trueskill-tt/src/time_slice.rs

//! A single time step's worth of events.
//!
//! Renamed from `Batch` in T2.

use std::collections::HashMap;

use crate::{
    Index, N_INF,
    arena::ScratchArena,
    drift::Drift,
    game::Game,
    gaussian::Gaussian,
    rating::Rating,
    storage::{CompetitorStore, SkillStore},
    time::Time,
    tuple_gt, tuple_max,
};

#[derive(Debug)]
pub(crate) struct Skill {
    pub(crate) forward: Gaussian,
    backward: Gaussian,
    likelihood: Gaussian,
    pub(crate) elapsed: i64,
    pub(crate) online: Gaussian,
}

impl Skill {
    pub(crate) fn posterior(&self) -> Gaussian {
        self.likelihood * self.backward * self.forward
    }
}

impl Default for Skill {
    fn default() -> Self {
        Self {
            forward: N_INF,
            backward: N_INF,
            likelihood: N_INF,
            elapsed: 0,
            online: N_INF,
        }
    }
}

#[derive(Debug)]
struct Item {
    agent: Index,
    likelihood: Gaussian,
}

impl Item {
    fn within_prior<T: Time, D: Drift<T>>(
        &self,
        online: bool,
        forward: bool,
        skills: &SkillStore,
        agents: &CompetitorStore<T, D>,
    ) -> Rating<T, D> {
        let r = &agents[self.agent].rating;
        let skill = skills.get(self.agent).unwrap();

        if online {
            Rating::new(skill.online, r.beta, r.drift)
        } else if forward {
            Rating::new(skill.forward, r.beta, r.drift)
        } else {
            Rating::new(skill.posterior() / self.likelihood, r.beta, r.drift)
        }
    }
}

#[derive(Debug)]
struct Team {
    items: Vec<Item>,
    output: f64,
}

#[derive(Debug)]
pub(crate) struct Event {
    teams: Vec<Team>,
    evidence: f64,
    weights: Vec<Vec<f64>>,
}

impl Event {
    fn outputs(&self) -> Vec<f64> {
        self.teams
            .iter()
            .map(|team| team.output)
            .collect::<Vec<_>>()
    }

    pub(crate) fn within_priors<T: Time, D: Drift<T>>(
        &self,
        online: bool,
        forward: bool,
        skills: &SkillStore,
        agents: &CompetitorStore<T, D>,
    ) -> Vec<Vec<Rating<T, D>>> {
        self.teams
            .iter()
            .map(|team| {
                team.items
                    .iter()
                    .map(|item| item.within_prior(online, forward, skills, agents))
                    .collect::<Vec<_>>()
            })
            .collect::<Vec<_>>()
    }
}

#[derive(Debug)]
pub struct TimeSlice<T: Time = i64> {
    pub(crate) events: Vec<Event>,
    pub(crate) skills: SkillStore,
    pub(crate) time: T,
    p_draw: f64,
    arena: ScratchArena,
}

impl<T: Time> TimeSlice<T> {
    pub fn new(time: T, p_draw: f64) -> Self {
        Self {
            events: Vec::new(),
            skills: SkillStore::new(),
            time,
            p_draw,
            arena: ScratchArena::new(),
        }
    }

    pub fn add_events<D: Drift<T>>(
        &mut self,
        composition: Vec<Vec<Vec<Index>>>,
        results: Vec<Vec<f64>>,
        weights: Vec<Vec<Vec<f64>>>,
        agents: &CompetitorStore<T, D>,
    ) {
        let mut unique = Vec::with_capacity(10);

        let this_agent = composition.iter().flatten().flatten().filter(|idx| {
            if !unique.contains(idx) {
                unique.push(*idx);

                return true;
            }

            false
        });

        for idx in this_agent {
            let elapsed = compute_elapsed(agents[*idx].last_time.as_ref(), &self.time);

            if let Some(skill) = self.skills.get_mut(*idx) {
                skill.elapsed = elapsed;
                skill.forward = agents[*idx].receive(&self.time);
            } else {
                self.skills.insert(
                    *idx,
                    Skill {
                        forward: agents[*idx].receive(&self.time),
                        elapsed,
                        ..Default::default()
                    },
                );
            }
        }

        let events = composition.iter().enumerate().map(|(e, event)| {
            let teams = event
                .iter()
                .enumerate()
                .map(|(t, team)| {
                    let items = team
                        .iter()
                        .map(|&agent| Item {
                            agent,
                            likelihood: N_INF,
                        })
                        .collect::<Vec<_>>();

