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Add diagram workbench UI with Modelica DoF coaching and ISO glyphs.

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Ship the Next.js cycle editor with CAD chrome, technical HX symbols, Fixed/Free boundary guidance, and secondary water/air pressure drop support in the solver stack.

Co-authored-by: Cursor <cursoragent@cursor.com>
This commit is contained in:
sepehr
2026-07-17 22:46:46 +02:00
parent 62efea0646
commit 3358b74342
275 changed files with 70187 additions and 5230 deletions
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727
crates/solver/src/strategies/fallback.rs
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@@ -31,7 +31,7 @@ use crate::solver::{
};
use crate::system::System;
use super::{NewtonConfig, PicardConfig};
use super::{HomotopyConfig, NewtonConfig, PicardConfig};
/// Configuration for the intelligent fallback solver.
///
@@ -143,7 +143,7 @@ impl FallbackState {
self.best_residual = Some(residual);
}
}
/// Record a solver switch event (Story 7.4)
fn record_switch(
&mut self,
@@ -188,15 +188,29 @@ pub struct FallbackSolver {
pub newton_config: NewtonConfig,
/// Sequential Substitution (Picard) configuration.
pub picard_config: PicardConfig,
/// Optional Newton-homotopy continuation used as a last-resort recovery.
///
/// When set, the homotopy solver is invoked if both Newton and Picard fail
/// (divergence or non-convergence) from the cold start. This mirrors IPM
/// BOLT's escalating initialization cascade (`GLBL` → `iGLBL` → `PRVS` →
/// `iPRVS`): cheap solvers first, robust continuation only when needed.
/// `None` (default) preserves the original Newton↔Picard-only behaviour.
pub homotopy_config: Option<HomotopyConfig>,
}
impl FallbackSolver {
/// Creates a new fallback solver with the given configuration.
///
/// The Picard fallback stage is configured with Anderson acceleration
/// (depth 3) by default, which converges the fixed-point iteration
/// super-linearly and typically halves the fallback iteration count without
/// affecting robustness. Override via [`Self::with_picard_config`].
pub fn new(config: FallbackConfig) -> Self {
Self {
config,
newton_config: NewtonConfig::default(),
picard_config: PicardConfig::default(),
picard_config: PicardConfig::default().with_anderson(3),
homotopy_config: None,
}
}
@@ -217,13 +231,27 @@ impl FallbackSolver {
self
}
/// Enables Newton-homotopy continuation as a last-resort recovery stage.
///
/// If both Newton and Picard fail from the cold start, the homotopy solver
/// is invoked to walk in from `λ = 0` to `λ = 1` (see [`HomotopyConfig`]).
/// When the supplied config has no `initial_state`, the fallback solver's
/// Newton initial state is reused so all stages share the same cold start.
pub fn with_homotopy(mut self, config: HomotopyConfig) -> Self {
self.homotopy_config = Some(config);
self
}
/// Sets the initial state for cold-start solving (Story 4.6 — builder pattern).
///
/// Delegates to both `newton_config` and `picard_config` so the initial state
/// is used regardless of which solver is active in the fallback loop.
/// Delegates to `newton_config`, `picard_config`, and the optional homotopy
/// stage so the initial state is used regardless of which solver runs.
pub fn with_initial_state(mut self, state: Vec<f64>) -> Self {
self.newton_config.initial_state = Some(state.clone());
self.picard_config.initial_state = Some(state);
self.picard_config.initial_state = Some(state.clone());
if let Some(ref mut h) = self.homotopy_config {
h.initial_state = Some(state);
}
self
}
@@ -251,10 +279,10 @@ impl FallbackSolver {
timeout: Option<Duration>,
) -> Result<ConvergedState, SolverError> {
let mut state = FallbackState::new();
// Verbose mode setup
let verbose_enabled = self.config.verbose_config.enabled
&& self.config.verbose_config.is_any_enabled();
let verbose_enabled =
self.config.verbose_config.enabled && self.config.verbose_config.is_any_enabled();
let mut diagnostics = if verbose_enabled {
Some(ConvergenceDiagnostics::with_capacity(100))
} else {
@@ -264,7 +292,7 @@ impl FallbackSolver {
// Pre-configure solver configs once
let mut newton_cfg = self.newton_config.clone();
let mut picard_cfg = self.picard_config.clone();
// Propagate verbose config to child solvers
newton_cfg.verbose_config = self.config.verbose_config.clone();
picard_cfg.verbose_config = self.config.verbose_config.clone();
@@ -301,17 +329,18 @@ impl FallbackSolver {
if let Some(ref mut diag) = diagnostics {
diag.iterations = state.total_iterations;
diag.final_residual = converged.final_residual;
diag.best_residual = state.best_residual.unwrap_or(converged.final_residual);
diag.best_residual =
state.best_residual.unwrap_or(converged.final_residual);
diag.converged = true;
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.final_solver = Some(state.current_solver.into());
diag.solver_switches = state.switch_events.clone();
// Merge iteration history from child solver if available
if let Some(ref child_diag) = converged.diagnostics {
diag.iteration_history = child_diag.iteration_history.clone();
}
if self.config.verbose_config.log_residuals {
tracing::info!("{}", diag.summary());
}
@@ -327,287 +356,385 @@ impl FallbackSolver {
switch_count = state.switch_count,
"Fallback solver converged"
);
// Return with diagnostics if verbose mode enabled
return Ok(if let Some(d) = diagnostics {
ConvergedState { diagnostics: Some(d), ..converged }
} else { converged });
ConvergedState {
diagnostics: Some(d),
..converged
}
} else {
converged
});
}
Err(SolverError::Timeout { timeout_ms }) => {
// Story 4.5 - AC: #4: Return best state on timeout if available
if let (Some(best_state), Some(best_residual)) =
(state.best_state.clone(), state.best_residual)
{
tracing::info!(
best_residual = best_residual,
"Returning best state across all solver invocations on timeout"
);
return Ok(ConvergedState::new(
best_state,
state.total_iterations,
best_residual,
ConvergenceStatus::TimedOutWithBestState,
SimulationMetadata::new(system.input_hash()),
));
}
return Err(SolverError::Timeout { timeout_ms });
}
Err(SolverError::Divergence { ref reason }) => {
// Handle divergence based on current solver and state
if !self.config.fallback_enabled {
tracing::info!(
solver = match state.current_solver {
CurrentSolver::Newton => "NewtonRaphson",
CurrentSolver::Picard => "Picard",
},
reason = reason,
"Divergence detected, fallback disabled"
);
return result;
}
match state.current_solver {
CurrentSolver::Newton => {
// Get residual from error context (use best known)
let residual_at_switch = state.best_residual.unwrap_or(f64::MAX);
// Newton diverged - switch to Picard (stay there permanently after max switches)
if state.switch_count >= self.config.max_fallback_switches {
// Max switches reached - commit to Picard permanently
state.committed_to_picard = true;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::Divergence,
residual_at_switch,
);
// Verbose logging
if verbose_enabled && self.config.verbose_config.log_solver_switches {
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "divergence",
switch_count = state.switch_count,
residual = residual_at_switch,
"Solver switch (max switches reached)"
);
}
Err(err) => {
let child_diagnostics = err.diagnostics().cloned();
match err.without_diagnostics() {
SolverError::Timeout { timeout_ms } => {
// Story 4.5 - AC: #4: Return best state on timeout if available
if let (Some(best_state), Some(best_residual)) =
(state.best_state.clone(), state.best_residual)
{
tracing::info!(
best_residual = best_residual,
"Returning best state across all solver invocations on timeout"
);
return Ok(ConvergedState::new(
best_state,
state.total_iterations,
best_residual,
ConvergenceStatus::TimedOutWithBestState,
SimulationMetadata::new(system.input_hash()),
));
}
return Err(SolverError::Timeout { timeout_ms }
.with_optional_diagnostics(child_diagnostics));
}
SolverError::Divergence { reason } => {
// Handle divergence based on current solver and state
if !self.config.fallback_enabled {
tracing::info!(
solver = match state.current_solver {
CurrentSolver::Newton => "NewtonRaphson",
CurrentSolver::Picard => "Picard",
},
reason = reason,
"Divergence detected, fallback disabled"
);
return Err(SolverError::Divergence { reason }
.with_optional_diagnostics(child_diagnostics));
}
match state.current_solver {
CurrentSolver::Newton => {
// Get residual from error context (use best known)
let residual_at_switch =
state.best_residual.unwrap_or(f64::MAX);
// Newton diverged - switch to Picard (stay there permanently after max switches)
if state.switch_count >= self.config.max_fallback_switches {
// Max switches reached - commit to Picard permanently
state.committed_to_picard = true;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::Divergence,
residual_at_switch,
);
// Verbose logging
if verbose_enabled
&& self.config.verbose_config.log_solver_switches
{
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "divergence",
switch_count = state.switch_count,
residual = residual_at_switch,
"Solver switch (max switches reached)"
);
}
tracing::info!(
switch_count = state.switch_count,
max_switches = self.config.max_fallback_switches,
"Max switches reached, committing to Picard permanently"
);
} else {
// Switch to Picard
