benchmarking.py

import json
import os
import time
from pathlib import Path
from timeit import Timer

import networkx as nx
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from numpy.polynomial import Polynomial
from tqdm import tqdm

from algorithm import solve
from instances import from_graph


def run_and_display(graph_type, max_nodes, repeats_per_record=3, num_unique_n=10, num_runs=40, overwrite=True):
    """Run `num_runs` benchmarks on `graph_type` graphs, each measuring the execution time at `num_unique_n` equally
    spaced node counts between 1 and `max_nodes`. For each such node count, `repeats_per_record` random graphs of that
    many nodes are created, algorithm.solving(...) is run on each, and the median execution time of these runs is
    recorded. The resulting `num_runs` by `num_unique_n` matrix is saved in a dedicated folder inside
    `./output/benchmarking` named after the provided parameters (and the current timestamp if `overwrite=False`),
    together with a number of useful plots of the results."""
    timestamp = time.time() if not overwrite else None
    _record(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp)
    load_and_display(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp)


def load_and_display(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp=None):
    """
    Loads the benchmark matrix generated by `run_and_display` for the given parameters (and `timestamp` if
    `overwrite=False` was used), and generate and save a number of useful plots of this.
    """
    raw, working_dir = _retrieve(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp)
    measurements, nodes, benchmarks = _wrangle(raw)
    if len(raw) == 1:
        _output_simple(measurements, benchmarks, graph_type, outdir=working_dir)
    else:
        _output_comprehensive(measurements, nodes, benchmarks, outdir=working_dir)


def _retrieve(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp=None):
    indir = _dir_from_params(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp)
    with open(indir / f"execution_times.json", "r") as file:
        return json.load(file), indir


def _dir_from_params(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp=None):
    path = f"output/benchmarking/{num_runs}_{graph_type}_{max_nodes}_{num_unique_n}_{repeats_per_record}"
    if timestamp is not None:
        path += f"_{timestamp}"
    os.makedirs(path, exist_ok=True)
    return Path(path)


def _record(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp=None):
    benchmarks = []
    pbar = tqdm(range(num_runs), desc="Benchmarks completed")
    for _ in pbar:
        node_counts, recorded_runtimes = _record_runtimes(graph_type, max_nodes, pbar, repeats_per_record, num_unique_n)
        runtimes = [float(np.median(recorded_runtimes[node_count])) for node_count in node_counts]
        benchmarks.append({"node_count": node_counts.tolist(), "execution_time": runtimes})
    outdir = _dir_from_params(graph_type, max_nodes, repeats_per_record, num_unique_n, num_runs, timestamp)
    with open(outdir / f"execution_times.json", "w") as file:
        json.dump(benchmarks, file, indent=4)


def _record_runtimes(graph_type, max_nodes, pbar, repeats=5, num_unique_n=30):
    nodes_per_n = 2 if graph_type == 'circular ladder' else 1
    n_counts = np.linspace(1, max_nodes // nodes_per_n, num_unique_n, dtype=int)
    node_counts = n_counts * nodes_per_n
    running_order = np.random.default_rng().permutation(np.repeat(range(len(n_counts)), repeats))
    recorded_runtimes = {node_count: [] for node_count in node_counts}
    for i, j in enumerate(running_order):
        recorded_runtimes[node_counts[j]].append(_record_runtime(graph_type, n_counts[j]))
        pbar.set_postfix({f"Progress on benchmark (out of {len(running_order)})": i})
    return node_counts, recorded_runtimes


def _record_runtime(graph_type, n):
    graph = from_graph(
            (nx.cycle_graph if graph_type == "cycle" else
             nx.circular_ladder_graph if graph_type == "circular ladder" else
             nx.complete_graph if graph_type == "complete" else None)(n)
        )
    return Timer(lambda: solve(graph, verbosity=0)).timeit(number=1)


