connor/differential-equations
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Errors still aren't quite right

Browse Source
This commit is contained in:
Connor Johnstone
2023-03-10 17:57:18 -07:00
parent fc96e2e9be
commit 2ec474a77a
4 changed files with 52 additions and 34 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
src/controller.rs
View File

@@ -35,6 +35,7 @@ where
let factor = self.factor_c2.max(self.factor_c1.min(factor_11 * self.factor_old.powf(-self.beta) / self.safety_factor));
let mut h_new = h / factor;
if err <= 1.0.into() {
println!("{:?}", f64::from(h));
// Accept the stepsize
self.factor_old = err.max(1.0e-4.into());
if h_new.abs() > self.h_max {
@@ -42,6 +43,7 @@ where
h_new = self.h_max.copysign(h_new);
}
(true, h_new)
// (true, h_new)
} else {
// Reject the stepsize and propose a smaller one
h_new = h / (self.factor_c1.min(factor_11 / self.safety_factor));

24
src/integrator.rs
View File

@@ -48,8 +48,8 @@ where
k0 * self.tableau().b[0] +
k1 * self.tableau().b[1];
let err = match self.tableau().b_star {
Some(b_star) => Some(sum + (k0 * b_star[0] +
k1 * b_star[1]) * T::from(-1.0_f64)),
Some(b_star) => Some(sum + ((k0 * b_star[0] +
k1 * b_star[1]) * T::from(-1.0_f64)) * h),
None => None
};
(ode.y + (sum * h), err)
@@ -73,9 +73,9 @@ where
k1 * self.tableau().b[1] +
k2 * self.tableau().b[2];
let err = match self.tableau().b_star {
Some(b_star) => Some(sum + (k0 * b_star[0] +
Some(b_star) => Some(sum + ((k0 * b_star[0] +
k1 * b_star[1] +
k2 * b_star[2]) * T::from(-1.0_f64)),
k2 * b_star[2]) * T::from(-1.0_f64)) * h),
None => None
};
(ode.y + (sum * h), err)
@@ -108,10 +108,10 @@ where
k2 * self.tableau().b[2] +
k3 * self.tableau().b[3];
let err = match self.tableau().b_star {
Some(b_star) => Some(sum + (k0 * b_star[0] +
Some(b_star) => Some(sum + ((k0 * b_star[0] +
k1 * b_star[1] +
k2 * b_star[2] +
k3 * b_star[3]) * T::from(-1.0_f64)),
k3 * b_star[3]) * T::from(-1.0_f64)) * h),
None => None
};
(ode.y + (sum * h), err)
@@ -154,11 +154,11 @@ where
k3 * self.tableau().b[3] +
k4 * self.tableau().b[4];
let err = match self.tableau().b_star {
Some(b_star) => Some(sum + (k0 * b_star[0] +
Some(b_star) => Some(sum + ((k0 * b_star[0] +
k1 * b_star[1] +
k2 * b_star[2] +
k3 * b_star[3] +
k4 * b_star[4]) * T::from(-1.0_f64)),
k4 * b_star[4]) * T::from(-1.0_f64)) * h),
None => None
};
(ode.y + (sum * h), err)
@@ -212,12 +212,12 @@ where
k4 * self.tableau().b[4] +
k5 * self.tableau().b[5];
let err = match self.tableau().b_star {
Some(b_star) => Some(sum + (k0 * b_star[0] +
Some(b_star) => Some((sum + (k0 * b_star[0] +
k1 * b_star[1] +
k2 * b_star[2] +
k3 * b_star[3] +
k4 * b_star[4] +
k5 * b_star[5]) * T::from(-1.0_f64)),
k5 * b_star[5]) * T::from(-1.0_f64)) * h),
None => None
};
(ode.y + (sum * h), err)
@@ -285,7 +285,7 @@ where
let tol = self.atol + yi.abs().max(next_yi.abs()) * self.rtol;
err += (err_array[i] / tol).powi(2);
});
(next_y, Some(err))
(next_y, Some(err.sqrt()))
}
}
@@ -347,7 +347,7 @@ mod tests {
let system = System {};
let y0 = Vector3::new(1.0, 1.0, 1.0);
let mut ode = ODE::new(system, 0.0, 10.0, y0);
let mut ode = ODE::new(system, 0.0, 30.0, y0);
let rk4 = FixedFourthOrder { tableau: RUNGE_KUTTA_4_TABLEAU };

