It works?!

src/factor_graph.rs

@@ -1,54 +1,396 @@
-use std::cmp;
+use std::collections::HashMap;
 
 use gaussian::Gaussian;
+use math;
+
+#[derive(Clone, Copy)]
+pub struct VariableId {
+    index: usize,
+}
+
+pub struct VariableArena {
+    variables: Vec<Variable>,
+}
+
+impl VariableArena {
+    pub fn new() -> VariableArena {
+        VariableArena {
+            variables: Vec::new(),
+        }
+    }
+
+    pub fn create(&mut self) -> VariableId {
+        let index = self.variables.len();
+
+        self.variables.push(Variable {
+            value: Gaussian::with_pi_tau(0.0, 0.0),
+            factors: HashMap::new(),
+        });
+
+        VariableId { index }
+    }
+
+    pub fn get(&mut self, id: VariableId) -> Option<&Variable> {
+        self.variables.get(id.index)
+    }
+
+    pub fn get_mut(&mut self, id: VariableId) -> Option<&mut Variable> {
+        self.variables.get_mut(id.index)
+    }
+}
 
 pub struct Variable {
-    gaussian: Gaussian,
+    value: Gaussian,
+    factors: HashMap<usize, Gaussian>,
 }
 
 impl Variable {
-    pub fn new() -> Variable {
-        Variable {
-            gaussian: Gaussian::new(0.0, 0.0),
-        }
+    pub fn attach_factor(&mut self, factor: usize) {
+        self.factors.insert(factor, Gaussian::new());
     }
 
-    fn delta(&self, other: &Variable) -> f32 {
-        let pi_delta = self.gaussian.pi - other.gaussian.pi;
+    pub fn update_value(&mut self, factor: usize, value: Gaussian) {
+        let old = self.factors[&factor];
 
-        if pi_delta.is_infinite() {
-            0.0
-        } else {
-            let tau_delta = (self.gaussian.tau - other.gaussian.tau).abs();
+        let intermediate = value * old;
+        let value = intermediate / self.value;
 
-            if pi_delta > tau_delta {
-               pi_delta
-            } else {
-                tau_delta
-            }
-        }
+        self.value = value;
     }
-}
 
-pub trait Factor {
-    fn down(&self) -> f32 {
-        0.0
+    pub fn get_value(&self) -> Gaussian {
+        self.value
+    }
+
+    pub fn update_message(&mut self, factor: usize, message: Gaussian) {
+        let old = self.factors[&factor];
+
+        let intermediate = self.value / old;
+        let value = intermediate * message;
+
+        self.value = value;
+
+        self.factors.insert(factor, message);
+    }
+
+    pub fn get_message(&self, factor: usize) -> Gaussian {
+        self.factors[&factor]
     }
 }
 
 pub struct PriorFactor {
-    variable: Variable,
-    dynamic: f32
+    id: usize,
+    variable: VariableId,
+    gaussian: Gaussian,
 }
 
 impl PriorFactor {
-    pub fn new(variable: Variable, dynamic: f32) -> PriorFactor {
-        PriorFactor { variable, dynamic }
+    pub fn new(
+        variable_arena: &mut VariableArena,
+        id: usize,
+        variable: VariableId,
+        gaussian: Gaussian,
+    ) -> PriorFactor {
+        if let Some(variable) = variable_arena.get_mut(variable) {
+            variable.attach_factor(id);
+        }
+
+        PriorFactor {
+            id,
+            variable,
+            gaussian,
+        }
+    }
+
+    pub fn start(&self, variable_arena: &mut VariableArena) {
+        if let Some(variable) = variable_arena.get_mut(self.variable) {
+            variable.update_value(self.id, self.gaussian);
+        }
     }
 }
 
