653 lines
20 KiB
Rust
653 lines
20 KiB
Rust
use crate::{
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approx, compute_margin, evidence,
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gaussian::Gaussian,
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message::{DiffMessage, TeamMessage},
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player::Player,
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sort_perm, tuple_gt, tuple_max, N00, N_INF,
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};
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#[derive(Debug)]
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pub struct Game<'a> {
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teams: Vec<Vec<Player>>,
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result: &'a [f64],
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weights: &'a [Vec<f64>],
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p_draw: f64,
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pub(crate) likelihoods: Vec<Vec<Gaussian>>,
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pub(crate) evidence: f64,
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}
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impl<'a> Game<'a> {
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pub fn new(
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teams: Vec<Vec<Player>>,
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result: &'a [f64],
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weights: &'a [Vec<f64>],
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p_draw: f64,
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) -> Self {
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debug_assert!(
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(result.len() == teams.len()),
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"result must have the same length as teams"
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);
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debug_assert!(
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weights
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.iter()
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.zip(teams.iter())
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.all(|(w, t)| w.len() == t.len()),
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"weights must have the same dimensions as teams"
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);
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debug_assert!(
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(0.0..1.0).contains(&p_draw),
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"draw probability.must be >= 0.0 and < 1.0"
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);
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debug_assert!(
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p_draw > 0.0 || {
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let mut r = result.to_vec();
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r.sort_unstable_by(|a, b| a.partial_cmp(b).unwrap());
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r.windows(2).all(|w| w[0] != w[1])
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},
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"draw must be > 0.0 if there is teams with draw"
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);
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let mut this = Self {
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teams,
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result,
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weights,
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p_draw,
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likelihoods: Vec::new(),
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evidence: 0.0,
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};
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this.likelihoods();
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this
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}
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fn likelihoods(&mut self) {
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let o = sort_perm(self.result, true);
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let mut team = o
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.iter()
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.map(|&e| {
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let performance = self.teams[e]
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.iter()
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.zip(self.weights[e].iter())
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.fold(N00, |p, (player, &weight)| {
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p + (player.performance() * weight)
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});
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TeamMessage {
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prior: performance,
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..Default::default()
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}
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})
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.collect::<Vec<_>>();
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let mut diff = team
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.windows(2)
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.map(|w| DiffMessage {
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prior: w[0].prior - w[1].prior,
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likelihood: N_INF,
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})
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.collect::<Vec<_>>();
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let tie = o
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.windows(2)
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.map(|e| self.result[e[0]] == self.result[e[1]])
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.collect::<Vec<_>>();
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let margin = if self.p_draw == 0.0 {
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vec![0.0; o.len() - 1]
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} else {
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o.windows(2)
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.map(|w| {
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let a: f64 = self.teams[w[0]].iter().map(|a| a.beta.powi(2)).sum();
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let b: f64 = self.teams[w[1]].iter().map(|a| a.beta.powi(2)).sum();
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compute_margin(self.p_draw, (a + b).sqrt())
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})
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.collect::<Vec<_>>()
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};
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self.evidence = 1.0;
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let mut step = (f64::INFINITY, f64::INFINITY);
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let mut iter = 0;
