#[cfg(test)]
mod tests {
use std::panic::{catch_unwind, AssertUnwindSafe};
use std::time::Instant;
use approx::assert_relative_eq;
use nalgebra::DVector;
use crate::numerical::Nonlinear_systems::engine::{
DiagnosticsOptions, NewtonMethod, SolveOptions,
};
use crate::numerical::Nonlinear_systems::error::SolveError;
use crate::numerical::Nonlinear_systems::prelude::{
DampedNewtonMethod, DampedNewtonMethodAdvanced, LevenbergMarquardtMethod,
LevenbergMarquardtMinpack, NielsenLevenbergMarquardtMethod,
NielsenLevenbergMarquardtMethodAdvanced, NonlinearSolverMethod, PowellDoglegMethod,
PreparedSymbolicNonlinearProblem, SymbolicNonlinearProblem, SymbolicProblemOptions,
TrustRegionLMMethod, TrustRegionMethod,
};
use crate::numerical::Nonlinear_systems::symbolic_aot_test_support::{
aot_solver_test_guard, register_parameterized_dense_backend,
};
use crate::numerical::Nonlinear_systems::symbolic_generated::{
SymbolicAotBuildPolicy, SymbolicGeneratedBackendConfig,
};
use crate::symbolic::codegen::codegen_aot_runtime_link::unregister_linked_dense_backend;
use crate::symbolic::codegen::rust_backend::codegen_aot_build::AotBuildProfile;
const RUNS: usize = 5;
fn equations() -> Vec<String> {
vec!["a*x+y-3".to_string(), "x-y".to_string()]
}
fn problem_options() -> SymbolicProblemOptions {
SymbolicProblemOptions::new()
.with_variables(vec!["x".to_string(), "y".to_string()])
.with_equation_parameters(vec!["a".to_string()])
}
fn solve_options() -> SolveOptions {
SolveOptions {
tolerance: 1e-10,
max_iterations: 32,
diagnostics: DiagnosticsOptions {
collect_history: false,
collect_statistics: true,
..DiagnosticsOptions::default()
},
..SolveOptions::default()
}
}
fn parameter_sweep() -> [(f64, f64); RUNS] {
[
(1.0, 1.5),
(2.0, 1.0),
(3.0, 0.75),
(4.0, 0.6),
(8.0, 1.0 / 3.0),
]
}
#[derive(Default)]
struct SweepSummary {
bind_solve_ms: Vec<f64>,
residual_ms: Vec<f64>,
jacobian_ms: Vec<f64>,
linear_ms: Vec<f64>,
final_errors: Vec<f64>,
}
fn run_sweep(prepared: &PreparedSymbolicNonlinearProblem) -> SweepSummary {
let mut summary = SweepSummary::default();
for (parameter, expected) in parameter_sweep() {
let started = Instant::now();
let bound = prepared
.bind_values(DVector::from_vec(vec![parameter]))
.expect("parameter binding should be valid");
let result = NonlinearSolverMethod::Newton(NewtonMethod)
.solve(&bound, DVector::from_vec(vec![0.5, 0.5]), solve_options())
.expect("parameter sweep solve should succeed");
summary
.bind_solve_ms
.push(started.elapsed().as_secs_f64() * 1e3);
summary
.residual_ms
.push(result.statistics.residual_duration.as_secs_f64() * 1e3);
summary
.jacobian_ms
.push(result.statistics.jacobian_duration.as_secs_f64() * 1e3);
summary
.linear_ms
.push(result.statistics.linear_solve_duration.as_secs_f64() * 1e3);
let expected_error =
((result.x[0] - expected).powi(2) + (result.x[1] - expected).powi(2)).sqrt();
summary.final_errors.push(expected_error);
assert_relative_eq!(result.x[0], expected, epsilon = 1e-9);
assert_relative_eq!(result.x[1], expected, epsilon = 1e-9);
}
summary
}
fn mean(values: &[f64]) -> f64 {
values.iter().sum::<f64>() / values.len() as f64
}
fn format_metric(values: &[f64]) -> String {
let average = mean(values);
let min = values.iter().copied().fold(f64::INFINITY, f64::min);
let max = values.iter().copied().fold(f64::NEG_INFINITY, f64::max);
format!("{average:.3}[{min:.3},{max:.3}]")
}
fn format_metric_with_std(values: &[f64]) -> String {
if values.is_empty() {
return "-".to_string();
