mirror of
https://github.com/titanscouting/tra-analysis.git
synced 2024-11-10 15:04:45 +00:00
261 lines
8.4 KiB
Python
261 lines
8.4 KiB
Python
|
# -*- coding: utf-8 -*-
|
||
|
|
"""
|
||
|
|
trueskill.mathematics
|
||
|
|
~~~~~~~~~~~~~~~~~~~~~
|
||
|
|
|
||
|
|
This module contains basic mathematics functions and objects for TrueSkill
|
||
|
|
algorithm. If you have not scipy, this module provides the fallback.
|
||
|
|
|
||
|
|
:copyright: (c) 2012-2016 by Heungsub Lee.
|
||
|
|
:license: BSD, see LICENSE for more details.
|
||
|
|
|
||
|
|
"""
|
||
|
|
from __future__ import absolute_import
|
||
|
|
|
||
|
|
import copy
|
||
|
|
import math
|
||
|
|
try:
|
||
|
|
from numbers import Number
|
||
|
|
except ImportError:
|
||
|
|
Number = (int, long, float, complex)
|
||
|
|
|
||
|
|
from six import iterkeys
|
||
|
|
|
||
|
|
|
||
|
|
__all__ = ['Gaussian', 'Matrix', 'inf']
|
||
|
|
|
||
|
|
|
||
|
|
inf = float('inf')
|
||
|
|
|
||
|
|
|
||
|
|
class Gaussian(object):
|
||
|
|
"""A model for the normal distribution."""
|
||
|
|
|
||
|
|
#: Precision, the inverse of the variance.
|
||
|
|
pi = 0
|
||
|
|
#: Precision adjusted mean, the precision multiplied by the mean.
|
||
|
|
tau = 0
|
||
|
|
|
||
|
|
def __init__(self, mu=None, sigma=None, pi=0, tau=0):
|
||
|
|
if mu is not None:
|
||
|
|
if sigma is None:
|
||
|
|
raise TypeError('sigma argument is needed')
|
||
|
|
elif sigma == 0:
|
||
|
|
raise ValueError('sigma**2 should be greater than 0')
|
||
|
|
pi = sigma ** -2
|
||
|
|
tau = pi * mu
|
||
|
|
self.pi = pi
|
||
|
|
self.tau = tau
|
||
|
|
|
||
|
|
@property
|
||
|
|
def mu(self):
|
||
|
|
"""A property which returns the mean."""
|
||
|
|
return self.pi and self.tau / self.pi
|
||
|
|
|
||
|
|
@property
|
||
|
|
def sigma(self):
|
||
|
|
"""A property which returns the the square root of the variance."""
|
||
|
|
return math.sqrt(1 / self.pi) if self.pi else inf
|
||
|
|
|
||
|
|
def __mul__(self, other):
|
||
|
|
pi, tau = self.pi + other.pi, self.tau + other.tau
|
||
|
|
return Gaussian(pi=pi, tau=tau)
|
||
|
|
|
||
|
|
def __truediv__(self, other):
|
||
|
|
pi, tau = self.pi - other.pi, self.tau - other.tau
|
||
|
|
return Gaussian(pi=pi, tau=tau)
|
||
|
|
|
||
|
|
__div__ = __truediv__ # for Python 2
|
||
|
|
|
||
|
|
def __eq__(self, other):
|
||
|
|
return self.pi == other.pi and self.tau == other.tau
|
||
|
|
|
||
|
|
def __lt__(self, other):
|
||
|
|
return self.mu < other.mu
|
||
|
|
|
||
|
|
def __le__(self, other):
|
||
|
|
return self.mu <= other.mu
|
||
|
|
|
||
|
|
def __gt__(self, other):
|
||
|
|
return self.mu > other.mu
|
||
|
|
|
||
|
|
def __ge__(self, other):
|
||
|
|
return self.mu >= other.mu
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return 'N(mu={:.3f}, sigma={:.3f})'.format(self.mu, self.sigma)
|
||
|
|
|
||
|
|
def _repr_latex_(self):
|
||
|
|
latex = r'\mathcal{{ N }}( {:.3f}, {:.3f}^2 )'.format(self.mu, self.sigma)
|
||
|
|
return '$%s$' % latex
|
||
|
|
|
||
|
|
|
||
|
|
class Matrix(list):
|
||
|
|
"""A model for matrix."""
