trueskill-tt/src/history.rs

use std::{borrow::Borrow, collections::HashMap, hash::Hash, marker::PhantomData};

use crate::{
    BETA, GAMMA, Index, MU, N_INF, P_DRAW, SIGMA,
    competitor::{self, Competitor},
    convergence::{ConvergenceOptions, ConvergenceReport},
    drift::{ConstantDrift, Drift},
    error::InferenceError,
    gaussian::Gaussian,
    key_table::KeyTable,
    observer::{NullObserver, Observer},
    rating::Rating,
    sort_time,
    storage::CompetitorStore,
    time::Time,
    time_slice::{self, TimeSlice},
    tuple_gt, tuple_max,
};

#[derive(Clone)]
pub struct HistoryBuilder<
    T: Time = i64,
    D: Drift<T> = ConstantDrift,
    O: Observer<T> = NullObserver,
    K: Eq + Hash + Clone = &'static str,
> {
    mu: f64,
    sigma: f64,
    beta: f64,
    drift: D,
    p_draw: f64,
    online: bool,
    convergence: ConvergenceOptions,
    observer: O,
    _time: PhantomData<T>,
    _key: PhantomData<K>,
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> HistoryBuilder<T, D, O, K> {
    pub fn mu(mut self, mu: f64) -> Self {
        self.mu = mu;
        self
    }

    pub fn sigma(mut self, sigma: f64) -> Self {
        self.sigma = sigma;
        self
    }

    pub fn beta(mut self, beta: f64) -> Self {
        self.beta = beta;
        self
    }

    pub fn drift<D2: Drift<T>>(self, drift: D2) -> HistoryBuilder<T, D2, O, K> {
        HistoryBuilder {
            drift,
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            p_draw: self.p_draw,
            online: self.online,
            convergence: self.convergence,
            observer: self.observer,
            _time: self._time,
            _key: self._key,
        }
    }

    pub fn p_draw(mut self, p_draw: f64) -> Self {
        self.p_draw = p_draw;
        self
    }

    pub fn online(mut self, online: bool) -> Self {
        self.online = online;
        self
    }

    pub fn convergence(mut self, opts: ConvergenceOptions) -> Self {
        self.convergence = opts;
        self
    }

    pub fn observer<O2: Observer<T>>(self, observer: O2) -> HistoryBuilder<T, D, O2, K> {
        HistoryBuilder {
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            drift: self.drift,
            p_draw: self.p_draw,
            online: self.online,
            convergence: self.convergence,
            observer,
            _time: self._time,
            _key: self._key,
        }
    }

    pub fn build(self) -> History<T, D, O, K> {
        History {
            size: 0,
            time_slices: Vec::new(),
            agents: CompetitorStore::new(),
            keys: KeyTable::new(),
            mu: self.mu,
            sigma: self.sigma,
            beta: self.beta,
            drift: self.drift,
            p_draw: self.p_draw,
            online: self.online,
            convergence: self.convergence,
            observer: self.observer,
        }
    }
}

impl Default for HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str> {
    fn default() -> Self {
        Self {
            mu: MU,
            sigma: SIGMA,
            beta: BETA,
            drift: ConstantDrift(GAMMA),
            p_draw: P_DRAW,
            online: false,
            convergence: ConvergenceOptions::default(),
            observer: NullObserver,
            _time: PhantomData,
            _key: PhantomData,
        }
    }
}

pub struct History<
    T: Time = i64,
    D: Drift<T> = ConstantDrift,
    O: Observer<T> = NullObserver,
    K: Eq + Hash + Clone = &'static str,
> {
    size: usize,
    pub(crate) time_slices: Vec<TimeSlice<T>>,
    pub(crate) agents: CompetitorStore<T, D>,
    keys: KeyTable<K>,
    mu: f64,
    sigma: f64,
    beta: f64,
    drift: D,
    p_draw: f64,
    online: bool,
    convergence: ConvergenceOptions,
    observer: O,
}

impl Default for History<i64, ConstantDrift, NullObserver, &'static str> {
    fn default() -> Self {
        HistoryBuilder::default().build()
    }
}

impl History<i64, ConstantDrift, NullObserver, &'static str> {
    pub fn builder() -> HistoryBuilder<i64, ConstantDrift, NullObserver, &'static str> {
        HistoryBuilder::default()
    }
}

