File size: 2,402 Bytes
d44a7b7 | 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 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | """Regenerate illustrative tables using 80-digit arithmetic.
These evaluate the explicit circle design. They are not interval-certified
finite-length global optima. No randomness, downloads, or external services.
"""
from pathlib import Path
import csv
import json
import mpmath as mp
def main() -> None:
mp.mp.dps = 80
output = Path(__file__).resolve().parent / "results"
output.mkdir(exist_ok=True)
sigma = mp.mpf("0.0001")
alpha = mp.mpf("0.05")
quantile = mp.sqrt(2) * mp.erfinv(1 - 2 * alpha)
rows = []
for parameter, length in [("0.5", "0.5"), ("0.1", "0.5"),
("0.01", "0.5"), ("0.5", "0.2"),
("0.5", "0.1"), ("0.001", "0.5")]:
lam, ell = mp.mpf(parameter), mp.mpf(length)
kappa = lam * (1-lam)
z = kappa*ell**2/(4*mp.pi**2)
beta = 2*mp.pi*z/(1+mp.sqrt(1-z))
deficit = 2*mp.sin(beta/2)**2
gram_min = mp.mpf(3)/2*mp.sin(beta)**2
condition = 2/mp.tan(beta)**2
real_samples = 4*sigma**2*quantile**2/deficit**2
rows.append({"lambda": parameter, "L": length,
"kappa": mp.nstr(kappa, 30),
"writer_angle": mp.nstr(beta, 35),
"writer_deficit": mp.nstr(deficit, 35),
"gram_min_d3": mp.nstr(gram_min, 35),
"gram_condition_d3": mp.nstr(condition, 35),
"real_sample_threshold": mp.nstr(real_samples, 35),
"illustrative_ceiling": str(int(mp.ceil(real_samples)))})
with (output/"circle_examples.csv").open("w", newline="", encoding="utf-8") as f:
writer = csv.DictWriter(f, fieldnames=list(rows[0]))
writer.writeheader(); writer.writerows(rows)
report = {"digits": 80, "sigma": str(sigma), "equal_prior_risk": str(alpha),
"scope": "Explicit circle design; not certified finite-L global optima.",
"rows": rows}
(output/"circle_examples.json").write_text(json.dumps(report, indent=2), encoding="utf-8")
for row in rows:
print(row["lambda"], row["L"],
"gap="+mp.nstr(mp.mpf(row["writer_deficit"]),7),
"Gram="+mp.nstr(mp.mpf(row["gram_min_d3"]),7),
"cond="+mp.nstr(mp.mpf(row["gram_condition_d3"]),7),
"n="+row["illustrative_ceiling"])
if __name__ == "__main__":
main()
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