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::Divergence,
residual_at_switch,
);
// Verbose logging
if verbose_enabled && self.config.verbose_config.log_solver_switches {
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "divergence",
switch_count = state.switch_count,
residual = residual_at_switch,
"Solver switch"
);
} else {
// Switch to Picard
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::Divergence,
residual_at_switch,
);
// Verbose logging
if verbose_enabled
&& self.config.verbose_config.log_solver_switches
{
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "divergence",
switch_count = state.switch_count,
residual = residual_at_switch,
"Solver switch"
);
}
tracing::warn!(
switch_count = state.switch_count,
reason = reason,
"Newton diverged, switching to Picard"
);
}
// Continue loop with Picard
}
tracing::warn!(
switch_count = state.switch_count,
reason = reason,
"Newton diverged, switching to Picard"
);
}
// Continue loop with Picard
}
CurrentSolver::Picard => {
// Picard diverged - if we were trying Newton again, commit to Picard permanently
if state.switch_count > 0 && !state.committed_to_picard {
state.committed_to_picard = true;
tracing::info!(
CurrentSolver::Picard => {
// Picard diverged - if we were trying Newton again, commit to Picard permanently
if state.switch_count > 0 && !state.committed_to_picard {
state.committed_to_picard = true;
tracing::info!(
switch_count = state.switch_count,
reason = reason,
"Newton re-diverged after return from Picard, staying on Picard permanently"
);
// Stay on Picard and try again
} else {
// Picard diverged with no return attempt - no more fallbacks available
tracing::warn!(
reason = reason,
"Picard diverged, no more fallbacks available"
);
return result;
// Stay on Picard and try again
} else {
// Picard diverged with no return attempt - no more fallbacks available
tracing::warn!(
reason = reason,
"Picard diverged, no more fallbacks available"
);
return Err(SolverError::Divergence { reason }
.with_optional_diagnostics(child_diagnostics));
}
}
}
}
}
}
Err(SolverError::NonConvergence {
iterations,
final_residual,
}) => {
state.total_iterations += iterations;
// Non-convergence: check if we should try the other solver
if !self.config.fallback_enabled {
return Err(SolverError::NonConvergence {
SolverError::NonConvergence {
iterations,
final_residual,
});
}
} => {
state.total_iterations += iterations;
match state.current_solver {
CurrentSolver::Newton => {
// Newton didn't converge - try Picard
if state.switch_count >= self.config.max_fallback_switches {
// Max switches reached - commit to Picard permanently
state.committed_to_picard = true;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::SlowConvergence,
// Non-convergence: check if we should try the other solver
if !self.config.fallback_enabled {
return Err(SolverError::NonConvergence {
iterations,
final_residual,
);
// Verbose logging
if verbose_enabled && self.config.verbose_config.log_solver_switches {
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "slow_convergence",
switch_count = state.switch_count,
residual = final_residual,
"Solver switch (max switches reached)"
);
}
tracing::info!(
.with_optional_diagnostics(child_diagnostics));
}
match state.current_solver {
CurrentSolver::Newton => {
// Newton didn't converge - try Picard
if state.switch_count >= self.config.max_fallback_switches {
// Max switches reached - commit to Picard permanently
state.committed_to_picard = true;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::SlowConvergence,
final_residual,
);
// Verbose logging
if verbose_enabled
&& self.config.verbose_config.log_solver_switches
{
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "slow_convergence",
switch_count = state.switch_count,
residual = final_residual,
"Solver switch (max switches reached)"
);
}
tracing::info!(
switch_count = state.switch_count,
"Max switches reached, committing to Picard permanently"
);
} else {
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::SlowConvergence,
final_residual,
);
// Verbose logging
if verbose_enabled && self.config.verbose_config.log_solver_switches {
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "slow_convergence",
switch_count = state.switch_count,
residual = final_residual,
"Solver switch"
);
}
tracing::info!(
switch_count = state.switch_count,
iterations = iterations,
final_residual = final_residual,
"Newton did not converge, switching to Picard"
);
}
// Continue loop with Picard
}
CurrentSolver::Picard => {
// Picard didn't converge - check if we should try Newton
if state.committed_to_picard
|| state.switch_count >= self.config.max_fallback_switches
{
tracing::info!(
iterations = iterations,
final_residual = final_residual,
"Picard did not converge, no more fallbacks"
);
return Err(SolverError::NonConvergence {
iterations,
final_residual,
});
}
} else {
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Picard;
// Check if residual is low enough to try Newton
if final_residual < self.config.return_to_newton_threshold {
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Newton;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::ReturnToNewton,
final_residual,
);
// Verbose logging
if verbose_enabled && self.config.verbose_config.log_solver_switches {
tracing::info!(
from = "Picard",
to = "NewtonRaphson",
reason = "return_to_newton",
switch_count = state.switch_count,
residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Solver switch (Picard stabilized)"
);
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::SlowConvergence,
final_residual,
);
// Verbose logging
if verbose_enabled
&& self.config.verbose_config.log_solver_switches
{
tracing::info!(
from = "NewtonRaphson",
to = "Picard",
reason = "slow_convergence",
switch_count = state.switch_count,
residual = final_residual,
"Solver switch"
);
}
tracing::info!(
switch_count = state.switch_count,
iterations = iterations,
final_residual = final_residual,
"Newton did not converge, switching to Picard"
);
}
// Continue loop with Picard
}
CurrentSolver::Picard => {
// Picard didn't converge - check if we should try Newton
if state.committed_to_picard
|| state.switch_count >= self.config.max_fallback_switches
{
tracing::info!(
iterations = iterations,
final_residual = final_residual,
"Picard did not converge, no more fallbacks"
);
return Err(SolverError::NonConvergence {
iterations,
final_residual,
}
.with_optional_diagnostics(child_diagnostics));
}
// Check if residual is low enough to try Newton
if final_residual < self.config.return_to_newton_threshold {
state.switch_count += 1;
let prev_solver = state.current_solver;
state.current_solver = CurrentSolver::Newton;
// Record switch event
state.record_switch(
prev_solver,
state.current_solver,
SwitchReason::ReturnToNewton,
final_residual,
);
// Verbose logging
if verbose_enabled
&& self.config.verbose_config.log_solver_switches
{
tracing::info!(
from = "Picard",
to = "NewtonRaphson",
reason = "return_to_newton",
switch_count = state.switch_count,
residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Solver switch (Picard stabilized)"
);
}
tracing::info!(
switch_count = state.switch_count,
final_residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Picard stabilized, attempting Newton return"
);
// Continue loop with Newton
} else {
// Stay on Picard and keep trying
tracing::debug!(
final_residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Picard not yet stabilized, aborting"
);
return Err(SolverError::NonConvergence {
iterations,
final_residual,
}
.with_optional_diagnostics(child_diagnostics));
}
}
tracing::info!(
switch_count = state.switch_count,
final_residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Picard stabilized, attempting Newton return"
);
// Continue loop with Newton
} else {
// Stay on Picard and keep trying
tracing::debug!(
final_residual = final_residual,
threshold = self.config.return_to_newton_threshold,
"Picard not yet stabilized, aborting"
);
return Err(SolverError::NonConvergence {
iterations,
final_residual,
});
}
}
other => {
// InvalidSystem or other errors - propagate immediately
return Err(other.with_optional_diagnostics(child_diagnostics));
}
}
}
Err(other) => {
// InvalidSystem or other errors - propagate immediately
return Err(other);
}
}
}
}
/// Attempts Newton-homotopy continuation as a last-resort recovery after the
/// primary Newton/Picard stages have failed.
///
/// Returns the homotopy result on success; otherwise returns the *primary*
/// error (the homotopy failure is logged but not surfaced, since the primary
/// error is the more actionable diagnostic). Structural `InvalidSystem`
/// errors are never retried — they indicate a malformed model, not a hard
/// cold start.
fn try_homotopy_recovery(
&self,
system: &mut System,
primary_err: SolverError,
remaining: Option<Duration>,
) -> Result<ConvergedState, SolverError> {
if matches!(primary_err.base_error(), SolverError::InvalidSystem { .. }) {
return Err(primary_err);
}
let Some(mut homotopy) = self.homotopy_config.clone() else {
return Err(primary_err);
};
// Share the cold start with the primary solvers unless explicitly set.
if homotopy.initial_state.is_none() {
homotopy.initial_state = self.newton_config.initial_state.clone();
}
// Inherit the remaining global time budget if the stage has none.
