Verner 7 Integrator (#1)
Co-authored-by: Connor Johnstone <connor.johnstone@arcfield.com> Reviewed-on: #1
This commit is contained in:
254
benches/vern7_comparison.rs
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254
benches/vern7_comparison.rs
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use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
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use nalgebra::{Vector1, Vector2, Vector6};
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use ordinary_diffeq::prelude::*;
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use std::hint::black_box;
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// Tight tolerance benchmarks - where Vern7 should excel
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// Vern7 is designed for tolerances in the range 1e-8 to 1e-12
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// Simple 1D exponential problem
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// y' = y, y(0) = 1, solution: y(t) = e^t
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fn bench_exponential_tight_tol(c: &mut Criterion) {
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type Params = ();
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fn derivative(_t: f64, y: Vector1<f64>, _p: &Params) -> Vector1<f64> {
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Vector1::new(y[0])
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}
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let y0 = Vector1::new(1.0);
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let controller = PIController::default();
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let mut group = c.benchmark_group("exponential_tight_tol");
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// Tight tolerance - where Vern7 should excel
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let tol = 1e-10;
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group.bench_function("bs3_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 4.0, y0, ());
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let bs3 = BS3::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, bs3, controller).solve();
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});
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});
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});
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group.bench_function("dp5_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 4.0, y0, ());
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let dp45 = DormandPrince45::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, dp45, controller).solve();
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});
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});
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});
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group.bench_function("vern7_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 4.0, y0, ());
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let vern7 = Vern7::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, vern7, controller).solve();
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});
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});
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});
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group.finish();
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}
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// 2D harmonic oscillator - smooth periodic system
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// y'' + y = 0, or as system: y1' = y2, y2' = -y1
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fn bench_harmonic_oscillator_tight_tol(c: &mut Criterion) {
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type Params = ();
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fn derivative(_t: f64, y: Vector2<f64>, _p: &Params) -> Vector2<f64> {
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Vector2::new(y[1], -y[0])
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}
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let y0 = Vector2::new(1.0, 0.0);
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let controller = PIController::default();
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let mut group = c.benchmark_group("harmonic_oscillator_tight_tol");
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let tol = 1e-10;
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group.bench_function("bs3_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 20.0, y0, ());
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let bs3 = BS3::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, bs3, controller).solve();
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});
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});
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});
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group.bench_function("dp5_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 20.0, y0, ());
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let dp45 = DormandPrince45::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, dp45, controller).solve();
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});
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});
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});
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group.bench_function("vern7_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 20.0, y0, ());
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let vern7 = Vern7::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, vern7, controller).solve();
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});
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});
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});
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group.finish();
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}
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// 6D orbital mechanics - high dimensional problem where tight tolerances matter
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fn bench_orbit_tight_tol(c: &mut Criterion) {
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let mu = 3.98600441500000e14;
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type Params = (f64,);
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let params = (mu,);
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fn derivative(_t: f64, state: Vector6<f64>, p: &Params) -> Vector6<f64> {
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let acc = -(p.0 * state.fixed_rows::<3>(0)) / (state.fixed_rows::<3>(0).norm().powi(3));
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Vector6::new(state[3], state[4], state[5], acc[0], acc[1], acc[2])
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}
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let y0 = Vector6::new(
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4.263868426884883e6,
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5.146189057155391e6,
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1.1310208421331816e6,
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-5923.454461876975,
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4496.802639690076,
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1870.3893008991558,
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);
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let controller = PIController::new(0.37, 0.04, 10.0, 0.2, 1000.0, 0.9, 0.01);
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let mut group = c.benchmark_group("orbit_tight_tol");
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// Tight tolerance for orbital mechanics
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let tol = 1e-10;
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group.bench_function("dp5_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 10000.0, y0, params);
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let dp45 = DormandPrince45::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, dp45, controller).solve();
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});
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});
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});
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group.bench_function("vern7_tol_1e-10", |b| {
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let ode = ODE::new(&derivative, 0.0, 10000.0, y0, params);
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let vern7 = Vern7::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, vern7, controller).solve();
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});
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});
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});
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group.finish();
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}
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// Benchmark interpolation performance with lazy dense output
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fn bench_vern7_interpolation(c: &mut Criterion) {
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type Params = ();
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fn derivative(_t: f64, y: Vector1<f64>, _p: &Params) -> Vector1<f64> {
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Vector1::new(y[0])
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}
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let y0 = Vector1::new(1.0);
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let controller = PIController::default();
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let mut group = c.benchmark_group("vern7_interpolation");
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let tol = 1e-10;
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// Vern7 with interpolation (should compute extra stages lazily)
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group.bench_function("vern7_with_interpolation", |b| {
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b.iter(|| {
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black_box({
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let ode = ODE::new(&derivative, 0.0, 5.0, y0, ());
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let vern7 = Vern7::new().a_tol(tol).r_tol(tol);
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let mut problem = Problem::new(ode, vern7, controller);
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let solution = problem.solve();
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// Interpolate at 100 points - first one computes extra stages
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let _: Vec<_> = (0..100).map(|i| solution.interpolate(i as f64 * 0.05)).collect();
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});
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});
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});
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// DP5 with interpolation for comparison
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group.bench_function("dp5_with_interpolation", |b| {
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b.iter(|| {
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black_box({
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let ode = ODE::new(&derivative, 0.0, 5.0, y0, ());
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let dp45 = DormandPrince45::new().a_tol(tol).r_tol(tol);
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let mut problem = Problem::new(ode, dp45, controller);
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let solution = problem.solve();
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let _: Vec<_> = (0..100).map(|i| solution.interpolate(i as f64 * 0.05)).collect();
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});
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});
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});
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group.finish();
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}
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// Tolerance scaling for Vern7 vs lower-order methods
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fn bench_tolerance_scaling_vern7(c: &mut Criterion) {
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type Params = ();
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fn derivative(_t: f64, y: Vector1<f64>, _p: &Params) -> Vector1<f64> {
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Vector1::new(-y[0])
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}
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let y0 = Vector1::new(1.0);
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let controller = PIController::default();
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let mut group = c.benchmark_group("tolerance_scaling_vern7");
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// Focus on tight tolerances where Vern7 excels
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let tolerances = [1e-6, 1e-7, 1e-8, 1e-9, 1e-10];
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for &tol in &tolerances {
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group.bench_with_input(BenchmarkId::new("dp5", tol), &tol, |b, &tol| {
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let ode = ODE::new(&derivative, 0.0, 10.0, y0, ());
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let dp45 = DormandPrince45::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, dp45, controller).solve();
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});
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});
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});
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group.bench_with_input(BenchmarkId::new("vern7", tol), &tol, |b, &tol| {
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let ode = ODE::new(&derivative, 0.0, 10.0, y0, ());
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let vern7 = Vern7::new().a_tol(tol).r_tol(tol);
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b.iter(|| {
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black_box({
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Problem::new(ode, vern7, controller).solve();
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});
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});
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});
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}
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group.finish();
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}
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criterion_group!(
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benches,
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bench_exponential_tight_tol,
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bench_harmonic_oscillator_tight_tol,
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bench_orbit_tight_tol,
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bench_vern7_interpolation,
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bench_tolerance_scaling_vern7,
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);
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criterion_main!(benches);
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