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| from __future__ import annotations | |
| import base64 | |
| import html | |
| import math | |
| COLORS = ("#2563eb", "#059669", "#d97706", "#dc2626") | |
| def line_svg(title: str, x_label: str, y_label: str, series: list[dict], log_x: bool = False, log_y: bool = False) -> str: | |
| width, height = 760, 430 | |
| left, right, top, bottom = 90, 30, 55, 70 | |
| plot_w, plot_h = width - left - right, height - top - bottom | |
| all_x = [value for item in series for value in item["x"]] | |
| all_y = [value for item in series for value in item["y"]] | |
| tx = (lambda value: math.log10(value)) if log_x else (lambda value: value) | |
| ty = (lambda value: math.log10(value)) if log_y else (lambda value: value) | |
| x_values = [tx(value) for value in all_x] | |
| y_values = [ty(value) for value in all_y] | |
| x_min, x_max = min(x_values), max(x_values) | |
| y_min, y_max = min(y_values), max(y_values) | |
| x_pad = (x_max - x_min or 1.0) * 0.04 | |
| y_pad = (y_max - y_min or 1.0) * 0.08 | |
| x_min, x_max = x_min - x_pad, x_max + x_pad | |
| y_min, y_max = y_min - y_pad, y_max + y_pad | |
| def px(value: float) -> float: | |
| return left + (tx(value) - x_min) / (x_max - x_min) * plot_w | |
| def py(value: float) -> float: | |
| return top + (y_max - ty(value)) / (y_max - y_min) * plot_h | |
| parts = [ | |
| f'<svg xmlns="http://www.w3.org/2000/svg" width="{width}" height="{height}" viewBox="0 0 {width} {height}" role="img">', | |
| f"<title>{html.escape(title)}</title>", | |
| '<rect width="100%" height="100%" fill="white"/>', | |
| f'<text x="{width/2}" y="28" text-anchor="middle" font-family="sans-serif" font-size="19" font-weight="700">{html.escape(title)}</text>', | |
| ] | |
| for tick in range(6): | |
| fraction = tick / 5 | |
| x = left + fraction * plot_w | |
| y = top + fraction * plot_h | |
| x_value = x_min + fraction * (x_max - x_min) | |
| y_value = y_max - fraction * (y_max - y_min) | |
| x_text = f"10^{x_value:.1f}" if log_x else f"{x_value:.3g}" | |
| y_text = f"10^{y_value:.1f}" if log_y else f"{y_value:.3g}" | |
| parts.extend([ | |
| f'<line x1="{x:.2f}" y1="{top}" x2="{x:.2f}" y2="{top+plot_h}" stroke="#e5e7eb"/>', | |
| f'<line x1="{left}" y1="{y:.2f}" x2="{left+plot_w}" y2="{y:.2f}" stroke="#e5e7eb"/>', | |
| f'<text x="{x:.2f}" y="{top+plot_h+22}" text-anchor="middle" font-family="sans-serif" font-size="11">{x_text}</text>', | |
| f'<text x="{left-10}" y="{y+4:.2f}" text-anchor="end" font-family="sans-serif" font-size="11">{y_text}</text>', | |
| ]) | |
| parts.extend([ | |
| f'<line x1="{left}" y1="{top+plot_h}" x2="{left+plot_w}" y2="{top+plot_h}" stroke="#111827"/>', | |
| f'<line x1="{left}" y1="{top}" x2="{left}" y2="{top+plot_h}" stroke="#111827"/>', | |
| f'<text x="{left+plot_w/2}" y="{height-18}" text-anchor="middle" font-family="sans-serif" font-size="13">{html.escape(x_label)}</text>', | |
| f'<text x="20" y="{top+plot_h/2}" text-anchor="middle" transform="rotate(-90 20 {top+plot_h/2})" font-family="sans-serif" font-size="13">{html.escape(y_label)}</text>', | |
| ]) | |
| for index, item in enumerate(series): | |
| color = COLORS[index % len(COLORS)] | |
| points = " ".join(f"{px(x):.2f},{py(y):.2f}" for x, y in zip(item["x"], item["y"])) | |
