//! Performance Optimization Demo
//!
//! This example demonstrates how to use the performance monitoring and profiling
//! capabilities to identify bottlenecks and optimize numerical algorithms.
//!
//! The example compares different integration methods while monitoring their
//! performance characteristics and providing optimization recommendations.
use ndarray::{Array1, Array2, ArrayView1};
use scirs2_integrate::{
monte_carlo::{monte_carlo, MonteCarloOptions},
// Standard integration methods
ode::{solve_ivp, ODEMethod, ODEOptions},
// Parallel optimization
parallel_optimization::{
ArithmeticOp, ParallelOptimizer, ReductionOp, VectorOperation, VectorizedComputeTask,
},
// Performance monitoring
performance_monitor::{PerformanceAnalyzer, PerformanceProfiler, PerformanceReport},
quad::quad,
romberg::romberg,
IntegrateResult,
};
use std::time::{Duration, Instant};
/// Benchmark different integration methods with performance monitoring
#[allow(dead_code)]
fn main() -> IntegrateResult<()> {
println!("=== Performance Optimization Demo ===\n");
// Benchmark 1: ODE solving with different methods
benchmark_ode_methods()?;
// Benchmark 2: Quadrature methods comparison
benchmark_quadrature_methods()?;
// Benchmark 3: Parallel optimization showcase
benchmark_parallel_operations()?;
// Benchmark 4: Memory usage optimization
benchmark_memory_efficiency()?;
Ok(())
}
/// Benchmark different ODE solving methods
#[allow(dead_code)]
fn benchmark_ode_methods() -> IntegrateResult<()> {
println!("1. ODE Methods Performance Comparison");
println!(" Solving stiff Van der Pol oscillator...\n");
let methods = vec![
("RK45", ODEMethod::RK45),
("BDF", ODEMethod::Bdf),
("Radau", ODEMethod::Radau),
];
// Van der Pol oscillator: y'' - μ(1-y²)y' + y = 0
// Convert to first-order system
let mu = 10.0; // Stiffness parameter
let ode_fn = move |_t: f64, y: ArrayView1<f64>| {
Array1::from_vec(vec![y[1], mu * (1.0 - y[0] * y[0]) * y[1] - y[0]])
};
let t_span = [0.0, 20.0];
let y0 = Array1::from_vec(vec![2.0, 0.0]);
for (method_name, method) in methods {
let mut profiler = PerformanceProfiler::new();
profiler.start_phase("ode_solving");
let options = ODEOptions {
method,
rtol: 1e-6,
atol: 1e-9,
max_step: Some(0.1),
h0: Some(1e-3),
..Default::default()
};
let start_memory = estimate_memory_usage();
let result = solve_ivp(ode_fn, t_span, y0.clone(), Some(options));
let peak_memory = estimate_memory_usage();
profiler.end_phase("ode_solving");
profiler.update_memory_stats(start_memory, peak_memory);
// Estimate function evaluations based on method and solution points
let estimated_evaluations = if let Ok(ref solution) = result {
match method {
ODEMethod::RK45 => solution.t.len() * 6, // 6 evaluations per step for RK45
ODEMethod::Bdf => solution.t.len() * 3, // Fewer for implicit methods
ODEMethod::Radau => solution.t.len() * 4,
}
} else {
100 // Default estimate
};
for _ in 0..estimated_evaluations {
profiler.record_function_evaluation();
}
if let Ok(solution) = result {
// Record convergence information
for y_step in &solution.y {
let residual = (y_step[0].powi(2) + y_step[1].powi(2)).sqrt();
profiler.record_convergence(residual);
}
profiler.record_metric("solution_points", solution.t.len() as f64);
profiler.record_metric("final_time", *solution.t.last().unwrap());
}
let metrics = profiler.finalize();
print_method_performance(method_name, &metrics);
}
Ok(())
}
/// Benchmark quadrature methods
#[allow(dead_code)]
fn benchmark_quadrature_methods() -> IntegrateResult<()> {
println!("\n2. Quadrature Methods Performance Comparison");
println!(" Integrating oscillatory function...\n");
