Move stuff around
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0ae05fd730
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110
src/bin/flat/fns.rs
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110
src/bin/flat/fns.rs
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@ -0,0 +1,110 @@
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use crate::FloatExt2;
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pub struct LinearLimiter {
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pub min: f32,
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pub max: f32,
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}
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impl LinearLimiter {
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pub fn value(&self, x: f32) -> f32 { (self.min, self.max).inverse_lerp(x.abs()).clamp(0.0, 1.0) }
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pub fn derivative(&self, x: f32) -> f32 { if x.abs() > self.min && x.abs() < self.max { x.signum() / (self.max - self.min) } else { 0.0 } }
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}
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pub struct QuadraticAccelerator {
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pub internal: f32,
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pub external: f32,
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}
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/// Продолжает функцию f с [-lim, lim] линейно в предположении f(±lim) = ±val, f'(±lim) = 1.
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fn extend_linear(t: f32, f: impl FnOnce(f32) -> f32, lim: f32, val: f32) -> f32 {
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if t.abs() <= lim { f(t) } else { t + t.signum() * (val - lim) }
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}
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/// Продолжает функцию f с [-lim, lim] константой в предположении f(±lim) = val, f'(±lim) = 0.
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fn extend_const(t: f32, f: impl FnOnce(f32) -> f32, lim: f32, val: f32) -> f32 {
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if t.abs() <= lim { f(t) } else { val }
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}
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impl QuadraticAccelerator {
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fn a(&self) -> f32 { -(self.external - self.internal) / self.internal.powi(2) }
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fn b(&self) -> f32 { 2.0 * self.external / self.internal - 1.0 }
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fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x.abs()).sqrt() }
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pub fn x(&self, u: f32) -> f32 { extend_linear(u, |u| (self.a() * u.abs() + self.b()) * u, self.internal, self.external) }
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pub fn u(&self, x: f32) -> f32 { extend_linear(x, |x| 0.5 * x.signum() * (-self.b() + self.root(x)) / self.a(), self.external, self.internal) }
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pub fn dx(&self, u: f32) -> f32 { extend_const(u, |u| 2.0 * self.a() * u.abs() + self.b(), self.internal, 1.0) }
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pub fn du(&self, x: f32) -> f32 { extend_const(x, |x| 1.0 / self.root(x), self.external, 1.0) }
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pub fn d2u(&self, x: f32) -> f32 { extend_const(x, |x| -2.0 * x.signum() * self.a() * self.root(x).powi(-3), self.external, 0.0) }
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}
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#[cfg(test)]
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mod test {
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use approx::{abs_diff_eq, AbsDiffEq, assert_abs_diff_eq};
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#[test]
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fn test_linear_limiter() {
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let testee = super::LinearLimiter { min: 20.0, max: 30.0 };
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let ε = 1.0e-4f32;
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let δ = 1.0 / 8.0; // Mathematically, you want this to be small. Computationally, you don’t.
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let margin = 1.0 / 16.0;
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let mul = 1.0 + margin;
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for x in itertools_num::linspace(0., testee.min, 10) {
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assert_abs_diff_eq!(testee.value(x), 0., epsilon = ε);
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assert_abs_diff_eq!(testee.value(-x), 0., epsilon = ε);
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}
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for x in itertools_num::linspace(testee.max, mul * testee.max, 10) {
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assert_abs_diff_eq!(testee.value(x), 1., epsilon = ε);
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assert_abs_diff_eq!(testee.value(-x), 1., epsilon = ε);
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}
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for x in itertools_num::linspace(-mul * testee.max, mul * testee.max, 100) {
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// Currently, the derivative is discontinuous at ±min and ±max... let’s just skip these for now.
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if x.abs().abs_diff_eq(&testee.min, δ) || x.abs().abs_diff_eq(&testee.max, δ) {
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continue;
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}
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let df_num = (testee.value(x + δ) - testee.value(x - δ)) / (2. * δ);
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let df_expl = testee.derivative(x);
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assert!(abs_diff_eq!(df_expl, df_num, epsilon = ε), "At x={x}, df/dx:\nnumerical: {df_num}\nexplicit: {df_expl}\n");
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}
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}
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#[test]
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fn test_quadratic_accelerator() {
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let testee = super::QuadraticAccelerator { internal: 100.0, external: 150.0 };
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let ε = 1.0e-4f32;
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let δ = 1.0 / 8.0; // Mathematically, you want this to be small. Computationally, you don’t.
