Cross-repo recipe package system.

scripts/slave/recipe_modules/math_utils/api.py

-# Copyright 2015 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.
-
-"""General statistical or mathematical functions."""
-
-import math
-
-from recipe_engine import recipe_api
-
-
-class MathUtilsApi(recipe_api.RecipeApi):
-
-  @staticmethod
-  def truncated_mean(data_set, truncate_fraction):
-    """Calculates the truncated mean of a set of values.
-
-    Note that this isn't just the mean of the set of values with the highest
-    and lowest values discarded; the non-discarded values are also weighted
-    differently depending how many values are discarded.
-
-    Args:
-      data_set: Non-empty list of values.
-      truncate_fraction: How much of the upper and lower portions of the data
-          set to discard, expressed as a value in [0, 0.5).
-
-    Returns:
-      The truncated mean as a float.
-
-    Raises:
-      TypeError: The data set was empty after discarding values.
-    """
-    if truncate_fraction >= 0.5:
-      raise ValueError('Trying to truncate %d percent of the list.' %
-                       (200 * truncate_fraction))
-    if len(data_set) > 2:
-      data_set = sorted(data_set)
-
-      discard_num_float = len(data_set) * truncate_fraction
-      discard_num_int = int(math.floor(discard_num_float))
-      kept_weight = len(data_set) - discard_num_float * 2
-
-      data_set = data_set[discard_num_int:len(data_set)-discard_num_int]
-
-      weight_left = 1.0 - (discard_num_float - discard_num_int)
-
-      if weight_left < 1:
-        # If the % to discard leaves a fractional portion, need to weight those
-        # values.
-        unweighted_vals = data_set[1:len(data_set)-1]
-        weighted_vals = [data_set[0], data_set[len(data_set)-1]]
-        weighted_vals = [w * weight_left for w in weighted_vals]
-        data_set = weighted_vals + unweighted_vals
-    else:
-      kept_weight = len(data_set)
-
-    _truncated_mean = reduce(lambda x, y: float(x) + float(y),
-                             data_set) / kept_weight
-    return _truncated_mean
-
-  @staticmethod
-  def mean(values):
-    """Calculates the arithmetic mean of a list of values."""
-    return MathUtilsApi.truncated_mean(values, 0.0)
-
-  @staticmethod
-  def variance(values):
-    """Calculates the sample variance."""
-    if len(values) == 1:
-      return 0.0
-    mean = MathUtilsApi.mean(values)
-    differences_from_mean = [float(x) - mean for x in values]
-    squared_differences = [float(x * x) for x in differences_from_mean]
-    _variance = sum(squared_differences) / (len(values) - 1)
-    return _variance
-
-  @staticmethod
-  def standard_deviation(values):
-    """Calculates the sample standard deviation of the given list of values."""
-    return math.sqrt(MathUtilsApi.variance(values))
-
-  @staticmethod
-  def relative_change(before, after):
-    """Returns the relative change of before and after, relative to before.
-
-    There are several different ways to define relative difference between
-    two numbers; sometimes it is defined as relative to the smaller number,
-    or to the mean of the two numbers. This version returns the difference
-    relative to the first of the two numbers.
-
-    Args:
-      before: A number representing an earlier value.
-      after: Another number, representing a later value.
-
-    Returns:
-      A non-negative floating point number; 0.1 represents a 10% change.
-    """
-    if before == after:
-      return 0.0
-    if before == 0:
-      return float('nan')
-    difference = after - before
-    return math.fabs(difference / before)
-
-  @staticmethod
-  def pooled_standard_error(work_sets):
-    """Calculates the pooled sample standard error for a set of samples.
-
-    Args:
-      work_sets: A collection of collections of numbers.
-
-    Returns:
-      Pooled sample standard error.
