def coco_stats():
"""
http://stattrek.com/online-calculator/hypergeometric.aspx
CommandLine:
python -m mtgmonte.stats --exec-coco_stats --show
Example:
>>> # DISABLE_DOCTEST
>>> from mtgmonte.stats import * # NOQA
>>> result = coco_stats()
>>> print(result)
>>> ut.show_if_requested()
"""
import plottool as pt
from scipy.stats import hypergeom
N = pop_size = 60 # cards in deck # NOQA
K = num_success = 21 # number of creatures in deck # NOQA
n = sample_size = 6 # cards seen by coco # NOQA
# prob of at least that many hits
hypergeom
prb = hypergeom(N, K, n)
k = number_of_success = 1 # number of hits you want # NOQA
prb.pmf(k) # P(X = k)
#
prb.cdf(k) # P(X <= k)
1 - prb.cdf(k) # P(X > k)
(1 - prb.cdf(k)) + prb.pmf(k) # P(X >= k)
def prob_ge(k, prb=prb):
return (1 - prb.cdf(k)) + prb.pmf(k) # P(X >= k)
pt.ensure_pylab_qt4()
import numpy as np
k = np.arange(1, 3)
K_list = np.arange(15, 30)
label_list = [str(K_) + " creatures in deck" for K_ in K_list]
ydata_list = [prob_ge(k, prb=hypergeom(N, K_, n)) for K_ in K_list]
pt.multi_plot(
k,
ydata_list,
label_list=label_list,
title="probability of at least k hits with coco",
xlabel="k",
ylabel="prob",
num_xticks=len(k),
use_darkbackground=True,
)
def land_stats():
"""
http://stattrek.com/online-calculator/hypergeometric.aspx
CommandLine:
python -m mtgmonte.stats --exec-land_stats --show
Example:
>>> # DISABLE_DOCTEST
>>> from mtgmonte.stats import * # NOQA
>>> result = land_stats()
>>> print(result)
>>> ut.show_if_requested()
"""
import plottool as pt
from scipy.stats import hypergeom
N = pop_size = 60 # cards in deck # NOQA
# K = num_success = 25 # lands in deck # NOQA
n = sample_size = 6 # cards seen by coco # NOQA
# prob of at least that many hits
def prob_ge(k, prb):
return (1 - prb.cdf(k)) + prb.pmf(k) # P(X >= k)
pt.ensure_pylab_qt4()
N = deck_size = 60 # NOQA
land_range = (24, 27 + 1)
# N = deck_size = 40 # NOQA
# land_range = (15, 18 + 1)
xdata = range(0, 15) # turn
ydata_list = [[hypergeom(N, K, x + 7).expect() for x in xdata] for K in range(*land_range)]
spread_list = [[hypergeom(N, K, x + 7).std() for x in xdata] for K in range(*land_range)]
# spread_list = None
import numpy as np
label_list = ["%d lands" % (K,) for K in range(*land_range)]
pt.multi_plot(
xdata, ydata_list, spread_list=spread_list, label_list=label_list, num_xticks=15, num_yticks=13, fnum=1
)
min_lands_acceptable = np.minimum(np.array(xdata), [1, 2, 3, 4, 5, 6] + [6] * (len(xdata) - 6))
pt.multi_plot(
xdata,
[min_lands_acceptable, (np.array(xdata) ** 0.9) * 0.5 + 4],
label_list=["minimum ok", "maximum ok"],
num_xticks=15,
num_yticks=13,
fnum=1,
marker="o",
)
def ewma():
import plottool as pt
import ubelt as ub
import numpy as np
pt.qtensure()
# Investigate the span parameter
span = 20
alpha = 2 / (span + 1)