|
||
|
|
|
||
|
|
def __init__(self, src, height=None, width=None):
|
||
|
|
if callable(src):
|
||
|
|
f, src = src, {}
|
||
|
|
size = [height, width]
|
||
|
|
if not height:
|
||
|
|
def set_height(height):
|
||
|
|
size[0] = height
|
||
|
|
size[0] = set_height
|
||
|
|
if not width:
|
||
|
|
def set_width(width):
|
||
|
|
size[1] = width
|
||
|
|
size[1] = set_width
|
||
|
|
try:
|
||
|
|
for (r, c), val in f(*size):
|
||
|
|
src[r, c] = val
|
||
|
|
except TypeError:
|
||
|
|
raise TypeError('A callable src must return an interable '
|
||
|
|
'which generates a tuple containing '
|
||
|
|
'coordinate and value')
|
||
|
|
height, width = tuple(size)
|
||
|
|
if height is None or width is None:
|
||
|
|
raise TypeError('A callable src must call set_height and '
|
||
|
|
'set_width if the size is non-deterministic')
|
||
|
|
if isinstance(src, list):
|
||
|
|
is_number = lambda x: isinstance(x, Number)
|
||
|
|
unique_col_sizes = set(map(len, src))
|
||
|
|
everything_are_number = filter(is_number, sum(src, []))
|
||
|
|
if len(unique_col_sizes) != 1 or not everything_are_number:
|
||
|
|
raise ValueError('src must be a rectangular array of numbers')
|
||
|
|
two_dimensional_array = src
|
||
|
|
elif isinstance(src, dict):
|
||
|
|
if not height or not width:
|
||
|
|
w = h = 0
|
||
|
|
for r, c in iterkeys(src):
|
||
|
|
if not height:
|
||
|
|
h = max(h, r + 1)
|
||
|
|
if not width:
|
||
|
|
w = max(w, c + 1)
|
||
|
|
if not height:
|
||
|
|
height = h
|
||
|
|
if not width:
|
||
|
|
width = w
|
||
|
|
two_dimensional_array = []
|
||
|
|
for r in range(height):
|
||
|
|
row = []
|
||
|
|
two_dimensional_array.append(row)
|
||
|
|
for c in range(width):
|
||
|
|
row.append(src.get((r, c), 0))
|
||
|
|
else:
|
||
|
|
raise TypeError('src must be a list or dict or callable')
|
||
|
|
super(Matrix, self).__init__(two_dimensional_array)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def height(self):
|
||
|
|
return len(self)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def width(self):
|
||
|
|
return len(self[0])
|
||
|
|
|
||
|
|
def transpose(self):
|
||
|
|
height, width = self.height, self.width
|
||
|
|
src = {}
|
||
|
|
for c in range(width):
|
||
|
|
for r in range(height):
|
||
|
|
src[c, r] = self[r][c]
|
||
|
|
return type(self)(src, height=width, width=height)
|
||
|
|
|
||
|
|
def minor(self, row_n, col_n):
|
||
|
|
height, width = self.height, self.width
|
||
|
|
if not (0 <= row_n < height):
|
||
|
|
raise ValueError('row_n should be between 0 and %d' % height)
|
||
|
|
elif not (0 <= col_n < width):
|
||
|
|
raise ValueError('col_n should be between 0 and %d' % width)
|
||
|
|
two_dimensional_array = []
|
||
|
|
for r in range(height):
|
||
|
|
if r == row_n:
|
||
|
|
continue
|
||
|
|
row = []
|
||
|
|
two_dimensional_array.append(row)
|
||
|
|
for c in range(width):
|
||
|
|
if c == col_n:
|
||
|
|
continue
|
||
|
|
row.append(self[r][c])
|
||
|
|
return type(self)(two_dimensional_array)
|
||
|
|
|
||
|
|
def determinant(self):
|
||
|
|
height, width = self.height, self.width
|
||
|
|
if height != width:
|
||
|
|
raise ValueError('Only square matrix can calculate a determinant')
|
||
|
|
tmp, rv = copy.deepcopy(self), 1.