impl<K: Eq + Hash + Clone> History<i64, ConstantDrift, NullObserver, K> {
    /// Like `builder()` but uses a custom key type `K` instead of the default `&'static str`.
    pub fn builder_with_key() -> HistoryBuilder<i64, ConstantDrift, NullObserver, K> {
        HistoryBuilder {
            mu: MU,
            sigma: SIGMA,
            beta: BETA,
            drift: ConstantDrift(GAMMA),
            p_draw: P_DRAW,
            online: false,
            convergence: ConvergenceOptions::default(),
            observer: NullObserver,
            _time: PhantomData,
            _key: PhantomData,
        }
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    pub fn intern<Q>(&mut self, key: &Q) -> Index
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        self.keys.get_or_create(key)
    }

    pub fn lookup<Q>(&self, key: &Q) -> Option<Index>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        self.keys.get(key)
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    fn iteration(&mut self) -> (f64, f64) {
        let mut step = (0.0, 0.0);

        competitor::clean(self.agents.values_mut(), false);

        for j in (0..self.time_slices.len() - 1).rev() {
            for agent in self.time_slices[j + 1].skills.keys() {
                self.agents.get_mut(agent).unwrap().message =
                    self.time_slices[j + 1].backward_prior_out(&agent, &self.agents);
            }

            let old = self.time_slices[j].posteriors();

            self.time_slices[j].new_backward_info(&self.agents);

            let new = self.time_slices[j].posteriors();

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

        competitor::clean(self.agents.values_mut(), false);

        for j in 1..self.time_slices.len() {
            for agent in self.time_slices[j - 1].skills.keys() {
                self.agents.get_mut(agent).unwrap().message =
                    self.time_slices[j - 1].forward_prior_out(&agent);
            }

            let old = self.time_slices[j].posteriors();

            self.time_slices[j].new_forward_info(&self.agents);

            let new = self.time_slices[j].posteriors();

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

        if self.time_slices.len() == 1 {
            let old = self.time_slices[0].posteriors();

            self.time_slices[0].iteration(0, &self.agents);

            let new = self.time_slices[0].posteriors();

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

        step
    }

    /// Learning curves for all competitors, keyed by their user-facing key.
    ///
    /// Note: `key(idx)` is O(n) per lookup; this method is therefore O(n²)
    /// in the number of competitors. Acceptable for T2; T3 may optimize.
    pub fn learning_curves(&self) -> HashMap<K, Vec<(T, Gaussian)>> {
        let mut data: HashMap<K, Vec<(T, Gaussian)>> = HashMap::new();
        for slice in &self.time_slices {
            for (idx, skill) in slice.skills.iter() {
                if let Some(key) = self.keys.key(idx).cloned() {
                    data.entry(key)
                        .or_default()
                        .push((slice.time, skill.posterior()));
                }
            }
        }
        data
    }

    /// Skill estimate at the latest time slice the competitor appears in.
    pub fn current_skill<Q>(&self, key: &Q) -> Option<Gaussian>
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let idx = self.keys.get(key)?;
        self.time_slices
            .iter()
            .rev()
            .find_map(|ts| ts.skills.get(idx).map(|sk| sk.posterior()))
    }

    /// Learning curve for a single key: (time, posterior) pairs in time order.
    pub fn learning_curve<Q>(&self, key: &Q) -> Vec<(T, Gaussian)>
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let Some(idx) = self.keys.get(key) else {
            return Vec::new();
        };
        self.time_slices
            .iter()
            .filter_map(|ts| ts.skills.get(idx).map(|sk| (ts.time, sk.posterior())))
            .collect()
    }

    pub(crate) fn log_evidence_internal(&mut self, forward: bool, targets: &[Index]) -> f64 {
        self.time_slices
            .iter()
            .map(|ts| ts.log_evidence(self.online, targets, forward, &self.agents))
            .sum()
    }

    /// Total log-evidence across the history.
    pub fn log_evidence(&mut self) -> f64 {
        self.log_evidence_internal(false, &[])
    }

    /// Log-evidence restricted to time slices containing at least one of the
    /// given keys. Useful for leave-one-out cross-validation.
    pub fn log_evidence_for<Q>(&mut self, keys: &[&Q]) -> f64
    where
        K: std::borrow::Borrow<Q>,
        Q: std::hash::Hash + Eq + ?Sized,
    {
        let targets: Vec<Index> = keys.iter().filter_map(|k| self.keys.get(*k)).collect();
        self.log_evidence_internal(false, &targets)
    }

