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