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use super::rk_adaptive_settings::RKAdaptiveSettings;
use super::types::*;
pub trait RKAdaptive<const N: usize, const NI: usize> {
// Butcher Tableau Coefficients
const A: [[f64; N]; N];
const C: [f64; N];
const B: [f64; N];
const BERR: [f64; N];
// Interpolation coefficients
const BI: [[f64; NI]; N];
// order
const ORDER: usize;
/// First Same as Last
/// (first compute of next iteration is same as last compute of last iteration)
const FSAL: bool;
fn interpolate<S: ODEState>(xinterp: f64, sol: &ODESolution<S>) -> ODEResult<S> {
if sol.dense.is_none() {
return Err(Box::new(ODEError::NoDenseOutputInSolution));
}
let dense = sol.dense.as_ref().unwrap();
// These could probably be combined into a single function, but...
// keeping forward and backward separate makes it simpler in my mind
if sol.x > dense.x[0] {
return Self::interpolate_forward(xinterp, sol);
} else {
return Self::interpolate_backward(xinterp, sol);
}
}
/// Interpolate densely calculated solution onto
/// values that are evenly spaced in "x"
/// for forward direction
fn interpolate_forward<S: ODEState>(xinterp: f64, sol: &ODESolution<S>) -> ODEResult<S> {
if sol.dense.is_none() {
return Err(Box::new(ODEError::NoDenseOutputInSolution));
}
let dense = sol.dense.as_ref().unwrap();
// Check if interpolation point is within bounds
if sol.x < xinterp {
return Err(Box::new(ODEError::InterpExceedsSolutionBounds {
interp: xinterp,
start: dense.x[0],
stop: sol.x,
}));
}
if xinterp < dense.x[0] {
return Err(Box::new(ODEError::InterpExceedsSolutionBounds {
interp: xinterp,
start: dense.x[0],
stop: sol.x,
}));
}
// We know indices are monotonically increasing, so only search from
// last found position in the array forward
let mut idx = match dense.x.iter().position(|x| *x >= xinterp) {
Some(v) => v,
None => dense.x.len(),
};
if idx > 0 {
idx -= 1;
}
// t is fractional distance beween x at idx and idx+1
// and is in range [0,1]
let t = (xinterp - dense.x[idx]) / dense.h[idx];
// Compute interpolant coefficient as funciton of t
// note that t is in range [0,1]
//
// This is equation (6) of
// https://link.springer.com/article/10.1023/A:1021190918665
//
// Note: equation (6) of paper incorrectly has sum index "j"
// starting from 0. It should start from 1.
//
let bi: Vec<f64> = Self::BI
.iter()
.map(|biarr| {
// Coefficients multiply increasing powers of t
let mut tj = 1.0;
biarr.iter().fold(0.0, |acc, bij| {
tj = tj * t;
acc + bij * tj
})
})
.collect();
//
// Compute interpolated value
//
// This is equation(5) of:
// https://link.springer.com/article/10.1023/A:1021190918665
//
let mut y = dense.yprime[idx]
.iter()
.enumerate()
.fold(dense.y[idx].clone() / dense.h[idx], |acc, (ix, k)| {
acc + k.clone() * bi[ix]
});
y = y * dense.h[idx];
Ok(y)
}
/// Interpolate densely calculated solution onto
/// values that are evenly spaced in "x"
/// for backward direction
fn interpolate_backward<S: ODEState>(xinterp: f64, sol: &ODESolution<S>) -> ODEResult<S> {
if sol.dense.is_none() {
return Err(Box::new(ODEError::NoDenseOutputInSolution));
}
let dense = sol.dense.as_ref().unwrap();
// Check if interpolation point is within bounds
if sol.x > xinterp {
return Err(Box::new(ODEError::InterpExceedsSolutionBounds {
interp: xinterp,
start: dense.x[0],
stop: sol.x,
}));
}
if xinterp > dense.x[0] {
return Err(Box::new(ODEError::InterpExceedsSolutionBounds {
interp: xinterp,
start: dense.x[0],
stop: sol.x,
}));
}
// We know indices are monotonically increasing, so only search from
// last found position in the array forward
let mut idx = match dense.x.iter().position(|x| *x <= xinterp) {
Some(v) => v,
None => dense.x.len(),
};
if idx > 0 {
idx -= 1;
}
// t is fractional distance beween x at idx and idx+1
// and is in range [0,1]
let t = (xinterp - dense.x[idx]) / dense.h[idx];
// Compute interpolant coefficient as funciton of t
// note that t is in range [0,1]
//
// This is equation (6) of
// https://link.springer.com/article/10.1023/A:1021190918665
//
// Note: equation (6) of paper incorrectly has sum index "j"
// starting from 0. It should start from 1.