    /// Draw-probability quality metric for the given teams (key slices).
    ///
    /// Values range roughly [0, 1]; 1 == perfectly matched.
    pub fn predict_quality(&self, teams: &[&[&K]]) -> f64 {
        let groups: Vec<Vec<Gaussian>> = teams
            .iter()
            .map(|team| {
                team.iter()
                    .filter_map(|k| self.keys.get(*k))
                    .filter_map(|idx| {
                        self.time_slices
                            .iter()
                            .rev()
                            .find_map(|ts| ts.skills.get(idx).map(|s| s.posterior()))
                    })
                    .collect()
            })
            .collect();
        let group_refs: Vec<&[Gaussian]> = groups.iter().map(|g| g.as_slice()).collect();
        crate::quality(&group_refs, self.beta)
    }

    /// 2-team win probability: returns `[P(team0 wins), P(team1 wins)]`.
    ///
    /// Panics if `teams.len() != 2`. N-team support lands in T4.
    pub fn predict_outcome(&self, teams: &[&[&K]]) -> Vec<f64> {
        assert_eq!(teams.len(), 2, "predict_outcome T2: 2 teams only");
        let gather = |team: &[&K]| -> Gaussian {
            team.iter()
                .filter_map(|k| self.keys.get(*k))
                .filter_map(|idx| {
                    self.time_slices
                        .iter()
                        .rev()
                        .find_map(|ts| ts.skills.get(idx).map(|s| s.posterior()))
                })
                .fold(crate::N00, |acc, g| acc + g.forget(self.beta.powi(2)))
        };
        let a = gather(teams[0]);
        let b = gather(teams[1]);
        let diff = a - b;
        let p_a = 1.0 - crate::cdf(0.0, diff.mu(), diff.sigma());
        vec![p_a, 1.0 - p_a]
    }

    /// Run the full forward+backward convergence loop and return a summary.
    pub fn converge(&mut self) -> Result<ConvergenceReport, InferenceError> {
        use std::time::Instant;

        use smallvec::SmallVec;

        let opts = self.convergence;
        let mut step = (f64::INFINITY, f64::INFINITY);
        let mut i = 0;
        let mut per_iter: SmallVec<[std::time::Duration; 32]> = SmallVec::new();
        while tuple_gt(step, opts.epsilon) && i < opts.max_iter {
            let t0 = Instant::now();
            step = self.iteration();
            per_iter.push(t0.elapsed());
            i += 1;
            self.observer.on_iteration_end(i, step);
        }
        let converged = !tuple_gt(step, opts.epsilon);
        let log_evidence = self.log_evidence_internal(false, &[]);
        self.observer.on_converged(i, step, converged);
        Ok(ConvergenceReport {
            iterations: i,
            final_step: step,
            log_evidence,
            converged,
            per_iteration_time: per_iter,
            slices_skipped: 0,
        })
    }
}

impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O, K> {
    pub(crate) fn add_events_with_prior(
        &mut self,
        composition: Vec<Vec<Vec<Index>>>,
        results: Vec<Vec<f64>>,
        times: Vec<T>,
        weights: Vec<Vec<Vec<f64>>>,
        mut priors: HashMap<Index, Rating<T, D>>,
    ) -> Result<(), InferenceError> {
        if !results.is_empty() && results.len() != composition.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "results",
                expected: composition.len(),
                got: results.len(),
            });
        }
        if times.len() != composition.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "times",
                expected: composition.len(),
                got: times.len(),
            });
        }
        if !weights.is_empty() && weights.len() != composition.len() {
            return Err(InferenceError::MismatchedShape {
                kind: "weights",
                expected: composition.len(),
                got: weights.len(),
            });
        }

        competitor::clean(self.agents.values_mut(), true);

        let mut this_agent = Vec::with_capacity(1024);

        for agent in composition.iter().flatten().flatten() {
            if this_agent.contains(agent) {
                continue;
            }

            this_agent.push(*agent);

            if !self.agents.contains(*agent) {
                self.agents.insert(
                    *agent,
                    Competitor {
                        rating: priors.remove(agent).unwrap_or_else(|| {
                            Rating::new(
                                Gaussian::from_ms(self.mu, self.sigma),
                                self.beta,
                                self.drift,
                            )
                        }),
                        message: N_INF,
                        last_time: None,
                    },
                );
            }
        }

        let n = composition.len();
        let o = sort_time(&times, false);

        let mut i = 0;
        let mut k = 0;

        while i < n {
            let mut j = i + 1;
            let t = times[o[i]];

            while j < n && times[o[j]] == t {
                j += 1;
            }

            while self.time_slices.len() > k && self.time_slices[k].time < t {
                let time_slice = &mut self.time_slices[k];

                if k > 0 {
                    time_slice.new_forward_info(&self.agents);
                }

                for agent_idx in &this_agent {
                    if let Some(skill) = time_slice.skills.get_mut(*agent_idx) {
                        skill.elapsed = time_slice::compute_elapsed(
                            self.agents[*agent_idx].last_time.as_ref(),
                            &time_slice.time,
                        );