                    Team {
                        items,
                        output: if results.is_empty() {
                            (event.len() - (t + 1)) as f64
                        } else {
                            results[e][t]
                        },
                    }
                })
                .collect::<Vec<_>>();

            let weights = if weights.is_empty() {
                teams
                    .iter()
                    .map(|team| vec![1.0; team.items.len()])
                    .collect::<Vec<_>>()
            } else {
                weights[e].clone()
            };

            Event {
                teams,
                evidence: 0.0,
                weights,
            }
        });

        let from = self.events.len();

        self.events.extend(events);

        self.iteration(from, agents);
    }

    pub(crate) fn posteriors(&self) -> HashMap<Index, Gaussian> {
        self.skills
            .iter()
            .map(|(idx, skill)| (idx, skill.posterior()))
            .collect::<HashMap<_, _>>()
    }

    pub fn iteration<D: Drift<T>>(&mut self, from: usize, agents: &CompetitorStore<T, D>) {
        for event in self.events.iter_mut().skip(from) {
            let teams = event.within_priors(false, false, &self.skills, agents);
            let result = event.outputs();

            let g = Game::new(teams, &result, &event.weights, self.p_draw, &mut self.arena);

            for (t, team) in event.teams.iter_mut().enumerate() {
                for (i, item) in team.items.iter_mut().enumerate() {
                    let old_likelihood = self.skills.get(item.agent).unwrap().likelihood;
                    let new_likelihood = (old_likelihood / item.likelihood) * g.likelihoods[t][i];
                    self.skills.get_mut(item.agent).unwrap().likelihood = new_likelihood;
                    item.likelihood = g.likelihoods[t][i];
                }
            }

            event.evidence = g.evidence;
        }
    }

    #[allow(dead_code)]
    pub(crate) fn convergence<D: Drift<T>>(&mut self, agents: &CompetitorStore<T, D>) -> usize {
        let epsilon = 1e-6;
        let iterations = 20;

        let mut step = (f64::INFINITY, f64::INFINITY);
        let mut i = 0;

        while tuple_gt(step, epsilon) && i < iterations {
            let old = self.posteriors();

            self.iteration(0, agents);

            let new = self.posteriors();

            step = old.iter().fold((0.0, 0.0), |step, (a, old)| {
                tuple_max(step, old.delta(new[a]))
            });

            i += 1;
        }

        i
    }

    pub(crate) fn forward_prior_out(&self, agent: &Index) -> Gaussian {
        let skill = self.skills.get(*agent).unwrap();
        skill.forward * skill.likelihood
    }

    pub(crate) fn backward_prior_out<D: Drift<T>>(
        &self,
        agent: &Index,
        agents: &CompetitorStore<T, D>,
    ) -> Gaussian {
        let skill = self.skills.get(*agent).unwrap();
        let n = skill.likelihood * skill.backward;
        n.forget(
            agents[*agent]
                .rating
                .drift
                .variance_for_elapsed(skill.elapsed),
        )
    }

    pub(crate) fn new_backward_info<D: Drift<T>>(&mut self, agents: &CompetitorStore<T, D>) {
        for (agent, skill) in self.skills.iter_mut() {
            skill.backward = agents[agent].message;
        }
        self.iteration(0, agents);
    }

    pub(crate) fn new_forward_info<D: Drift<T>>(&mut self, agents: &CompetitorStore<T, D>) {
        for (agent, skill) in self.skills.iter_mut() {
            skill.forward = agents[agent].receive_for_elapsed(skill.elapsed);
        }
        self.iteration(0, agents);
    }

