113 lines
3.3 KiB
Markdown
113 lines
3.3 KiB
Markdown
# Benchmarks
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This directory contains performance benchmarks for the ODE solver library.
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## Running Benchmarks
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To run all benchmarks:
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```bash
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cargo bench
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```
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To run a specific benchmark file:
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```bash
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cargo bench --bench bs3_vs_dp5
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cargo bench --bench simple_1d
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cargo bench --bench orbit
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```
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## Benchmark Suites
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### `bs3_vs_dp5.rs` - BS3 vs DP5 Comparison
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Comprehensive performance comparison between the Bogacki-Shampine 3(2) method (BS3) and Dormand-Prince 4(5) method (DP5).
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**Test Problems:**
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1. **Exponential Decay** - Simple 1D problem: `y' = -0.5*y`
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2. **Harmonic Oscillator** - 2D conservative system: `y'' + y = 0`
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3. **Nonlinear Pendulum** - Nonlinear 2D system with trigonometric terms
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4. **Orbital Mechanics** - 6D system with gravitational dynamics
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5. **Interpolation** - Performance of dense output interpolation
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6. **Tolerance Scaling** - How methods perform across tolerance ranges (1e-3 to 1e-7)
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**Expected Results:**
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- **BS3** should be faster for moderate tolerances (1e-3 to 1e-6) on simple problems
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- Lower overhead: 4 stages vs 7 stages for DP5
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- FSAL property: effective cost ~3 function evaluations per step
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- **DP5** should be faster for tight tolerances (< 1e-7)
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- Higher order allows larger steps
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- Better for problems requiring high accuracy
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- **Interpolation**: DP5 has more sophisticated interpolation, may be faster/more accurate
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### `simple_1d.rs` - Simple 1D Problem
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Basic benchmark for a simple 1D exponential decay problem using DP5.
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### `orbit.rs` - Orbital Mechanics
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6D orbital mechanics problem using DP5.
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## Benchmark Results Interpretation
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Criterion outputs timing statistics for each benchmark:
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- **Time**: Mean execution time with confidence interval
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- **Outliers**: Number of measurements significantly different from the mean
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- **Plots**: Stored in `target/criterion/` (if gnuplot is available)
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### Performance Comparison
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When comparing BS3 vs DP5:
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1. **For moderate accuracy (tol ~ 1e-5)**:
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- BS3 typically uses ~1.5-2x the time per problem
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- But this can vary by problem characteristics
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2. **For high accuracy (tol ~ 1e-7)**:
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- DP5 becomes more competitive or faster
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- Higher order allows fewer steps
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3. **Memory usage**:
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- BS3: Stores 4 values for dense output [y0, y1, f0, f1]
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- DP5: Stores 5 values for dense output [rcont1..rcont5]
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- Difference is minimal for most problems
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## Notes
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- Benchmarks use `std::hint::black_box()` to prevent compiler optimizations
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- Each benchmark runs multiple iterations to get statistically significant results
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- Results may vary based on:
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- System load
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- CPU frequency scaling
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- Compiler optimizations
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- Problem characteristics (stiffness, nonlinearity, dimension)
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## Adding New Benchmarks
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To add a new benchmark:
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1. Create a new file in `benches/` (e.g., `my_benchmark.rs`)
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2. Add benchmark configuration to `Cargo.toml`:
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```toml
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[[bench]]
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name = "my_benchmark"
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harness = false
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```
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3. Use the Criterion framework:
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```rust
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use criterion::{criterion_group, criterion_main, Criterion};
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use std::hint::black_box;
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fn my_bench(c: &mut Criterion) {
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c.bench_function("my_test", |b| {
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b.iter(|| {
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black_box({
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// Code to benchmark
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});
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});
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});
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}
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criterion_group!(benches, my_bench);
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criterion_main!(benches);
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```
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