// Highly oscillatory function: cos(50x) * exp(-x²)
let test_function = |x: f64| (50.0 * x).cos() * (-x * x).exp();
let methods = vec![
("Adaptive Quad", "adaptive"),
("Romberg", "romberg"),
("Monte Carlo", "monte_carlo"),
];
for (method_name, method_type) in methods {
let mut profiler = PerformanceProfiler::new();
profiler.start_phase("integration");
let start_memory = estimate_memory_usage();
let (result, function_evals) = match method_type {
"adaptive" => {
let quad_result = quad(test_function, -2.0, 2.0, None)?;
profiler.record_metric("error_estimate", quad_result.abs_error);
(quad_result.value, quad_result.n_evals)
}
"romberg" => {
let romberg_result = romberg(test_function, -2.0, 2.0, None)?;
profiler.record_metric("error_estimate", romberg_result.abs_error);
(
romberg_result.value,
2_usize.pow(romberg_result.n_iters as u32 + 1) - 1,
)
}
"monte_carlo" => {
let options = MonteCarloOptions {
n_samples: 100000,
seed: Some(42),
..Default::default()
};
let mc_result = monte_carlo(
|x: ArrayView1<f64>| test_function(x[0]),
&[(-2.0, 2.0)],
Some(options),
)?;
profiler.record_metric("error_estimate", mc_result.std_error);
(mc_result.value, mc_result.n_evals)
}
_ => unreachable!(),
};
let peak_memory = estimate_memory_usage();
profiler.end_phase("integration");
profiler.update_memory_stats(start_memory, peak_memory);
// Record function evaluations
for _ in 0..function_evals {
profiler.record_function_evaluation();
}
profiler.record_metric("integration_result", result);
let metrics = profiler.finalize();
print_method_performance(method_name, &metrics);
}
Ok(())
}
/// Benchmark parallel operations
#[allow(dead_code)]
fn benchmark_parallel_operations() -> IntegrateResult<()> {
println!("\n3. Parallel Operations Performance Benchmark");
println!(" Testing vectorized operations with different configurations...\n");
let mut optimizer = ParallelOptimizer::new(4);
optimizer.initialize()?;
// Create test data
let sizes = vec![1000, 5000, 10000];
let operations = vec![
(
"Exponential",
VectorOperation::ElementWise(ArithmeticOp::Exp),
),
("Sine", VectorOperation::ElementWise(ArithmeticOp::Sin)),
(
"Sum Reduction",
VectorOperation::Reduction(ReductionOp::Sum),
),
(
"Power 2",
VectorOperation::ElementWise(ArithmeticOp::Power(2.0)),
),
];
for size in sizes {
println!(" Matrix size: {}x{}", size, size / 10);
let test_matrix = Array2::from_shape_fn((size, size / 10), |(i, j)| {
(i as f64 * 0.1 + j as f64 * 0.05).sin()
});
for (op_name, operation) in &operations {
let mut profiler = PerformanceProfiler::new();
profiler.start_phase("parallel_operation");
let task = VectorizedComputeTask {
input: test_matrix.clone(),
operation: operation.clone(),
chunk_size: size / 20,
prefer_simd: true,
};
let start_memory = estimate_memory_usage();
let start_time = Instant::now();
let _result = optimizer.execute_vectorized(task)?;
let duration = start_time.elapsed();
let peak_memory = estimate_memory_usage();
profiler.end_phase("parallel_operation");
profiler.update_memory_stats(start_memory, peak_memory);
profiler.estimate_flops(size * (size / 10), duration);
let metrics = profiler.finalize();
println!(
" {}: {:.2}ms, {:.1} MFLOPS, {:.1}MB peak",
op_name,
duration.as_millis(),
metrics.cache_stats.flops.unwrap_or(0.0) / 1e6,
metrics.memory_stats.peak_memory as f64 / (1024.0 * 1024.0)
);
}
println!();
}
Ok(())
}
/// Benchmark memory efficiency
#[allow(dead_code)]
fn benchmark_memory_efficiency() -> IntegrateResult<()> {
println!("4. Memory Efficiency Analysis");
println!(" Comparing memory usage patterns...\n");
let test_scenarios = vec![
("Small frequent allocations", 1000, 100),
