Initial commit.

src/lib.rs

@@ -0,0 +1,110 @@
+mod matrix;
+
+use matrix::Matrix;
+
+/// Default initial mean of ratings.
+const MU: f32 = 25.0;
+
+/// Default initial standard deviation of ratings.
+const SIGMA: f32 = MU / 3.0;
+
+///  Default distance that guarantees about 76% chance of winning.
+const BETA: f32 = SIGMA / 2.0;
+
+///  Default dynamic factor.
+const TAU: f32 = SIGMA / 100.0;
+
+///  Default draw probability of the game.
+const DRAW_PROBABILITY: f32 = 0.10;
+
+///  A basis to check reliability of the result.
+const DELTA: f32 = 0.0001;
+
+#[derive(Debug, PartialEq)]
+struct Rating {
+    mu: f32,
+    sigma: f32,
+}
+
+impl Default for Rating {
+    fn default() -> Rating {
+        Rating {
+            mu: MU,
+            sigma: SIGMA,
+        }
+    }
+}
+
+fn quality(rating_groups: &[&[Rating]]) -> f32 {
+    let flatten_ratings = rating_groups.iter().flat_map(|group| group.iter()).collect::<Vec<_>>();
+    let flatten_weights = vec![1.0; flatten_ratings.len()].into_boxed_slice();
+
+    let length = flatten_ratings.len();
+
+    let mut mean_matrix = Matrix::new(length, 1);
+
+    for (i, rating) in flatten_ratings.iter().enumerate() {
+        mean_matrix[(i, 0)] = rating.mu;
+    }
+
+    let mut variance_matrix = Matrix::new(length, length);
+
+    for (i, rating) in flatten_ratings.iter().enumerate() {
+        variance_matrix[(i, i)] = rating.sigma.powi(2);
+    }
+
+    let mut rotated_a_matrix = Matrix::new(rating_groups.len() - 1, length);
+
+    let mut t = 0;
+    let mut x = 0;
+
+    for (row, group) in rating_groups.windows(2).enumerate() {
+        let current = group[0];
+        let next = group[1];
+
+        for n in t..t + current.len() {
+            rotated_a_matrix[(row, n)] = flatten_weights[n];
+            t += 1;
+            x += 1;
+        }
+
+        for n in x..x + next.len() {
+            rotated_a_matrix[(row, n)] = -flatten_weights[n];
+            x += 1;
+        }
+    }
+
+    let a_matrix = rotated_a_matrix.transpose();
+
+    let _ata = BETA.powi(2) * &rotated_a_matrix * &a_matrix;
+    let _atsa = &rotated_a_matrix * &variance_matrix * &a_matrix;
+    let start = mean_matrix.transpose() * &a_matrix;
+    let middle = &_ata + &_atsa;
+    let end = &rotated_a_matrix * &mean_matrix;
+
+    let e_arg = (-0.5 * &start * &middle.inverse() * &end).determinant();
+    let s_arg = _ata.determinant() / middle.determinant();
+
+    e_arg.exp() * s_arg.sqrt()
+}
+
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_quality_1vs1() {
+        let alice = Rating {
+            mu: 25.0,
+            sigma: SIGMA,
+        };
+
+        let bob = Rating {
+            mu: 30.0,
+            sigma: SIGMA,
+        };
+
+        assert_eq!(quality(&[&[alice], &[bob]]), 0.41614607);
+    }
+}