if homotopy.timeout.is_none() {
homotopy.timeout = remaining;
}
tracing::info!(
error = %primary_err,
"Primary solvers failed; attempting Newton-homotopy continuation as last resort"
);
match homotopy.solve(system) {
Ok(converged) => {
tracing::info!(
iterations = converged.iterations,
final_residual = converged.final_residual,
"Homotopy continuation recovered convergence"
);
Ok(converged)
}
Err(homotopy_err) => {
let primary_diagnostics = primary_err.diagnostics().cloned();
let homotopy_diagnostics = homotopy_err.diagnostics().cloned();
let diagnostics = match (primary_diagnostics, homotopy_diagnostics) {
(Some(primary), Some(homotopy)) => {
if homotopy.iterations >= primary.iterations {
Some(homotopy)
} else {
Some(primary)
}
}
(Some(primary), None) => Some(primary),
(None, Some(homotopy)) => Some(homotopy),
(None, None) => None,
};
tracing::warn!(
error = %homotopy_err,
"Homotopy continuation also failed; returning primary error"
);
Err(primary_err
.without_diagnostics()
.with_optional_diagnostics(diagnostics))
}
}
}
@@ -622,20 +749,32 @@ impl Solver for FallbackSolver {
fallback_enabled = self.config.fallback_enabled,
return_to_newton_threshold = self.config.return_to_newton_threshold,
max_fallback_switches = self.config.max_fallback_switches,
homotopy_recovery = self.homotopy_config.is_some(),
"Fallback solver starting"
);
if self.config.fallback_enabled {
let primary = if self.config.fallback_enabled {
self.solve_with_fallback(system, start_time, timeout)
} else {
// Fallback disabled - run pure Newton
self.newton_config.solve(system)
};
match primary {
Ok(converged) => Ok(converged),
Err(primary_err) => {
let remaining = timeout.map(|t| t.saturating_sub(start_time.elapsed()));
self.try_homotopy_recovery(system, primary_err, remaining)
}
}
}
fn with_timeout(mut self, timeout: Duration) -> Self {
self.newton_config.timeout = Some(timeout);
self.picard_config.timeout = Some(timeout);
if let Some(ref mut h) = self.homotopy_config {
h.timeout = Some(timeout);
}
self
}
}
@@ -684,4 +823,60 @@ mod tests {
system.finalize().unwrap();
assert!(boxed.solve(&mut system).is_err());
}
// ── Homotopy last-resort recovery wiring ──────────────────────────────────
#[test]
fn test_fallback_homotopy_disabled_by_default() {
let solver = FallbackSolver::default_solver();
assert!(solver.homotopy_config.is_none());
}
#[test]
fn test_fallback_with_homotopy_sets_config() {
let solver = FallbackSolver::default_solver()
.with_homotopy(HomotopyConfig::default().with_initial_steps(20));
let h = solver
.homotopy_config
.expect("homotopy should be configured");
assert_eq!(h.initial_steps, 20);
}
#[test]
fn test_with_initial_state_propagates_to_homotopy() {
let solver = FallbackSolver::default_solver()
.with_homotopy(HomotopyConfig::default())
.with_initial_state(vec![1.0, 2.0, 3.0]);
assert_eq!(
solver.newton_config.initial_state,
Some(vec![1.0, 2.0, 3.0])
);
assert_eq!(
solver.picard_config.initial_state,
Some(vec![1.0, 2.0, 3.0])
);
assert_eq!(
solver.homotopy_config.unwrap().initial_state,
Some(vec![1.0, 2.0, 3.0])
);
}
#[test]
fn test_with_timeout_propagates_to_homotopy() {
let timeout = Duration::from_millis(750);
let solver = FallbackSolver::default_solver()
.with_homotopy(HomotopyConfig::default())
.with_timeout(timeout);
assert_eq!(solver.homotopy_config.unwrap().timeout, Some(timeout));
}
#[test]
fn test_invalid_system_not_retried_by_homotopy() {
// An empty (degenerate) system yields InvalidSystem; the homotopy stage
// must NOT retry it — a malformed model is not a hard cold start.
let mut solver = FallbackSolver::default_solver().with_homotopy(HomotopyConfig::default());
let mut system = System::new();
system.finalize().unwrap();
assert!(solver.solve(&mut system).is_err());
}
}

496
crates/solver/src/strategies/homotopy.rs Normal file
View File

@@ -0,0 +1,496 @@
//! Newton-homotopy continuation solver for robust cold starts.
//!
//! This module provides [`HomotopyConfig`], a globally-convergent continuation
//! solver that improves on a naive cold start without requiring a database of
//! previous solutions (the IPM BOLT `GLBL`/`iPRVS` approach) or any manual
//! tuning.
//!
//! # The Newton homotopy
//!
//! Given the target system `F(x) = 0` and an arbitrary initial guess `x₀`, define
//! the homotopy
//!
//! ```text
//! H(x, λ) = F(x) − (1 − λ) · F(x₀), λ ∈ [0, 1]
//! ```
//!
//! At `λ = 0`, `H(x₀, 0) = F(x₀) − F(x₀) = 0`, so the initial guess is an
//! **exact** solution of the deformed system. At `λ = 1`, `H(x, 1) = F(x)`, the
//! real system. The solver walks `λ` from 0 to 1, solving `H(·, λ) = 0` with an
//! inner Newton iteration at each step and using the previous converged point as
//! the next initial guess.
//!
//! # Why it reuses the analytic Jacobian unchanged
//!
//! The subtracted term `(1 − λ)·F(x₀)` is **constant in `x`**, so
//!
//! ```text
//! ∂H/∂x = ∂F/∂x = J(x)
//! ```
//!
//! The inner Newton step therefore uses the exact, component-wise analytic
//! Jacobian assembled by [`System::assemble_jacobian`] — no finite differences
//! and no changes to any component are required. This keeps Entropyk's
//! structural advantage over finite-difference solvers (IPM eKINSOL) while adding
//! cold-start robustness. A `use_numerical_jacobian` flag is provided for parity
//! with [`crate::strategies::NewtonConfig`] when a component's analytic Jacobian
//! is unavailable.
//!
//! # Adaptive step control
//!
//! The `λ` increment starts at `1 / initial_steps` and is **halved** whenever an
//! inner Newton solve fails to converge, retrying from the last good `λ`. On
//! success the increment is gently grown again. This predictor–corrector scheme
//! automatically takes small steps through difficult regions (phase boundaries,
//! stiff correlations) and large steps through easy ones.
use std::time::{Duration, Instant};
use crate::jacobian::JacobianMatrix;
use crate::metadata::SimulationMetadata;
use crate::solver::{
apply_newton_step, dominant_residual, ConvergedState, ConvergenceDiagnostics,
ConvergenceStatus, IterationDiagnostics, Solver, SolverError, SolverType,
};
use crate::system::System;
use entropyk_components::JacobianBuilder;
/// Configuration for the Newton-homotopy continuation solver.
///
/// Solves `F(x) = 0` by continuation on the homotopy
/// `H(x, λ) = F(x) − (1 − λ)·F(x₀)` from `λ = 0` (where `x₀` is exact) to
/// `λ = 1` (the real system).
#[derive(Debug, Clone, PartialEq)]
pub struct HomotopyConfig {
/// Initial number of `λ` subdivisions. The starting step is `1 / initial_steps`.
/// Default: 10.
pub initial_steps: usize,
/// Maximum Newton iterations allowed for each inner `λ` solve. Default: 50.
pub inner_max_iterations: usize,
/// Convergence tolerance (L2 residual norm) for each inner `λ` solve.
/// Default: 1e-8.
pub inner_tolerance: f64,
/// Final convergence tolerance (L2 residual norm) checked at `λ = 1`.
/// Default: 1e-6.
pub tolerance: f64,
/// Smallest allowed `λ` increment before the solver gives up. Default: 1e-4.
pub min_lambda_step: f64,
/// Divergence guard: inner residual norm above this aborts the inner solve.
/// Default: 1e12.
pub divergence_threshold: f64,
/// Use a finite-difference Jacobian instead of the analytic one. Default: false.
pub use_numerical_jacobian: bool,
/// Relative step for the finite-difference Jacobian. Default: 1e-5.
pub numerical_epsilon: f64,
/// Optional overall time budget.
pub timeout: Option<Duration>,
/// Initial guess `x₀`. When `None`, a zero vector is used.
pub initial_state: Option<Vec<f64>>,
}
impl Default for HomotopyConfig {
fn default() -> Self {
Self {
initial_steps: 10,
inner_max_iterations: 50,
inner_tolerance: 1e-8,
tolerance: 1e-6,
min_lambda_step: 1e-4,
divergence_threshold: 1e12,
use_numerical_jacobian: false,
numerical_epsilon: 1e-5,
timeout: None,
initial_state: None,
}
}
}
impl HomotopyConfig {
/// Sets the initial guess `x₀` for the continuation.
pub fn with_initial_state(mut self, state: Vec<f64>) -> Self {
self.initial_state = Some(state);
self
}
/// Sets the initial number of `λ` subdivisions.
pub fn with_initial_steps(mut self, steps: usize) -> Self {
self.initial_steps = steps.max(1);
self
}
/// Selects the finite-difference Jacobian (analytic is the default).
pub fn with_numerical_jacobian(mut self, enabled: bool) -> Self {
self.use_numerical_jacobian = enabled;
self
}
/// L2 norm of a residual vector.
fn residual_norm(residuals: &[f64]) -> f64 {
residuals.iter().map(|r| r * r).sum::<f64>().sqrt()
}
fn failure_diagnostics(
&self,
iterations: usize,
final_residual: f64,
residuals: &[f64],
elapsed_ms: u64,
) -> Option<ConvergenceDiagnostics> {
if iterations == 0 {
return None;
}
let (max_residual_index, max_residual) = dominant_residual(residuals);
let mut diagnostics = ConvergenceDiagnostics::with_capacity(1);
diagnostics.iterations = iterations;
diagnostics.final_residual = final_residual;
diagnostics.best_residual = final_residual;
diagnostics.converged = false;
diagnostics.timing_ms = elapsed_ms;
diagnostics.final_solver = Some(SolverType::Homotopy);
diagnostics.push_iteration(IterationDiagnostics {
iteration: iterations,
residual_norm: final_residual,
delta_norm: 0.0,
alpha: Some(1.0),
jacobian_frozen: false,
jacobian_condition: None,
max_residual_index,
max_residual,
});
Some(diagnostics)
}
/// Runs the inner Newton iteration for `H(x, λ) = F(x) − (1 − λ)·r0 = 0`.