| parts.append(f'<polyline points="{points}" fill="none" stroke="{color}" stroke-width="2.5"/>') | |
| for x, y in zip(item["x"], item["y"]): | |
| parts.append(f'<circle cx="{px(x):.2f}" cy="{py(y):.2f}" r="4" fill="{color}"/>') | |
| legend_x = left + 12 + (index % 2) * 280 | |
| legend_y = top + 18 + (index // 2) * 20 | |
| parts.extend([ | |
| f'<line x1="{legend_x}" y1="{legend_y}" x2="{legend_x+24}" y2="{legend_y}" stroke="{color}" stroke-width="3"/>', | |
| f'<text x="{legend_x+31}" y="{legend_y+4}" font-family="sans-serif" font-size="12">{html.escape(item["label"])}</text>', | |
| ]) | |
| parts.append("</svg>") | |
| return "\n".join(parts) + "\n" | |
| def make_figures(claims: list[dict]) -> dict[str, str]: | |
| by_id = {claim["claim_id"]: claim for claim in claims} | |
| claim1 = by_id["claim1"] | |
| primary = [ | |
| {"label": f"omega={item['omega']:.4g}", "x": [row["T"] for row in item["rows"]], "y": [row["mean_squared_parameter_error"] for row in item["rows"]]} | |
| for item in claim1["problems"] | |
| ] | |
| primary.append({"label": "constant-step control", "x": [row["T"] for row in claim1["negative_control"]["rows"]], "y": [row["mean_squared_parameter_error"] for row in claim1["negative_control"]["rows"]]}) | |
| base = claim1["problems"][0] | |
| claim2 = by_id["claim2"] | |
| claim3 = by_id["claim3"] | |
| claim4 = by_id["claim4"] | |
| rho = [0.6, 0.9, 0.99] | |
| figures = { | |
| "headline_td_scaling.svg": line_svg("Exact exponential schedule converges; constant step stalls", "horizon T (log scale)", "last-iterate MSE (log scale)", primary, True, True), | |
| "bound_calibration.svg": line_svg("Observed error remains below Theorem 3.4's explicit bound", "horizon T (log scale)", "MSE / upper bound (log scale)", [{"label": "observed MSE", "x": [row["T"] for row in base["rows"]], "y": [row["mean_squared_parameter_error"] for row in base["rows"]]}, {"label": "explicit bound", "x": [row["T"] for row in base["rows"]], "y": [row["theorem_upper_bound"] for row in base["rows"]]}], True, True), | |
| "omega_dependency.svg": line_svg("Standard eta0 needs omega; regularized eta0 does not", "omega", "eta0 at T=1e6 (log scale)", [{"label": "Theorem 4.10 standard", "x": list(claim2["omega_values"]), "y": claim2["eta0_values_at_T_1e6"]}, {"label": "Theorem 4.12 regularized", "x": list(claim3["omega_values"]), "y": claim3["eta0_at_T_1e6_for_each_omega"]}], False, True), | |
| "mixing_factor.svg": line_svg("The displayed mixing factor spans 86 orders of magnitude", "tau_0.05", "log10 exp(m/log(1/rho))", [{"label": "Theorem 4.12 factor", "x": [row["tau_0.05"] for row in claim4["mixing_sweep"]], "y": [row["log10_bound_factor"] for row in claim4["mixing_sweep"]]}]), | |
| "feasible_horizons.svg": line_svg("Exact Markovian theorem regimes begin at extreme horizons", "rho", "first feasible log10(T)", [{"label": "standard", "x": rho, "y": [claim2["calibrated_first_feasible_horizons"][str(value)]["log10_T_first_feasible"] for value in rho]}, {"label": "regularized", "x": rho, "y": [claim3["calibrated_first_feasible_horizons"][str(value)]["log10_T_first_feasible"] for value in rho]}]), | |
| } | |
| return {name: base64.b64encode(svg.encode()).decode() for name, svg in figures.items()} | |