    pub(crate) fn log_evidence<D: Drift<T>>(
        &self,
        online: bool,
        targets: &[Index],
        forward: bool,
        agents: &CompetitorStore<T, D>,
    ) -> f64 {
        // log_evidence is infrequent; a local arena avoids needing &mut self.
        let mut arena = ScratchArena::new();

        if targets.is_empty() {
            if online || forward {
                self.events
                    .iter()
                    .map(|event| {
                        Game::new(
                            event.within_priors(online, forward, &self.skills, agents),
                            &event.outputs(),
                            &event.weights,
                            self.p_draw,
                            &mut arena,
                        )
                        .evidence
                        .ln()
                    })
                    .sum()
            } else {
                self.events.iter().map(|event| event.evidence.ln()).sum()
            }
        } else if online || forward {
            self.events
                .iter()
                .enumerate()
                .filter(|(_, event)| {
                    event
                        .teams
                        .iter()
                        .flat_map(|team| &team.items)
                        .any(|item| targets.contains(&item.agent))
                })
                .map(|(_, event)| {
                    Game::new(
                        event.within_priors(online, forward, &self.skills, agents),
                        &event.outputs(),
                        &event.weights,
                        self.p_draw,
                        &mut arena,
                    )
                    .evidence
                    .ln()
                })
                .sum()
        } else {
            self.events
                .iter()
                .filter(|event| {
                    event
                        .teams
                        .iter()
                        .flat_map(|team| &team.items)
                        .any(|item| targets.contains(&item.agent))
                })
                .map(|event| event.evidence.ln())
                .sum()
        }
    }

    pub fn get_composition(&self) -> Vec<Vec<Vec<Index>>> {
        self.events
            .iter()
            .map(|event| {
                event
                    .teams
                    .iter()
                    .map(|team| team.items.iter().map(|item| item.agent).collect::<Vec<_>>())
                    .collect::<Vec<_>>()
            })
            .collect::<Vec<_>>()
    }

    pub fn get_results(&self) -> Vec<Vec<f64>> {
        self.events
            .iter()
            .map(|event| {
                event
                    .teams
                    .iter()
                    .map(|team| team.output)
                    .collect::<Vec<_>>()
            })
            .collect::<Vec<_>>()
    }
}

pub(crate) fn compute_elapsed<T: Time>(last: Option<&T>, current: &T) -> i64 {
    last.map(|l| l.elapsed_to(current).max(0)).unwrap_or(0)
}

#[cfg(test)]
mod tests {
    use approx::assert_ulps_eq;

    use super::*;
    use crate::{
        KeyTable, competitor::Competitor, drift::ConstantDrift, rating::Rating,
        storage::CompetitorStore,
    };

    #[test]
    fn test_one_event_each() {
        let mut index_map = KeyTable::new();

        let a = index_map.get_or_create("a");
        let b = index_map.get_or_create("b");
        let c = index_map.get_or_create("c");
        let d = index_map.get_or_create("d");
        let e = index_map.get_or_create("e");
        let f = index_map.get_or_create("f");

        let mut agents: CompetitorStore<i64, ConstantDrift> = CompetitorStore::new();

        for agent in [a, b, c, d, e, f] {
            agents.insert(
                agent,
                Competitor {
                    rating: Rating::new(
                        Gaussian::from_ms(25.0, 25.0 / 3.0),
                        25.0 / 6.0,
                        ConstantDrift(25.0 / 300.0),
                    ),
                    ..Default::default()
                },
            );
        }

        let mut time_slice = TimeSlice::new(0i64, 0.0);

        time_slice.add_events(
            vec![
                vec![vec![a], vec![b]],
                vec![vec![c], vec![d]],
                vec![vec![e], vec![f]],
            ],
            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
            vec![],
            &agents,
        );

        let post = time_slice.posteriors();

