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use super::traits::*;
use ndarray::*;
use ndarray_linalg::*;
#[derive(Debug, Clone)]
pub struct Euler<F: Explicit> {
f: F,
dt: <F::Scalar as Scalar>::Real,
x: Array<F::Scalar, F::Dim>,
}
impl<A: Scalar, F: Explicit<Scalar = A>> TimeStep for Euler<F> {
type Time = A::Real;
fn get_dt(&self) -> Self::Time {
self.dt
}
fn set_dt(&mut self, dt: Self::Time) {
self.dt = dt;
}
}
impl<F: Explicit> Scheme for Euler<F> {
type Core = F;
fn new(f: F, dt: Self::Time) -> Self {
let x = Array::zeros(f.model_size());
Self { f, dt, x }
}
fn core(&self) -> &Self::Core {
&self.f
}
fn core_mut(&mut self) -> &mut Self::Core {
&mut self.f
}
}
impl<F: Explicit> ModelSpec for Euler<F> {
type Scalar = F::Scalar;
type Dim = F::Dim;
fn model_size(&self) -> <Self::Dim as Dimension>::Pattern {
self.f.model_size()
}
}
impl<F: Explicit> TimeEvolution for Euler<F> {
fn iterate<'a, S>(&mut self, x: &'a mut ArrayBase<S, F::Dim>) -> &'a mut ArrayBase<S, Self::Dim>
where
S: DataMut<Elem = Self::Scalar>,
{
self.x.zip_mut_with(x, |buf, x| *buf = *x);
let fx = self.f.rhs(x);
Zip::from(&mut *fx).and(&self.x).for_each(|vfx, vx| {
*vfx = *vx + vfx.mul_real(self.dt);
});
fx
}
}
#[derive(Debug, Clone)]
pub struct Heun<F: Explicit> {
f: F,
dt: <F::Scalar as Scalar>::Real,
x: Array<F::Scalar, F::Dim>,
k1: Array<F::Scalar, F::Dim>,
}
impl<A: Scalar, F: Explicit<Scalar = A>> TimeStep for Heun<F> {
type Time = A::Real;
fn get_dt(&self) -> Self::Time {
self.dt
}
fn set_dt(&mut self, dt: Self::Time) {
self.dt = dt;
}
}
impl<F: Explicit> Scheme for Heun<F> {
type Core = F;
fn new(f: F, dt: Self::Time) -> Self {
let x = Array::zeros(f.model_size());
let k1 = Array::zeros(f.model_size());
Self { f, dt, x, k1 }
}
fn core(&self) -> &Self::Core {
&self.f
}
fn core_mut(&mut self) -> &mut Self::Core {
&mut self.f
}
}
impl<F: Explicit> ModelSpec for Heun<F> {
type Scalar = F::Scalar;
type Dim = F::Dim;
fn model_size(&self) -> <Self::Dim as Dimension>::Pattern {
self.f.model_size()
}
}
impl<F: Explicit> TimeEvolution for Heun<F> {
fn iterate<'a, S>(&mut self, x: &'a mut ArrayBase<S, F::Dim>) -> &'a mut ArrayBase<S, Self::Dim>
where
S: DataMut<Elem = Self::Scalar>,
{
let dt = self.dt;
let dt_2 = self.dt * F::Scalar::real(0.5);
self.x.zip_mut_with(x, |buf, x| *buf = *x);
let k1 = self.f.rhs(x);
self.k1.zip_mut_with(k1, |buf, k1| *buf = *k1);
Zip::from(&mut *k1).and(&self.x).for_each(|k1, &x_| {
*k1 = k1.mul_real(dt) + x_;
});
let k2 = self.f.rhs(k1);
Zip::from(&mut *k2)
.and(&self.x)
.and(&self.k1)
.for_each(|k2, &x_, &k1_| {
*k2 = x_ + (k1_ + *k2).mul_real(dt_2);
});
k2
}
}
#[derive(Debug, Clone)]
pub struct RK4<F: Explicit> {
f: F,
dt: <F::Scalar as Scalar>::Real,
x: Array<F::Scalar, F::Dim>,
k1: Array<F::Scalar, F::Dim>,
k2: Array<F::Scalar, F::Dim>,
k3: Array<F::Scalar, F::Dim>,
}
impl<A: Scalar, F: Explicit<Scalar = A>> TimeStep for RK4<F> {
type Time = A::Real;
fn get_dt(&self) -> Self::Time {
self.dt
}
fn set_dt(&mut self, dt: Self::Time) {
self.dt = dt;
}
}
impl<F: Explicit> Scheme for RK4<F> {
type Core = F;
fn new(f: F, dt: Self::Time) -> Self {
let x = Array::zeros(f.model_size());
let k1 = Array::zeros(f.model_size());
let k2 = Array::zeros(f.model_size());
let k3 = Array::zeros(f.model_size());
Self {
f,
dt,
x,
k1,
k2,
k3,
}
}
fn core(&self) -> &Self::Core {
&self.f
}
fn core_mut(&mut self) -> &mut Self::Core {
&mut self.f
}
}
impl<F: Explicit> ModelSpec for RK4<F> {
type Scalar = F::Scalar;
type Dim = F::Dim;
fn model_size(&self) -> <Self::Dim as Dimension>::Pattern {
self.f.model_size()
}
}
impl<F: Explicit> TimeEvolution for RK4<F> {
fn iterate<'a, S>(&mut self, x: &'a mut ArrayBase<S, F::Dim>) -> &'a mut ArrayBase<S, Self::Dim>
where
S: DataMut<Elem = Self::Scalar>,
{
let two = F::Scalar::real(2.0);
let dt = self.dt;
let dt_2 = self.dt * F::Scalar::real(0.5);
let dt_6 = self.dt / F::Scalar::real(6.0);
self.x.zip_mut_with(x, |buf, x| *buf = *x);
let k1 = self.f.rhs(x);
self.k1.zip_mut_with(k1, |buf, k1| *buf = *k1);
Zip::from(&mut *k1).and(&self.x).for_each(|k1, &x| {
*k1 = k1.mul_real(dt_2) + x;
});
let k2 = self.f.rhs(k1);
self.k2.zip_mut_with(k2, |buf, k| *buf = *k);
Zip::from(&mut *k2).and(&self.x).for_each(|k2, &x| {
*k2 = x + k2.mul_real(dt_2);
});
let k3 = self.f.rhs(k2);
self.k3.zip_mut_with(k3, |buf, k| *buf = *k);
Zip::from(&mut *k3).and(&self.x).for_each(|k3, &x| {
*k3 = x + k3.mul_real(dt);
});
let k4 = self.f.rhs(k3);
Zip::from(&mut *k4)
.and(&self.x)
.and(&self.k1)
.and(&self.k2)
.and(&self.k3)
.for_each(|k4, &x, &k1, &k2, &k3| {
*k4 = x + (k1 + (k2 + k3).mul_real(two) + *k4).mul_real(dt_6);
});
k4
}
}