                        let agent = self.agents.get_mut(*agent_idx).unwrap();

                        agent.last_time = Some(time_slice.time);
                        agent.message = time_slice.forward_prior_out(agent_idx);
                    }
                }

                k += 1;
            }

            let composition = (i..j)
                .map(|e| composition[o[e]].clone())
                .collect::<Vec<_>>();

            let results = if results.is_empty() {
                Vec::new()
            } else {
                (i..j).map(|e| results[o[e]].clone()).collect::<Vec<_>>()
            };

            let weights = if weights.is_empty() {
                Vec::new()
            } else {
                (i..j).map(|e| weights[o[e]].clone()).collect::<Vec<_>>()
            };

            if self.time_slices.len() > k && self.time_slices[k].time == t {
                let time_slice = &mut self.time_slices[k];
                time_slice.add_events(composition, results, weights, &self.agents);

                for agent_idx in time_slice.skills.keys() {
                    let agent = self.agents.get_mut(agent_idx).unwrap();

                    agent.last_time = Some(t);
                    agent.message = time_slice.forward_prior_out(&agent_idx);
                }
            } else {
                let mut time_slice = TimeSlice::new(t, self.p_draw);
                time_slice.add_events(composition, results, weights, &self.agents);

                self.time_slices.insert(k, time_slice);

                let time_slice = &self.time_slices[k];

                for agent_idx in time_slice.skills.keys() {
                    let agent = self.agents.get_mut(agent_idx).unwrap();

                    agent.last_time = Some(t);
                    agent.message = time_slice.forward_prior_out(&agent_idx);
                }

                k += 1;
            }

            i = j;
        }

        while self.time_slices.len() > k {
            let time_slice = &mut self.time_slices[k];

            time_slice.new_forward_info(&self.agents);

            for agent_idx in &this_agent {
                if let Some(skill) = time_slice.skills.get_mut(*agent_idx) {
                    skill.elapsed = time_slice::compute_elapsed(
                        self.agents[*agent_idx].last_time.as_ref(),
                        &time_slice.time,
                    );

                    let agent = self.agents.get_mut(*agent_idx).unwrap();

                    agent.last_time = Some(time_slice.time);
                    agent.message = time_slice.forward_prior_out(agent_idx);
                }
            }

            k += 1;
        }

        self.size += n;
        Ok(())
    }

    pub fn record_winner<Q>(&mut self, winner: &Q, loser: &Q, time: T) -> Result<(), InferenceError>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        let w = self.intern(winner);
        let l = self.intern(loser);
        self.add_events_with_prior(
            vec![vec![vec![w], vec![l]]],
            vec![vec![1.0, 0.0]],
            vec![time],
            vec![],
            HashMap::new(),
        )
    }

    pub fn record_draw<Q>(&mut self, a: &Q, b: &Q, time: T) -> Result<(), InferenceError>
    where
        K: Borrow<Q>,
        Q: Hash + Eq + ToOwned<Owned = K> + ?Sized,
    {
        let a_idx = self.intern(a);
        let b_idx = self.intern(b);
        self.add_events_with_prior(
            vec![vec![vec![a_idx], vec![b_idx]]],
            vec![vec![0.0, 0.0]],
            vec![time],
            vec![],
            HashMap::new(),
        )
    }

    /// Start a fluent event builder for a single match at `time`.
    pub fn event(&mut self, time: T) -> crate::event_builder::EventBuilder<'_, T, D, O, K> {
        crate::event_builder::EventBuilder::new(self, time)
    }