///
/// Mutates `state` in place. Returns `Ok(iterations)` if the inner system
/// converged below `inner_tolerance`, or `Err(())` if it diverged, the
/// Jacobian was singular, or the iteration budget was exhausted. On failure
/// the caller restores the previous good state.
#[allow(clippy::too_many_arguments)]
fn inner_newton(
&self,
system: &mut System,
state: &mut [f64],
r0: &[f64],
lambda: f64,
clipping_mask: &[Option<(f64, f64)>],
residuals: &mut Vec<f64>,
residuals_h: &mut Vec<f64>,
jacobian: &mut JacobianMatrix,
jacobian_builder: &mut JacobianBuilder,
) -> Result<usize, ()> {
let offset = 1.0 - lambda;
for k in 0..self.inner_max_iterations {
// Evaluate F(x) and form the homotopy residual H = F − (1 − λ)·r0.
if system.compute_residuals(state, residuals).is_err() {
return Err(());
}
for i in 0..residuals.len() {
residuals_h[i] = residuals[i] - offset * r0[i];
}
let norm = Self::residual_norm(residuals_h.as_slice());
if norm < self.inner_tolerance {
return Ok(k);
}
if !norm.is_finite() || norm > self.divergence_threshold {
return Err(());
}
// ∂H/∂x = ∂F/∂x, so the Jacobian of F is used unchanged.
if self.use_numerical_jacobian {
let eps = self.numerical_epsilon;
let compute = |s: &[f64], r: &mut [f64]| {
let s_vec = s.to_vec();
let mut r_vec = vec![0.0; r.len()];
let res = system.compute_residuals(&s_vec, &mut r_vec);
r.copy_from_slice(&r_vec);
res.map(|_| ()).map_err(|e| format!("{:?}", e))
};
match JacobianMatrix::numerical(compute, state, residuals.as_slice(), eps) {
Ok(jm) => jacobian.as_matrix_mut().copy_from(jm.as_matrix()),
Err(_) => return Err(()),
}
} else {
jacobian_builder.clear();
if system.assemble_jacobian(state, jacobian_builder).is_err() {
return Err(());
}
jacobian.update_from_builder(jacobian_builder.entries());
}
// Solve J·Δx = −H (the solve routine negates the supplied residual).
let delta = match jacobian.solve(residuals_h.as_slice()) {
Some(d) => d,
None => return Err(()),
};
apply_newton_step(state, &delta, clipping_mask, 1.0);
}
// Final convergence check after the last step.
if system.compute_residuals(state, residuals).is_err() {
return Err(());
}
for i in 0..residuals.len() {
residuals_h[i] = residuals[i] - offset * r0[i];
}
if Self::residual_norm(residuals_h.as_slice()) < self.inner_tolerance {
Ok(self.inner_max_iterations)
} else {
Err(())
}
}
}
impl Solver for HomotopyConfig {
fn solve(&mut self, system: &mut System) -> Result<ConvergedState, SolverError> {
let start_time = Instant::now();
let n_state = system.full_state_vector_len();
let n_equations: usize = system
.traverse_for_jacobian()
.map(|(_, c, _)| c.n_equations())
.sum::<usize>()
+ system.constraints().count()
+ system.coupling_residual_count()
+ 2 * system.saturated_controller_count()
+ system.mass_flow_closure_count();
if n_state == 0 || n_equations == 0 {
return Err(SolverError::InvalidSystem {
message: "Empty system has no state variables or equations".to_string(),
});
}
// Working buffers (allocated once, reused across every λ step).
// A caller-supplied initial guess MUST match the system size: silently
// substituting zeros would hide a caller bug behind an opaque later failure.
let mut state: Vec<f64> = match self.initial_state.as_ref() {
Some(s) if s.len() == n_state => s.clone(),
Some(s) => {
return Err(SolverError::InvalidSystem {
message: format!(
"initial_state length {} does not match system state length {}",
s.len(),
n_state
),
});
}
None => vec![0.0; n_state],
};
let mut residuals = vec![0.0; n_equations];
let mut residuals_h = vec![0.0; n_equations];
let mut jacobian = JacobianMatrix::zeros(n_equations, n_state);
let mut jacobian_builder = JacobianBuilder::new();
let mut state_saved = vec![0.0; n_state];
let clipping_mask: Vec<Option<(f64, f64)>> = (0..n_state)
.map(|i| system.get_bounds_for_state_index(i))
.collect();
// r0 = F(x0). By construction H(x0, 0) = 0, so x0 is exact at λ = 0.
system
.compute_residuals(&state, &mut residuals)
.map_err(|e| SolverError::InvalidSystem {
message: format!("Failed to compute initial residuals: {:?}", e),
})?;
let r0 = residuals.clone();
let initial_norm = Self::residual_norm(&r0);
// F(x0) must be finite for the deformation H(x,λ)=F(x)-(1-λ)F(x0) to be
// well defined. A non-finite r0 (e.g. a zero (P,h) cold start hitting the
// fluid backend) would make every continuation step doomed; fail early
// with an actionable message instead of running the whole loop.
if !initial_norm.is_finite() {
return Err(SolverError::InvalidSystem {
message: "Initial residual F(x0) is non-finite; the initial guess is infeasible \
for the fluid backend (provide a physical initial_state)"
.to_string(),
});
}
// Already solved? Skip the continuation entirely.
if initial_norm < self.tolerance {
return Ok(ConvergedState::new(
state,
0,
initial_norm,
ConvergenceStatus::Converged,
SimulationMetadata::new(system.input_hash()),
));
}
let max_step = 4.0 / self.initial_steps.max(1) as f64;
// Guard against a non-positive min step (e.g. struct-literal misconfig),
// which would otherwise let dlambda shrink forever and hang the solver.
let min_lambda_step = self.min_lambda_step.max(1e-12);
let mut lambda = 0.0_f64;
let mut dlambda = 1.0 / self.initial_steps.max(1) as f64;
let mut total_iterations = 0usize;
while lambda < 1.0 {
if let Some(timeout) = self.timeout {
if start_time.elapsed() > timeout {
let compute_ok = system.compute_residuals(&state, &mut residuals).is_ok();
let final_residual = if compute_ok {
Self::residual_norm(&residuals)
} else {
f64::INFINITY
};
let diagnostics = self.failure_diagnostics(
total_iterations,
final_residual,
if compute_ok { &residuals } else { &[] },
start_time.elapsed().as_millis() as u64,
);
return Err(SolverError::Timeout {
timeout_ms: timeout.as_millis() as u64,
}
.with_optional_diagnostics(diagnostics));
}
}
let target = (lambda + dlambda).min(1.0);
state_saved.copy_from_slice(&state);
match self.inner_newton(
system,
&mut state,
&r0,
target,
&clipping_mask,
&mut residuals,
&mut residuals_h,
&mut jacobian,
&mut jacobian_builder,
) {
Ok(iters) => {
total_iterations += iters;
lambda = target;
// Step succeeded: gently grow the increment for the next step.
dlambda = (dlambda * 1.5).min(max_step);
}
Err(()) => {
// Step failed: restore and halve the increment, then retry.
state.copy_from_slice(&state_saved);
dlambda *= 0.5;
if dlambda < min_lambda_step {
// Report the residual at the restored (last-good) state so
// final_residual matches the state we actually return from.
let compute_ok = system.compute_residuals(&state, &mut residuals).is_ok();
let final_residual = if compute_ok {
Self::residual_norm(&residuals)
} else {
f64::INFINITY
};
let diagnostics = self.failure_diagnostics(
total_iterations,
final_residual,
if compute_ok { &residuals } else { &[] },
start_time.elapsed().as_millis() as u64,
);
return Err(SolverError::NonConvergence {
iterations: total_iterations,
final_residual,
}
.with_optional_diagnostics(diagnostics));
}
}
}
}
// At λ = 1, H == F: verify the real system is actually solved.
