"""Draws the report's SVG figures from results/*.json. Usage: python figures.py Requires matplotlib (tested with 3.10.7). """ import json import sys from pathlib import Path import plistlib import subprocess # Work-around: on macOS 27, `system_profiler SPFontsDataType` output lacks # the "_items" key that matplotlib's font scan expects, so the call is # answered with an empty list (fonts are still found by directory scan). _check_output = subprocess.check_output def _patched(cmd, *a, **k): if isinstance(cmd, (list, tuple)) and cmd and cmd[0] == "system_profiler": return plistlib.dumps([{"_items": []}]) return _check_output(cmd, *a, **k) subprocess.check_output = _patched import matplotlib # noqa: E402 matplotlib.use("svg") import matplotlib.pyplot as plt # noqa: E402 res = Path(sys.argv[1]) out = Path(sys.argv[2]) out.mkdir(parents=True, exist_ok=True) INK = "#1d2330" MUTED = "#5b6475" GRID = "#e3e6ec" BLUE = "#2f5bd3" ORANGE = "#d9692b" GREEN = "#1f8a5b" GREY = "#8a93a5" PURPLE = "#7a4bc2" plt.rcParams.update({ "svg.fonttype": "none", "font.family": ["Helvetica", "Arial", "DejaVu Sans", "sans-serif"], "font.size": 13, "axes.titlesize": 14, "axes.labelsize": 13, "xtick.labelsize": 12.5, "ytick.labelsize": 12.5, "legend.fontsize": 12.5, "axes.edgecolor": MUTED, "axes.labelcolor": INK, "xtick.color": MUTED, "ytick.color": MUTED, "text.color": INK, "axes.grid": True, "grid.color": GRID, "grid.linewidth": 0.8, "axes.spines.top": False, "axes.spines.right": False, "figure.facecolor": "white", "axes.facecolor": "white", "savefig.facecolor": "white", }) def save(fig, name, top=1.0): fig.tight_layout(rect=(0, 0, 1, top)) fig.savefig(out / name, format="svg", metadata={"Date": None}) plt.close(fig) from matplotlib.ticker import FixedLocator, FuncFormatter, NullLocator # noqa: E402 def plain_log_y(ax, ticks): ax.yaxis.set_major_locator(FixedLocator(ticks)) ax.yaxis.set_minor_locator(NullLocator()) ax.yaxis.set_major_formatter(FuncFormatter(lambda v, _: f"{v:,.0f}" if v >= 1 else f"{v:g}")) def ci(s): return s["mean"], s["mean"] - s["ci95"][0], s["ci95"][1] - s["mean"] e1 = json.loads((res / "e1_summary.json").read_text()) ms = [r["m"] for r in e1["byExpenseCount"]] # Figure 1 (hero): money created or destroyed per ledger. fig, ax = plt.subplots(figsize=(7.0, 4.2)) y, lo, hi = zip(*[ci(r["round_money_created_minor"]) for r in e1["byExpenseCount"]]) ax.errorbar(ms, y, yerr=[lo, hi], color=ORANGE, marker="o", lw=2.2, capsize=4, label="Doubles, each share rounded to the minor unit") for m, v in zip(ms, y): ax.annotate(f"{v:,.0f}", (m, v), textcoords="offset points", xytext=(-8, 9), ha="right", color=ORANGE, fontsize=12.5) ax.plot(ms, [0.5] * len(ms), color=BLUE, marker="s", lw=2.2, label="Integer package: exactly 0 in every ledger") ax.set_xscale("log") ax.set_yscale("log") ax.set_ylim(0.3, 4000) ax.yaxis.set_minor_locator(NullLocator()) ax.set_yticks([0.5, 1, 10, 100, 1000]) ax.set_yticklabels(["0", "1", "10", "100", "1,000"]) ax.set_xticks(ms) ax.xaxis.set_minor_locator(NullLocator()) ax.set_xticklabels([f"{m:,}" for m in ms]) ax.set_xlabel("Expenses in the ledger") ax.set_ylabel("Minor units created or lost\n(mean per ledger, 95% CI)") ax.set_title("Rounding each share separately leaks money; integers do not", loc="left") ax.legend(loc="upper left", frameon=False) save(fig, "fig1-money-leak.svg") # Figure 2: long-run allocation bias of the remainder rule. fig, ax = plt.subplots(figsize=(7.0, 4.2)) series = [ ("int_max_dev_from_exact_minor", "Package rule (heaviest weight, then id)", BLUE, "s"), ("hamilton_max_dev_from_exact_minor", "Largest remainder, ties by id", GREY, "^"), ("rotated_max_dev_from_exact_minor", "Largest remainder, ties rotated per expense", GREEN, "o"), ] for key, label, col, mk in series: y, lo, hi = zip(*[ci(r[key]) for r in