[pinpoint] Move mann_whitney_u.py to models/

dashboard/dashboard/pinpoint/mann_whitney_u.py

-# Copyright 2016 The Chromium Authors. All rights reserved.
-# Use of this source code is governed by a BSD-style license that can be
-# found in the LICENSE file.
-
-"""Pure Python implementation of the Mann-Whitney U test.
-
-This code is adapted from SciPy:
-  https://github.com/scipy/scipy/blob/master/scipy/stats/stats.py
-Which is provided under a BSD-style license.
-
-There is also a JavaScript version in Catapult:
-  https://github.com/catapult-project/catapult/blob/master/tracing/third_party/mannwhitneyu/mannwhitneyu.js
-"""
-
-import itertools
-import math
-
-
-def MannWhitneyU(x, y):
-  """Computes the Mann-Whitney rank test on samples x and y.
-
-  The distribution of U is approximately normal for large samples. This
-  implementation uses the normal approximation, so it's recommended to have
-  sample sizes > 20.
-  """
-  n1 = len(x)
-  n2 = len(y)
-  ranked = _RankData(x + y)
-  rankx = ranked[0:n1]  # get the x-ranks
-  u1 = n1*n2 + n1*(n1+1)/2.0 - sum(rankx)  # calc U for x
-  u2 = n1*n2 - u1  # remainder is U for y
-  t = _TieCorrectionFactor(ranked)
-  if t == 0:
-    raise ValueError('All numbers are identical in mannwhitneyu')
-  sd = math.sqrt(t * n1 * n2 * (n1+n2+1) / 12.0)
-
-  mean_rank = n1*n2/2.0 + 0.5
-  big_u = max(u1, u2)
-
-  z = (big_u - mean_rank) / sd
-  return 2 * _NormSf(abs(z))
-
-
-def _RankData(a):
-  """Assigns ranks to data. Ties are given the mean of the ranks of the items.
-
-  This is called "fractional ranking":
-    https://en.wikipedia.org/wiki/Ranking
-  """
-  sorter = _ArgSortReverse(a)
-  ranked_min = [0] * len(sorter)
-  for i, j in reversed(list(enumerate(sorter))):
-    ranked_min[j] = i
-
-  sorter = _ArgSort(a)
-  ranked_max = [0] * len(sorter)
-  for i, j in enumerate(sorter):
-    ranked_max[j] = i
-
-  return [1 + (x+y)/2.0 for x, y in zip(ranked_min, ranked_max)]
-
-
-def _ArgSort(a):
-  """Returns the indices that would sort an array.
-
-  Ties are given indices in ordinal order."""
-  return sorted(range(len(a)), key=a.__getitem__)
-
-
-def _ArgSortReverse(a):
-  """Returns the indices that would sort an array.
-
-  Ties are given indices in reverse ordinal order."""
-  return list(reversed(sorted(range(len(a)), key=a.__getitem__, reverse=True)))
-
-
-def _TieCorrectionFactor(rankvals):
-  """Tie correction factor for ties in the Mann-Whitney U test."""
-  arr = sorted(rankvals)
-  cnt = [len(list(group)) for _, group in itertools.groupby(arr)]
-  size = len(arr)
-  if size < 2:
-    return 1.0
-  else:
-    return 1.0 - sum(x**3 - x for x in cnt) / float(size**3 - size)
-
-
-def _NormSf(x):
-  """Survival function of the standard normal distribution. (1 - cdf)"""
-  return (1 - math.erf(x/math.sqrt(2))) / 2