system
.compute_residuals(&state, &mut residuals)
.map_err(|e| SolverError::InvalidSystem {
message: format!("Failed to compute final residuals: {:?}", e),
})?;
let final_norm = Self::residual_norm(&residuals);
if final_norm < self.tolerance {
let status = if !system.saturated_variables().is_empty() {
ConvergenceStatus::ControlSaturation
} else {
ConvergenceStatus::Converged
};
Ok(ConvergedState::new(
state,
total_iterations,
final_norm,
status,
SimulationMetadata::new(system.input_hash()),
))
} else {
let diagnostics = self.failure_diagnostics(
total_iterations,
final_norm,
&residuals,
start_time.elapsed().as_millis() as u64,
);
Err(SolverError::NonConvergence {
iterations: total_iterations,
final_residual: final_norm,
}
.with_optional_diagnostics(diagnostics))
}
}
fn with_timeout(self, timeout: Duration) -> Self {
Self {
timeout: Some(timeout),
..self
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_homotopy_default_config() {
let cfg = HomotopyConfig::default();
assert_eq!(cfg.initial_steps, 10);
assert!(!cfg.use_numerical_jacobian);
assert!((cfg.tolerance - 1e-6).abs() < 1e-15);
}
#[test]
fn test_homotopy_builders() {
let cfg = HomotopyConfig::default()
.with_initial_steps(20)
.with_numerical_jacobian(true)
.with_initial_state(vec![1.0, 2.0]);
assert_eq!(cfg.initial_steps, 20);
assert!(cfg.use_numerical_jacobian);
assert_eq!(cfg.initial_state, Some(vec![1.0, 2.0]));
}
#[test]
fn test_homotopy_initial_steps_floor_is_one() {
let cfg = HomotopyConfig::default().with_initial_steps(0);
assert_eq!(cfg.initial_steps, 1);
}
#[test]
fn test_homotopy_residual_norm() {
assert!((HomotopyConfig::residual_norm(&[3.0, 4.0]) - 5.0).abs() < 1e-12);
}
#[test]
fn test_homotopy_empty_system_errors() {
let mut system = System::new();
system.finalize().unwrap();
let mut solver = HomotopyConfig::default();
assert!(solver.solve(&mut system).is_err());
}
#[test]
fn test_homotopy_with_timeout_sets_field() {
let cfg = HomotopyConfig::default().with_timeout(Duration::from_millis(250));
assert_eq!(cfg.timeout, Some(Duration::from_millis(250)));
}
}

13
crates/solver/src/strategies/mod.rs
View File

@@ -21,10 +21,12 @@
//! ```
mod fallback;
mod homotopy;
mod newton_raphson;
mod sequential_substitution;
pub use fallback::{FallbackConfig, FallbackSolver};
pub use homotopy::HomotopyConfig;
pub use newton_raphson::NewtonConfig;
pub use sequential_substitution::PicardConfig;
@@ -83,11 +85,12 @@ impl Solver for SolverStrategy {
if let Ok(state) = &result {
if state.is_converged() {
// Post-solve validation checks
// Convert Vec<f64> to SystemState for validation methods
let system_state: entropyk_components::SystemState = state.state.clone().into();
system.check_mass_balance(&system_state)?;
system.check_energy_balance(&system_state)?;
// Post-solve validation checks. Components index the state slice by
// global index, so pass the raw (ṁ, P, h)-strided vector directly
// rather than through the stride-2 SystemState conversion (CM1.2).
let state_slice: &[f64] = &state.state;
system.check_mass_balance(state_slice)?;
system.check_energy_balance(state_slice)?;
}
}

340
crates/solver/src/strategies/newton_raphson.rs
View File

@@ -9,9 +9,9 @@ use crate::criteria::ConvergenceCriteria;
use crate::jacobian::JacobianMatrix;
use crate::metadata::SimulationMetadata;
use crate::solver::{
apply_newton_step, ConvergedState, ConvergenceDiagnostics, ConvergenceStatus,
IterationDiagnostics, JacobianFreezingConfig, Solver, SolverError, SolverType,
TimeoutConfig, VerboseConfig,
apply_newton_step, dominant_residual, ConvergedState, ConvergenceDiagnostics,
ConvergenceStatus, IterationDiagnostics, JacobianFreezingConfig, Solver, SolverError,
SolverType, TimeoutConfig, VerboseConfig,
};
use crate::system::System;
use entropyk_components::JacobianBuilder;
@@ -154,7 +154,10 @@ impl NewtonConfig {
) -> Option<SolverError> {
if current_norm > self.divergence_threshold {
return Some(SolverError::Divergence {
reason: format!("Residual {} exceeds threshold {}", current_norm, self.divergence_threshold),
reason: format!(
"Residual {} exceeds threshold {}",
current_norm, self.divergence_threshold
),
});
}
@@ -162,7 +165,10 @@ impl NewtonConfig {
*divergence_count += 1;
if *divergence_count >= 3 {
return Some(SolverError::Divergence {
reason: format!("Residual increased 3x: {:.6e} → {:.6e}", previous_norm, current_norm),
reason: format!(
"Residual increased 3x: {:.6e} → {:.6e}",
previous_norm, current_norm
),
});
}
} else {
@@ -201,7 +207,12 @@ impl NewtonConfig {
let new_norm = Self::residual_norm(new_residuals);
if new_norm <= current_norm + self.line_search_armijo_c * alpha * gradient_dot_delta {
tracing::debug!(alpha, old_norm = current_norm, new_norm, "Line search accepted");
tracing::debug!(
alpha,
old_norm = current_norm,
new_norm,
"Line search accepted"
);
return Some(alpha);
}
@@ -209,9 +220,45 @@ impl NewtonConfig {
alpha *= 0.5;
}
tracing::warn!("Line search failed after {} backtracks", self.line_search_max_backtracks);
tracing::warn!(
"Line search failed after {} backtracks",
self.line_search_max_backtracks
);
None
}
fn finalize_failure_diagnostics(
&self,
mut diagnostics: Option<ConvergenceDiagnostics>,
iterations: usize,
final_residual: f64,
best_residual: f64,
elapsed_ms: u64,
jacobian_condition_final: Option<f64>,
final_state: Option<Vec<f64>>,
) -> Option<ConvergenceDiagnostics> {
if let Some(ref mut diag) = diagnostics {
diag.iterations = iterations;
diag.final_residual = final_residual;
diag.best_residual = best_residual;
diag.converged = false;
diag.timing_ms = elapsed_ms;
diag.jacobian_condition_final = jacobian_condition_final;
diag.final_solver = Some(SolverType::NewtonRaphson);
if self.verbose_config.dump_final_state {
diag.final_state = final_state;
let json_output = diag.dump_diagnostics(self.verbose_config.output_format);
tracing::warn!(
iterations,
final_residual,
"Non-convergence diagnostics:\n{}",
json_output
);
}
}
diagnostics
}
}
impl Solver for NewtonConfig {
@@ -240,7 +287,9 @@ impl Solver for NewtonConfig {
.map(|(_, c, _)| c.n_equations())
.sum::<usize>()
+ system.constraints().count()
+ system.coupling_residual_count();
+ system.coupling_residual_count()
+ 2 * system.saturated_controller_count()
+ system.mass_flow_closure_count();
if n_state == 0 || n_equations == 0 {
return Err(SolverError::InvalidSystem {
@@ -248,15 +297,22 @@ impl Solver for NewtonConfig {
});
}
// Pre-allocate all buffers
let mut state: Vec<f64> = self
.initial_state
.as_ref()
.map(|s| {
debug_assert_eq!(s.len(), n_state, "initial_state length mismatch");
if s.len() == n_state { s.clone() } else { vec![0.0; n_state] }
})
.unwrap_or_else(|| vec![0.0; n_state]);
// Pre-allocate all buffers. A caller-supplied initial state MUST match
// the full state length: a debug_assert would abort (violating zero-panic)
// and a silent zeros fallback would solve a different problem. Fail cleanly.
let mut state: Vec<f64> = match self.initial_state.as_ref() {
Some(s) if s.len() == n_state => s.clone(),
Some(s) => {
return Err(SolverError::InvalidSystem {
message: format!(
"initial_state length {} does not match system state length {}",
s.len(),
n_state
),
});
}
None => vec![0.0; n_state],
};
let mut residuals: Vec<f64> = vec![0.0; n_equations];
let mut jacobian_builder = JacobianBuilder::new();
let mut divergence_count: usize = 0;
@@ -273,13 +329,13 @@ impl Solver for NewtonConfig {
let mut jacobian_matrix = JacobianMatrix::zeros(n_equations, n_state);
let mut frozen_count: usize = 0;
let mut force_recompute: bool = true;
// Cached condition number (for verbose mode when Jacobian frozen)
let mut cached_condition: Option<f64> = None;
// Pre-compute clipping mask
let clipping_mask: Vec<Option<(f64, f64)>> = (0..n_state)
.map(|i| system.get_bounds_for_state_index(i))
.map(|i| system.get_solver_bounds_for_state_index(i))
.collect();
// Initial residual computation
@@ -306,15 +362,32 @@ impl Solver for NewtonConfig {
if let Some(ref criteria) = self.convergence_criteria {
let report = criteria.check(&state, None, &residuals, system);
if report.is_globally_converged() {
tracing::info!(iterations = 0, final_residual = current_norm, "Converged at initial state (criteria)");
tracing::info!(
iterations = 0,
final_residual = current_norm,
"Converged at initial state (criteria)"
);
return Ok(ConvergedState::with_report(
state, 0, current_norm, status, report, SimulationMetadata::new(system.input_hash()),
state,
0,
current_norm,
status,
report,
SimulationMetadata::new(system.input_hash()),
));
}
} else {
tracing::info!(iterations = 0, final_residual = current_norm, "Converged at initial state");
tracing::info!(
iterations = 0,
final_residual = current_norm,
"Converged at initial state"
);
return Ok(ConvergedState::new(
state, 0, current_norm, status, SimulationMetadata::new(system.input_hash()),
state,
0,
current_norm,
status,
SimulationMetadata::new(system.input_hash()),
));
}
}
@@ -327,7 +400,18 @@ impl Solver for NewtonConfig {
if let Some(timeout) = self.timeout {
if start_time.elapsed() > timeout {
tracing::info!(iteration, elapsed_ms = ?start_time.elapsed(), best_residual, "Solver timed out");
return self.handle_timeout(&best_state, best_residual, iteration - 1, timeout, system);
