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explicit.rs
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/
explicit.rs
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//! Define explicit schemes
use ndarray::*;
use super::traits::*;
macro_rules! def_explicit {
($method:ident, $constructor:ident) => {
#[derive(new)]
pub struct $method<F> {
f: F,
dt: f64,
}
pub fn $constructor<F>(f: F, dt: f64) -> $method<F> {
$method::new(f, dt)
}
impl<F> TimeStep for $method<F> {
fn get_dt(&self) -> f64 {
self.dt
}
fn set_dt(&mut self, dt: f64) {
self.dt = dt;
}
}
}} // def_explicit
def_explicit!(Euler, euler);
def_explicit!(Heun, heun);
def_explicit!(RK4, rk4);
macro_rules! impl_time_evolution {
( $($mut_:tt), * ) => {
impl<'a, A, D, F> TimeEvolution<A, OwnedRcRepr<A>, D> for &'a $($mut_),* Euler<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b> &'b $($mut_),* F: EOM<A, OwnedRcRepr<A>, D>
{
#[inline(always)]
fn iterate(self, x: RcArray<A, D>) -> RcArray<A, D> {
let fx = self.f.rhs(x.clone());
x + fx * self.dt
}
}
impl<'a, A, D, F> TimeEvolution<A, ViewRepr<&'a mut A>, D> for &'a $($mut_),* Euler<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b, 'c> &'b $($mut_),* F: EOM<A, ViewRepr<&'c mut A>, D>
{
#[inline(always)]
fn iterate(self, x: ArrayViewMut<A, D>) -> ArrayViewMut<A, D> {
let x_ = x.to_owned();
let mut fx = self.f.rhs(x);
azip!(mut fx, x_ in { *fx = x_ + *fx * self.dt });
fx
}
}
impl<'a, A, D, F> TimeEvolution<A, OwnedRcRepr<A>, D> for &'a $($mut_),* Heun<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b> &'b $($mut_),* F: EOM<A, OwnedRcRepr<A>, D>
{
#[inline(always)]
fn iterate(self, x: RcArray<A, D>) -> RcArray<A, D> {
let k1 = self.f.rhs(x.clone()) * self.dt;
let k2 = self.f.rhs(x.clone() + k1.clone()) * self.dt;
x + (k1 + k2) * 0.5
}
}
impl<'a, A, D, F> TimeEvolution<A, ViewRepr<&'a mut A>, D> for &'a $($mut_),* Heun<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b, 'c> &'b $($mut_),* F: EOM<A, ViewRepr<&'c mut A>, D>
{
#[inline(always)]
fn iterate(self, x: ArrayViewMut<A, D>) -> ArrayViewMut<A, D> {
let dt = self.dt;
let dt_2 = self.dt * 0.5;
let x_ = x.to_owned();
let mut k1 = self.f.rhs(x);
let k1_ = k1.to_owned();
azip!(mut k1, x_ in { *k1 = *k1 * dt + x_ });
let mut k2 = self.f.rhs(k1);
azip!(mut k2, x_, k1_ in { *k2 = x_ + (k1_ + *k2) * dt_2 });
k2
}
}
impl<'a, A, D, F> TimeEvolution<A, OwnedRcRepr<A>, D> for &'a $($mut_),* RK4<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b> &'b $($mut_),* F: EOM<A, OwnedRcRepr<A>, D>
{
#[inline(always)]
fn iterate(self, x: RcArray<A, D>) -> RcArray<A, D> {
let dt_2 = 0.5 * self.dt;
let dt_6 = self.dt / 6.0;
let k1 = self.f.rhs(x.clone());
let l1 = k1.clone() * dt_2 + &x;
let k2 = self.f.rhs(l1);
let l2 = k2.clone() * dt_2 + &x;
let k3 = self.f.rhs(l2);
let l3 = k3.clone() * self.dt + &x;
let k4 = self.f.rhs(l3);
x + (k1 + (k2 + k3) * 2.0 + k4) * dt_6
}
}
impl<'a, A, D, F> TimeEvolution<A, ViewRepr<&'a mut A>, D> for &'a $($mut_),* RK4<F>
where A: OdeScalar<f64>,
D: Dimension,
for<'b, 'c> &'b $($mut_),* F: EOM<A, ViewRepr<&'c mut A>, D>
{
#[inline(always)]
fn iterate(self, x: ArrayViewMut<A, D>) -> ArrayViewMut<A, D> {
let dt = self.dt;
let dt_2 = self.dt * 0.5;
let dt_6 = self.dt / 6.0;
let x_ = x.to_owned();
// k1
let mut k1 = self.f.rhs(x);
let k1_ = k1.to_owned();
azip!(mut k1, x_ in { *k1 = *k1 * dt_2 + x_ });
// k2
let mut k2 = self.f.rhs(k1);
let k2_ = k2.to_owned();
azip!(mut k2, x_ in { *k2 = x_ + *k2 * dt_2 });
// k3
let mut k3 = self.f.rhs(k2);
let k3_ = k3.to_owned();
azip!(mut k3, x_ in { *k3 = x_ + *k3 * dt });
let mut k4 = self.f.rhs(k3);
azip!(mut k4, x_, k1_, k2_, k3_ in {
*k4 = x_ + (k1_ + (k2_ + k3_) * 2.0 + *k4) * dt_6
});
k4
}
}
}} // impl_time_evolution!
impl_time_evolution!();
impl_time_evolution!(mut);