mirror of
https://github.com/titanscouting/tra-analysis.git
synced 2024-11-10 15:04:45 +00:00
136 lines
3.7 KiB
Python
136 lines
3.7 KiB
Python
# -*- coding: utf-8 -*-
|
|
"""
|
|
trueskill.backends
|
|
~~~~~~~~~~~~~~~~~~
|
|
|
|
Provides mathematical statistics backend chooser.
|
|
|
|
:copyright: (c) 2012-2016 by Heungsub Lee.
|
|
:license: BSD, see LICENSE for more details.
|
|
|
|
"""
|
|
from __future__ import absolute_import
|
|
|
|
import math
|
|
|
|
from six.moves import range
|
|
|
|
|
|
__all__ = ['available_backends', 'choose_backend', 'cdf', 'pdf', 'ppf']
|
|
|
|
|
|
def _gen_erfcinv(erfc, math=math):
|
|
"""Generates the inverse function of erfc by the given erfc function and
|
|
math module.
|
|
"""
|
|
def erfcinv(y):
|
|
"""The inverse function of erfc."""
|
|
if y >= 2:
|
|
return -100.
|
|
elif y <= 0:
|
|
return 100.
|
|
zero_point = y < 1
|
|
if not zero_point:
|
|
y = 2 - y
|
|
t = math.sqrt(-2 * math.log(y / 2.))
|
|
x = -0.70711 * \
|
|
((2.30753 + t * 0.27061) / (1. + t * (0.99229 + t * 0.04481)) - t)
|
|
for i in range(2):
|
|
err = erfc(x) - y
|
|
x += err / (1.12837916709551257 * math.exp(-(x ** 2)) - x * err)
|
|
return x if zero_point else -x
|
|
return erfcinv
|
|
|
|
|
|
def _gen_ppf(erfc, math=math):
|
|
"""ppf is the inverse function of cdf. This function generates cdf by the
|
|
given erfc and math module.
|
|
"""
|
|
erfcinv = _gen_erfcinv(erfc, math)
|
|
def ppf(x, mu=0, sigma=1):
|
|
"""The inverse function of cdf."""
|
|
return mu - sigma * math.sqrt(2) * erfcinv(2 * x)
|
|
return ppf
|
|
|
|
|
|
def erfc(x):
|
|
"""Complementary error function (via `http://bit.ly/zOLqbc`_)"""
|
|
z = abs(x)
|
|
t = 1. / (1. + z / 2.)
|
|
r = t * math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (
|
|
0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (
|
|
0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (
|
|
-0.82215223 + t * 0.17087277
|
|
)))
|
|
)))
|
|
)))
|
|
return 2. - r if x < 0 else r
|
|
|
|
|
|
def cdf(x, mu=0, sigma=1):
|
|
"""Cumulative distribution function"""
|
|
return 0.5 * erfc(-(x - mu) / (sigma * math.sqrt(2)))
|
|
|
|
|
|
def pdf(x, mu=0, sigma=1):
|
|
"""Probability density function"""
|
|
return (1 / math.sqrt(2 * math.pi) * abs(sigma) *
|
|
math.exp(-(((x - mu) / abs(sigma)) ** 2 / 2)))
|
|
|
|
|
|
ppf = _gen_ppf(erfc)
|
|
|
|
|
|
def choose_backend(backend):
|
|
"""Returns a tuple containing cdf, pdf, ppf from the chosen backend.
|
|
|
|
>>> cdf, pdf, ppf = choose_backend(None)
|
|
>>> cdf(-10)
|
|
7.619853263532764e-24
|
|
>>> cdf, pdf, ppf = choose_backend('mpmath')
|
|
>>> cdf(-10)
|
|
mpf('7.6198530241605255e-24')
|
|
|
|
.. versionadded:: 0.3
|
|
|
|
"""
|
|
if backend is None: # fallback
|
|
return cdf, pdf, ppf
|
|
elif backend == 'mpmath':
|
|
try:
|
|
import mpmath
|
|
except ImportError:
|
|
raise ImportError('Install "mpmath" to use this backend')
|
|
return mpmath.ncdf, mpmath.npdf, _gen_ppf(mpmath.erfc, math=mpmath)
|
|
elif backend == 'scipy':
|
|
try:
|
|
from scipy.stats import norm
|
|
except ImportError:
|
|
raise ImportError('Install "scipy" to use this backend')
|
|
return norm.cdf, norm.pdf, norm.ppf
|
|
raise ValueError('%r backend is not defined' % backend)
|
|
|
|
|
|
def available_backends():
|
|
"""Detects list of available backends. All of defined backends are
|
|
``None`` -- internal implementation, "mpmath", "scipy".
|
|
|
|
You can check if the backend is available in the current environment with
|
|
this function::
|
|
|
|
if 'mpmath' in available_backends():
|
|
# mpmath can be used in the current environment
|
|
setup(backend='mpmath')
|
|
|
|
.. versionadded:: 0.3
|
|
|
|
"""
|
|
backends = [None]
|
|
for backend in ['mpmath', 'scipy']:
|
|
try:
|
|
__import__(backend)
|
|
except ImportError:
|
|
continue
|
|
backends.append(backend)
|
|
return backends
|