Added nba history example, and implemented kernel matern32.

src/kernel/matern32.rs

@@ -0,0 +1,73 @@
+use ndarray::prelude::*;
+
+use super::Kernel;
+
+#[derive(Clone)]
+pub struct Matern32 {
+    var: f64,
+    l_scale: f64,
+    lambda: f64,
+}
+
+impl Matern32 {
+    pub fn new(var: f64, l_scale: f64) -> Self {
+        Matern32 {
+            var,
+            l_scale,
+            lambda: 3.0f64.sqrt() / l_scale,
+        }
+    }
+}
+
+impl Kernel for Matern32 {
+    fn k_diag(&self, ts: &[f64]) -> Array1<f64> {
+        Array1::ones(ts.len()) * self.var
+    }
+
+    fn order(&self) -> usize {
+        2
+    }
+
+    fn state_mean(&self, t: f64) -> Array1<f64> {
+        Array1::zeros(2)
+    }
+
+    fn state_cov(&self, t: f64) -> Array2<f64> {
+        let a = self.lambda;
+
+        array![[1.0, 0.0], [0.0, a * a]] * self.var
+    }
+
+    fn measurement_vector(&self) -> Array1<f64> {
+        array![1.0, 0.0]
+    }
+
+    fn feedback(&self) -> Array2<f64> {
+        let a = self.lambda;
+
+        array![[0.0, 1.0], [-a.powi(2), -2.0 * a]]
+    }
+
+    fn transition(&self, t0: f64, t1: f64) -> Array2<f64> {
+        let d = t1 - t0;
+        let a = self.lambda;
+
+        let ba = array![[d * a + 1.0, d], [-d * a * a, 1.0 - d * a]];
+
+        (-d * a).exp() * ba
+    }
+
+    fn noise_cov(&self, t0: f64, t1: f64) -> Array2<f64> {
+        let d = t1 - t0;
+        let a = self.lambda;
+        let da = d * a;
+
+        let c = (-2.0 * da).exp();
+
+        let x11 = 1.0 - c * (2.0 * da * da + 2.0 * da + 1.0);
+        let x12 = c * (2.0 * da * da * a);
+        let x22 = a * a * (1.0 - c * (2.0 * da * da - 2.0 * da + 1.0));
+
+        self.var * array![[x11, x12], [x12, x22]]
+    }
+}