284 lines
8.5 KiB
Python
284 lines
8.5 KiB
Python
from bisect import bisect
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from math import pi, sqrt, tanh
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from operator import attrgetter, itemgetter
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from django.db import transaction
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from django.db.models import Count, OuterRef, Subquery
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from django.db.models.functions import Coalesce
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from django.utils import timezone
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BETA2 = 328.33**2
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RATING_INIT = 1200 # Newcomer's rating when applying the rating floor/ceiling
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MEAN_INIT = 1400.0
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VAR_INIT = 250**2 * (BETA2 / 212**2)
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SD_INIT = sqrt(VAR_INIT)
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VALID_RANGE = MEAN_INIT - 20 * SD_INIT, MEAN_INIT + 20 * SD_INIT
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VAR_PER_CONTEST = 1219.047619 * (BETA2 / 212**2)
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VAR_LIM = (
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sqrt(VAR_PER_CONTEST**2 + 4 * BETA2 * VAR_PER_CONTEST) - VAR_PER_CONTEST
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) / 2
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SD_LIM = sqrt(VAR_LIM)
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TANH_C = sqrt(3) / pi
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def tie_ranker(iterable, key=attrgetter("points")):
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rank = 0
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delta = 1
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last = None
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buf = []
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for item in iterable:
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new = key(item)
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if new != last:
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for _ in buf:
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yield rank + (delta - 1) / 2.0
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rank += delta
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delta = 0
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buf = []
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delta += 1
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buf.append(item)
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last = key(item)
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for _ in buf:
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yield rank + (delta - 1) / 2.0
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def eval_tanhs(tanh_terms, x):
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return sum((wt / sd) * tanh((x - mu) / (2 * sd)) for mu, sd, wt in tanh_terms)
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def solve(tanh_terms, y_tg, lin_factor=0, bounds=VALID_RANGE):
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L, R = bounds
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Ly, Ry = None, None
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while R - L > 2:
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x = (L + R) / 2
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y = lin_factor * x + eval_tanhs(tanh_terms, x)
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if y > y_tg:
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R, Ry = x, y
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elif y < y_tg:
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L, Ly = x, y
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else:
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return x
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# Use linear interpolation to be slightly more accurate.
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if Ly is None:
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Ly = lin_factor * L + eval_tanhs(tanh_terms, L)
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if y_tg <= Ly:
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return L
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if Ry is None:
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Ry = lin_factor * R + eval_tanhs(tanh_terms, R)
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if y_tg >= Ry:
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return R
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ratio = (y_tg - Ly) / (Ry - Ly)
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return L * (1 - ratio) + R * ratio
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def get_var(times_ranked, cache=[VAR_INIT]):
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while times_ranked >= len(cache):
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next_var = 1.0 / (1.0 / (cache[-1] + VAR_PER_CONTEST) + 1.0 / BETA2)
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cache.append(next_var)
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return cache[times_ranked]
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def recalculate_ratings(ranking, old_mean, times_ranked, historical_p):
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n = len(ranking)
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new_p = [0.0] * n
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new_mean = [0.0] * n
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# Note: pre-multiply delta by TANH_C to improve efficiency.
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delta = [TANH_C * sqrt(get_var(t) + VAR_PER_CONTEST + BETA2) for t in times_ranked]
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p_tanh_terms = [(m, d, 1) for m, d in zip(old_mean, delta)]
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# Calculate performance at index i.
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def solve_idx(i, bounds=VALID_RANGE):
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r = ranking[i]
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y_tg = 0
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for d, s in zip(delta, ranking):
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if s > r: # s loses to r
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y_tg += 1.0 / d
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elif s < r: # s beats r
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y_tg -= 1.0 / d
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# Otherwise, this is a tie that counts as half a win, as per Elo-MMR.
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new_p[i] = solve(p_tanh_terms, y_tg, bounds=bounds)
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# Fill all indices between i and j, inclusive. Use the fact that new_p is non-increasing.
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def divconq(i, j):
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if j - i > 1:
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k = (i + j) // 2
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solve_idx(k, bounds=(new_p[j], new_p[i]))
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divconq(i, k)
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divconq(k, j)
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if n < 2:
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new_p = list(old_mean)
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new_mean = list(old_mean)
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else:
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# Calculate performance.
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solve_idx(0)
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solve_idx(n - 1)
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divconq(0, n - 1)
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# Calculate mean.
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for i, r in enumerate(ranking):
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tanh_terms = []
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w_prev = 1.0
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w_sum = 0.0
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for j, h in enumerate([new_p[i]] + historical_p[i]):
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gamma2 = VAR_PER_CONTEST if j > 0 else 0
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h_var = get_var(times_ranked[i] + 1 - j)
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k = h_var / (h_var + gamma2)
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w = w_prev * k**2
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# Future optimization: If j is around 20, then w < 1e-3 and it is possible to break early.