("Large infrequent allocations", 10, 10000),
("Balanced allocations", 100, 1000),
];
for (scenario_name, n_allocs, alloc_size) in test_scenarios {
let mut profiler = PerformanceProfiler::new();
profiler.start_phase("memory_test");
let _start_memory = estimate_memory_usage();
let mut data_storage = Vec::new();
// Simulate different allocation patterns
for i in 0..n_allocs {
let data = Array1::from_shape_fn(alloc_size, |j| (i as f64 + j as f64 * 0.1).sin());
data_storage.push(data);
// Record allocation
let current_memory = estimate_memory_usage();
profiler.update_memory_stats(current_memory, current_memory);
}
let _peak_memory = estimate_memory_usage();
// Simulate some computation
let _sum: f64 = data_storage.iter().flat_map(|arr| arr.iter()).sum();
profiler.end_phase("memory_test");
let metrics = profiler.finalize();
let report = PerformanceAnalyzer::generate_report(&metrics);
println!(" {scenario_name}: ");
println!(
" Peak memory: {:.1} MB",
metrics.memory_stats.peak_memory as f64 / (1024.0 * 1024.0)
);
println!(
" Allocations: {}",
metrics.memory_stats.allocation_count
);
if !report.recommendations.is_empty() {
println!(" Recommendations:");
for rec in &report.recommendations {
println!(" - {}: {}", rec.category, rec.suggestion);
}
}
println!();
}
Ok(())
}
/// Print performance metrics for a method
#[allow(dead_code)]
fn print_method_performance(
method_name: &str,
metrics: &scirs2_integrate::performance_monitor::PerformanceMetrics,
) {
println!(" {method_name}: ");
println!(" Time: {:.3}s", metrics.total_time.as_secs_f64());
println!(
" Function evaluations: {}",
metrics.function_evaluations
);
if let Some(eval_rate) = metrics.algorithm_metrics.get("evaluations_per_second") {
println!(" Evaluation rate: {eval_rate:.1} evals/sec");
}
println!(
" Peak memory: {:.1} MB",
metrics.memory_stats.peak_memory as f64 / (1024.0 * 1024.0)
);
// Print convergence information if available
if !metrics.convergence_history.is_empty() {
let final_residual = metrics.convergence_history.last().unwrap();
println!(" Final residual: {final_residual:.2e}");
}
println!();
}
/// Estimate current memory usage (simplified)
#[allow(dead_code)]
fn estimate_memory_usage() -> usize {
// This is a simplified memory estimation
// In a real application, you might use system calls or memory profiling tools
// Return a rough estimate based on typical allocation patterns
// In practice, you'd want to use tools like jemalloc's stats or system APIs
std::mem::size_of::<usize>() * 1024 // Placeholder value
}
/// Create an optimization report
#[allow(dead_code)]
fn create_optimization_report() -> PerformanceReport {
// This would typically be generated from actual performance data
let metrics = scirs2_integrate::performance_monitor::PerformanceMetrics::default();
scirs2_integrate::performance_monitor::PerformanceAnalyzer::generate_report(&metrics)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_performance_demo_components() {
// Test that the basic components work
let _profiler = PerformanceProfiler::new();
let _optimizer = ParallelOptimizer::new(2);
let _memory_estimate = estimate_memory_usage();
assert!(true); // Basic sanity check
}
#[test]
fn test_optimization_workflow() {
// Test a complete optimization workflow
let mut profiler = PerformanceProfiler::new();
profiler.start_phase("test");
// Simulate some work
std::thread::sleep(Duration::from_millis(1));
profiler.end_phase("test");
profiler.record_function_evaluation();
let metrics = profiler.finalize();
assert!(metrics.total_time > Duration::ZERO);
assert_eq!(metrics.function_evaluations, 1);
}
}