    /// Bulk-ingest typed events.
    pub fn add_events<I>(&mut self, events: I) -> Result<(), InferenceError>
    where
        I: IntoIterator<Item = crate::event::Event<T, K>>,
    {
        use crate::event::Event;
        let events: Vec<Event<T, K>> = events.into_iter().collect();
        if events.is_empty() {
            return Ok(());
        }

        let mut composition: Vec<Vec<Vec<Index>>> = Vec::with_capacity(events.len());
        let mut results: Vec<Vec<f64>> = Vec::with_capacity(events.len());
        let mut times: Vec<T> = Vec::with_capacity(events.len());
        let mut weights: Vec<Vec<Vec<f64>>> = Vec::with_capacity(events.len());
        let mut priors: HashMap<Index, Rating<T, D>> = HashMap::new();

        for ev in events {
            let ranks = ev.outcome.as_ranks();
            if ranks.len() != ev.teams.len() {
                return Err(InferenceError::MismatchedShape {
                    kind: "outcome ranks vs teams",
                    expected: ev.teams.len(),
                    got: ranks.len(),
                });
            }

            let mut event_comp: Vec<Vec<Index>> = Vec::with_capacity(ev.teams.len());
            let mut event_weights: Vec<Vec<f64>> = Vec::with_capacity(ev.teams.len());

            for team in ev.teams {
                let mut team_indices: Vec<Index> = Vec::with_capacity(team.members.len());
                let mut team_weights: Vec<f64> = Vec::with_capacity(team.members.len());
                for member in team.members {
                    let idx = self.keys.get_or_create(&member.key);
                    team_indices.push(idx);
                    team_weights.push(member.weight);
                    if let Some(prior) = member.prior {
                        priors.insert(idx, Rating::new(prior, self.beta, self.drift));
                    }
                }
                event_comp.push(team_indices);
                event_weights.push(team_weights);
            }
            composition.push(event_comp);
            weights.push(event_weights);

            let max_rank = ranks.iter().copied().max().unwrap_or(0) as f64;
            let inverted: Vec<f64> = ranks.iter().map(|&r| max_rank - r as f64).collect();
            results.push(inverted);
            times.push(ev.time);
        }

        self.add_events_with_prior(composition, results, times, weights, priors)
    }
}

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

    use super::*;
    use crate::{
        ConstantDrift, EPSILON, Event, Game, Gaussian, Member, Outcome, P_DRAW, Team,
        arena::ScratchArena,
    };

    fn make_events_1v1(
        pairs: &[(&'static str, &'static str)],
        outcomes: &[Outcome],
        times: &[i64],
    ) -> Vec<Event<i64, &'static str>> {
        pairs
            .iter()
            .copied()
            .zip(outcomes.iter().cloned())
            .zip(times.iter().copied())
            .map(|(((a, b), outcome), time)| Event {
                time,
                teams: smallvec![
                    Team::with_members([Member::new(a)]),
                    Team::with_members([Member::new(b)]),
                ],
                outcome,
            })
            .collect()
    }

    #[test]
    fn test_init() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let p0 = h.time_slices[0].posteriors();

        assert_ulps_eq!(
            p0[&a],
            Gaussian::from_ms(29.205220, 7.194481),
            epsilon = 1e-6
        );

        let observed = h.time_slices[1].skills.get(a).unwrap().forward.sigma();
        let gamma: f64 = 0.15 * 25.0 / 3.0;
        let expected = (gamma.powi(2)
            + h.time_slices[0]
                .skills
                .get(a)
                .unwrap()
                .posterior()
                .sigma()
                .powi(2))
        .sqrt();

        assert_ulps_eq!(observed, expected, epsilon = 0.000001);

        let observed = h.time_slices[1].skills.get(a).unwrap().posterior();

        let w = [vec![1.0], vec![1.0]];
        let p = Game::ranked_with_arena(
            h.time_slices[1].events[0].within_priors(
                false,
                false,
                &h.time_slices[1].skills,
                &h.agents,
            ),
            &[0.0, 1.0],
            &w,
            P_DRAW,
            &mut ScratchArena::new(),
        )
        .posteriors();
        let expected = p[0][0];

        assert_ulps_eq!(observed, expected, epsilon = 1e-6);

        let _ = (b, c);
    }

    #[test]
    fn test_one_batch() {
        let mut h1 = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(0.15 * 25.0 / 3.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 1, 1],
        );
        h1.add_events(events).unwrap();

        let a = h1.keys.get("a").unwrap();
        let c = h1.keys.get("c").unwrap();

        assert_ulps_eq!(
            h1.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(22.904409, 6.010330),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h1.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.110318, 5.866311),
            epsilon = 1e-6
        );

        h1.converge().unwrap();

        assert_ulps_eq!(
            h1.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h1.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.000000, 5.419212),
            epsilon = 1e-6
        );

        let mut h2 = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h2.add_events(events).unwrap();

