#!/usr/bin/env python3 """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()