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while tuple_gt(step, 1e-6) && iter < 10 {
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step = (0.0, 0.0);
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for e in 0..diff.len() - 1 {
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diff[e].prior = team[e].posterior_win() - team[e + 1].posterior_lose();
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if iter == 0 {
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self.evidence *= evidence(&diff, &margin, &tie, e);
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}
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diff[e].likelihood = approx(diff[e].prior, margin[e], tie[e]) / diff[e].prior;
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let likelihood_lose = team[e].posterior_win() - diff[e].likelihood;
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step = tuple_max(step, team[e + 1].likelihood_lose.delta(likelihood_lose));
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team[e + 1].likelihood_lose = likelihood_lose;
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}
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for e in (1..diff.len()).rev() {
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diff[e].prior = team[e].posterior_win() - team[e + 1].posterior_lose();
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if iter == 0 && e == diff.len() - 1 {
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self.evidence *= evidence(&diff, &margin, &tie, e);
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}
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diff[e].likelihood = approx(diff[e].prior, margin[e], tie[e]) / diff[e].prior;
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let likelihood_win = team[e + 1].posterior_lose() + diff[e].likelihood;
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step = tuple_max(step, team[e].likelihood_win.delta(likelihood_win));
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team[e].likelihood_win = likelihood_win;
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}
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iter += 1;
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}
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if diff.len() == 1 {
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self.evidence = evidence(&diff, &margin, &tie, 0);
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diff[0].prior = team[0].posterior_win() - team[1].posterior_lose();
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diff[0].likelihood = approx(diff[0].prior, margin[0], tie[0]) / diff[0].prior;
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}
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let t_end = team.len() - 1;
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let d_end = diff.len() - 1;
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team[0].likelihood_win = team[1].posterior_lose() + diff[0].likelihood;
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team[t_end].likelihood_lose = team[t_end - 1].posterior_win() - diff[d_end].likelihood;
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let m_t_ft = o.into_iter().map(|e| team[e].likelihood());
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self.likelihoods = self
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.teams
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.iter()
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.zip(self.weights.iter())
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.zip(m_t_ft)
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.map(|((p, w), m)| {
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let performance = p.iter().zip(w.iter()).fold(N00, |p, (player, &weight)| {
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p + (player.performance() * weight)
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});
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p.iter()
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.zip(w.iter())
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.map(|(p, &w)| {
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((m - performance.exclude(p.performance() * w)) * (1.0 / w))
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.forget(p.beta, 1)
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})
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.collect::<Vec<_>>()
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})
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.collect::<Vec<_>>();
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}
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pub fn posteriors(&self) -> Vec<Vec<Gaussian>> {
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self.likelihoods
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.iter()
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.zip(self.teams.iter())
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.map(|(l, t)| {
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l.iter()
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.zip(t.iter())
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.map(|(&l, p)| l * p.prior)
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.collect::<Vec<_>>()
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})
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.collect::<Vec<_>>()
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}
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}
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#[cfg(test)]
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mod tests {
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use ::approx::assert_ulps_eq;
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use crate::{Gaussian, Player, GAMMA, N_INF};
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use super::*;
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#[test]
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fn test_1vs1() {
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let t_a = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let t_b = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let w = [vec![1.0], vec![1.0]];
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let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(20.794779, 7.194481), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(29.205220, 7.194481), epsilon = 1e-6);
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let t_a = Player::new(Gaussian::from_ms(29.0, 1.0), 25.0 / 6.0, GAMMA);
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let t_b = Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, GAMMA);
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let w = [vec![1.0], vec![1.0]];
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let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(28.896475, 0.996604), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(32.189211, 6.062063), epsilon = 1e-6);
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let t_a = Player::new(Gaussian::from_ms(1.139, 0.531), 1.0, 0.2125);
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let t_b = Player::new(Gaussian::from_ms(15.568, 0.51), 1.0, 0.2125);