        let a = h2.keys.get("a").unwrap();
        let c = h2.keys.get("c").unwrap();

        assert_ulps_eq!(
            h2.time_slices[2].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(22.903522, 6.011017),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h2.time_slices[2].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.110702, 5.866811),
            epsilon = 1e-6
        );

        h2.converge().unwrap();

        assert_ulps_eq!(
            h2.time_slices[2].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(24.998668, 5.420053),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h2.time_slices[2].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(25.000532, 5.419827),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_learning_curves() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "c"), ("c", "a")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[5, 6, 7],
        );
        h.add_events(events).unwrap();
        h.converge().unwrap();

        let lc_a = h.learning_curve("a");
        let lc_c = h.learning_curve("c");

        let aj_e = lc_a.len();
        let cj_e = lc_c.len();

        assert_eq!(lc_a[0].0, 5);
        assert_eq!(lc_a[aj_e - 1].0, 7);

        assert_ulps_eq!(
            lc_a[aj_e - 1].1,
            Gaussian::from_ms(24.998668, 5.420053),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_c[cj_e - 1].1,
            Gaussian::from_ms(25.000532, 5.419827),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_env_ttt() {
        let mut h = History::builder()
            .mu(25.0)
            .sigma(25.0 / 3.0)
            .beta(25.0 / 6.0)
            .drift(ConstantDrift(25.0 / 300.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();
        h.converge().unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(25.000267, 5.419423),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(24.999198, 5.419512),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(25.001332, 5.420054),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_teams() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(6.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events: Vec<Event<i64, &'static str>> = vec![
            Event {
                time: 1,
                teams: smallvec![
                    Team::with_members([Member::new("a"), Member::new("b")]),
                    Team::with_members([Member::new("c"), Member::new("d")]),
                ],
                outcome: Outcome::winner(0, 2),
            },
            Event {
                time: 2,
                teams: smallvec![
                    Team::with_members([Member::new("e"), Member::new("f")]),
                    Team::with_members([Member::new("b"), Member::new("c")]),
                ],
                outcome: Outcome::winner(1, 2),
            },
            Event {
                time: 3,
                teams: smallvec![
                    Team::with_members([Member::new("a"), Member::new("d")]),
                    Team::with_members([Member::new("e"), Member::new("f")]),
                ],
                outcome: Outcome::winner(0, 2),
            },
        ];
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();
        let d = h.keys.get("d").unwrap();
        let e = h.keys.get("e").unwrap();
        let f = h.keys.get("f").unwrap();

        let trueskill_log_evidence = h.log_evidence_internal(false, &[]);
        let trueskill_log_evidence_online = h.log_evidence_internal(true, &[]);

        assert_ulps_eq!(
            trueskill_log_evidence,
            trueskill_log_evidence_online,
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior().mu(),
            -h.time_slices[0].skills.get(c).unwrap().posterior().mu(),
            epsilon = 1e-6
        );

        let evidence_second_event = h.log_evidence_internal(false, &[b]).exp() * 2.0;
        assert_ulps_eq!(0.5, evidence_second_event, epsilon = 1e-6);

        let evidence_third_event = h.log_evidence_internal(false, &[a]).exp() * 2.0;
        assert_ulps_eq!(0.669885, evidence_third_event, epsilon = 1e-6);

        h.converge().unwrap();

        let loocv_hat = h.log_evidence_internal(false, &[]).exp();
        let p_d_m_hat = h.log_evidence_internal(true, &[]).exp();

        assert_ulps_eq!(loocv_hat, 0.241027, epsilon = 1e-6);
        assert_ulps_eq!(p_d_m_hat, 0.172432, epsilon = 1e-6);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[0].skills.get(d).unwrap().posterior(),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[1].skills.get(e).unwrap().posterior(),
            h.time_slices[1].skills.get(f).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(4.084902, 5.106919),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            Gaussian::from_ms(-0.533029, 5.106919),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(e).unwrap().posterior(),
            Gaussian::from_ms(-3.551872, 5.154569),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_add_events() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        h.converge().unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[4, 5, 6],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 6);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[5].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_only_add_events() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        h.converge().unwrap();

        assert_eq!(h.time_slices[2].skills.get(b).unwrap().elapsed, 2);
        assert_eq!(h.time_slices[2].skills.get(c).unwrap().elapsed, 1);

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[2].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 1.300610),
            epsilon = 1e-6
        );