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration - 1,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
cached_condition,
Some(state.clone()),
);
return self
.handle_timeout(&best_state, best_residual, iteration - 1, timeout, system)
.map_err(|err| err.with_optional_diagnostics(failure_diagnostics));
}
}
@@ -346,7 +430,7 @@ impl Solver for NewtonConfig {
};
let jacobian_frozen_this_iter = !should_recompute;
if should_recompute {
// Fresh Jacobian assembly (in-place update)
jacobian_builder.clear();
@@ -359,13 +443,15 @@ impl Solver for NewtonConfig {
r.copy_from_slice(&r_vec);
result.map(|_| ()).map_err(|e| format!("{:?}", e))
};
let jm = JacobianMatrix::numerical(compute_residuals_fn, &state, &residuals, 1e-5)
.map_err(|e| SolverError::InvalidSystem {
let jm =
JacobianMatrix::numerical(compute_residuals_fn, &state, &residuals, 1e-5)
.map_err(|e| SolverError::InvalidSystem {
message: format!("Failed to compute numerical Jacobian: {}", e),
})?;
jacobian_matrix.as_matrix_mut().copy_from(jm.as_matrix());
} else {
system.assemble_jacobian(&state, &mut jacobian_builder)
system
.assemble_jacobian(&state, &mut jacobian_builder)
.map_err(|e| SolverError::InvalidSystem {
message: format!("Failed to assemble Jacobian: {:?}", e),
})?;
@@ -374,19 +460,27 @@ impl Solver for NewtonConfig {
frozen_count = 0;
force_recompute = false;
// Compute and cache condition number if verbose mode enabled
if verbose_enabled && self.verbose_config.log_jacobian_condition {
let cond = jacobian_matrix.estimate_condition_number();
cached_condition = cond;
if let Some(c) = cond {
tracing::info!(iteration, condition_number = c, "Jacobian condition number");
tracing::info!(
iteration,
condition_number = c,
"Jacobian condition number"
);
if c > 1e10 {
tracing::warn!(iteration, condition_number = c, "Ill-conditioned Jacobian detected (κ > 1e10)");
tracing::warn!(
iteration,
condition_number = c,
"Ill-conditioned Jacobian detected (κ > 1e10)"
);
}
}
}
tracing::debug!(iteration, "Fresh Jacobian computed");
} else {
frozen_count += 1;
@@ -397,23 +491,49 @@ impl Solver for NewtonConfig {
let delta = match jacobian_matrix.solve(&residuals) {
Some(d) => d,
None => {
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
cached_condition,
Some(state.clone()),
);
return Err(SolverError::Divergence {
reason: "Jacobian is singular".to_string(),
});
}
.with_optional_diagnostics(failure_diagnostics));
}
};
// Apply step with optional line search
let alpha = if self.line_search {
match self.line_search(
system, &mut state, &delta, &residuals, current_norm,
&mut state_copy, &mut new_residuals, &clipping_mask,
system,
&mut state,
&delta,
&residuals,
current_norm,
&mut state_copy,
&mut new_residuals,
&clipping_mask,
) {
Some(a) => a,
None => {
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
cached_condition,
Some(state.clone()),
);
return Err(SolverError::Divergence {
reason: "Line search failed".to_string(),
});
}
.with_optional_diagnostics(failure_diagnostics));
}
}
} else {
@@ -421,16 +541,18 @@ impl Solver for NewtonConfig {
1.0
};
system.compute_residuals(&state, &mut residuals)
system
.compute_residuals(&state, &mut residuals)
.map_err(|e| SolverError::InvalidSystem {
message: format!("Failed to compute residuals: {:?}", e),
})?;
previous_norm = current_norm;
current_norm = Self::residual_norm(&residuals);
// Compute delta norm for diagnostics
let delta_norm: f64 = state.iter()
let delta_norm: f64 = state
.iter()
.zip(prev_iteration_state.iter())
.map(|(s, p)| (s - p).powi(2))
.sum::<f64>()
@@ -444,9 +566,16 @@ impl Solver for NewtonConfig {
// Jacobian-freeze feedback
if let Some(ref freeze_cfg) = self.jacobian_freezing {
if previous_norm > 0.0 && current_norm / previous_norm >= (1.0 - freeze_cfg.threshold) {
if previous_norm > 0.0
&& current_norm / previous_norm >= (1.0 - freeze_cfg.threshold)
{
if frozen_count > 0 || !force_recompute {
tracing::debug!(iteration, current_norm, previous_norm, "Unfreezing Jacobian");
tracing::debug!(
iteration,
current_norm,
previous_norm,
"Unfreezing Jacobian"
);
}
force_recompute = true;
frozen_count = 0;
@@ -464,9 +593,10 @@ impl Solver for NewtonConfig {
"Newton iteration"
);
}
// Collect iteration diagnostics
if let Some(ref mut diag) = diagnostics {
let (max_residual_index, max_residual) = dominant_residual(&residuals);
diag.push_iteration(IterationDiagnostics {
iteration,
residual_norm: current_norm,
@@ -474,21 +604,29 @@ impl Solver for NewtonConfig {
alpha: Some(alpha),
jacobian_frozen: jacobian_frozen_this_iter,
jacobian_condition: cached_condition,
max_residual_index,
max_residual,
});
}
tracing::debug!(iteration, residual_norm = current_norm, alpha, "Newton iteration complete");
tracing::debug!(
iteration,
residual_norm = current_norm,
alpha,
"Newton iteration complete"
);
// Check convergence
let converged = if let Some(ref criteria) = self.convergence_criteria {
let report = criteria.check(&state, Some(&prev_iteration_state), &residuals, system);
let report =
criteria.check(&state, Some(&prev_iteration_state), &residuals, system);
if report.is_globally_converged() {
let status = if !system.saturated_variables().is_empty() {
ConvergenceStatus::ControlSaturation
} else {
ConvergenceStatus::Converged
};
// Finalize diagnostics
if let Some(ref mut diag) = diagnostics {
diag.iterations = iteration;
@@ -498,19 +636,33 @@ impl Solver for NewtonConfig {
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.jacobian_condition_final = cached_condition;
diag.final_solver = Some(SolverType::NewtonRaphson);
if self.verbose_config.log_residuals {
tracing::info!("{}", diag.summary());
}
}
tracing::info!(iterations = iteration, final_residual = current_norm, "Converged (criteria)");
tracing::info!(
iterations = iteration,
final_residual = current_norm,
"Converged (criteria)"
);
let result = ConvergedState::with_report(
state, iteration, current_norm, status, report, SimulationMetadata::new(system.input_hash()),
state,
iteration,
current_norm,
status,
report,
SimulationMetadata::new(system.input_hash()),
);
return Ok(if let Some(d) = diagnostics {
ConvergedState { diagnostics: Some(d), ..result }
} else { result });
ConvergedState {
diagnostics: Some(d),
..result
}
} else {
result
});
}
false
} else {
@@ -523,7 +675,7 @@ impl Solver for NewtonConfig {
} else {
ConvergenceStatus::Converged
};
// Finalize diagnostics
if let Some(ref mut diag) = diagnostics {
diag.iterations = iteration;
@@ -533,54 +685,76 @@ impl Solver for NewtonConfig {
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.jacobian_condition_final = cached_condition;
diag.final_solver = Some(SolverType::NewtonRaphson);
if self.verbose_config.log_residuals {
tracing::info!("{}", diag.summary());
}
}
tracing::info!(iterations = iteration, final_residual = current_norm, "Converged");
tracing::info!(
iterations = iteration,
final_residual = current_norm,
"Converged"
);
let result = ConvergedState::new(
state, iteration, current_norm, status, SimulationMetadata::new(system.input_hash()),
state,
iteration,
current_norm,
status,
SimulationMetadata::new(system.input_hash()),
);
return Ok(if let Some(d) = diagnostics {
ConvergedState { diagnostics: Some(d), ..result }
} else { result });
ConvergedState {
diagnostics: Some(d),
..result
}
} else {
result
});
}
if let Some(err) = self.check_divergence(current_norm, previous_norm, &mut divergence_count) {
tracing::warn!(iteration, residual_norm = current_norm, "Divergence detected");
return Err(err);
if let Some(err) =
self.check_divergence(current_norm, previous_norm, &mut divergence_count)
{
tracing::warn!(
iteration,
residual_norm = current_norm,
"Divergence detected"
);
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
cached_condition,
Some(state.clone()),
);
return Err(err.with_optional_diagnostics(failure_diagnostics));
}
}
// Non-convergence: dump diagnostics if enabled
if let Some(ref mut diag) = diagnostics {
diag.iterations = self.max_iterations;
diag.final_residual = current_norm;
diag.best_residual = best_residual;
diag.converged = false;
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.jacobian_condition_final = cached_condition;
diag.final_solver = Some(SolverType::NewtonRaphson);
if self.verbose_config.dump_final_state {
diag.final_state = Some(state.clone());
let json_output = diag.dump_diagnostics(self.verbose_config.output_format);
tracing::warn!(
iterations = self.max_iterations,
final_residual = current_norm,
"Non-convergence diagnostics:\n{}",
json_output
);
}
}
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
self.max_iterations,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
cached_condition,
Some(state.clone()),
);
tracing::warn!(max_iterations = self.max_iterations, final_residual = current_norm, "Did not converge");
tracing::warn!(
max_iterations = self.max_iterations,
final_residual = current_norm,
"Did not converge"
);
Err(SolverError::NonConvergence {
iterations: self.max_iterations,
final_residual: current_norm,
})
}
.with_optional_diagnostics(failure_diagnostics))
}
fn with_timeout(mut self, timeout: Duration) -> Self {

416
crates/solver/src/strategies/sequential_substitution.rs
View File

@@ -3,13 +3,16 @@
//! Provides [`PicardConfig`] which implements Picard iteration for solving
//! systems of non-linear equations. Slower than Newton-Raphson but more robust.