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let margin = 1.0 / 16.0;
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let mul = 1.0 + margin;
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assert_abs_diff_eq!(testee.u(testee.external), testee.internal, epsilon = ε);
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assert_abs_diff_eq!(testee.u(-testee.external), -testee.internal, epsilon = ε);
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assert_abs_diff_eq!(testee.du(testee.external), 1., epsilon = ε);
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assert_abs_diff_eq!(testee.du(-testee.external), 1., epsilon = ε);
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for x in itertools_num::linspace(-mul * testee.external, mul * testee.external, 100) {
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let ux = testee.u(x);
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let xux = testee.x(ux);
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assert!(abs_diff_eq!(x, xux, epsilon = ε), "At x={x}:\nu(x): {ux}\nx(u(x)): {xux}\n");
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let du_num = (testee.u(x + δ) - testee.u(x - δ)) / (2. * δ);
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let du_expl = testee.du(x);
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assert!(abs_diff_eq!(du_expl, du_num, epsilon = ε), "At x={x}, du/dx:\nnumerical: {du_num}\nexplicit: {du_expl}\n");
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let dudx = du_expl * testee.dx(ux);
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assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At x={x}:\ndu/dx * dx/du: {dudx}\n");
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let d2u_num = (testee.du(x + δ) - testee.du(x - δ)) / (2. * δ);
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let d2u_expl = testee.d2u(x);
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assert!(abs_diff_eq!(d2u_expl, d2u_num, epsilon = ε), "At x={x}, d^2u/dx^2:\nnumerical: {d2u_num}\nexplicit: {d2u_expl}\n");
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}
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for u in itertools_num::linspace(-mul * testee.internal, mul * testee.internal, 100) {
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let xu = testee.x(u);
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let uxu = testee.u(xu);
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assert!(abs_diff_eq!(u, uxu, epsilon = ε), "At u={u}:\nx(u): {xu}\nu(x(u)): {uxu}\n");
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let dx_num = (testee.x(u + δ) - testee.x(u - δ)) / (2. * δ);
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let dx_expl = testee.dx(u);
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assert!(abs_diff_eq!(dx_expl, dx_num, epsilon = ε), "At u={u}, dx/du:\nnumerical: {dx_num}\nexplicit: {dx_expl}\n");
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let dudx = testee.du(xu) * dx_expl;
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assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At u={u}:\ndu/dx * dx/du: {dudx}\n");
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}
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}
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}
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@ -4,6 +4,7 @@ use flo_canvas::*;
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use glam::*;
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mod riemann;
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mod fns;
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use riemann::{Tens2, Decomp2, Metric, trace_iter};
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use shape::Shape;
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@ -624,129 +625,6 @@ impl Tube {
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pub fn dv(&self, y: f32) -> f32 { self.fy().du(y) }
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}
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mod fns {
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use crate::FloatExt2;
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pub struct LinearLimiter {
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pub min: f32,
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pub max: f32,
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}
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impl LinearLimiter {
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pub fn value(&self, x: f32) -> f32 { (self.min, self.max).inverse_lerp(x.abs()).clamp(0.0, 1.0) }
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pub fn derivative(&self, x: f32) -> f32 { if x.abs() > self.min && x.abs() < self.max { x.signum() / (self.max - self.min) } else { 0.0 } }
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}
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pub struct QuadraticAccelerator {
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pub internal: f32,
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pub external: f32,
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}
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/// Продолжает функцию f с [-lim, lim] линейно в предположении f(±lim) = ±val, f'(±lim) = 1.
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fn extend_linear(t: f32, f: impl FnOnce(f32) -> f32, lim: f32, val: f32) -> f32 {
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if t.abs() <= lim { f(t) } else { t + t.signum() * (val - lim) }
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}
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/// Продолжает функцию f с [-lim, lim] константой в предположении f(±lim) = val, f'(±lim) = 0.
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fn extend_const(t: f32, f: impl FnOnce(f32) -> f32, lim: f32, val: f32) -> f32 {
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if t.abs() <= lim { f(t) } else { val }
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}
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impl QuadraticAccelerator {
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fn a(&self) -> f32 { -(self.external - self.internal) / self.internal.powi(2) }
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fn b(&self) -> f32 { 2.0 * self.external / self.internal - 1.0 }
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fn root(&self, x: f32) -> f32 { (self.b().powi(2) + 4.0 * self.a() * x.abs()).sqrt() }
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pub fn x(&self, u: f32) -> f32 { extend_linear(u, |u| (self.a() * u.abs() + self.b()) * u, self.internal, self.external) }
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pub fn u(&self, x: f32) -> f32 { extend_linear(x, |x| 0.5 * x.signum() * (-self.b() + self.root(x)) / self.a(), self.external, self.internal) }
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pub fn dx(&self, u: f32) -> f32 { extend_const(u, |u| 2.0 * self.a() * u.abs() + self.b(), self.internal, 1.0) }
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pub fn du(&self, x: f32) -> f32 { extend_const(x, |x| 1.0 / self.root(x), self.external, 1.0) }
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pub fn d2u(&self, x: f32) -> f32 { extend_const(x, |x| -2.0 * x.signum() * self.a() * self.root(x).powi(-3), self.external, 0.0) }
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}
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#[cfg(test)]
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mod test {
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use approx::{abs_diff_eq, AbsDiffEq, assert_abs_diff_eq};
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#[test]
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fn test_linear_limiter() {
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let testee = super::LinearLimiter { min: 20.0, max: 30.0 };
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let ε = 1.0e-4f32;
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let δ = 1.0 / 8.0; // Mathematically, you want this to be small. Computationally, you don’t.