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[4, 5, 6],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 6);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![a], vec![c]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(a).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[3].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            h.time_slices[5].skills.get(b).unwrap().posterior(),
            Gaussian::from_ms(0.000000, 0.931236),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_log_evidence() {
        use crate::ConvergenceOptions;

        let mut h: History<i64, _, _, &'static str> = History::builder().build();

        // empty results in the old API = team 0 wins; reproduce with Outcome::winner(0,2)
        let events = make_events_1v1(
            &[("a", "b"), ("b", "a")],
            &[Outcome::winner(0, 2), Outcome::winner(0, 2)],
            &[1, 2],
        );
        h.add_events(events).unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();

        let p_d_m_2 = h.log_evidence_internal(false, &[]).exp() * 2.0;

        assert_ulps_eq!(p_d_m_2, 0.17650911, epsilon = 1e-6);
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(true, &[]).exp() * 2.0,
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(true, &[a]).exp() * 2.0,
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            p_d_m_2,
            h.log_evidence_internal(false, &[a]).exp() * 2.0,
            epsilon = 1e-6
        );

        // run exactly 11 iterations (old test used convergence(11, ...))
        h.convergence = ConvergenceOptions {
            max_iter: 11,
            epsilon: EPSILON,
        };
        h.converge().unwrap();

        let loocv_approx_2 = h.log_evidence_internal(false, &[]).exp().sqrt();

        assert_ulps_eq!(loocv_approx_2, 0.001976774, epsilon = 0.000001);

        let p_d_m_approx_2 = h.log_evidence_internal(true, &[]).exp() * 2.0;

        assert!(loocv_approx_2 - p_d_m_approx_2 < 1e-4);

        assert_ulps_eq!(
            loocv_approx_2,
            h.log_evidence_internal(true, &[b]).exp() * 2.0,
            epsilon = 1e-4
        );

        let mut h2: History<i64, _, _, &'static str> = History::builder().build();

        let events = make_events_1v1(
            &[("a", "b"), ("b", "a")],
            &[Outcome::winner(0, 2), Outcome::winner(0, 2)],
            &[1, 2],
        );
        h2.add_events(events).unwrap();

        assert_ulps_eq!(
            ((0.5f64 * 0.1765).ln() / 2.0).exp(),
            (h2.log_evidence_internal(false, &[]) / 2.0).exp(),
            epsilon = 1e-4
        );
    }

    #[test]
    fn test_add_events_with_time() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[0, 10, 20],
        );
        h.add_events(events).unwrap();
        h.converge().unwrap();

        let a = h.keys.get("a").unwrap();
        let b = h.keys.get("b").unwrap();
        let c = h.keys.get("c").unwrap();

        let events2 = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[15, 10, 0],
        );
        h.add_events(events2).unwrap();

        assert_eq!(h.time_slices.len(), 4);

        assert_eq!(
            h.time_slices
                .iter()
                .map(|ts| ts.events.len())
                .collect::<Vec<_>>(),
            vec![2, 2, 1, 1]
        );

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]], vec![vec![b], vec![c]]],
                vec![vec![vec![a], vec![c]], vec![vec![a], vec![c]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        assert_eq!(
            h.time_slices
                .iter()
                .map(|b| b.get_results())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![0.0, 1.0], vec![0.0, 1.0]],
                vec![vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]]
            ]
        );

        let end = h.time_slices.len() - 1;

        assert_eq!(h.time_slices[0].skills.get(c).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[end].skills.get(c).unwrap().elapsed, 10);

        assert_eq!(h.time_slices[0].skills.get(a).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[2].skills.get(a).unwrap().elapsed, 5);

        assert_eq!(h.time_slices[0].skills.get(b).unwrap().elapsed, 0);
        assert_eq!(h.time_slices[end].skills.get(b).unwrap().elapsed, 5);

        h.converge().unwrap();

        assert_ulps_eq!(
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            h.time_slices[end].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[end].skills.get(c).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h.time_slices[0].skills.get(c).unwrap().posterior(),
            h.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        // second scenario: team-0 wins (empty results in old API), different composition order

        let mut h2: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("c", "a"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[0, 10, 20],
        );
        h2.add_events(events).unwrap();
        h2.converge().unwrap();

        let a = h2.keys.get("a").unwrap();
        let b = h2.keys.get("b").unwrap();
        let c = h2.keys.get("c").unwrap();

        let events2 = make_events_1v1(
            &[("a", "b"), ("c", "a"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
                Outcome::winner(0, 2),
            ],
            &[15, 10, 0],
        );
        h2.add_events(events2).unwrap();

        assert_eq!(h2.time_slices.len(), 4);