|
||
|
|
for c in range(width - 1, 0, -1):
|
||
|
|
pivot, r = max((abs(tmp[r][c]), r) for r in range(c + 1))
|
||
|
|
pivot = tmp[r][c]
|
||
|
|
if not pivot:
|
||
|
|
return 0.
|
||
|
|
tmp[r], tmp[c] = tmp[c], tmp[r]
|
||
|
|
if r != c:
|
||
|
|
rv = -rv
|
||
|
|
rv *= pivot
|
||
|
|
fact = -1. / pivot
|
||
|
|
for r in range(c):
|
||
|
|
f = fact * tmp[r][c]
|
||
|
|
for x in range(c):
|
||
|
|
tmp[r][x] += f * tmp[c][x]
|
||
|
|
return rv * tmp[0][0]
|
||
|
|
|
||
|
|
def adjugate(self):
|
||
|
|
height, width = self.height, self.width
|
||
|
|
if height != width:
|
||
|
|
raise ValueError('Only square matrix can be adjugated')
|
||
|
|
if height == 2:
|
||
|
|
a, b = self[0][0], self[0][1]
|
||
|
|
c, d = self[1][0], self[1][1]
|
||
|
|
return type(self)([[d, -b], [-c, a]])
|
||
|
|
src = {}
|
||
|
|
for r in range(height):
|
||
|
|
for c in range(width):
|
||
|
|
sign = -1 if (r + c) % 2 else 1
|
||
|
|
src[r, c] = self.minor(r, c).determinant() * sign
|
||
|
|
return type(self)(src, height, width)
|
||
|
|
|
||
|
|
def inverse(self):
|
||
|
|
if self.height == self.width == 1:
|
||
|
|
return type(self)([[1. / self[0][0]]])
|
||
|
|
return (1. / self.determinant()) * self.adjugate()
|
||
|
|
|
||
|
|
def __add__(self, other):
|
||
|
|
height, width = self.height, self.width
|
||
|
|
if (height, width) != (other.height, other.width):
|
||
|
|
raise ValueError('Must be same size')
|
||
|
|
src = {}
|
||
|
|
for r in range(height):
|
||
|
|
for c in range(width):
|
||
|
|
src[r, c] = self[r][c] + other[r][c]
|
||
|
|
return type(self)(src, height, width)
|
||
|
|
|
||
|
|
def __mul__(self, other):
|
||
|
|
if self.width != other.height:
|
||
|
|
raise ValueError('Bad size')
|
||
|
|
height, width = self.height, other.width
|
||
|
|
src = {}
|
||
|
|
for r in range(height):
|
||
|
|
for c in range(width):
|
||
|
|
src[r, c] = sum(self[r][x] * other[x][c]
|
||
|
|
for x in range(self.width))
|
||
|
|
return type(self)(src, height, width)
|
||
|
|
|
||
|
|
def __rmul__(self, other):
|
||
|
|
if not isinstance(other, Number):
|
||
|
|
raise TypeError('The operand should be a number')
|
||
|
|
height, width = self.height, self.width
|
||
|
|
src = {}
|
||
|
|
for r in range(height):
|
||
|
|
for c in range(width):
|
||
|
|
src[r, c] = other * self[r][c]
|
||
|
|
return type(self)(src, height, width)
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return '{}({})'.format(type(self).__name__, super(Matrix, self).__repr__())
|
||
|
|
|
||
|
|
def _repr_latex_(self):
|
||
|
|
rows = [' && '.join(['%.3f' % cell for cell in row]) for row in self]
|
||
|
|
latex = r'\begin{matrix} %s \end{matrix}' % r'\\'.join(rows)
|
||
|
|
return '$%s$' % latex
|