-    """
-    numerator = 0.0
-    denominator1 = 0.0
-    denominator2 = 0.0
-
-    for current_set in work_sets:
-      std_dev = MathUtilsApi.standard_deviation(current_set)
-      numerator += (len(current_set) - 1) * std_dev ** 2
-      denominator1 += len(current_set) - 1
-      if len(current_set) > 0:
-        denominator2 += 1.0 / len(current_set)
-
-    if denominator1 == 0:
-      return 0.0
-
-    return math.sqrt(numerator / denominator1) * math.sqrt(denominator2)
-
-  @staticmethod
-  def standard_error(values):
-    """Calculates the standard error of a list of values."""
-    if len(values) <= 1:
-      return 0.0
-    std_dev = MathUtilsApi.standard_deviation(values)
-    return std_dev / math.sqrt(len(values))
-
-  #Copied this from BisectResults
-  @staticmethod
-  def confidence_score(sample1, sample2,
-                       accept_single_bad_or_good=False):
-    """Calculates a confidence score.
-
-    This score is a percentage which represents our degree of confidence in the
-    proposition that the good results and bad results are distinct groups, and
-    their differences aren't due to chance alone.
-
-
-    Args:
-      sample1: A flat list of "good" result numbers.
-      sample2: A flat list of "bad" result numbers.
-      accept_single_bad_or_good: If True, computes confidence even if there is
-          just one bad or good revision, otherwise single good or bad revision
-          always returns 0.0 confidence. This flag will probably get away when
-          we will implement expanding the bisect range by one more revision for
-          such case.
-
-    Returns:
-      A number in the range [0, 100].
-    """
-    # If there's only one item in either list, this means only one revision was
-    # classified good or bad; this isn't good enough evidence to make a
-    # decision. If an empty list was passed, that also implies zero confidence.
-    if not accept_single_bad_or_good:
-      if len(sample1) <= 1 or len(sample2) <= 1:
-        return 0.0
-
-    # If there were only empty lists in either of the lists (this is unexpected
-    # and normally shouldn't happen), then we also want to return 0.
-    if not sample1 or not sample2:
-      return 0.0
-
-    # The p-value is approximately the probability of obtaining the given set
-    # of good and bad values just by chance.
-    _, _, p_value = MathUtilsApi.welchs_t_test(sample1, sample2)
-    return 100.0 * (1.0 - p_value)
-
-  @staticmethod
-  def welchs_t_test(sample1, sample2):
-    """Performs Welch's t-test on the two samples.
-
-    Welch's t-test is an adaptation of Student's t-test which is used when the
-    two samples may have unequal variances. It is also an independent two-sample
-    t-test.
-
-    Args:
-      sample1: A collection of numbers.
-      sample2: Another collection of numbers.
-
-    Returns:
-      A 3-tuple (t-statistic, degrees of freedom, p-value).
-    """
-    mean1 = MathUtilsApi.mean(sample1)
-    mean2 = MathUtilsApi.mean(sample2)
-    v1 = MathUtilsApi.variance(sample1)
-    v2 = MathUtilsApi.variance(sample2)
-    n1 = len(sample1)
-    n2 = len(sample2)
-    t = MathUtilsApi._t_value(mean1, mean2, v1, v2, n1, n2)
-    df = MathUtilsApi._degrees_of_freedom(v1, v2, n1, n2)
-    p = MathUtilsApi._lookup_p_value(t, df)
-    return t, df, p
-
-  @staticmethod
-  def _t_value(mean1, mean2, v1, v2, n1, n2):
-    """Calculates a t-statistic value using the formula for Welch's t-test.
-
-    The t value can be thought of as a signal-to-noise ratio; a higher t-value
-    tells you that the groups are more different.
-
-    Args:
-      mean1: Mean of sample 1.
-      mean2: Mean of sample 2.
-      v1: Variance of sample 1.
-      v2: Variance of sample 2.
-      n1: Sample size of sample 1.
-      n2: Sample size of sample 2.
-
-    Returns:
-      A t value, which may be negative or positive.
-    """
-    # If variance of both segments is zero, return some large t-value.