# how long does it take for the estimation to hit 0?
# (ie, it no longer cares about the initial 1?)
# about 93 iterations to get to 1e-4
# about 47 iterations to get to 1e-2
# about 24 iterations to get to 1e-1
# 20 iterations goes to .135
data = ([1] + [0] * 20 + [1] * 40 + [0] * 20 + [1] * 50 + [0] * 20 +
[1] * 60 + [0] * 20 + [1] * 165 + [0] * 20 + [0])
mave = []
iter_ = iter(data)
current = next(iter_)
mave += [current]
for x in iter_:
current = (alpha * x) + (1 - alpha) * current
mave += [current]
if False:
pt.figure(fnum=1, doclf=True)
pt.plot(data)
pt.plot(mave)
np.where(np.array(mave) < 1e-1)
import sympy as sym
# span, alpha, n = sym.symbols('span, alpha, n')
n = sym.symbols('n', integer=True, nonnegative=True, finite=True)
span = sym.symbols('span', integer=True, nonnegative=True, finite=True)
thresh = sym.symbols('thresh', real=True, nonnegative=True, finite=True)
# alpha = 2 / (span + 1)
a, b, c = sym.symbols('a, b, c', real=True, nonnegative=True, finite=True)
sym.solve(sym.Eq(b**a, c), a)
current = 1
x = 0
steps = []
for _ in range(10):
current = (alpha * x) + (1 - alpha) * current
steps.append(current)
alpha = sym.symbols('alpha', real=True, nonnegative=True, finite=True)
base = sym.symbols('base', real=True, finite=True)
alpha = 2 / (span + 1)
thresh_expr = (1 - alpha)**n
thresthresh_exprh_expr = base**n
n_expr = sym.ceiling(sym.log(thresh) / sym.log(1 - 2 / (span + 1)))
sym.pprint(sym.simplify(thresh_expr))
sym.pprint(sym.simplify(n_expr))
print(sym.latex(sym.simplify(n_expr)))
# def calc_n2(span, thresh):
# return np.log(thresh) / np.log(1 - 2 / (span + 1))
def calc_n(span, thresh):
return np.log(thresh) / np.log((span - 1) / (span + 1))
def calc_thresh_val(n, span):
alpha = 2 / (span + 1)
return (1 - alpha)**n
span = np.arange(2, 200)
n_frac = calc_n(span, thresh=.5)
n = np.ceil(n_frac)
calc_thresh_val(n, span)
pt.figure(fnum=1, doclf=True)
ydatas = ut.odict([('thresh=%f' % thresh,
np.ceil(calc_n(span, thresh=thresh)))
for thresh in [1e-3, .01, .1, .2, .3, .4, .5]])
pt.multi_plot(
span,
ydatas,
xlabel='span',
ylabel='n iters to acheive thresh',
marker='',
# num_xticks=len(span),
fnum=1)
pt.gca().set_aspect('equal')
def both_sides(eqn, func):
return sym.Eq(func(eqn.lhs), func(eqn.rhs))
eqn = sym.Eq(thresh_expr, thresh)
n_expr = sym.solve(eqn,
n)[0].subs(base,
(1 - alpha)).subs(alpha, (2 / (span + 1)))
eqn = both_sides(eqn, lambda x: sym.log(x, (1 - alpha)))
lhs = eqn.lhs
from sympy.solvers.inequalities import solve_univariate_inequality
def eval_expr(span_value, n_value):
return np.array(
[thresh_expr.subs(span, span_value).subs(n, n_) for n_ in n_value],
dtype=np.float)
eval_expr(20, np.arange(20))
def linear(x, a, b):
return a * x + b
def sigmoidal_4pl(x, a, b, c, d):
return d + (a - d) / (1 + (x / c)**b)
def exponential(x, a, b, c):
return a + b * np.exp(-c * x)
import scipy.optimize
# Determine how to choose span, such that you get to .01 from 1
# in n timesteps
thresh_to_span_to_n = []
thresh_to_n_to_span = []
for thresh_value in ub.ProgIter([.0001, .001, .01, .1, .2, .3, .4, .5]):
print('')
test_vals = sorted([2, 3, 4, 5, 6])
n_to_span = []
for n_value in ub.ProgIter(test_vals):