-impl Factor for PriorFactor {
-    fn down(&self) -> f32 {
-        0.0
+pub struct LikelihoodFactor {
+    id: usize,
+    mean: VariableId,
+    value: VariableId,
+    variance: f32,
+}
+
+impl LikelihoodFactor {
+    pub fn new(
+        variable_arena: &mut VariableArena,
+        id: usize,
+        mean: VariableId,
+        value: VariableId,
+        variance: f32,
+    ) -> LikelihoodFactor {
+        if let Some(variable) = variable_arena.get_mut(mean) {
+            variable.attach_factor(id);
+        }
+
+        if let Some(variable) = variable_arena.get_mut(value) {
+            variable.attach_factor(id);
+        }
+
+        LikelihoodFactor {
+            id,
+            mean,
+            value,
+            variance,
+        }
+    }
+
+    pub fn update_mean(&self, variable_arena: &mut VariableArena) {
+        let x = variable_arena
+            .get(self.value)
+            .map(|variable| variable.get_value())
+            .unwrap();
+        let fx = variable_arena
+            .get_mut(self.value)
+            .map(|variable| variable.get_message(self.id))
+            .unwrap();
+
+        let a = 1.0 / (1.0 + self.variance * (x.pi - fx.pi));
+
+        let gaussian = Gaussian::with_pi_tau(a * (x.pi - fx.pi), a * (x.tau - fx.tau));
+
+        if let Some(variable) = variable_arena.get_mut(self.mean) {
+            variable.update_message(self.id, gaussian);
+        }
+    }
+
+    pub fn update_value(&self, variable_arena: &mut VariableArena) {
+        let y = variable_arena
+            .get(self.mean)
+            .map(|variable| variable.get_value())
+            .unwrap();
+        let fy = variable_arena
+            .get(self.mean)
+            .map(|variable| variable.get_message(self.id))
+            .unwrap();
+
+        let a = 1.0 / (1.0 + self.variance * (y.pi - fy.pi));
+
+        let gaussian = Gaussian::with_pi_tau(a * (y.pi - fy.pi), a * (y.tau - fy.tau));
+
+        if let Some(variable) = variable_arena.get_mut(self.value) {
+            variable.update_message(self.id, gaussian);
+        }
+    }
+}
+
+pub struct SumFactor {
+    id: usize,
+    sum: VariableId,
+    terms: Vec<VariableId>,
+    coeffs: Vec<f32>,
+}
+
+impl SumFactor {
+    pub fn new(
+        variable_arena: &mut VariableArena,
+        id: usize,
+        sum: VariableId,
+        terms: Vec<VariableId>,
+        coeffs: Vec<f32>,
+    ) -> SumFactor {
+        if let Some(variable) = variable_arena.get_mut(sum) {
+            variable.attach_factor(id);
+        }
+
+        for term in &terms {
+            if let Some(variable) = variable_arena.get_mut(*term) {
+                variable.attach_factor(id);
+            }
+        }
+
+        SumFactor {
+            id,
+            sum,
+            terms,
+            coeffs,
+        }
+    }
+
+    fn internal_update(
+        &self,
+        variable_arena: &mut VariableArena,
+        variable: VariableId,
+        y: Vec<Gaussian>,
+        fy: Vec<Gaussian>,
+        a: &Vec<f32>,
+    ) {
+        let size = a.len();
+
+        let mut sum_pi = 0.0;
+        let mut sum_tau = 0.0;
+
+        for i in 0..size {
+            let da = a[i];
+            let gy = y[i];
+            let gfy = fy[i];
+
+            sum_pi += da.powi(2) / (gy.pi - gfy.pi);
+            sum_tau += da * (gy.tau - gfy.tau) / (gy.pi - gfy.pi);
+        }
+
+        let new_pi = 1.0 / sum_pi;
+        let new_tau = new_pi * sum_tau;
+
+        let gaussian = Gaussian::with_pi_tau(new_pi, new_tau);
+
+        if let Some(variable) = variable_arena.get_mut(variable) {
+            variable.update_value(self.id, gaussian);
+        }
+    }
+
+    pub fn update_sum(&self, variable_arena: &mut VariableArena) {