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|ts| ts.events.len())
                .collect::<Vec<_>>(),
            vec![2, 2, 1, 1]
        );

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|b| b.get_composition())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![vec![a], vec![b]], vec![vec![b], vec![c]]],
                vec![vec![vec![c], vec![a]], vec![vec![c], vec![a]]],
                vec![vec![vec![a], vec![b]]],
                vec![vec![vec![b], vec![c]]]
            ]
        );

        assert_eq!(
            h2.time_slices
                .iter()
                .map(|b| b.get_results())
                .collect::<Vec<_>>(),
            vec![
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![1.0, 0.0], vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]],
                vec![vec![1.0, 0.0]]
            ]
        );

        let end = h2.time_slices.len() - 1;

        assert_eq!(h2.time_slices[0].skills.get(c).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[end].skills.get(c).unwrap().elapsed, 10);

        assert_eq!(h2.time_slices[0].skills.get(a).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[2].skills.get(a).unwrap().elapsed, 5);

        assert_eq!(h2.time_slices[0].skills.get(b).unwrap().elapsed, 0);
        assert_eq!(h2.time_slices[end].skills.get(b).unwrap().elapsed, 5);

        h2.converge().unwrap();

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(b).unwrap().posterior(),
            h2.time_slices[end].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(c).unwrap().posterior(),
            h2.time_slices[end].skills.get(c).unwrap().posterior(),
            epsilon = 1e-6
        );

        assert_ulps_eq!(
            h2.time_slices[0].skills.get(c).unwrap().posterior(),
            h2.time_slices[0].skills.get(b).unwrap().posterior(),
            epsilon = 1e-6
        );
    }

    #[test]
    fn test_1vs1_weighted() {
        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(2.0)
            .sigma(6.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .build();

        // empty results in old API = team 0 wins: a wins event 1, b wins event 2
        let events: Vec<Event<i64, &'static str>> = vec![
            Event {
                time: 1,
                teams: smallvec![
                    Team::with_members([Member::new("a").with_weight(5.0)]),
                    Team::with_members([Member::new("b").with_weight(4.0)]),
                ],
                outcome: Outcome::winner(0, 2),
            },
            Event {
                time: 2,
                teams: smallvec![
                    Team::with_members([Member::new("b").with_weight(5.0)]),
                    Team::with_members([Member::new("a").with_weight(4.0)]),
                ],
                outcome: Outcome::winner(0, 2),
            },
        ];
        h.add_events(events).unwrap();

        let lc_a = h.learning_curve("a");
        let lc_b = h.learning_curve("b");

        assert_ulps_eq!(
            lc_a[0].1,
            Gaussian::from_ms(5.537659, 4.758722),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_b[0].1,
            Gaussian::from_ms(-0.830127, 5.239568),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_a[1].1,
            Gaussian::from_ms(1.792277, 4.099566),
            epsilon = 1e-6
        );
        assert_ulps_eq!(
            lc_b[1].1,
            Gaussian::from_ms(4.845533, 3.747616),
            epsilon = 1e-6
        );

        h.converge().unwrap();

        let lc_a = h.learning_curve("a");
        let lc_b = h.learning_curve("b");

        assert_ulps_eq!(lc_a[0].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_b[0].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_a[1].1, lc_a[0].1, epsilon = 1e-6);
        assert_ulps_eq!(lc_b[1].1, lc_a[0].1, epsilon = 1e-6);
    }

    #[test]
    fn test_converge_returns_report() {
        use crate::ConvergenceOptions;

        let mut h: History<i64, _, _, &'static str> = History::builder()
            .mu(0.0)
            .sigma(2.0)
            .beta(1.0)
            .drift(ConstantDrift(0.0))
            .convergence(ConvergenceOptions {
                max_iter: 30,
                epsilon: 1e-6,
            })
            .build();

        let events = make_events_1v1(
            &[("a", "b"), ("a", "c"), ("b", "c")],
            &[
                Outcome::winner(0, 2),
                Outcome::winner(1, 2),
                Outcome::winner(0, 2),
            ],
            &[1, 2, 3],
        );
        h.add_events(events).unwrap();

        let report = h.converge().unwrap();
        assert!(report.converged);
        assert!(report.iterations > 0);
        assert!(report.iterations < 30);
        assert!(report.final_step.0 <= 1e-6);
    }
}