# In n iterations I want to choose a span that the expression go
# less than a threshold
constraint = thresh_expr.subs(n, n_value) < thresh_value
solution = solve_univariate_inequality(constraint, span)
try:
lowbound = np.ceil(float(solution.args[0].lhs))
highbound = np.floor(float(solution.args[1].rhs))
assert lowbound <= highbound
span_value = lowbound
except AttributeError:
span_value = np.floor(float(solution.rhs))
n_to_span.append((n_value, span_value))
# Given a threshold, find a minimum number of steps
# that brings you up to that threshold given a span
test_vals = sorted(set(list(range(2, 1000, 50)) + [2, 3, 4, 5, 6]))
span_to_n = []
for span_value in ub.ProgIter(test_vals):
constraint = thresh_expr.subs(span, span_value) < thresh_value
solution = solve_univariate_inequality(constraint, n)
n_value = solution.lhs
span_to_n.append((span_value, n_value))
thresh_to_n_to_span.append((thresh_value, n_to_span))
thresh_to_span_to_n.append((thresh_value, span_to_n))
thresh_to_params = []
for thresh_value, span_to_n in thresh_to_span_to_n:
xdata, ydata = [np.array(_, dtype=np.float) for _ in zip(*span_to_n)]
p0 = (1 / np.diff((ydata - ydata[0])[1:]).mean(), ydata[0])
func = linear
popt, pcov = scipy.optimize.curve_fit(func, xdata, ydata, p0)
# popt, pcov = scipy.optimize.curve_fit(exponential, xdata, ydata)
if False:
yhat = func(xdata, *popt)
pt.figure(fnum=1, doclf=True)
pt.plot(xdata, ydata, label='measured')
pt.plot(xdata, yhat, label='predicteed')
pt.legend()
# slope = np.diff(ydata).mean()
# pt.plot(d)
thresh_to_params.append((thresh_value, popt))
# pt.plt.plot(*zip(*thresh_to_slope), 'x-')
# for thresh_value=.01, we get a rough line with slop ~2.302,
# for thresh_value=.5, we get a line with slop ~34.66
# if we want to get to 0 in n timesteps, with a thresh_value of
# choose span=f(thresh_value) * (n + 2))
# f is some inverse exponential
# 0.0001, 460.551314197147
# 0.001, 345.413485647860,
# 0.01, 230.275657098573,
# 0.1, 115.137828549287,
# 0.2, 80.4778885203347,
# 0.3, 60.2031233261536,
# 0.4, 45.8179484913827,
# 0.5, 34.6599400289520
# Seems to be 4PL symetrical sigmoid
# f(x) = -66500.85 + (66515.88 - -66500.85) / (1 + (x/0.8604672)^0.001503716)
# f(x) = -66500.85 + (66515.88 - -66500.85)/(1 + (x/0.8604672)^0.001503716)
def f(x):
return -66500.85 + (66515.88 -
-66500.85) / (1 + (x / 0.8604672)**0.001503716)
# return (10000 * (-6.65 + (13.3015) / (1 + (x/0.86) ** 0.00150)))
# f(.5) * (n - 1)
# f(
solve_rational_inequalities(thresh_expr < .01, n)
def demo_refresh():
r"""
CommandLine:
python -m ibeis.algo.graph.refresh demo_refresh \
--num_pccs=40 --size=2 --show
Example:
>>> # ENABLE_DOCTEST
>>> from ibeis.algo.graph.refresh import * # NOQA
>>> demo_refresh()
>>> ut.show_if_requested()
"""
from ibeis.algo.graph import demo
demokw = ut.argparse_dict({'num_pccs': 50, 'size': 4})
refreshkw = ut.argparse_funckw(RefreshCriteria)
# make an inference object
infr = demo.demodata_infr(size_std=0, **demokw)
edges = list(infr.dummy_verif.find_candidate_edges(K=100))
scores = np.array(infr.dummy_verif.predict_edges(edges))
sortx = scores.argsort()[::-1]
edges = ut.take(edges, sortx)
scores = scores[sortx]
ys = infr.match_state_df(edges)[POSTV].values