e1["byExpenseCount"]]) ax.errorbar(ms, y, yerr=[lo, hi], color=col, marker=mk, lw=2, capsize=3, label=label) ax.set_xscale("log") ax.set_yscale("log") ax.set_xticks(ms) ax.xaxis.set_minor_locator(NullLocator()) ax.set_xticklabels([f"{m:,}" for m in ms]) ax.set_xlabel("Expenses in the ledger") ax.set_ylabel("Largest gap from the exact\nrational balance (minor units)") plain_log_y(ax, [1, 10, 100, 1000]) ax.set_title("Exact totals, but a fixed tie-break drifts against one person", loc="left") ax.legend(loc="upper left", frameon=False) save(fig, "fig2-tiebreak-bias.svg") # Figure 3: simplifier optimality gap. e2 = json.loads((res / "e2_summary.json").read_text()) fig, axes = plt.subplots(1, 3, figsize=(9.6, 3.9), sharey=True) names = {"uniform": "Uneven multi-payer bills", "round": "Round equal splits", "pairs": "One-to-one IOUs"} cols = [BLUE, ORANGE, PURPLE, INK] for ax, g in zip(axes, ["uniform", "round", "pairs"]): rows = [r for r in e2["byGenAndSize"] if r["gen"] == g and r["n"] <= 10] ns = [r["n"] for r in rows] bottom = [0.0] * len(rows) for gap, col in zip(["0", "1", "2", "3"], cols): vals = [r["greedyGapHistogram"].get(gap, 0) / r["instances"] for r in rows] ax.bar(ns, vals, bottom=bottom, color=col, width=0.75, label={"0": "optimal", "1": "+1 transfer", "2": "+2", "3": "+3"}[gap]) bottom = [b + v for b, v in zip(bottom, vals)] ax.set_title(names[g], loc="left", fontsize=13) ax.set_xticks(ns) ax.set_xlabel("People in the group") ax.grid(axis="x", visible=False) axes[0].set_ylabel("Share of 2,000 ledgers") axes[0].set_ylim(0, 1) h, l = axes[0].get_legend_handles_labels() fig.legend(h, l, loc="upper center", ncol=4, frameon=False, bbox_to_anchor=(0.5, 1.0)) save(fig, "fig3-simplifier-gap.svg", top=0.9) # Figure 4: routed payments. e3 = json.loads((res / "e3_summary.json").read_text()) fig, axes = plt.subplots(1, 2, figsize=(9.6, 3.9), sharey=True) strat = [("naiveClamp", "Plain payment (clamped pair)", ORANGE, "o"), ("bridge", "Routed bridge", BLUE, "s"), ("guarded", "Bridge + fall back to direct", GREEN, "^")] for ax, g in zip(axes, ["uniform", "pairs"]): rows = [r for r in e3["byGenAndSize"] if r["gen"] == g] ns = [r["n"] for r in rows] for key, label, col, mk in strat: y = [r[key]["unsettledFraction"] * 100 for r in rows] lo = [max(0.0, (r[key]["unsettledFraction"] - r[key]["unsettledWilson95"][0]) * 100) for r in rows] hi = [max(0.0, (r[key]["unsettledWilson95"][1] - r[key]["unsettledFraction"]) * 100) for r in rows] ax.errorbar(ns, y, yerr=[lo, hi], color=col, marker=mk, lw=2, capsize=3, label=label) ax.set_title(names[g], loc="left", fontsize=13) ax.set_xticks(ns) ax.set_xlabel("People in the group") ax.set_ylim(-3, 103) axes[0].set_ylabel("Ledgers left unsettled after\npaying every simplified row (%)") h, l = axes[0].get_legend_handles_labels() fig.legend(h, l, loc="upper center", ncol=3, frameon=False, bbox_to_anchor=(0.5, 1.0)) save(fig, "fig4-routed-payments.svg", top=0.9) # Figure 5: runtime. e5 = json.loads((res / "e5_runtime.json").read_text()) fig, ax = plt.subplots(figsize=(7.0, 4.2)) ops = [("netBalances", "Net balances", BLUE, "s"), ("settlementsDirect", "Direct plan", GREEN, "o"), ("settlementsSimplified", "Simplified plan", ORANGE, "^"), ("decomposeWholePlan", "Decompose every simplified row", PURPLE, "D")] for op, label, col, mk in ops: rows = [r for r in e5["rows"] if r["op"] == op and r["n"] == 10] ax.plot([r["m"] for r in rows], [r["cpu_min_us"] for r in rows], color=col, marker=mk, lw=2, label=label) ax.set_xscale("log") ax.set_yscale("log") ax.set_xticks([10, 100, 1000]) ax.xaxis.set_minor_locator(NullLocator()) ax.set_xticklabels(["10", "100", "1,000"]) ax.set_xlabel("Expenses (group of 10 people)") ax.set_ylabel("CPU time per call, best of 21 (µs)") plain_log_y(ax, [1, 10, 100, 1000, 10000]) ax.set_title("Cost grows linearly with expenses", loc="left") ax.legend(loc="upper left", frameon=False) save(fig, "fig5-runtime.svg") print("figures written to", out)