trueskill-rs/src/factor_graph.rs

use std::collections::HashMap;

use gaussian::Gaussian;
use math;

#[derive(Clone, Copy, Debug, PartialEq)]
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::from_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 {
    value: Gaussian,
    factors: HashMap<usize, Gaussian>,
}

impl Variable {
    pub fn attach_factor(&mut self, factor: usize) {
        self.factors.insert(factor, Gaussian::from_pi_tau(0.0, 0.0));
    }

    pub fn update_value(&mut self, factor: usize, value: Gaussian) {
        let old = self.factors[&factor];

        let intermediate = value * old;
        self.factors.insert(factor, intermediate / self.value);

        self.value = value;
    }

    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 {
    id: usize,
    variable: VariableId,
    gaussian: Gaussian,
}

impl PriorFactor {
    pub fn new(
        variable_arena: &mut VariableArena,
        id: usize,
        variable: VariableId,
        gaussian: Gaussian,
    ) -> PriorFactor {
        variable_arena.get_mut(variable).unwrap().attach_factor(id);

        PriorFactor {
            id,
            variable,
            gaussian,
        }
    }

    pub fn start(&self, variable_arena: &mut VariableArena) {
        variable_arena
            .get_mut(self.variable)
            .unwrap()
            .update_value(self.id, self.gaussian);
    }
}

pub struct LikelihoodFactor {
    id: usize,
    mean: VariableId,
    value: VariableId,
    variance: f64,
}

impl LikelihoodFactor {
    pub fn new(
        variable_arena: &mut VariableArena,
        id: usize,
        mean: VariableId,
        value: VariableId,
        variance: f64,
    ) -> LikelihoodFactor {
        variable_arena.get_mut(mean).unwrap().attach_factor(id);
        variable_arena.get_mut(value).unwrap().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::from_pi_tau(a * (x.pi() - fx.pi()), a * (x.tau() - fx.tau()));

        variable_arena
            .get_mut(self.mean)
            .unwrap()
            .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::from_pi_tau(a * (y.pi() - fy.pi()), a * (y.tau() - fy.tau()));

        variable_arena
            .get_mut(self.value)
            .unwrap()
            .update_message(self.id, gaussian);
    }
}

pub struct SumFactor {
    id: usize,
    sum: VariableId,
    terms: Vec<VariableId>,
    coeffs: Vec<f64>,
}

impl SumFactor {
    pub fn new(
        variable_arena: &mut VariableArena,
        id: usize,
        sum: VariableId,
        terms: Vec<VariableId>,
        coeffs: Vec<f64>,
    ) -> SumFactor {
        variable_arena.get_mut(sum).unwrap().attach_factor(id);

        for term in &terms {
            variable_arena.get_mut(*term).unwrap().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<f64>,
    ) {
        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::from_pi_tau(new_pi, new_tau);

        variable_arena
            .get_mut(variable)
            .unwrap()
            .update_message(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: f64, e: f64) -> f64 {
    math::pdf(t - e) / math::cdf(t - e)
}

fn w_win(t: f64, e: f64) -> f64 {
    let vwin = v_win(t, e);

    vwin * (vwin + t - e)
}

fn v_draw(t: f64, e: f64) -> f64 {
    (math::pdf(-e - t) - math::pdf(e - t)) / (math::cdf(e - t) - math::cdf(-e - t))
}

fn w_draw(t: f64, e: f64) -> f64 {
    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: f64,
    draw: bool,
}

impl TruncateFactor {
    pub fn new(
        variable_arena: &mut VariableArena,
        id: usize,
        variable: VariableId,
        epsilon: f64,
        draw: bool,
    ) -> TruncateFactor {
        variable_arena.get_mut(variable).unwrap().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::from_pi_tau(c / m_w, (d + sqrt_c * v) / m_w);

        variable_arena
            .get_mut(self.variable)
            .unwrap()
            .update_value(self.id, gaussian);
    }
}