lib.rs 5.36 KB
Newer Older
1 2 3
#[cfg(test)]
extern crate matplotrust;

4
extern crate rand;
5

Rui Vieira's avatar
Rui Vieira committed
6 7
use rand::prelude::*;
use rand::distributions::Normal as N;
8
use std::f64::consts::PI;
Rui Vieira's avatar
Rui Vieira committed
9

10 11 12
mod utils;
mod timeseries;

Rui Vieira's avatar
Rui Vieira committed
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
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;
    }
41 42 43 44 45 46 47 48

    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();
    }
Rui Vieira's avatar
Rui Vieira committed
49 50
}

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
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 {
86 87 88
                let alpha = slopes[i] / secants[i];
                let beta = slopes[i + 1] / secants[i];
                let h = alpha.hypot(beta);
89 90
                if h > 9.0 {
                    let t = 3.0 / h;
91 92
                    slopes[i] = t * alpha * secants[i];
                    slopes[i + 1] = t * beta * secants[i];
93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135
                }
            }
        }

        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()));
    }

Rui Vieira's avatar
Rui Vieira committed
136
    fn partial(x: Vec<f64>, y: Vec<f64>) -> impl Fn(f64) -> f64 {
137 138 139 140 141 142
        move |p| {
            let mut spline = MonotonicCubicSpline::new(&x, &y);
            spline.interpolate(p)
        }
    }

143 144
}

Rui Vieira's avatar
Rui Vieira committed
145
#[cfg(test)]
146
mod test_normal {
Rui Vieira's avatar
Rui Vieira committed
147 148 149 150 151

    use super::*;

    #[test]
    fn sample_mean_std() {
152
        let n = 0..1000000;
Rui Vieira's avatar
Rui Vieira committed
153
        let mut normal = Normal::new(0.0, 1.0);
Rui Vieira's avatar
Rui Vieira committed
154
        let samples = n.map(|_i| normal.sample()).collect::<Vec<f64>>();
Rui Vieira's avatar
Rui Vieira committed
155 156 157 158
        let mu = mean(&samples);
        assert_delta!(0.0, mu, 1e-3);
    }

159 160 161 162 163 164 165 166 167 168 169 170 171 172 173
    #[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);
    }

174

175 176 177 178 179 180 181
    #[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];

Rui Vieira's avatar
Rui Vieira committed
182
        let smooth = MonotonicCubicSpline::partial(x.clone(), y.clone());
183 184 185 186 187 188

        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);
189
            y_interp.push(smooth(p));
190 191 192 193 194 195 196 197 198 199
        }
        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);

    }

Rui Vieira's avatar
Rui Vieira committed
200
}