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//! Adaptive Runge-Kutta methods for ODEs
use crate::{
error::Error,
interpolate::{Interpolation, cubic_hermite_interpolate},
methods::{Adaptive, ExplicitRungeKutta, Ordinary, h_init::InitialStepSize},
ode::{ODE, OrdinaryNumericalMethod},
stats::Evals,
status::Status,
traits::{Real, State},
utils::{constrain_step_size, validate_step_size_parameters},
};
impl<T: Real, Y: State<T>, const O: usize, const S: usize, const I: usize>
OrdinaryNumericalMethod<T, Y> for ExplicitRungeKutta<Ordinary, Adaptive, T, Y, O, S, I>
{
fn init<F>(&mut self, ode: &F, t0: T, tf: T, y0: &Y) -> Result<Evals, Error<T, Y>>
where
F: ODE<T, Y> + ?Sized,
{
let mut evals = Evals::new();
// If h0 is zero, calculate initial step size
if self.h0 == T::zero() {
// Only use adaptive step size calculation if the method supports it
self.h0 = InitialStepSize::<Ordinary>::compute(
ode, t0, tf, y0, self.order, &self.rtol, &self.atol, self.h_min, self.h_max,
&mut evals,
);
evals.function += 2;
}
// Check bounds
match validate_step_size_parameters::<T, Y>(self.h0, self.h_min, self.h_max, t0, tf) {
Ok(h0) => self.h = (self.filter)(h0),
Err(status) => return Err(status),
}
// Initialize Statistics
self.stiffness_counter = 0;
// Initialize State
self.t = t0;
self.y = y0.clone();
self.dydt = y0.zeros_like();
self.y_prev = y0.clone();
self.dydt_prev = y0.zeros_like();
self.k = core::array::from_fn(|_| y0.zeros_like());
self.cont = core::array::from_fn(|_| y0.zeros_like());
ode.diff(self.t, &self.y, &mut self.dydt);
evals.function += 1;
// Initialize previous state
self.t_prev = self.t;
self.y_prev = self.y.clone();
self.dydt_prev = self.dydt.clone();
// Initialize Status
self.status = Status::Initialized;
Ok(evals)
}
fn step<F>(&mut self, ode: &F) -> Result<Evals, Error<T, Y>>
where
F: ODE<T, Y> + ?Sized,
{
let mut evals = Evals::new();
// Check step size
if self.h.abs() < self.h_prev.abs() * T::from_f64(1e-14).unwrap() {
self.status = Status::Error(Error::StepSize {
t: self.t,
y: self.y.clone(),
});
return Err(Error::StepSize {
t: self.t,
y: self.y.clone(),
});
}
// Check max steps
if self.steps >= self.max_steps {
self.status = Status::Error(Error::MaxSteps {
t: self.t,
y: self.y.clone(),
});
return Err(Error::MaxSteps {
t: self.t,
y: self.y.clone(),
});
}
self.steps += 1;
// Save k[0] as the current derivative
self.k[0] = self.dydt.clone();
// Compute stages
for i in 1..self.stages {
let mut y_stage = self.y.clone();
for j in 0..i {
y_stage.add_scaled(self.a[i][j] * self.h, &self.k[j]);
}
ode.diff(self.t + self.c[i] * self.h, &y_stage, &mut self.k[i]);
}
evals.function += self.stages - 1; // We already have k[0]
// For adaptive methods with error estimation
// Compute higher order solution
let mut y_high = self.y.clone();
for i in 0..self.stages {
y_high.add_scaled(self.b[i] * self.h, &self.k[i]);
}
// Compute lower order solution for error estimation
let mut y_low = self.y.clone();
let bh = &self.bh.unwrap();
for i in 0..self.stages {
y_low.add_scaled(bh[i] * self.h, &self.k[i]);
}
// Calculate error norm
let err = y_high.minus(&y_low);
let err_norm = self.y.error_norm_inf(&y_high, &err, &self.atol, &self.rtol);
// Step size scale factor
let order = T::from_usize(self.order).unwrap();
let error_exponent = T::one() / order;
let mut scale = self.safety_factor * err_norm.powf(-error_exponent);
// Clamp scale factor to prevent extreme step size changes