//
let bi: Vec<f64> = Self::BI
.iter()
.map(|biarr| {
// Coefficients multiply increasing powers of t
let mut tj = 1.0;
biarr.iter().fold(0.0, |acc, bij| {
tj = tj * t;
acc + bij * tj
})
})
.collect();
//
// Compute interpolated value
//
// This is equation(5) of:
// https://link.springer.com/article/10.1023/A:1021190918665
//
let mut y = dense.yprime[idx]
.iter()
.enumerate()
.fold(dense.y[idx].clone() / dense.h[idx], |acc, (ix, k)| {
acc + k.clone() * bi[ix]
});
y = y * dense.h[idx];
Ok(y)
}
fn integrate<S: ODEState>(
start: f64,
stop: f64,
y0: &S,
ydot: impl Fn(f64, &S) -> ODEResult<S>,
settings: &RKAdaptiveSettings,
) -> ODEResult<ODESolution<S>> {
let mut nevals: usize = 0;
let mut naccept: usize = 0;
let mut nreject: usize = 0;
let mut x = start.clone();
let mut y = y0.clone();
let mut qold: f64 = 1.0e-4;
let tdir = match stop > start {
true => 1.0,
false => -1.0,
};
// Take guess at initial stepsize
let mut h = {
// Adapted from OrdinaryDiffEq.jl
let sci = (y0.ode_abs() * settings.relerror).ode_scalar_add(settings.abserror);
let d0 = y0.ode_elem_div(&sci).ode_norm();
let ydot0 = ydot(start.clone(), &y0)?;
let d1 = ydot0.ode_elem_div(&sci).ode_norm();
let h0 = 0.01 * d0 / d1 * tdir;
let y1 = y0.clone() + ydot0.clone() * h0;
let ydot1 = ydot(start + h0, &y1)?;
let d2 = (ydot1 - ydot0).ode_elem_div(&sci).ode_norm() / h0;
let dmax = f64::max(d1, d2);
let h1: f64 = match dmax < 1e-15 {
false => (10.0 as f64).powf(-(2.0 + dmax.log10()) / (Self::ORDER as f64)),
true => f64::max(1e-6, h0.abs() * 1e-3),
};
nevals += 2;
f64::min(100.0 * h0.abs(), h1.abs()) * tdir
};
let mut accepted_steps: Option<DenseOutput<S>> = match settings.dense_output {
false => None,
true => Some(DenseOutput {
x: Vec::new(),
h: Vec::new(),
yprime: Vec::new(),
y: Vec::new(),
}),
};
// OK ... lets integrate!
loop {
if (tdir > 0.0 && (x + h) >= stop) || (tdir < 0.0 && (x + h) <= stop) {
h = stop - x;
}
let mut karr = Vec::with_capacity(N);
karr.push(ydot(x, &y)?);
// Create the "k"s
for k in 1..N {
karr.push(ydot(
x + h * Self::C[k],
&(karr.iter().enumerate().fold(y.clone(), |acc, (idx, ki)| {
acc + ki.clone() * Self::A[k][idx] * h
})),
)?);
}
// Sum the "k"s
let ynp1 = karr
.iter()
.enumerate()
.fold(y.clone() * 1.0 / h, |acc, (idx, k)| {
acc + k.clone() * Self::B[idx]
})
* h;
// Compute the "error" state by differencing the p and p* orders
let yerr = karr
.iter()
.enumerate()
.fold(S::ode_zero(), |acc, (idx, k)| {
if Self::BERR[idx].abs() > 1.0e-9 {
acc + k.clone() * Self::BERR[idx]
} else {
acc
}
})
* h;
// Compute normalized error
let enorm = {
let mut ymax = y.ode_abs().ode_elem_max(&ynp1.ode_abs()) * settings.relerror;
ymax = ymax.ode_scalar_add(settings.abserror);
let ydiv = yerr.ode_elem_div(&ymax);
ydiv.ode_norm()
};
nevals += N;
if !enorm.is_finite() {
return Err(Box::new(ODEError::StepErrorToSmall));
}
// Run proportional-integral controller on error
let beta1 = 7.0 / (5.0 * Self::ORDER as f64);
let beta2 = 2.0 / (5.0 * Self::ORDER as f64);
let q11 = enorm.powf(beta1);
let q = {
let q = q11 / qold.powf(beta2);
f64::max(
1.0 / settings.maxfac,
f64::min(1.0 / settings.minfac, q / settings.gamma),
)
};
if (enorm < 1.0) || (h.abs() <= settings.dtmin) {
// If dense output requested, record dense output
match settings.dense_output {
true => {
let astep = accepted_steps.as_mut().unwrap();
astep.x.push(x);
astep.h.push(h);
astep.yprime.push(karr);
astep.y.push(y.clone());
}
false => {}
}
// Adjust step size
qold = f64::max(enorm, 1.0e-4);
x += h;
y = ynp1;
h = h / q;
naccept += 1;
if (tdir > 0.0 && x >= stop) || (tdir < 0.0 && x <= stop) {
break;
}
} else {
nreject += 1;
h = h / f64::min(1.0 / settings.minfac, q11 / settings.gamma);
}
}
Ok(ODESolution {
nevals: nevals,
naccept: naccept,
nreject: nreject,
x: x,
y: y,
dense: accepted_steps,
})
}
}