y_remainsum = ys[::-1].cumsum()[::-1]
# Do oracle reviews and wait to converge
refresh = RefreshCriteria(**refreshkw)
xdata = []
pprob_any = []
rfrac_any = []
for count, (edge, y) in enumerate(zip(edges, ys)):
refresh.add(y, user_id='user:oracle')
rfrac_any.append(y_remainsum[count] / y_remainsum[0])
pprob_any.append(refresh.prob_any_remain())
xdata.append(count + 1)
if refresh.check():
break
xdata = xdata
ydatas = ut.odict([
('Est. probability any remain', pprob_any),
('Fraction remaining', rfrac_any),
])
ut.quit_if_noshow()
import plottool as pt
pt.qtensure()
from ibeis.scripts.thesis import TMP_RC
import matplotlib as mpl
mpl.rcParams.update(TMP_RC)
pt.multi_plot(
xdata, ydatas, xlabel='# manual reviews', rcParams=TMP_RC, marker='',
ylim=(0, 1), use_legend=False,
)
demokw = ut.map_keys({'num_pccs': '#PCC', 'size': 'PCC size'},
demokw)
thresh = refreshkw.pop('thresh')
refreshkw['span'] = refreshkw.pop('window')
pt.relative_text((.02, .58 + .0), ut.get_cfg_lbl(demokw, sep=' ')[1:],
valign='bottom')
pt.relative_text((.02, .68 + .0), ut.get_cfg_lbl(refreshkw, sep=' ')[1:],
valign='bottom')
legend = pt.gca().legend()
legend.get_frame().set_alpha(1.0)
pt.plt.plot([xdata[0], xdata[-1]], [thresh, thresh], 'g--', label='thresh')
def limited_power_toughness_histogram():
r"""
CommandLine:
python -m mtgmonte.stats --exec-limited_power_toughness_histogram --show
Example:
>>> # DISABLE_DOCTEST
>>> from mtgmonte.stats import * # NOQA
>>> result = limited_power_toughness_histogram()
>>> print(result)
>>> ut.show_if_requested()
"""
from mtgmonte import mtgobjs
from mtglib.gatherer_request import SearchRequest
from mtglib.card_extractor import CardExtractor
# from mtglib.card_renderer import CardList
request = SearchRequest({"set": "Oath of the Gatewatch"})
def add_page(url, page):
parts = url.split("/")
part1 = "/".join(parts[:-1])
part2 = "/Default.aspx?page=%d&" % (page,)
part3 = parts[-1].replace("Default.aspx?", "")
url2 = part1 + part2 + part3
return url2
card_list = []
for page in range(0, 10):
url = request.url
url2 = add_page(url, page)
extract = CardExtractor(url2)
card_list0 = extract.cards
for card in card_list0:
card2 = mtgobjs.Card2()
card2.__dict__.update(card.__dict__)
card_list.append(card2)
if len(card_list0) != 100:
break
for c in card_list:
c.nice_attrs += ["rarity"]
creats = [_card2 for _card2 in card_list if "Creature" in card2.types]
creats = [_card2 for _card2 in creats if _card2.rarity in ["Common", "Uncommon"]]
powtough = []
for c in creats:
try:
powtough.append((int(c.power), int(c.toughness)))
except ValueError:
pass
import plottool as pt
pt.ensure_pylab_qt4()
import numpy as np
scores_list = np.array(list(zip(*powtough)))
xdata = np.arange(0, np.max(scores_list) + 1)
powhist = np.histogram(scores_list[0], bins=xdata)[0]
toughist = np.histogram(scores_list[1], bins=xdata)[0]
pt.multi_plot(xdata, [powhist, toughist], label_list=["power", "toughness"], kind="bar")
bothhist = ut.dict_hist(powtough)
xdata = np.arange(len(bothhist))
dat = sorted(bothhist.items())
xticklabels = ut.take_column(dat, 0)
ydata = ut.take_column(dat, 1)
pt.multi_plot(xdata, [ydata], xticklabels=xticklabels, kind="bar")