        assert_ulps_eq!(
            post[&a],
            Gaussian::from_ms(29.205220, 7.194481),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&b],
            Gaussian::from_ms(20.794779, 7.194481),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&c],
            Gaussian::from_ms(20.794779, 7.194481),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&d],
            Gaussian::from_ms(29.205220, 7.194481),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&e],
            Gaussian::from_ms(29.205220, 7.194481),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&f],
            Gaussian::from_ms(20.794779, 7.194481),
            epsilon = 1e-6
        );

        assert_eq!(time_slice.convergence(&agents), 1);
    }

    #[test]
    fn test_same_strength() {
        let mut index_map = KeyTable::new();

        let a = index_map.get_or_create("a");
        let b = index_map.get_or_create("b");
        let c = index_map.get_or_create("c");
        let d = index_map.get_or_create("d");
        let e = index_map.get_or_create("e");
        let f = index_map.get_or_create("f");

        let mut agents: CompetitorStore<i64, ConstantDrift> = CompetitorStore::new();

        for agent in [a, b, c, d, e, f] {
            agents.insert(
                agent,
                Competitor {
                    rating: Rating::new(
                        Gaussian::from_ms(25.0, 25.0 / 3.0),
                        25.0 / 6.0,
                        ConstantDrift(25.0 / 300.0),
                    ),
                    ..Default::default()
                },
            );
        }

        let mut time_slice = TimeSlice::new(0i64, 0.0);

        time_slice.add_events(
            vec![
                vec![vec![a], vec![b]],
                vec![vec![a], vec![c]],
                vec![vec![b], vec![c]],
            ],
            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
            vec![],
            &agents,
        );

        let post = time_slice.posteriors();

        assert_ulps_eq!(
            post[&a],
            Gaussian::from_ms(24.960978, 6.298544),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&b],
            Gaussian::from_ms(27.095590, 6.010330),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&c],
            Gaussian::from_ms(24.889681, 5.866311),
            epsilon = 1e-6
        );

        assert!(time_slice.convergence(&agents) > 1);

        let post = time_slice.posteriors();

        assert_ulps_eq!(
            post[&a],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&b],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&c],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_add_events() {
        let mut index_map = KeyTable::new();

        let a = index_map.get_or_create("a");
        let b = index_map.get_or_create("b");
        let c = index_map.get_or_create("c");
        let d = index_map.get_or_create("d");
        let e = index_map.get_or_create("e");
        let f = index_map.get_or_create("f");

        let mut agents: CompetitorStore<i64, ConstantDrift> = CompetitorStore::new();

        for agent in [a, b, c, d, e, f] {
            agents.insert(
                agent,
                Competitor {
                    rating: Rating::new(
                        Gaussian::from_ms(25.0, 25.0 / 3.0),
                        25.0 / 6.0,
                        ConstantDrift(25.0 / 300.0),
                    ),
                    ..Default::default()
                },
            );
        }

        let mut time_slice = TimeSlice::new(0i64, 0.0);

        time_slice.add_events(
            vec![
                vec![vec![a], vec![b]],
                vec![vec![a], vec![c]],
                vec![vec![b], vec![c]],
            ],
            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
            vec![],
            &agents,
        );

        time_slice.convergence(&agents);

        let post = time_slice.posteriors();

        assert_ulps_eq!(
            post[&a],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&b],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&c],
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );

        time_slice.add_events(
            vec![
                vec![vec![a], vec![b]],
                vec![vec![a], vec![c]],
                vec![vec![b], vec![c]],
            ],
            vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]],
            vec![],
            &agents,
        );

        assert_eq!(time_slice.events.len(), 6);

        time_slice.convergence(&agents);

        let post = time_slice.posteriors();

        assert_ulps_eq!(
            post[&a],
            Gaussian::from_ms(25.000003, 3.880150),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&b],
            Gaussian::from_ms(25.000003, 3.880150),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            post[&c],
            Gaussian::from_ms(25.000003, 3.880150),
            epsilon = 1e-6
        );
    }
}