+        let mut y = Vec::new();
+
+        for term in &self.terms {
+            let value = variable_arena
+                .get(*term)
+                .map(|variable| variable.get_value())
+                .unwrap();
+
+            y.push(value);
+        }
+
+        let mut fy = Vec::new();
+
+        for term in &self.terms {
+            let value = variable_arena
+                .get(*term)
+                .map(|variable| variable.get_message(self.id))
+                .unwrap();
+
+            fy.push(value);
+        }
+
+        self.internal_update(variable_arena, self.sum, y, fy, &self.coeffs);
+    }
+
+    pub fn update_term(&self, variable_arena: &mut VariableArena, index: usize) {
+        let size = self.coeffs.len();
+        let idx_coeff = self.coeffs[index];
+
+        let mut a = vec![0.0; size];
+
+        for i in 0..size {
+            if i != index {
+                a[i] = -self.coeffs[i] / idx_coeff;
+            }
+        }
+
+        a[index] = 1.0 / idx_coeff;
+
+        let idx_term = self.terms[index];
+
+        let mut y = Vec::new();
+        let mut fy = Vec::new();
+
+        let mut v = self.terms.clone();
+
+        v[index] = self.sum;
+
+        for term in v {
+            let value = variable_arena
+                .get(term)
+                .map(|variable| variable.get_value())
+                .unwrap();
+
+            y.push(value);
+
+            let value = variable_arena
+                .get(term)
+                .map(|variable| variable.get_message(self.id))
+                .unwrap();
+
+            fy.push(value);
+        }
+
+        self.internal_update(variable_arena, idx_term, y, fy, &a);
+    }
+}
+
+fn v_win(t: f32, e: f32) -> f32 {
+    math::pdf(t - e) / math::cdf(t - e)
+}
+
+fn w_win(t: f32, e: f32) -> f32 {
+    let vwin = v_win(t, e);
+
+    vwin * (vwin + t - e)
+}
+
+fn v_draw(t: f32, e: f32) -> f32 {
+    (math::pdf(-e - t) - math::pdf(e - t)) / (math::cdf(e - t) - math::cdf(-e - t))
+}
+
+fn w_draw(t: f32, e: f32) -> f32 {
+    let vdraw = v_draw(t, e);
+    let n = (vdraw * vdraw) + ((e - t) * math::pdf(e - t) + (e + t) * math::pdf(e + t));
+    let d = math::cdf(e - t) - math::cdf(-e - t);
+
+    n / d
+}
+
+pub struct TruncateFactor {
+    id: usize,
+    variable: VariableId,
+    epsilon: f32,
+    draw: bool,
+}
+
+impl TruncateFactor {
+    pub fn new(
+        variable_arena: &mut VariableArena,
+        id: usize,
+        variable: VariableId,
+        epsilon: f32,
+        draw: bool,
+    ) -> TruncateFactor {
+        if let Some(variable) = variable_arena.get_mut(variable) {
+            variable.attach_factor(id);
+        }
+
+        TruncateFactor {
+            id,
+            variable,
+            epsilon,
+            draw,
+        }
+    }
+
+    pub fn update(&self, variable_arena: &mut VariableArena) {
+        let x = variable_arena
+            .get(self.variable)
+            .map(|variable| variable.get_value())
+            .unwrap();
+        let fx = variable_arena
+            .get_mut(self.variable)
+            .map(|variable| variable.get_message(self.id))
+            .unwrap();
+
+        let c = x.pi - fx.pi;
+        let d = x.tau - fx.tau;
+        let sqrt_c = c.sqrt();
+
+        let t = d / sqrt_c;
+        let e = self.epsilon * sqrt_c;
+
+        let (v, w) = if self.draw {
+            (v_draw(t, e), w_draw(t, e))
+        } else {
+            (v_win(t, e), w_win(t, e))
+        };
+
+        let m_w = 1.0 - w;
+
+        let gaussian = Gaussian::with_pi_tau(c / m_w, (d + sqrt_c * v) / m_w);
+
+        if let Some(variable) = variable_arena.get_mut(self.variable) {
+            variable.update_value(self.id, gaussian);
+        }
     }
 }

