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#[cfg(test)] extern crate matplotrust; extern crate rand; use rand::prelude::*; use rand::distributions::Normal as N; use std::f64::consts::PI; mod utils; mod timeseries; macro_rules! assert_delta { ($x:expr, $y:expr, $d:expr) => { if !(($x - $y).abs() < $d || ($y - $x).abs() < $d) { panic!(); } } } fn mean(numbers: &Vec<f64>) -> f64 { numbers.iter().sum::<f64>() as f64 / numbers.len() as f64 } pub struct Normal { mean : f64, std : f64 } impl Normal { pub fn new(mean: f64, std: f64) -> Normal { return Normal { mean : mean, std: std, } } pub fn sample(&mut self) -> f64 { let normal = N::new(self.mean, self.std); let v = normal.sample(&mut rand::thread_rng()); return v; } pub fn logpdf(&mut self, x: f64) -> f64 { return -0.5 * (2.0 * PI).ln() - self.std.ln() - (x - self.mean).powi(2) / (2.0 * self.std * self.std) } pub fn pdf(&mut self, x: f64) -> f64 { return self.logpdf(x).exp(); } } pub struct MonotonicCubicSpline { m_x: Vec<f64>, m_y: Vec<f64>, m_m: Vec<f64> } impl MonotonicCubicSpline { pub fn new(x : &Vec<f64>, y : &Vec<f64>) -> MonotonicCubicSpline { assert!(x.len() == y.len() && x.len() >= 2 && y.len() >= 2, "Must have at least 2 control points."); let n = x.len(); let mut secants = vec![0.0 ; n - 1]; let mut slopes = vec![0.0 ; n]; for i in 0..(n-1) { let h = *x.get(i + 1).unwrap() - *x.get(i).unwrap(); assert!(h > 0.0, "Control points must be monotonically increasing."); secants[i] = (*y.get(i + 1).unwrap() - *y.get(i).unwrap()) / h; } slopes[0] = secants[0]; for i in 1..(n-1) { slopes[i] = (secants[i - 1] + secants[i]) * 0.5; } slopes[n - 1] = secants[n - 2]; for i in 0..(n-1) { if secants[i] == 0.0 { slopes[i] = 0.0; slopes[i + 1] = 0.0; } else { let alpha = slopes[i] / secants[i]; let beta = slopes[i + 1] / secants[i]; let h = alpha.hypot(beta); if h > 9.0 { let t = 3.0 / h; slopes[i] = t * alpha * secants[i]; slopes[i + 1] = t * beta * secants[i]; } } } let spline = MonotonicCubicSpline { m_x: x.clone(), m_y: y.clone(), m_m: slopes }; return spline; } pub fn hermite(point: f64, x : (f64, f64), y: (f64, f64), m: (f64, f64)) -> f64 { let h: f64 = x.1 - x.0; let t = (point - x.0) / h; return (y.0 * (1.0 + 2.0 * t) + h * m.0 * t) * (1.0 - t) * (1.0 - t) + (y.1 * (3.0 - 2.0 * t) + h * m.1 * (t - 1.0)) * t * t; } pub fn interpolate(&mut self, point : f64) -> f64 { let n = self.m_x.len(); if point <= *self.m_x.get(0).unwrap() { return *self.m_y.get(0).unwrap(); } if point >= *self.m_x.get(n - 1).unwrap() { return *self.m_y.get(n - 1).unwrap(); } let mut i = 0; while point >= *self.m_x.get(i + 1).unwrap() { i += 1; if point == *self.m_x.get(i).unwrap() { return *self.m_y.get(i).unwrap(); } } return MonotonicCubicSpline::hermite(point, (*self.m_x.get(i).unwrap(), *self.m_x.get(i+1).unwrap()), (*self.m_y.get(i).unwrap(), *self.m_y.get(i+1).unwrap()), (*self.m_m.get(i).unwrap(), *self.m_m.get(i+1).unwrap())); } fn partial(x: Vec<f64>, y: Vec<f64>) -> impl Fn(f64) -> f64 { move |p| { let mut spline = MonotonicCubicSpline::new(&x, &y); spline.interpolate(p) } } } #[cfg(test)] mod test_normal { use super::*; #[test] fn sample_mean_std() { let n = 0..1000000; let mut normal = Normal::new(0.0, 1.0); let samples = n.map(|_i| normal.sample()).collect::<Vec<f64>>(); let mu = mean(&samples); assert_delta!(0.0, mu, 1e-3); } #[test] fn logpdf() { let mut normal = Normal::new(0.0, 1.0); let _logpdf = normal.logpdf(0.0); print!("{:?}", _logpdf); assert_delta!(-0.9189385, _logpdf, 1e-5); } fn pdf() { let mut normal = Normal::new(0.0, 1.0); let _pdf = normal.pdf(0.0); print!("{:?}", _pdf); assert_delta!(0.3989423, _pdf, 1e-5); } #[test] fn interpolation() { use matplotrust::*; let x = vec![0.0, 2.0, 3.0, 10.0]; let y = vec![1.0, 4.0, 8.0, 10.5]; let smooth = MonotonicCubicSpline::partial(x.clone(), y.clone()); let mut x_interp = Vec::new(); let mut y_interp = Vec::new(); for i in 0..100 { let p = i as f64 / 10.0; x_interp.push(p); y_interp.push(smooth(p)); } let mut figure = Figure::new(); let points = scatter_plot::<f64, f64>(x, y, None); let interpolation = line_plot::<f64, f64>(x_interp, y_interp, None); figure.add_plot(points); figure.add_plot(interpolation); figure.save("./docs/figures/monotonic_cubic_spline.png", None); } }