}
let average = mean(values);
let variance = values
.iter()
.map(|value| (value - average).powi(2))
.sum::<f64>()
/ values.len() as f64;
let min = values.iter().copied().fold(f64::INFINITY, f64::min);
let max = values.iter().copied().fold(f64::NEG_INFINITY, f64::max);
format!("{average:.3}+/-{:.3}[{min:.3},{max:.3}]", variance.sqrt())
}
fn invalid_parameter_updates_are_atomic() -> usize {
let mut problem = SymbolicNonlinearProblem::from_strings_with_options(
equations(),
problem_options().with_equation_parameter_values(DVector::from_vec(vec![2.0])),
)
.expect("parameterized problem should be valid");
let key_before = problem
.prepare_dense_aot_problem(Default::default())
.problem_key();
let jacobian_before = problem.symbolic_jacobian().to_vec();
let invalid_updates = [
DVector::from_vec(vec![]),
DVector::from_vec(vec![f64::NAN]),
DVector::from_vec(vec![f64::INFINITY]),
];
let invalid_update_count = invalid_updates.len();
for candidate in invalid_updates {
let error = problem
.set_parameter_values(candidate)
.expect_err("invalid parameter update must be rejected");
assert!(matches!(
error,
SolveError::DimensionMismatch {
context: "nonlinear parameter values",
..
} | SolveError::NonFiniteParameterValue { .. }
));
assert_eq!(
problem.parameter_values().expect("old values").as_slice(),
&[2.0]
);
}
problem
.set_parameter_values(DVector::from_vec(vec![4.0]))
.expect("valid parameter update should succeed");
assert_eq!(
problem.parameter_values().expect("new values").as_slice(),
&[4.0]
);
assert_eq!(
problem
.prepare_dense_aot_problem(Default::default())
.problem_key(),
key_before
);
assert_eq!(problem.symbolic_jacobian(), jacobian_before.as_slice());
invalid_update_count
}
#[test]
fn parameter_sweep_rejects_invalid_updates_without_mutating_prepared_state() {
assert_eq!(invalid_parameter_updates_are_atomic(), 3);
}
#[test]
fn lambdify_realistic_coupled_corpus_reports_uniform_stage_metrics() {
const DIMENSION: usize = 16;
const RUNS: usize = 3;
let target = (0..DIMENSION)
.map(|index| 1.0 + index as f64 * 0.015)
.collect::<Vec<_>>();
let equations = (0..DIMENSION)
.map(|index| {
let variable = format!("x{index}");
let mut equation =
format!("a*({variable}^2-{:.17})", target[index] * target[index]);
if index > 0 {
equation.push_str(&format!("+0.04*(x{}-{:.17})", index - 1, target[index - 1]));
}
if index + 1 < DIMENSION {
equation.push_str(&format!("+0.04*(x{}-{:.17})", index + 1, target[index + 1]));
}
equation
})
.collect::<Vec<_>>();
let variables = (0..DIMENSION)
.map(|index| format!("x{index}"))
.collect::<Vec<_>>();
let prepared = PreparedSymbolicNonlinearProblem::from_strings(
equations,
SymbolicProblemOptions::new()
.with_variables(variables)
.with_equation_parameters(vec!["a".to_string()])
.with_lambdify_backend(),
)
.expect("realistic Lambdify corpus should prepare");
let methods = vec![
NonlinearSolverMethod::Newton(
crate::numerical::Nonlinear_systems::engine::NewtonMethod,
),
NonlinearSolverMethod::DampedNewton(DampedNewtonMethod::default()),
NonlinearSolverMethod::DampedNewtonAdvanced(DampedNewtonMethodAdvanced::default()),
NonlinearSolverMethod::LevenbergMarquardt(LevenbergMarquardtMethod::default()),
NonlinearSolverMethod::LevenbergMarquardtMinpack(LevenbergMarquardtMinpack::default()),
NonlinearSolverMethod::NielsenLevenbergMarquardt(
NielsenLevenbergMarquardtMethod::default(),
),
NonlinearSolverMethod::NielsenLevenbergMarquardtAdvanced(
NielsenLevenbergMarquardtMethodAdvanced::default(),