39
src/lib.rs
View File

@@ -11,38 +11,55 @@ pub mod problem;
mod tests {
use nalgebra::Vector6;
use approx::assert_relative_eq;
use crate::integrator::{AdaptiveSixthOrder, RUNGE_KUTTA_FEHLBERG_54_TABLEAU};
use crate::integrator::*;
use crate::controller::{PIController};
use crate::ode::{SystemTrait, ODE};
use crate::problem::Problem;
use std::f64::consts::PI;
#[test]
fn test_ode_creation() {
fn test_orbit() {
struct System {
mu: f64,
}
impl SystemTrait<f64,6> for System {
fn derivative(&self, _t: f64, state: Vector6<f64>) -> Vector6<f64> {
let acc = -(self.mu * state.fixed_rows<3>(0)) / (state.fixed_rows<3>(0).norm.powi(3));
let acc = -(self.mu * state.fixed_rows::<3>(0)) / (state.fixed_rows::<3>(0).norm().powi(3));
Vector6::new(state[3], state[4], state[5], acc[0], acc[1], acc[2])
}
}
let system = System { mu: 3.98600441500000e14 };
let y0 = Vector3::new(1.0, 0.0, 0.0);
let ode = ODE::new(system, 0.0, 10.0, y0);
let controller = PIController::new(0.17, 0.04, 10.0, 0.2, 10.0, 0.9, 1e-4);
let y0 = Vector6::new(
4.26387250e+06,
5.14619397e+06,
1.13102192e+06,
-5.92345023e+03,
4.49679662e+03,
1.87038714e+03,
);
let a = 6.7781363e6_f64;
let period = 2.0 * PI * (a.powi(3)/system.mu).sqrt();
println!("{}", period);
let ode = ODE::new(system, 0.0, period, y0);
let controller = PIController::new(0.17, 0.04, 10.0, 0.2, 10000.0, 0.9, 1.0);
let rkf54 = AdaptiveSixthOrder {
tableau: RUNGE_KUTTA_FEHLBERG_54_TABLEAU,
atol: 1e-8_f64,
rtol: 1e-8_f64,
atol: 1e-12_f64,
rtol: 1e-7_f64,
};
let mut problem = Problem::new(ode, rkf54, controller);
let solution = problem.solve();
solution.times.iter().zip(solution.states.iter()).for_each(|(time, state)| {
assert_relative_eq!(state[0], time.exp(), max_relative=1e-7);
})
println!("{}", solution.times.len());
// panic!();
assert_relative_eq!(solution.times[solution.states.len()-1], period, max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][0], y0[0], max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][1], y0[1], max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][2], y0[2], max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][3], y0[3], max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][4], y0[4], max_relative=1e-7);
assert_relative_eq!(solution.states[solution.states.len()-1][5], y0[5], max_relative=1e-7);
}
}

21
src/problem.rs
View File

@@ -67,10 +67,10 @@ where
let mut times: Vec::<T> = Vec::new();
let mut states: Vec::<SVector<T,D1>> = Vec::new();
let mut step: T = self.controller.old_h;
while self.ode.t < self.ode.t_end {
let (mut new_y, mut err_option) = self.integrator.step(&self.ode, step);
times.push(self.ode.t);
states.push(self.ode.y);
while self.ode.t < self.ode.t_end {
let (mut new_y, mut err_option) = self.integrator.step(&self.ode, step);
match err_option {
Some(mut err) => {
// Adaptive Step Size
@@ -81,15 +81,14 @@ where
err = err_option.unwrap();
}
self.controller.old_h = step;
self.controller.h_max = self.ode.t_end - self.ode.t - step;
},
None => {},
};
self.ode.y = new_y;
self.ode.t += step;
},
None => {
// Fixed Step Size
self.ode.y = new_y;
self.ode.t += self.controller.old_h;
},
};
times.push(self.ode.t);
states.push(self.ode.y);
}
Solution {
times: times,
@@ -111,8 +110,8 @@ mod tests {
use crate::integrator::{AdaptiveSixthOrder, RUNGE_KUTTA_FEHLBERG_54_TABLEAU};
use crate::controller::{PIController};
#[test]
fn test_ode_creation() {
// #[test]
fn test_problem() {
struct System {}
impl SystemTrait<f64,3> for System {