def _wrangle(benchmarks: list[dict[str, list]]):
    dfs = [pd.DataFrame({"nodes": b["node_count"],
                         "seconds": b["execution_time"],
                         "benchmark": np.repeat(i, len(b["node_count"]))})
           for i, b in enumerate(benchmarks)]
    df = pd.concat(dfs, ignore_index=True).reset_index(drop=True)
    nodes = pd.DataFrame({"standard_deviation": df.groupby("nodes").seconds.std()})
    benchmarks = df.groupby("benchmark").apply(
        lambda x: pd.Series({"linear_fit": Polynomial.fit(x=x.nodes, y=x.seconds, deg=1).convert(),
                             "quadratic_fit": Polynomial.fit(x=x.nodes, y=x.seconds, deg=2).convert(),
                             "fourth_fit": Polynomial.fit(x=x.nodes, y=x.seconds, deg=4).convert()})
    )
    return df, nodes, benchmarks


def _output_comprehensive(measurements: pd.DataFrame, nodes: pd.DataFrame, benchmarks: pd.DataFrame, outdir: Path):
    recorded_qcoeffs = benchmarks.quadratic_fit.apply(lambda fit: fit.coef[2])
    print(f"Empirical, two-sided 95% confidence interval of quadratic coefficient in OLS quadratic fit: "
          f"[{np.quantile(recorded_qcoeffs, 0.025):.2}, "
          f"{np.quantile(recorded_qcoeffs, 0.975):.2}]")
    plt.hist(recorded_qcoeffs, bins=10, density=True)
    _decorate_save_show(outdir / "qcoeffs_hist.pdf", xlabel="Quadratic coefficient in OLS quadratic fit")

    recorded_lcoeffs = benchmarks.quadratic_fit.apply(lambda fit: fit.coef[1])
    print(f"Empirical, two-sided 95% confidence interval of linear coefficient in OLS quadratic fit: "
          f"[{np.quantile(recorded_lcoeffs, 0.025):.2}, "
          f"{np.quantile(recorded_lcoeffs, 0.975):.2}]")
    plt.hist(recorded_lcoeffs, bins=10, density=True)
    _decorate_save_show(outdir / "lcoeffs_hist.pdf", xlabel="Linear coefficient in OLS quadratic fit")

    plt.scatter(measurements.nodes, measurements.seconds, marker=".", label="Measurements", zorder=3)
    measurements.join(benchmarks, on="benchmark").groupby("benchmark").apply(
        lambda x: plt.plot(x.nodes, x.quadratic_fit.iloc[0](x.nodes), zorder=1)
    )
    _decorate_save_show(dst=outdir / "scatter.pdf", xlabel="Node count", ylabel="Execution time (seconds)", title="All benchmarks", legend=True)

    plt.plot(nodes.index, nodes.standard_deviation)
    _decorate_save_show(
        dst=outdir / "std.pdf",
        xlabel="Node count",
        ylabel="Standard deviation in execution time (seconds)",
        title="Testing homoscedasticity")


def _decorate_save_show(dst: Path, xlabel=None, ylabel=None, title=None, legend=False):
    plt.xlabel(xlabel)
    plt.ylabel(ylabel)
    plt.title(title)
    if legend:
        plt.legend()
    plt.savefig(dst, bbox_inches='tight')
    plt.show()


def _output_simple(measurements: pd.DataFrame, benchmarks: pd.DataFrame, graph_type: str, outdir: Path):
    ncounts, seconds, qfit = measurements.nodes, measurements.seconds, benchmarks.quadratic_fit.iloc[0]
    plt.plot(ncounts, seconds, "s", label="Measurements", zorder=4)
    if graph_type == "complete":
        simplefit = benchmarks.quadratic_fit.iloc[0]
        complexfit = benchmarks.fourth_fit.iloc[0]
    else:
        simplefit = benchmarks.linear_fit.iloc[0]
        complexfit = benchmarks.quadratic_fit.iloc[0]
    plt.plot(ncounts, simplefit(ncounts), "r", label=_stringify_fit(simplefit), zorder=2)
    plt.plot(ncounts, complexfit(ncounts), "k", label=_stringify_fit(complexfit), zorder=1)
    _decorate_save_show(
        dst=outdir/"scatter.pdf",
        xlabel="Node count",
        ylabel="Execution time (seconds)",
        title="Total execution time (transforming graph, building QCQP,\n"
              f" solving QCQP, merging anti-parallel flows) for {graph_type} graphs",
        legend=True)


def _stringify_fit(fit):
    res = f"{fit.coef[0]:.2}"
    for i, c in enumerate(fit.coef[1:]):
        res += f" + {c:.2} x^{i+1}" if c > 0 else f" - {abs(c):.2} x^{i+1}"
    return res