| |
| """Optional publication figures; requires numpy and matplotlib. |
| |
| The exact regression suite remains standard-library only. Figures 1 and 2 |
| read executed exact result files. Figure 3 uses floating-point singular values |
| to illustrate a proved conditioning counterexample; it is not a rank proof. |
| """ |
| from pathlib import Path |
| from itertools import combinations |
| import json |
| import os |
| import tempfile |
|
|
| ROOT = Path(__file__).resolve().parents[1] |
| os.environ.setdefault("MPLCONFIGDIR", str(Path(tempfile.gettempdir()) / "eve-aithrael-matplotlib")) |
| import numpy as np |
| import matplotlib |
| matplotlib.use("Agg") |
| import matplotlib.pyplot as plt |
|
|
| PALETTE = ["#007F86", "#B46B22", "#8B3B64", "#25364D"] |
| plt.rcParams.update({"font.family": "DejaVu Sans", "font.size": 10, |
| "axes.titlesize": 13, "axes.labelsize": 10, |
| "axes.spines.top": False, "axes.spines.right": False, |
| "axes.edgecolor": "#76818B", "axes.labelcolor": "#25364D", |
| "text.color": "#25364D", "xtick.color": "#526170", |
| "ytick.color": "#526170", "grid.color": "#E4E8EC", |
| "figure.facecolor": "white", "savefig.facecolor": "white", |
| "pdf.fonttype": 42, "ps.fonttype": 42}) |
|
|
|
|
| def save(fig, name): |
| folder = ROOT / "figures" |
| folder.mkdir(exist_ok=True) |
| target = folder / (name+".pdf") |
| fig.savefig(target, bbox_inches="tight", metadata={"Title": name.replace("_", " "), |
| "Author": "Eve, OpenAI AI assistant; prepared for Maciej Nowicki"}) |
| preview = ROOT.parent / "work" / "figure_previews" |
| preview.mkdir(parents=True, exist_ok=True) |
| fig.savefig(preview / (name+".png"), dpi=155, bbox_inches="tight") |
| plt.close(fig) |
| return {"file": str(target.relative_to(ROOT)), "bytes": target.stat().st_size} |
|
|
|
|
| def main(): |
| results_path = ROOT / "results" / "robust_results.json" |
| results = json.loads(results_path.read_text()) |
| assert results["status"] == "passed" |
| outputs = [] |
| profiles = results["dense_fault_recovery"]["profiles"] |
| fig, ax = plt.subplots(figsize=(7.0, 4.4), layout="constrained") |
| for j, profile in enumerate(profiles): |
| if profile: |
| ax.plot(range(1, len(profile)+1), profile, marker="o", linewidth=2.1, |
| markersize=7, color=PALETTE[j], label=f"Column {j}: dimension {len(profile)}") |
| ax.axhline(3, color="#677381", linestyle=(0, (4, 3)), linewidth=1.1) |
| ax.text(1.04, 3.16, "One erasure + one arbitrary error: distance must exceed 3", fontsize=9) |
| ax.set(xlabel="Surviving ambiguity dimension k", ylabel="Minimum channels removed", |
| title="Complete four-node DAG: exact failure profiles", |
| xlim=(0.9, 3.12), ylim=(2.7, 6.45), xticks=[1, 2, 3], yticks=[3, 4, 5, 6]) |
| ax.grid(axis="y") |
| ax.legend(loc="lower right", frameon=False, bbox_to_anchor=(1.0, 0.18)) |
| outputs.append(save(fig, "complete_four_failure_profiles")) |
|
|
| cases = results["causal_stars"] |
| distances = [cases["same_pattern_generic"]["causal_distance"], |
| cases["same_pattern_exceptional"]["causal_distance"]] |
| assert distances == [3, 2] |
| fig, ax = plt.subplots(figsize=(7.0, 4.5), layout="constrained") |
| bars = ax.bar([0, 1], distances, width=0.52, color=[PALETTE[0], PALETTE[2]]) |
| ax.bar_label(bars, labels=["Distance 3", "Distance 2"], padding=7, fontsize=12) |
| ax.axhline(3, color="#677381", linestyle=(0, (4, 3)), linewidth=1.0) |
| ax.text(1.39, 3.12, "Minimum for one\narbitrary error", ha="right", va="bottom", fontsize=9) |
| ax.set(xticks=[0, 1], xticklabels=["Distinct column ratios\nSecond row: 1, 2, 3, 4", |
| "Repeated column ratio\nSecond row: 1, 1, 3, 4"], |
| ylabel="Exact channel distance", title="Identical entry supports, different robustness", |
| ylim=(0, 4.15), xlim=(-0.55, 1.55), yticks=[0, 1, 2, 3, 4]) |
| ax.text(0, 0.18, "Corrects one error", ha="center", va="bottom", color="white", fontsize=10) |
| ax.text(1, 0.18, "Cannot correct one error", ha="center", va="bottom", color="white", fontsize=9) |
| ax.grid(axis="y", zorder=0) |
| ax.set_axisbelow(True) |
| outputs.append(save(fig, "same_support_coefficient_dependence")) |
|
|
| epsilons = np.logspace(-6, 0, 31) |
| parameters = np.arange(1, 6, dtype=float) |
| margins = [] |
| for eps in epsilons: |
| C = np.column_stack((np.ones(5), 1+eps*parameters))/(2+eps*parameters)[:, None] |
| assert np.all(C > 0) and np.max(np.abs(C.sum(axis=1)-1)) < 1e-14 |
| margin = min(float(np.linalg.svd(C[list(K)], compute_uv=False)[-1]) |
| for K in combinations(range(5), 2)) |
| assert margin > 0 |
| margins.append(margin) |
| fig, ax = plt.subplots(figsize=(7.0, 4.4), layout="constrained") |
| ax.loglog(epsilons, margins, color=PALETTE[0], marker="o", markersize=3.6, linewidth=1.8) |
| ax.set(xlabel="Separation parameter epsilon", ylabel="Worst retained-row singular value", |
| title="Optimal exact correction can be poorly conditioned") |
| ax.grid(which="major", alpha=0.9) |
| ax.text(0.04, 0.96, "5 positive convex-average channels; every pair independent\n" |
| "Exact distance = 4 for every epsilon > 0\n" |
| "Retain any 2 rows after the combined fault budget", |
| transform=ax.transAxes, va="top", fontsize=9, |
| bbox={"facecolor": "white", "edgecolor": "#E4E8EC", "pad": 7}) |
| outputs.append(save(fig, "normalized_conditioning_margin")) |
| data = {"source": "results/robust_results.json", |
| "exact_complete_four_profiles": profiles, |
| "exact_equal_support_distances": distances, |
| "conditioning_example": { |
| "status": "floating-point illustration of a separately proved formula", |
| "rows": "(1, 1+epsilon*a)/(2+epsilon*a), a=1,...,5", |
| "known_erasures": 1, "arbitrary_errors": 1, "combined_budget": 3, |
| "rows_retained": 2, "exact_distance_for_positive_epsilon": 4, |
| "epsilon": epsilons.tolist(), "minimum_singular_value": margins}, |
| "figures": outputs} |
| target = ROOT / "results" / "figure_data.json" |
| target.write_text(json.dumps(data, indent=2)+"\n") |
| print(json.dumps({"status": "created", "figures": outputs, |
| "data": str(target.relative_to(ROOT))}, indent=2)) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
