| """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() |
|
|
