File size: 6,426 Bytes
6773986 | 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 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | #!/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()
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