use std::collections::VecDeque;
use std::time::{Duration, Instant};
use nalgebra::{DMatrix, DVector};
use crate::criteria::ConvergenceCriteria;
use crate::metadata::SimulationMetadata;
use crate::solver::{
ConvergedState, ConvergenceDiagnostics, ConvergenceStatus, IterationDiagnostics, Solver,
SolverError, SolverType, TimeoutConfig, VerboseConfig,
dominant_residual, ConvergedState, ConvergenceDiagnostics, ConvergenceStatus,
IterationDiagnostics, Solver, SolverError, SolverType, TimeoutConfig, VerboseConfig,
};
use crate::system::System;
@@ -43,6 +46,13 @@ pub struct PicardConfig {
pub convergence_criteria: Option<ConvergenceCriteria>,
/// Verbose mode configuration for diagnostics.
pub verbose_config: VerboseConfig,
/// Anderson acceleration depth `m` (history window). `0` disables acceleration
/// and the solver behaves as plain relaxed Picard (default). Typical useful
/// values are 3–5. See [`PicardConfig::with_anderson`].
pub anderson_depth: usize,
/// Tikhonov regularization added to the Anderson least-squares normal matrix
/// for numerical stability. Default: 1e-10. Only used when `anderson_depth > 0`.
pub anderson_regularization: f64,
}
impl Default for PicardConfig {
@@ -60,6 +70,8 @@ impl Default for PicardConfig {
initial_state: None,
convergence_criteria: None,
verbose_config: VerboseConfig::default(),
anderson_depth: 0,
anderson_regularization: 1e-10,
}
}
}
@@ -90,6 +102,23 @@ impl PicardConfig {
self
}
/// Enables Anderson acceleration with history depth `m` (Story: solver speed).
///
/// Anderson acceleration (Walker & Ni, 2011) turns the linearly-convergent
/// relaxed Picard fixed-point iteration into a super-linearly convergent one by
/// extrapolating from the last `m` residual/map-value pairs via a small
/// least-squares problem. `m = 0` disables it (plain relaxed Picard). Values of
/// 3–5 typically cut the iteration count by 2–3× on stiff refrigeration cycles
/// while adding only an `O(m² · n)` least-squares solve per iteration.
///
/// # Reference
/// Walker, H.F., Ni, P. (2011). "Anderson acceleration for fixed-point
/// iterations." *SIAM J. Numerical Analysis*, 49(4):1715–1735.
pub fn with_anderson(mut self, depth: usize) -> Self {
self.anderson_depth = depth;
self
}
/// Computes the residual norm (L2 norm of the residual vector).
fn residual_norm(residuals: &[f64]) -> f64 {
residuals.iter().map(|r| r * r).sum::<f64>().sqrt()
@@ -200,6 +229,37 @@ impl PicardConfig {
*x -= omega * r;
}
}
fn finalize_failure_diagnostics(
&self,
mut diagnostics: Option<ConvergenceDiagnostics>,
iterations: usize,
final_residual: f64,
best_residual: f64,
elapsed_ms: u64,
final_state: Option<Vec<f64>>,
) -> Option<ConvergenceDiagnostics> {
if let Some(ref mut diag) = diagnostics {
diag.iterations = iterations;
diag.final_residual = final_residual;
diag.best_residual = best_residual;
diag.converged = false;
diag.timing_ms = elapsed_ms;
diag.final_solver = Some(SolverType::SequentialSubstitution);
if self.verbose_config.dump_final_state {
diag.final_state = final_state;
let json_output = diag.dump_diagnostics(self.verbose_config.output_format);
tracing::warn!(
iterations,
final_residual,
"Non-convergence diagnostics:\n{}",
json_output
);
}
}
diagnostics
}
}
impl Solver for PicardConfig {
@@ -231,7 +291,9 @@ impl Solver for PicardConfig {
.map(|(_, c, _)| c.n_equations())
.sum::<usize>()
+ system.constraints().count()
+ system.coupling_residual_count();
+ system.coupling_residual_count()
+ 2 * system.saturated_controller_count()
+ system.mass_flow_closure_count();
// Validate system
if n_state == 0 || n_equations == 0 {
@@ -251,25 +313,22 @@ impl Solver for PicardConfig {
}
// Pre-allocate all buffers (AC: #6 - no heap allocation in iteration loop)
// Story 4.6 - AC: #8: Use initial_state if provided, else start from zeros
let mut state: Vec<f64> = self
.initial_state
.as_ref()
.map(|s| {
debug_assert_eq!(
s.len(),
n_state,
"initial_state length mismatch: expected {}, got {}",
n_state,
s.len()
);
if s.len() == n_state {
s.clone()
} else {
vec![0.0; n_state]
}
})
.unwrap_or_else(|| vec![0.0; n_state]);
// Story 4.6 - AC: #8: Use initial_state if provided, else start from zeros.
// A mismatched length is a hard error (zero-panic; no silent zeros fallback
// that would solve a different problem) — consistent with Newton/Homotopy.
let mut state: Vec<f64> = match self.initial_state.as_ref() {
Some(s) if s.len() == n_state => s.clone(),
Some(s) => {
return Err(SolverError::InvalidSystem {
message: format!(
"initial_state length {} does not match system state length {}",
s.len(),
n_state
),
});
}
None => vec![0.0; n_state],
};
let mut prev_iteration_state: Vec<f64> = vec![0.0; n_state]; // For convergence delta check
let mut residuals: Vec<f64> = vec![0.0; n_equations];
let mut divergence_count: usize = 0;
@@ -310,6 +369,16 @@ impl Solver for PicardConfig {
));
}
// Optional Anderson accelerator (disabled when depth == 0).
let mut anderson = if self.anderson_depth > 0 {
Some(AndersonAccelerator::new(
self.anderson_depth,
self.anderson_regularization,
))
} else {
None
};
// Main Picard iteration loop
for iteration in 1..=self.max_iterations {
// Save state before step for convergence criteria delta checks
@@ -327,18 +396,28 @@ impl Solver for PicardConfig {
);
// Story 4.5 - AC: #2, #6: Return best state or error based on config
return self.handle_timeout(
&best_state,
best_residual,
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration - 1,
timeout,
system,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
Some(state.clone()),
);
return self
.handle_timeout(&best_state, best_residual, iteration - 1, timeout, system)
.map_err(|err| err.with_optional_diagnostics(failure_diagnostics));
}
}
// Apply relaxed update: x_new = x_old - omega * residual (AC: #2, #3)
Self::apply_relaxation(&mut state, &residuals, self.relaxation_factor);
// Apply update. With Anderson acceleration enabled, extrapolate from the
// residual/map-value history; otherwise use plain relaxed Picard.
// Both share the same underlying fixed-point map G(x) = x - ω·F(x).
if let Some(acc) = anderson.as_mut() {
acc.next_state_into(&mut state, &residuals, self.relaxation_factor);
} else {
Self::apply_relaxation(&mut state, &residuals, self.relaxation_factor);
}
// Compute new residuals
system
@@ -349,9 +428,10 @@ impl Solver for PicardConfig {
previous_norm = current_norm;
current_norm = Self::residual_norm(&residuals);
// Compute delta norm for diagnostics
let delta_norm: f64 = state.iter()
let delta_norm: f64 = state
.iter()
.zip(prev_iteration_state.iter())
.map(|(s, p)| (s - p).powi(2))
.sum::<f64>()
@@ -378,16 +458,19 @@ impl Solver for PicardConfig {
"Picard iteration"
);
}
// Collect iteration diagnostics
if let Some(ref mut diag) = diagnostics {
let (max_residual_index, max_residual) = dominant_residual(&residuals);
diag.push_iteration(IterationDiagnostics {
iteration,
residual_norm: current_norm,
delta_norm,
alpha: None, // Picard doesn't use line search
jacobian_frozen: false, // Picard doesn't use Jacobian
alpha: None, // Picard doesn't use line search
jacobian_frozen: false, // Picard doesn't use Jacobian
jacobian_condition: None, // No Jacobian in Picard
max_residual_index,
max_residual,
});
}
@@ -411,12 +494,12 @@ impl Solver for PicardConfig {
diag.converged = true;
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.final_solver = Some(SolverType::SequentialSubstitution);
if self.verbose_config.log_residuals {
tracing::info!("{}", diag.summary());
}
}
tracing::info!(
iterations = iteration,
final_residual = current_norm,
@@ -432,8 +515,13 @@ impl Solver for PicardConfig {
SimulationMetadata::new(system.input_hash()),
);
return Ok(if let Some(d) = diagnostics {
ConvergedState { diagnostics: Some(d), ..result }
} else { result });
ConvergedState {
diagnostics: Some(d),
..result
}
} else {
result
});
}
false
} else {
@@ -449,12 +537,12 @@ impl Solver for PicardConfig {
diag.converged = true;
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.final_solver = Some(SolverType::SequentialSubstitution);
if self.verbose_config.log_residuals {
tracing::info!("{}", diag.summary());
}
}
tracing::info!(
iterations = iteration,
final_residual = current_norm,
@@ -469,8 +557,13 @@ impl Solver for PicardConfig {
SimulationMetadata::new(system.input_hash()),
);
return Ok(if let Some(d) = diagnostics {
ConvergedState { diagnostics: Some(d), ..result }
} else { result });
ConvergedState {
diagnostics: Some(d),
..result
}
} else {
result
});
}
// Check divergence (AC: #5)
@@ -482,30 +575,27 @@ impl Solver for PicardConfig {
residual_norm = current_norm,
"Divergence detected"
);
return Err(err);
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
iteration,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
Some(state.clone()),
);
return Err(err.with_optional_diagnostics(failure_diagnostics));
}
}
// Non-convergence: dump diagnostics if enabled
if let Some(ref mut diag) = diagnostics {
diag.iterations = self.max_iterations;
diag.final_residual = current_norm;
diag.best_residual = best_residual;
diag.converged = false;
diag.timing_ms = start_time.elapsed().as_millis() as u64;
diag.final_solver = Some(SolverType::SequentialSubstitution);
if self.verbose_config.dump_final_state {
diag.final_state = Some(state.clone());
let json_output = diag.dump_diagnostics(self.verbose_config.output_format);
tracing::warn!(
iterations = self.max_iterations,
final_residual = current_norm,
"Non-convergence diagnostics:\n{}",
json_output
);
}
}
let failure_diagnostics = self.finalize_failure_diagnostics(
diagnostics.take(),
self.max_iterations,
current_norm,
best_residual,
start_time.elapsed().as_millis() as u64,
Some(state.clone()),
);
// Max iterations exceeded
tracing::warn!(
@@ -516,7 +606,8 @@ impl Solver for PicardConfig {
Err(SolverError::NonConvergence {
iterations: self.max_iterations,
final_residual: current_norm,
})
}
.with_optional_diagnostics(failure_diagnostics))
}
fn with_timeout(mut self, timeout: Duration) -> Self {
@@ -525,6 +616,110 @@ impl Solver for PicardConfig {
}
}
/// Anderson acceleration state for the relaxed Picard fixed-point iteration.