src/gaussian.rs

@@ -1,10 +1,51 @@
+use std::ops;
+
+#[derive(Clone, Copy)]
 pub struct Gaussian {
     pub pi: f32,
     pub tau: f32,
 }
 
 impl Gaussian {
-    pub fn new(pi: f32, tau: f32) -> Gaussian {
+    pub fn new() -> Gaussian {
+        Gaussian::with_pi_tau(0.0, 0.0)
+    }
+
+    pub fn with_pi_tau(pi: f32, tau: f32) -> Gaussian {
         Gaussian { pi, tau }
     }
+
+    pub fn with_mu_sigma(mu: f32, sigma: f32) -> Gaussian {
+        let pi = 1.0 / sigma.powi(2);
+
+        Gaussian::with_pi_tau(pi, pi * mu)
+    }
+
+    pub fn mu(&self) -> f32 {
+        if self.pi == 0.0 {
+            0.0
+        } else {
+            self.tau / self.pi
+        }
+    }
+
+    pub fn sigma(&self) -> f32 {
+        (1.0 / self.pi).sqrt()
+    }
+}
+
+impl ops::Mul<Gaussian> for Gaussian {
+    type Output = Gaussian;
+
+    fn mul(self, rhs: Gaussian) -> Gaussian {
+        Gaussian::with_pi_tau(self.pi + rhs.pi, self.tau + rhs.tau)
+    }
+}
+
+impl ops::Div<Gaussian> for Gaussian {
+    type Output = Gaussian;
+
+    fn div(self, rhs: Gaussian) -> Gaussian {
+        Gaussian::with_pi_tau(self.pi - rhs.pi, self.tau - rhs.tau)
+    }
 }

src/lib.rs

@@ -1,9 +1,11 @@
-mod matrix;
 mod factor_graph;
 mod gaussian;
+mod math;
+mod matrix;
 
-use matrix::Matrix;
 use factor_graph::*;
+use gaussian::Gaussian;
+use matrix::Matrix;
 
 /// Default initial mean of ratings.
 const MU: f32 = 25.0;
@@ -24,9 +26,9 @@ const DRAW_PROBABILITY: f32 = 0.10;
 const DELTA: f32 = 0.0001;
 
 #[derive(Debug, PartialEq)]
-struct Rating {
-    mu: f32,
-    sigma: f32,
+pub struct Rating {
+    pub mu: f32,
+    pub sigma: f32,
 }
 
 impl Default for Rating {
@@ -38,42 +40,155 @@ impl Default for Rating {
     }
 }
 
-
-fn _team_sizes(rating_groups: &[&[Rating]]) -> Vec<usize> {
-    let mut team_sizes = Vec::new();
-
-    for group in rating_groups {
-        let last = team_sizes.last().map(|v| *v).unwrap_or(0);
-
-        team_sizes.push(group.len() + last);
-    }
-
-    team_sizes
-}
-
-fn factor_graph_builders(rating_groups: &[&[Rating]]) {
+fn rate(rating_groups: &[&[Rating]]) {
     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 size = flatten_ratings.len();
-    let group_size = rating_groups.len();
 
-    let rating_vars = (0..size).map(|_| Variable::new()).collect::<Vec<_>>();
-    let perf_vars = (0..size).map(|_| Variable::new()).collect::<Vec<_>>();
-    let team_perf_vars = (0..group_size).map(|_| Variable::new()).collect::<Vec<_>>();
-    let team_diff_vars = (0..group_size - 1).map(|_| Variable::new()).collect::<Vec<_>>();
+    let tau_sqr = TAU.powi(2);
+    let beta_sqr = BETA.powi(2);
 
-    let team_sizes = _team_sizes(rating_groups);
-}
+    let mut variable_arena = VariableArena::new();
 
