add more integration schemes
This commit is contained in:
Magnus Ulimoen
parent
29499c0c0c
commit
596605a8b7
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@ -1,13 +1,97 @@
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use super::Float;
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use ndarray::{Array3, Zip};
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use ndarray::Array3;
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pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
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pub trait ButcherTableau {
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const S: usize = Self::B.len();
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const A: &'static [&'static [Float]];
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const B: &'static [Float];
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const C: &'static [Float];
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}
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pub struct Rk4;
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impl ButcherTableau for Rk4 {
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const A: &'static [&'static [Float]] = &[&[0.5], &[0.0, 0.5], &[0.0, 0.0, 1.0]];
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const B: &'static [Float] = &[1.0 / 6.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 6.0];
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const C: &'static [Float] = &[0.5, 0.5, 1.0];
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}
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pub struct Rk4_38;
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impl ButcherTableau for Rk4_38 {
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const A: &'static [&'static [Float]] = &[&[1.0 / 3.0], &[-1.0 / 3.0, 1.0], &[1.0, -1.0, 1.0]];
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const B: &'static [Float] = &[1.0 / 8.0, 3.0 / 8.0, 3.0 / 8.0, 1.0 / 8.0];
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const C: &'static [Float] = &[1.0 / 3.0, 2.0 / 3.0, 1.0];
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}
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pub struct EulerMethod;
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impl ButcherTableau for EulerMethod {
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const A: &'static [&'static [Float]] = &[&[]];
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const B: &'static [Float] = &[1.0];
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const C: &'static [Float] = &[];
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}
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pub struct MidpointMethod;
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impl ButcherTableau for MidpointMethod {
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const A: &'static [&'static [Float]] = &[&[0.5]];
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const B: &'static [Float] = &[0.0, 1.0];
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const C: &'static [Float] = &[1.0 / 2.0];
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}
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/// Bit exessive...
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const SQRT_5: Float = 2.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275;
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pub struct Rk6;
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impl ButcherTableau for Rk6 {
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const A: &'static [&'static [Float]] = &[
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&[4.0 / 7.0],
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&[115.0 / 112.0, -5.0 / 16.0],
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&[589.0 / 630.0, 5.0 / 18.0, -16.0 / 45.0],
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&[
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229.0 / 1200.0 - 29.0 / 6000.0 * SQRT_5,
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119.0 / 240.0 - 187.0 / 1200.0 * SQRT_5,
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-14.0 / 75.0 + 34.0 / 375.0 * SQRT_5,
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-3.0 / 100.0 * SQRT_5,
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],
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&[
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71.0 / 2400.0 - 587.0 / 12000.0 * SQRT_5,
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187.0 / 480.0 - 391.0 / 2400.0 * SQRT_5,
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-38.0 / 75.0 + 26.0 / 375.0 * SQRT_5,
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27.0 / 80.0 - 3.0 / 400.0 * SQRT_5,
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(1.0 + SQRT_5) / 4.0,
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],
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&[
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-49.0 / 480.0 + 43.0 / 160.0 * SQRT_5,
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-425.0 / 96.0 + 51.0 / 32.0 * SQRT_5,
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52.0 / 15.0 - 4.0 / 5.0 * SQRT_5,
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-27.0 / 16.0 + 3.0 / 16.0 * SQRT_5,
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5.0 / 4.0 - 3.0 / 4.0 * SQRT_5,
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5.0 / 2.0 - 1.0 / 2.0 * SQRT_5,
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],
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];
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const B: &'static [Float] = &[
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1.0 / 12.0,
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0.0,
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0.0,
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0.0,
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5.0 / 12.0,
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5.0 / 12.0,
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1.0 / 12.0,
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];
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const C: &'static [Float] = &[
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4.0 / 7.0,
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5.0 / 7.0,
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6.0 / 7.0,
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(5.0 - SQRT_5) / 10.0,
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(5.0 + SQRT_5) / 10.0,
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1.0,
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];
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}
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pub fn integrate<'a, BTableau, F: 'a, RHS, MT, C>(
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rhs: RHS,
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prev: &F,
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fut: &mut F,
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time: &mut Float,
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dt: Float,
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k: &mut [F; 4],
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k: &mut [F],
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constants: C,
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mut mutables: &mut MT,
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@ -15,8 +99,10 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
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C: Copy,
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F: std::ops::Deref<Target = Array3<Float>> + std::ops::DerefMut<Target = Array3<Float>>,
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RHS: Fn(&mut F, &F, Float, C, &mut MT),
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BTableau: ButcherTableau,
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{
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assert_eq!(prev.shape(), fut.shape());
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assert!(k.len() >= BTableau::S);
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for i in 0.. {
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let simtime;
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@ -25,26 +111,24 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
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fut.assign(prev);
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simtime = *time;
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}
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1 | 2 => {
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i if i < BTableau::S => {
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fut.assign(prev);
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fut.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
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simtime = *time + dt / 2.0;
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for (&a, k) in BTableau::A[i - 1].iter().zip(k.iter()) {
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if a == 0.0 {
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continue;
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}
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fut.scaled_add(a * dt, &k);
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}
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simtime = *time + dt * BTableau::C[i - 1];
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}
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3 => {
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_ if i == BTableau::S => {
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fut.assign(prev);
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fut.scaled_add(dt, &k[i - 1]);
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simtime = *time + dt;
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}
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4 => {
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Zip::from(&mut **fut)
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.and(&**prev)
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.and(&*k[0])
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.and(&*k[1])
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.and(&*k[2])
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.and(&*k[3])
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
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*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
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});
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for (&b, k) in BTableau::B.iter().zip(k.iter()) {
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if b == 0.0 {
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continue;
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}
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fut.scaled_add(b * dt, &k);
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}
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*time += dt;
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return;
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}
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@ -56,3 +140,21 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
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rhs(&mut k[i], &fut, simtime, constants, &mut mutables);
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}
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}
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pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
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rhs: RHS,
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prev: &F,
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fut: &mut F,
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time: &mut Float,
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dt: Float,
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k: &mut [F; 4],
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constants: C,
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mutables: &mut MT,
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) where
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C: Copy,
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F: std::ops::Deref<Target = Array3<Float>> + std::ops::DerefMut<Target = Array3<Float>>,
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RHS: Fn(&mut F, &F, Float, C, &mut MT),
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{
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integrate::<Rk6, F, RHS, MT, C>(rhs, prev, fut, time, dt, k, constants, mutables)
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}
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