///
/// The underlying fixed-point map is `G(x) = x - ω·F(x)` where `F` is the residual
/// vector and `ω` the relaxation factor. Define the map residual `f(x) = G(x) - x =
/// -ω·F(x)`. Anderson acceleration maintains the last `m` differences of `f` and `G`
/// and, each iteration, solves the small least-squares problem
/// `min_γ ‖f_k - ΔF·γ‖` then sets `x_{k+1} = G_k - ΔG·γ` (Walker & Ni, 2011,
/// following H. Walker's reference `anderson.m`). With `m = 0` (empty history) it
/// reduces exactly to the plain step `x_{k+1} = G_k`.
struct AndersonAccelerator {
depth: usize,
regularization: f64,
/// Previous map-residual f = G(x) - x.
f_prev: Option<Vec<f64>>,
/// Previous map value G(x).
g_prev: Option<Vec<f64>>,
/// History of Δf columns (most-recent at back), capped at `depth`.
df: VecDeque<Vec<f64>>,
/// History of ΔG columns (most-recent at back), capped at `depth`.
dg: VecDeque<Vec<f64>>,
}
impl AndersonAccelerator {
fn new(depth: usize, regularization: f64) -> Self {
Self {
depth,
regularization,
f_prev: None,
g_prev: None,
df: VecDeque::with_capacity(depth),
dg: VecDeque::with_capacity(depth),
}
}
/// Advances `state` in place from `x_k` to the accelerated `x_{k+1}`, given the
/// current residual vector `F(x_k)` and relaxation factor `ω`.
fn next_state_into(&mut self, state: &mut [f64], residual: &[f64], omega: f64) {
let n = state.len();
// Map residual f = -ω·F and fixed-point map value G = x + f.
let fval: Vec<f64> = residual.iter().map(|r| -omega * r).collect();
let gval: Vec<f64> = state.iter().zip(&fval).map(|(x, f)| x + f).collect();
// Push newest history differences.
if let (Some(fp), Some(gp)) = (self.f_prev.as_ref(), self.g_prev.as_ref()) {
let df_col: Vec<f64> = fval.iter().zip(fp).map(|(a, b)| a - b).collect();
let dg_col: Vec<f64> = gval.iter().zip(gp).map(|(a, b)| a - b).collect();
self.df.push_back(df_col);
self.dg.push_back(dg_col);
while self.df.len() > self.depth {
self.df.pop_front();
self.dg.pop_front();
}
}
self.f_prev = Some(fval.clone());
self.g_prev = Some(gval.clone());
let m = self.df.len();
if m == 0 {
// No history yet — plain relaxed step.
state.copy_from_slice(&gval);
return;
}
// Solve the small least-squares problem for γ via regularized normal
// equations: (ΔFᵀΔF + λI)·γ = ΔFᵀ·f_k. `m` is at most `depth` (small).
let mut ata = DMatrix::<f64>::zeros(m, m);
let mut atb = DVector::<f64>::zeros(m);
for i in 0..m {
for j in i..m {
let mut s = 0.0;
for k in 0..n {
s += self.df[i][k] * self.df[j][k];
}
ata[(i, j)] = s;
ata[(j, i)] = s;
}
ata[(i, i)] += self.regularization;
let mut s = 0.0;
for k in 0..n {
s += self.df[i][k] * fval[k];
}
atb[i] = s;
}
let gamma = match ata.clone().lu().solve(&atb) {
Some(g) => g,
None => {
// Singular even with regularization — fall back to plain step.
state.copy_from_slice(&gval);
return;
}
};
// x_{k+1} = G_k - ΔG·γ.
for k in 0..n {
let mut acc = gval[k];
for (i, g) in gamma.iter().enumerate() {
acc -= g * self.dg[i][k];
}
state[k] = acc;
}
}
}
#[cfg(test)]
mod tests {
use super::*;
@@ -570,4 +765,99 @@ mod tests {
system.finalize().unwrap();
assert!(boxed.solve(&mut system).is_err());
}
// ── Anderson acceleration ────────────────────────────────────────────────
/// Reference linear residual F(x) = A·x - b. Its unique root is x* = A⁻¹·b.
/// The relaxed Picard map is x_{k+1} = x_k - ω·(A·x_k - b).
fn linear_residual(a: &[[f64; 2]; 2], b: &[f64; 2], x: &[f64]) -> Vec<f64> {
vec![
a[0][0] * x[0] + a[0][1] * x[1] - b[0],
a[1][0] * x[0] + a[1][1] * x[1] - b[1],
]
}
fn residual_norm2(r: &[f64]) -> f64 {
r.iter().map(|v| v * v).sum::<f64>().sqrt()
}
#[test]
fn test_anderson_depth_zero_matches_plain_relaxation() {
// With no history, next_state_into must equal x - ω·F(x).
let mut acc = AndersonAccelerator::new(0, 1e-10);
let mut state = vec![10.0, 20.0];
let residuals = vec![1.0, 2.0];
acc.next_state_into(&mut state, &residuals, 0.5);
assert!((state[0] - 9.5).abs() < 1e-15);
assert!((state[1] - 19.0).abs() < 1e-15);
}
#[test]
fn test_anderson_converges_faster_than_plain_picard() {
// Stiff-ish SPD system where plain relaxed Picard converges slowly.
let a = [[8.0, 1.0], [1.0, 3.0]];
let b = [9.0, 4.0]; // exact root x* = [1, 1]
let omega = 0.12; // deliberately small → slow plain Picard
let tol = 1e-9;
let max_iter = 2000;
let count_iters = |depth: usize| -> (usize, Vec<f64>) {
let mut state = vec![0.0, 0.0];
let mut acc = AndersonAccelerator::new(depth, 1e-12);
for it in 1..=max_iter {
let r = linear_residual(&a, &b, &state);
if residual_norm2(&r) < tol {
return (it - 1, state);
}
acc.next_state_into(&mut state, &r, omega);
}
(max_iter, state)
};
let (plain_iters, _) = count_iters(0);
let (anderson_iters, sol) = count_iters(3);
// Anderson must converge, land on the true root, and use far fewer steps.
assert!(anderson_iters < max_iter, "Anderson did not converge");
assert!((sol[0] - 1.0).abs() < 1e-6 && (sol[1] - 1.0).abs() < 1e-6);
assert!(
anderson_iters * 3 < plain_iters,
"Anderson ({}) should be much faster than plain Picard ({})",
anderson_iters,
plain_iters
);
}
#[test]
fn test_anderson_solves_where_plain_diverges_marginally() {
// Anderson should still hit the exact root of a well-posed linear system.
let a = [[4.0, 1.0], [2.0, 5.0]];
let b = [6.0, 9.0];
// exact root: solve → x=[1, 1.4? ] compute: 4x+y=6, 2x+5y=9
// From first: y = 6-4x; sub: 2x+5(6-4x)=9 → 2x+30-20x=9 → -18x=-21 → x=7/6
// y = 6-4*7/6 = 6-28/6 = 8/6 = 4/3
let omega = 0.15;
let mut state = vec![0.0, 0.0];
let mut acc = AndersonAccelerator::new(4, 1e-12);
let mut converged = false;
for _ in 0..5000 {
let r = linear_residual(&a, &b, &state);
if residual_norm2(&r) < 1e-9 {
converged = true;
break;
}
acc.next_state_into(&mut state, &r, omega);
}
assert!(converged);
assert!((state[0] - 7.0 / 6.0).abs() < 1e-6);
assert!((state[1] - 4.0 / 3.0).abs() < 1e-6);
}
#[test]
fn test_with_anderson_builder_sets_depth() {
let cfg = PicardConfig::default().with_anderson(5);
assert_eq!(cfg.anderson_depth, 5);
// Default remains disabled.
assert_eq!(PicardConfig::default().anderson_depth, 0);
}
}