),
NonlinearSolverMethod::TrustRegion(TrustRegionMethod::default()),
NonlinearSolverMethod::PowellDogleg(PowellDoglegMethod::default()),
NonlinearSolverMethod::TrustRegionLM(TrustRegionLMMethod::default()),
];
let options = SolveOptions {
tolerance: 1e-10,
max_iterations: 80,
bounds: Some(
crate::numerical::Nonlinear_systems::problem::Bounds::new(vec![
(0.0, 2.0);
DIMENSION
])
.expect("realistic corpus bounds should validate"),
),
diagnostics: DiagnosticsOptions {
collect_history: false,
collect_statistics: true,
..DiagnosticsOptions::default()
},
..SolveOptions::default()
};
println!(
"[Nonlinear Lambdify story] dimension={DIMENSION}, parameter_values=0.5/1.0/2.0, runs={RUNS}; timings are ms mean+/-std[min,max]"
);
println!(
"method | cases | converged | nonconverged | typed_errors | panics | total_ms | residual_ms | jacobian_ms | linear_ms | residual_calls | jacobian_calls | linear_calls | rejected"
);
for method_template in methods {
let method_name = method_template.name();
let mut total_ms = Vec::new();
let mut residual_ms = Vec::new();
let mut jacobian_ms = Vec::new();
let mut linear_ms = Vec::new();
let mut residual_calls = Vec::new();
let mut jacobian_calls = Vec::new();
let mut linear_calls = Vec::new();
let mut rejected_steps = Vec::new();
let mut converged = 0;
let mut nonconverged = 0;
let mut typed_errors = 0;
let mut panics = 0;
for parameter in [0.5, 1.0, 2.0] {
let bound = prepared
.bind_values(DVector::from_vec(vec![parameter]))
.expect("realistic parameter binding should validate");
for _ in 0..RUNS {
let initial = DVector::from_element(DIMENSION, 0.8);
let outcome = catch_unwind(AssertUnwindSafe(|| {
method_template
.clone()
.solve(&bound, initial, options.clone())
}));
let result = match outcome {
Ok(Ok(result)) => result,
Ok(Err(error)) => {
typed_errors += 1;
println!(
"[Nonlinear Lambdify story] method={method_name} typed_error={error}"
);
continue;
}
Err(_) => {
panics += 1;
continue;
}
};
assert!(
result.residual_norm.is_finite()
&& result.x.iter().all(|value| value.is_finite())
&& result.residual.iter().all(|value| value.is_finite()),
"{method_name} produced a non-finite realistic Lambdify result: residual={} termination={:?}",
result.residual_norm,
result.termination
);
if matches!(
result.termination,
crate::numerical::Nonlinear_systems::error::TerminationReason::Converged
) {
assert!(
result.residual_norm <= 1e-8,
"{method_name} reported convergence with an inaccurate solution: residual={}",
result.residual_norm
);
for (value, expected) in result.x.iter().zip(&target) {
assert!((value - expected).abs() <= 1e-7);
}
converged += 1;
} else {
nonconverged += 1;
}
let statistics = result.statistics;
total_ms.push(statistics.total_duration.as_secs_f64() * 1e3);
residual_ms.push(statistics.residual_duration.as_secs_f64() * 1e3);
jacobian_ms.push(statistics.jacobian_duration.as_secs_f64() * 1e3);
linear_ms.push(statistics.linear_solve_duration.as_secs_f64() * 1e3);
residual_calls.push(statistics.residual_evaluations as f64);
jacobian_calls.push(statistics.jacobian_evaluations as f64);
linear_calls.push(statistics.linear_solves as f64);
rejected_steps.push(statistics.rejected_steps as f64);
}
}
assert_eq!(panics, 0, "{method_name} panicked during the story");
println!(
"{method_name} | {} | {converged} | {nonconverged} | {typed_errors} | {panics} | {} | {} | {} | {} | {} | {} | {} | {}",
3 * RUNS,
format_metric_with_std(&total_ms),
format_metric_with_std(&residual_ms),