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let margin = 1.0 / 16.0;
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let mul = 1.0 + margin;
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for x in itertools_num::linspace(0., testee.min, 10) {
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assert_abs_diff_eq!(testee.value(x), 0., epsilon = ε);
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assert_abs_diff_eq!(testee.value(-x), 0., epsilon = ε);
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}
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for x in itertools_num::linspace(testee.max, mul * testee.max, 10) {
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assert_abs_diff_eq!(testee.value(x), 1., epsilon = ε);
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assert_abs_diff_eq!(testee.value(-x), 1., epsilon = ε);
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}
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for x in itertools_num::linspace(-mul * testee.max, mul * testee.max, 100) {
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// Currently, the derivative is discontinuous at ±min and ±max... let’s just skip these for now.
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if x.abs().abs_diff_eq(&testee.min, δ) || x.abs().abs_diff_eq(&testee.max, δ) {
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continue;
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}
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let df_num = (testee.value(x + δ) - testee.value(x - δ)) / (2. * δ);
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let df_expl = testee.derivative(x);
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assert!(abs_diff_eq!(df_expl, df_num, epsilon = ε), "At x={x}, df/dx:\nnumerical: {df_num}\nexplicit: {df_expl}\n");
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}
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}
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#[test]
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fn test_quadratic_accelerator() {
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let testee = super::QuadraticAccelerator { internal: 100.0, external: 150.0 };
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let ε = 1.0e-4f32;
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let δ = 1.0 / 8.0; // Mathematically, you want this to be small. Computationally, you don’t.
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let margin = 1.0 / 16.0;
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let mul = 1.0 + margin;
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assert_abs_diff_eq!(testee.u(testee.external), testee.internal, epsilon = ε);
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assert_abs_diff_eq!(testee.u(-testee.external), -testee.internal, epsilon = ε);
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assert_abs_diff_eq!(testee.du(testee.external), 1., epsilon = ε);
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assert_abs_diff_eq!(testee.du(-testee.external), 1., epsilon = ε);
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for x in itertools_num::linspace(-mul * testee.external, mul * testee.external, 100) {
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let ux = testee.u(x);
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let xux = testee.x(ux);
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assert!(abs_diff_eq!(x, xux, epsilon = ε), "At x={x}:\nu(x): {ux}\nx(u(x)): {xux}\n");
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let du_num = (testee.u(x + δ) - testee.u(x - δ)) / (2. * δ);
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let du_expl = testee.du(x);
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assert!(abs_diff_eq!(du_expl, du_num, epsilon = ε), "At x={x}, du/dx:\nnumerical: {du_num}\nexplicit: {du_expl}\n");
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let dudx = du_expl * testee.dx(ux);
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assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At x={x}:\ndu/dx * dx/du: {dudx}\n");
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let d2u_num = (testee.du(x + δ) - testee.du(x - δ)) / (2. * δ);
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let d2u_expl = testee.d2u(x);
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assert!(abs_diff_eq!(d2u_expl, d2u_num, epsilon = ε), "At x={x}, d^2u/dx^2:\nnumerical: {d2u_num}\nexplicit: {d2u_expl}\n");
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}
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for u in itertools_num::linspace(-mul * testee.internal, mul * testee.internal, 100) {
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let xu = testee.x(u);
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let uxu = testee.u(xu);
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assert!(abs_diff_eq!(u, uxu, epsilon = ε), "At u={u}:\nx(u): {xu}\nu(x(u)): {uxu}\n");
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let dx_num = (testee.x(u + δ) - testee.x(u - δ)) / (2. * δ);
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let dx_expl = testee.dx(u);
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assert!(abs_diff_eq!(dx_expl, dx_num, epsilon = ε), "At u={u}, dx/du:\nnumerical: {dx_num}\nexplicit: {dx_expl}\n");
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let dudx = testee.du(xu) * dx_expl;
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assert!(abs_diff_eq!(dudx, 1.0, epsilon = ε), "At u={u}:\ndu/dx * dx/du: {dudx}\n");
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}
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}
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}
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}
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trait FloatExt2 {
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fn lerp(&self, t: f32) -> f32;
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fn inverse_lerp(&self, y: f32) -> f32;
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}
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impl FloatExt2 for (f32, f32) {
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fn lerp(&self, t: f32) -> f32 { f32::lerp(self.0, self.1, t) }
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fn inverse_lerp(&self, y: f32) -> f32 { f32::inverse_lerp(self.0, self.1, y) }
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}
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impl Metric for Tube {
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fn sqrt_at(&self, pos: Vec2) -> Decomp2 {
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let sx = self.fx().value(pos.x);
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@ -802,3 +680,13 @@ fn test_tube_metric_derivs() {
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}
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}
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}
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trait FloatExt2 {
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fn lerp(&self, t: f32) -> f32;
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fn inverse_lerp(&self, y: f32) -> f32;
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}
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impl FloatExt2 for (f32, f32) {
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fn lerp(&self, t: f32) -> f32 { f32::lerp(self.0, self.1, t) }
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fn inverse_lerp(&self, y: f32) -> f32 { f32::inverse_lerp(self.0, self.1, y) }
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}
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