alpha']), tuple(record['word']))
def main() -> None:
records = json.loads((ROOT/'results'/'exact_certificates.json').read_text())
for record in records:
n = int(record['n'])
seeds = tuple(ratio(row) for row in record['seeds'])
ratios = [ratio(row) for row in record['ratios']]
branches = (matrix(record['A']), matrix(record['B']))
cert = ExteriorCertificate(
normalizer=matrix(record['normalizer']),
readouts=tuple(seed.numerator for seed in seeds), seeds=seeds,
branches=branches, ratios=ratios, R=matrix(record['R']),
transports=[matrix(H) for H in record['H']],
depth=max((len(r.word) for r in ratios), default=0))
if not cert.verify():
raise AssertionError(f'Failed certificate at n={n}')
if cert.normalizer*(branches[0]+branches[1]) != cert.normalizer:
raise AssertionError(f'Failed instrument normalization at n={n}')
print(f'n={n}: seed coverage, provenance, row integrity, positivity, '
'transport, and normalization all pass.')
if __name__ == '__main__':
main()
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