-fn rate(rating_groups: &[&[Rating]]) {
-    let ranks = (0..rating_groups.len()).collect::<Vec<_>>();
-    let weights = vec![1.0; rating_groups.len()];
-    let min_delta = DELTA;
+    let mut ss = Vec::new();
+    let mut ps = Vec::new();
+    let mut ts = Vec::new();
+    let mut ds = Vec::new();
+
+    for _ in 0..size {
+        ss.push(variable_arena.create());
+        ps.push(variable_arena.create());
+        ts.push(variable_arena.create());
+    }
+
+    for _ in 0..size - 1 {
+        ds.push(variable_arena.create());
+    }
+
+    let mut factor_id = 0;
+
+    let mut skill = Vec::new();
+
+    for (i, rating) in flatten_ratings.iter().enumerate() {
+        let variable = ss[i];
+        let gaussian = Gaussian::with_mu_sigma(rating.mu, (rating.sigma.powi(2) + tau_sqr).sqrt());
+
+        skill.push(PriorFactor::new(
+            &mut variable_arena,
+            factor_id,
+            variable,
+            gaussian,
+        ));
+
+        factor_id += 1;
+    }
+
+    let mut skill_to_perf = Vec::new();;
+
+    for i in 0..size {
+        let mean = ss[i];
+        let value = ps[i];
+
+        skill_to_perf.push(LikelihoodFactor::new(
+            &mut variable_arena,
+            factor_id,
+            mean,
+            value,
+            beta_sqr,
+        ));
+
+        factor_id += 1;
+    }
+
+    let mut perf_to_team = Vec::new();;
+
+    for i in 0..size {
+        perf_to_team.push(SumFactor::new(
+            &mut variable_arena,
+            factor_id,
+            ts[i],
+            vec![ps[i]],
+            vec![1.0],
+        ));
+
+        factor_id += 1;
+    }
+
+    let mut team_diff = Vec::new();;
+
+    for i in 0..size - 1 {
+        team_diff.push(SumFactor::new(
+            &mut variable_arena,
+            factor_id,
+            ds[i],
+            vec![ts[i], ts[i + 1]],
+            vec![1.0, -1.0],
+        ));
+
+        factor_id += 1;
+    }
+
+    let mut trunc = Vec::new();
+
+    for i in 0..size - 1 {
+        trunc.push(TruncateFactor::new(
+            &mut variable_arena,
+            factor_id,
+            ds[i],
+            DELTA,
+            false,
+        ));
+
+        factor_id += 1;
+    }
+
+    for factor in &skill {
+        factor.start(&mut variable_arena);
+    }
+
+    for factor in &skill_to_perf {
+        factor.update_value(&mut variable_arena);
+    }
+
+    for factor in &perf_to_team {
+        factor.update_sum(&mut variable_arena);
+    }
+
+    for factor in &team_diff {
+        factor.update_sum(&mut variable_arena);
+    }
+
+    for factor in &trunc {
+        factor.update(&mut variable_arena);
+    }
+
+    for factor in &team_diff {
+        factor.update_term(&mut variable_arena, 0);
+        factor.update_term(&mut variable_arena, 1);
+    }
+
+    for factor in &perf_to_team {
+        factor.update_term(&mut variable_arena, 0);
+    }
+
+    for factor in &skill_to_perf {
+        factor.update_mean(&mut variable_arena);
+    }
+
+    for i in 0..size {
+        let value = variable_arena
+            .get(ss[i])
+            .map(|variable| variable.get_value())
+            .unwrap();
+
+        let mu = value.mu();
+        let sigma = value.sigma();
+
+        println!("player={}, mu={}, sigma={}", i, mu, sigma);
+    }
 }
 
 fn quality(rating_groups: &[&[Rating]]) -> f32 {
@@ -151,4 +266,21 @@ mod tests {
 
         assert_eq!(quality(&[&[alice], &[bob]]), 0.41614607);
     }
+
+    #[test]
+    fn test_rate_1vs1() {
+        let alice = Rating {
+            mu: 25.0,
+            sigma: SIGMA,
+        };
+
+        let bob = Rating {
+            mu: 30.0,
+            sigma: SIGMA,
+        };
+
+        rate(&[&[alice], &[bob]]);
+
+        assert_eq!(true, false);
+    }
 }

src/math.rs

@@ -0,0 +1,30 @@
+use std::f32;
+
+fn erfc(x: f32) -> f32 {
+    let z = x.abs();
+    let t = 1.0 / (1.0 + z / 2.0);
+    let r = t
+        * (-z * z - 1.26551223
+            + t * (1.00002368
+                + t * (0.37409196
+                    + t * (0.09678418
+                        + t * (-0.18628806
+                            + t * (0.27886807
+                                + t * (-1.13520398
+                                    + t * (1.48851587 + t * (-0.82215223 + t * 0.17087277)))))))))
+            .exp();
+
+    if x < 0.0 {
+        2.0 - r
+    } else {
+        r
+    }
+}
+
+pub fn cdf(x: f32) -> f32 {
+    0.5 * erfc(-x / 2.0f32.sqrt())
+}
+
+pub fn pdf(x: f32) -> f32 {
+    1.0 / (2.0 * f32::consts::PI).sqrt() * (-((x / 1.0).powi(2) / 2.0)).exp()
+}