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let w = [vec![1.0], vec![1.0]];
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let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 1.0], &w, 0.0);
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assert_eq!(g.likelihoods[0][0], N_INF);
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assert_eq!(g.likelihoods[1][0], N_INF);
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}
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#[test]
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fn test_1vs1vs1() {
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let teams = vec![
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vec![Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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)],
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vec![Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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)],
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vec![Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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)],
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];
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let w = [vec![1.0], vec![1.0], vec![1.0]];
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let g = Game::new(teams.clone(), &[1.0, 2.0, 0.0], &w, 0.0);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(25.000000, 6.238469), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(31.311358, 6.698818), epsilon = 1e-6);
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let w = [vec![1.0], vec![1.0], vec![1.0]];
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let g = Game::new(teams.clone(), &[2.0, 1.0, 0.0], &w, 0.0);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(31.311358, 6.698818), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(25.000000, 6.238469), epsilon = 1e-6);
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let w = [vec![1.0], vec![1.0], vec![1.0]];
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let g = Game::new(teams, &[1.0, 2.0, 0.0], &w, 0.5);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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let c = p[2][0];
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assert_ulps_eq!(a, Gaussian::from_ms(24.999999, 6.092561), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(33.379314, 6.483575), epsilon = 1e-6);
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assert_ulps_eq!(c, Gaussian::from_ms(16.620685, 6.483575), epsilon = 1e-6);
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}
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#[test]
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fn test_1vs1_draw() {
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let t_a = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let t_b = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let w = [vec![1.0], vec![1.0]];
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let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 0.0], &w, 0.25);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(24.999999, 6.469480), epsilon = 1e-6);
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let t_a = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
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let t_b = Player::new(Gaussian::from_ms(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0);
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let w = [vec![1.0], vec![1.0]];
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let g = Game::new(vec![vec![t_a], vec![t_b]], &[0.0, 0.0], &w, 0.25);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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assert_ulps_eq!(a, Gaussian::from_ms(25.736001, 2.709956), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(28.672888, 1.916471), epsilon = 1e-6);
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}
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#[test]
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fn test_1vs1vs1_draw() {
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let t_a = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let t_b = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let t_c = Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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);
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let w = [vec![1.0], vec![1.0], vec![1.0]];
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let g = Game::new(
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vec![vec![t_a], vec![t_b], vec![t_c]],
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&[0.0, 0.0, 0.0],
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&w,
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0.25,
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);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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let c = p[2][0];
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assert_ulps_eq!(a, Gaussian::from_ms(24.999999, 5.729068), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(25.000000, 5.707423), epsilon = 1e-6);
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assert_ulps_eq!(c, Gaussian::from_ms(24.999999, 5.729068), epsilon = 1e-6);
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let t_a = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
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let t_b = Player::new(Gaussian::from_ms(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0);
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let t_c = Player::new(Gaussian::from_ms(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0);
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let w = [vec![1.0], vec![1.0], vec![1.0]];
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let g = Game::new(
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vec![vec![t_a], vec![t_b], vec![t_c]],
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&[0.0, 0.0, 0.0],
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&w,
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0.25,
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);
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let p = g.posteriors();
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let a = p[0][0];
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let b = p[1][0];
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let c = p[2][0];
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assert_ulps_eq!(a, Gaussian::from_ms(25.488507, 2.638208), epsilon = 1e-6);
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assert_ulps_eq!(b, Gaussian::from_ms(25.510671, 2.628751), epsilon = 1e-6);
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assert_ulps_eq!(c, Gaussian::from_ms(28.555920, 1.885689), epsilon = 1e-6);
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}
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#[test]
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fn test_2vs1vs2_mixed() {
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let t_a = vec![