format_metric_with_std(&jacobian_ms),
format_metric_with_std(&linear_ms),
format_metric(&residual_calls),
format_metric(&jacobian_calls),
format_metric(&linear_calls),
format_metric(&rejected_steps),
);
}
}
#[test]
#[ignore = "builds a generated nonlinear AOT artifact and measures warm parameter reuse"]
fn parameter_sweep_lambdify_vs_generated_aot_reuses_prepared_backend() {
let _guard = aot_solver_test_guard();
let invalid_updates = invalid_parameter_updates_are_atomic();
let lambdify_started = Instant::now();
let lambdify = PreparedSymbolicNonlinearProblem::from_strings(
equations(),
problem_options().with_lambdify_backend(),
)
.expect("Lambdify preparation should succeed");
let lambdify_prepare_ms = lambdify_started.elapsed().as_secs_f64() * 1e3;
let lambdify_summary = run_sweep(&lambdify);
let output_dir = tempfile::tempdir().expect("AOT output directory should exist");
let aot_started = Instant::now();
let built = crate::numerical::Nonlinear_systems::symbolic::SymbolicNonlinearProblem::from_strings_with_generated_backend(
equations(),
problem_options().with_lambdify_backend(),
SymbolicGeneratedBackendConfig::defaults()
.with_build_policy(SymbolicAotBuildPolicy::BuildIfMissing {
profile: AotBuildProfile::Release,
})
.with_output_parent_dir(Some(output_dir.path().to_path_buf())),
)
.expect("generated AOT build should succeed");
let aot_build_ms = aot_started.elapsed().as_secs_f64() * 1e3;
assert!(
built.build_result.is_some(),
"cold AOT build should be recorded"
);
let resolver = built
.updated_resolver
.clone()
.expect("AOT build should return a resolver");
let problem_key = resolver
.registry()
.problem_keys()
.into_iter()
.next()
.expect("AOT resolver should contain the parameterized problem");
register_parameterized_dense_backend(&problem_key);
let reuse_started = Instant::now();
let aot = crate::numerical::Nonlinear_systems::symbolic::SymbolicNonlinearProblem::from_strings_with_generated_backend(
equations(),
problem_options().with_lambdify_backend(),
SymbolicGeneratedBackendConfig::require_prebuilt().with_resolver(Some(resolver)),
)
.expect("RequirePrebuilt should reuse the generated backend");
let aot_reuse_ms = reuse_started.elapsed().as_secs_f64() * 1e3;
assert_eq!(
aot.selected_backend,
crate::numerical::Nonlinear_systems::symbolic_backend::
SelectedSymbolicNonlinearBackendKind::AotCompiled
);
assert!(
aot.build_result.is_none(),
"warm AOT reuse must not rebuild"
);
let aot_summary = run_sweep(&aot.into_prepared());
println!(
"[Nonlinear parameter sweep] runs={RUNS}; invalid_updates={invalid_updates}; warm metrics are mean[min,max] milliseconds"
);
println!(
"backend | prepare_or_build_ms | require_prebuilt_ms | bind_solve_ms | residual_ms | jacobian_ms | linear_ms | max_solution_error"
);
println!(
"Lambdify | {lambdify_prepare_ms:.3} | - | {} | {} | {} | {} | {:.3e}",
format_metric(&lambdify_summary.bind_solve_ms),
format_metric(&lambdify_summary.residual_ms),
format_metric(&lambdify_summary.jacobian_ms),
format_metric(&lambdify_summary.linear_ms),
lambdify_summary
.final_errors
.iter()
.copied()
.fold(0.0, f64::max),
);
println!(
"AOT | {aot_build_ms:.3} | {aot_reuse_ms:.3} | {} | {} | {} | {} | {:.3e}",
format_metric(&aot_summary.bind_solve_ms),
format_metric(&aot_summary.residual_ms),
format_metric(&aot_summary.jacobian_ms),
format_metric(&aot_summary.linear_ms),
aot_summary.final_errors.iter().copied().fold(0.0, f64::max),
);
unregister_linked_dense_backend(&problem_key);
}
}