scale = scale.max(self.min_scale).min(self.max_scale);
// Determine if step is accepted
if err_norm <= T::one() {
// Log previous state
self.t_prev = self.t;
self.y_prev = self.y.clone();
self.dydt_prev = self.k[0].clone();
self.h_prev = self.h;
if let Status::RejectedStep = self.status {
self.stiffness_counter = 0;
self.status = Status::Solving;
// Limit step size growth to avoid oscillations between accepted and rejected steps
scale = scale.min(T::one());
}
// If method has dense output stages, compute them
if self.bi.is_some() {
// Compute extra stages for dense output
for i in 0..(I - S) {
let mut y_stage = self.y.clone();
for j in 0..self.stages + i {
y_stage.add_scaled(self.a[self.stages + i][j] * self.h, &self.k[j]);
}
ode.diff(
self.t + self.c[self.stages + i] * self.h,
&y_stage,
&mut self.k[self.stages + i],
);
}
evals.function += I - S;
}
// Update state with the higher-order solution
self.t += self.h;
self.y = y_high;
// Compute the derivative for the next step
if self.fsal {
// If FSAL (First Same As Last) is enabled, we can reuse the last derivative
self.dydt = self.k[S - 1].clone();
} else {
// Otherwise, compute the new derivative
ode.diff(self.t, &self.y, &mut self.dydt);
evals.function += 1;
}
} else {
// Step rejected
self.status = Status::RejectedStep;
self.stiffness_counter += 1;
// Check for stiffness
if self.stiffness_counter >= self.max_rejects {
self.status = Status::Error(Error::Stiffness {
t: self.t,
y: self.y.clone(),
});
return Err(Error::Stiffness {
t: self.t,
y: self.y.clone(),
});
}
}
// Update step size
self.h *= scale;
// Ensure step size is within bounds
self.h = constrain_step_size(self.h, self.h_min, self.h_max);
// Apply step size filter
self.h = (self.filter)(self.h);
Ok(evals)
}
fn t(&self) -> T {
self.t
}
fn y(&self) -> &Y {
&self.y
}
fn t_prev(&self) -> T {
self.t_prev
}
fn y_prev(&self) -> &Y {
&self.y_prev
}
fn h(&self) -> T {
self.h
}
fn set_h(&mut self, h: T) {
self.h = (self.filter)(h);
}
fn status(&self) -> &Status<T, Y> {
&self.status
}
fn set_status(&mut self, status: Status<T, Y>) {
self.status = status;
}
}
impl<T: Real, Y: State<T>, const O: usize, const S: usize, const I: usize> Interpolation<T, Y>
for ExplicitRungeKutta<Ordinary, Adaptive, T, Y, O, S, I>
{
fn interpolate(&mut self, t_interp: T) -> Result<Y, Error<T, Y>> {
// Check if t is within bounds
if t_interp < self.t_prev || t_interp > self.t {
return Err(Error::OutOfBounds {
t_interp,
t_prev: self.t_prev,
t_curr: self.t,
});
}
// If method has dense output coefficients, use them
if let Some(bi) = self.bi.as_ref() {
// Calculate the normalized distance within the step [0, 1]
let s = (t_interp - self.t_prev) / self.h_prev;
let mut cont = [T::zero(); I];
// Compute the interpolation coefficients using Horner's method
for i in 0..self.dense_stages {
// Start with the highest-order term
cont[i] = bi[i][self.order - 1];
// Apply Horner's method
for j in (0..self.order - 1).rev() {
cont[i] = cont[i] * s + bi[i][j];
}
// Multiply by s
cont[i] *= s;
}
// Compute the interpolated value
let mut y_interp = self.y_prev.clone();
for i in 0..I {
y_interp.add_scaled(cont[i] * self.h_prev, &self.k[i]);
}
Ok(y_interp)
} else {
// Otherwise use cubic Hermite interpolation
let y_interp = cubic_hermite_interpolate(
self.t_prev,
self.t,
&self.y_prev,
&self.y,
&self.dydt_prev,
&self.dydt,
t_interp,
);
Ok(y_interp)
}
}
}