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Player::new(Gaussian::from_ms(12.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
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Player::new(Gaussian::from_ms(18.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
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];
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let t_b = vec![Player::new(
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Gaussian::from_ms(30.0, 3.0),
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25.0 / 6.0,
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25.0 / 300.0,
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)];
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let t_c = vec![
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Player::new(Gaussian::from_ms(14.0, 3.0), 25.0 / 6.0, 25.0 / 300.0),
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Player::new(Gaussian::from_ms(16., 3.0), 25.0 / 6.0, 25.0 / 300.0),
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];
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let w = [vec![1.0, 1.0], vec![1.0], vec![1.0, 1.0]];
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let g = Game::new(vec![t_a, t_b, t_c], &[1.0, 0.0, 0.0], &w, 0.25);
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let p = g.posteriors();
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assert_ulps_eq!(p[0][0], Gaussian::from_ms(13.051, 2.864), epsilon = 1e-3);
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assert_ulps_eq!(p[0][1], Gaussian::from_ms(19.051, 2.864), epsilon = 1e-3);
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assert_ulps_eq!(p[1][0], Gaussian::from_ms(29.292, 2.764), epsilon = 1e-3);
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assert_ulps_eq!(p[2][0], Gaussian::from_ms(13.658, 2.813), epsilon = 1e-3);
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assert_ulps_eq!(p[2][1], Gaussian::from_ms(15.658, 2.813), epsilon = 1e-3);
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}
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#[test]
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fn test_1vs1_weighted() {
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let w_a = vec![1.0];
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let w_b = vec![2.0];
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let t_a = vec![Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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0.0,
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)];
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let t_b = vec![Player::new(
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Gaussian::from_ms(25.0, 25.0 / 3.0),
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25.0 / 6.0,
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0.0,
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)];
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let w = [w_a, w_b];
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let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
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let p = g.posteriors();
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assert_ulps_eq!(
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p[0][0],
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Gaussian::from_ms(30.625173, 7.765472),
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epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(13.749653, 5.733840),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.0];
|
|
let w_b = vec![0.7];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(27.630080, 7.206676),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(23.158943, 7.801628),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.6];
|
|
let w_b = vec![0.7];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(26.142438, 7.573088),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(24.500183, 8.193278),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.0];
|
|
let w_b = vec![0.0];
|
|
|
|
let t_a = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
|
|
let t_b = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(5.557067, 4.052826),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(2.000000, 6.000000),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.0];
|
|
let w_b = vec![-1.0];
|
|
|
|
let t_a = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
|
|
let t_b = vec![Player::new(Gaussian::from_ms(2.0, 6.0), 1.0, 0.0)];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a, t_b], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(p[0][0], p[1][0], epsilon = 1e-6);
|
|
}
|
|
|
|
#[test]
|
|
fn test_2vs2_weighted() {
|
|
let t_a = vec![
|
|
Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
|
|
Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
|
|
];
|
|
let w_a = vec![0.4, 0.8];
|
|
|
|
let t_b = vec![
|
|
Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
|
|
Player::new(Gaussian::from_ms(25.0, 25.0 / 3.0), 25.0 / 6.0, 0.0),
|
|
];
|
|
let w_b = vec![0.9, 0.6];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(27.539023, 8.129639),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[0][1],
|
|
Gaussian::from_ms(30.078046, 7.485372),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(19.287197, 7.243465),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][1],
|
|
Gaussian::from_ms(21.191465, 7.867608),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.3, 1.5];
|
|
let w_b = vec![0.7, 0.4];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(25.190190, 8.220511),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[0][1],
|
|
Gaussian::from_ms(25.219450, 8.182783),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(24.897589, 8.300779),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][1],
|
|
Gaussian::from_ms(24.941479, 8.322717),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w_a = vec![1.6, 0.2];
|
|
let w_b = vec![0.7, 2.4];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a.clone(), t_b.clone()], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(
|
|
p[0][0],
|
|
Gaussian::from_ms(31.674697, 7.501180),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[0][1],
|
|
Gaussian::from_ms(25.834337, 8.320970),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][0],
|
|
Gaussian::from_ms(22.079819, 8.180607),
|
|
epsilon = 1e-6
|
|
);
|
|
assert_ulps_eq!(
|
|
p[1][1],
|
|
Gaussian::from_ms(14.987953, 6.308469),
|
|
epsilon = 1e-6
|
|
);
|
|
|
|
let w = [vec![1.0, 1.0], vec![1.0]];
|
|
let g = Game::new(
|
|
vec![
|
|
t_a.clone(),
|
|
vec![Player::new(
|
|
Gaussian::from_ms(25.0, 25.0 / 3.0),
|
|
25.0 / 6.0,
|
|
0.0,
|
|
)],
|
|
],
|
|
&[1.0, 0.0],
|
|
&w,
|
|
0.0,
|
|
);
|
|
let post_2vs1 = g.posteriors();
|
|
|
|
let w_a = vec![1.0, 1.0];
|
|
let w_b = vec![1.0, 0.0];
|
|
|
|
let w = [w_a, w_b];
|
|
let g = Game::new(vec![t_a, t_b.clone()], &[1.0, 0.0], &w, 0.0);
|
|
let p = g.posteriors();
|
|
|
|
assert_ulps_eq!(p[0][0], post_2vs1[0][0], epsilon = 1e-6);
|
|
assert_ulps_eq!(p[0][1], post_2vs1[0][1], epsilon = 1e-6);
|
|
assert_ulps_eq!(p[1][0], post_2vs1[1][0], epsilon = 1e-6);
|
|
assert_ulps_eq!(p[1][1], t_b[1].prior, epsilon = 1e-6);
|
|
}
|
|
}
|