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tanh_terms.append((h, sqrt(BETA2) * TANH_C, w))
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w_prev = w
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w_sum += w / BETA2
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w0 = 1.0 / get_var(times_ranked[i] + 1) - w_sum
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p0 = eval_tanhs(tanh_terms[1:], old_mean[i]) / w0 + old_mean[i]
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new_mean[i] = solve(tanh_terms, w0 * p0, lin_factor=w0)
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# Display a slightly lower rating to incentivize participation.
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# As times_ranked increases, new_rating converges to new_mean.
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new_rating = [
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max(1, round(m - (sqrt(get_var(t + 1)) - SD_LIM)))
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for m, t in zip(new_mean, times_ranked)
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]
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return new_rating, new_mean, new_p
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def rate_contest(contest):
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from judge.models import Rating, Profile
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from judge.models.profile import _get_basic_info
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rating_subquery = Rating.objects.filter(user=OuterRef("user"))
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rating_sorted = rating_subquery.order_by("-contest__end_time")
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users = (
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contest.users.order_by("is_disqualified", "-score", "cumtime", "tiebreaker")
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.annotate(
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submissions=Count("submission"),
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last_rating=Coalesce(
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Subquery(rating_sorted.values("rating")[:1]), RATING_INIT
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),
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last_mean=Coalesce(Subquery(rating_sorted.values("mean")[:1]), MEAN_INIT),
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times=Coalesce(
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Subquery(
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rating_subquery.order_by()
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.values("user_id")
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.annotate(count=Count("id"))
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.values("count")
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),
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0,
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),
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)
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.exclude(user_id__in=contest.rate_exclude.all())
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.filter(virtual=0)
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.values(
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"id",
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"user_id",
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"score",
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"cumtime",
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"tiebreaker",
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"last_rating",
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"last_mean",
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"times",
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)
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)
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if not contest.rate_all:
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users = users.filter(submissions__gt=0)
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if contest.rating_floor is not None:
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users = users.exclude(last_rating__lt=contest.rating_floor)
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if contest.rating_ceiling is not None:
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users = users.exclude(last_rating__gt=contest.rating_ceiling)
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users = list(users)
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participation_ids = list(map(itemgetter("id"), users))
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user_ids = list(map(itemgetter("user_id"), users))
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ranking = list(tie_ranker(users, key=itemgetter("score", "cumtime", "tiebreaker")))
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old_mean = list(map(itemgetter("last_mean"), users))
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times_ranked = list(map(itemgetter("times"), users))
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historical_p = [[] for _ in users]
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user_id_to_idx = {uid: i for i, uid in enumerate(user_ids)}
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for h in (
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Rating.objects.filter(user_id__in=user_ids)
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.order_by("-contest__end_time")
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.values("user_id", "performance")
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):
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idx = user_id_to_idx[h["user_id"]]
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historical_p[idx].append(h["performance"])
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rating, mean, performance = recalculate_ratings(
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ranking, old_mean, times_ranked, historical_p
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)
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now = timezone.now()
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ratings = [
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Rating(
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user_id=i,
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contest=contest,
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rating=r,
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mean=m,
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performance=perf,
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last_rated=now,
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participation_id=pid,
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rank=z,
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)
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for i, pid, r, m, perf, z in zip(
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user_ids, participation_ids, rating, mean, performance, ranking
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)
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]
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with transaction.atomic():
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Rating.objects.bulk_create(ratings)
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Profile.objects.filter(
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contest_history__contest=contest, contest_history__virtual=0
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).update(
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rating=Subquery(
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Rating.objects.filter(user=OuterRef("id"))
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.order_by("-contest__end_time")
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.values("rating")[:1]
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)
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)
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_get_basic_info.dirty_multi([(uid,) for uid in user_ids])
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RATING_LEVELS = [
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"Newbie",
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"Amateur",
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"Expert",
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"Candidate Master",
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"Master",
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"Grandmaster",
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"Target",
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]
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RATING_VALUES = [1000, 1400, 1700, 1900, 2100, 2400, 3000]
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RATING_CLASS = [
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"rate-newbie",
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"rate-amateur",
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"rate-specialist",
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"rate-expert",
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"rate-candidate-master",
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"rate-master",
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"rate-grandmaster",
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"rate-target",
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]
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def rating_level(rating):
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return bisect(RATING_VALUES, rating)
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def rating_name(rating):
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return RATING_LEVELS[rating_level(rating)]
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def rating_class(rating):
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return RATING_CLASS[rating_level(rating)]
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def rating_progress(rating):
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level = bisect(RATING_VALUES, rating)
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if level == len(RATING_VALUES):
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return 1.0
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prev = 0 if not level else RATING_VALUES[level - 1]
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next = RATING_VALUES[level]
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return (rating - prev + 0.0) / (next - prev)
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