-    if v1 == 0 and v2 == 0:
-      return 1000.0
-    return (mean1 - mean2) / (math.sqrt(v1 / n1 + v2 / n2))
-
-  @staticmethod
-  def _degrees_of_freedom(v1, v2, n1, n2):
-    """Calculates degrees of freedom using the Welch-Satterthwaite formula.
-
-    Degrees of freedom is a measure of sample size. For other types of tests,
-    degrees of freedom is sometimes N - 1, where N is the sample size. However,
-
-    Args:
-      v1: Variance of sample 1.
-      v2: Variance of sample 2.
-      n1: Size of sample 2.
-      n2: Size of sample 2.
-
-    Returns:
-      An estimate of degrees of freedom. Must be at least 1.0.
-    """
-    # When there's no variance in either sample, return 1.
-    if v1 == 0 and v2 == 0:
-      return 1
-    # If the sample size is too small, also return the minimum (1).
-    if n1 <= 1 or n2 <= 2:
-      return 1
-    df = (((v1 / n1 + v2 / n2) ** 2) /
-          ((v1 ** 2) / ((n1 ** 2) * (n1 - 1)) +
-           (v2 ** 2) / ((n2 ** 2) * (n2 - 1))))
-    return max(1, df)
-
-  # Below is a hard-coded table for looking up p-values.
-  #
-  # Normally, p-values are calculated based on the t-distribution formula.
-  # Looking up pre-calculated values is a less accurate but less complicated
-  # alternative.
-  #
-  # Reference: http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
-
-  # A list of p-values for a two-tailed test. The entries correspond to to
-  # entries in the rows of the table below.
-  TWO_TAIL = [1, 0.20, 0.10, 0.05, 0.02, 0.01, 0.005, 0.002, 0.001]
-
-  # A map of degrees of freedom to lists of t-values. The index of the t-value
-  # can be used to look up the corresponding p-value.
-  TABLE = {
-      1: [0, 3.078, 6.314, 12.706, 31.820, 63.657, 127.321, 318.309, 636.619],
-      2: [0, 1.886, 2.920, 4.303, 6.965, 9.925, 14.089, 22.327, 31.599],
-      3: [0, 1.638, 2.353, 3.182, 4.541, 5.841, 7.453, 10.215, 12.924],
-      4: [0, 1.533, 2.132, 2.776, 3.747, 4.604, 5.598, 7.173, 8.610],
-      5: [0, 1.476, 2.015, 2.571, 3.365, 4.032, 4.773, 5.893, 6.869],
-      6: [0, 1.440, 1.943, 2.447, 3.143, 3.707, 4.317, 5.208, 5.959],
-      7: [0, 1.415, 1.895, 2.365, 2.998, 3.499, 4.029, 4.785, 5.408],
-      8: [0, 1.397, 1.860, 2.306, 2.897, 3.355, 3.833, 4.501, 5.041],
-      9: [0, 1.383, 1.833, 2.262, 2.821, 3.250, 3.690, 4.297, 4.781],
-      10: [0, 1.372, 1.812, 2.228, 2.764, 3.169, 3.581, 4.144, 4.587],
-      11: [0, 1.363, 1.796, 2.201, 2.718, 3.106, 3.497, 4.025, 4.437],
-      12: [0, 1.356, 1.782, 2.179, 2.681, 3.055, 3.428, 3.930, 4.318],
-      13: [0, 1.350, 1.771, 2.160, 2.650, 3.012, 3.372, 3.852, 4.221],
-      14: [0, 1.345, 1.761, 2.145, 2.625, 2.977, 3.326, 3.787, 4.140],
-      15: [0, 1.341, 1.753, 2.131, 2.602, 2.947, 3.286, 3.733, 4.073],
-      16: [0, 1.337, 1.746, 2.120, 2.584, 2.921, 3.252, 3.686, 4.015],
-      17: [0, 1.333, 1.740, 2.110, 2.567, 2.898, 3.222, 3.646, 3.965],
-      18: [0, 1.330, 1.734, 2.101, 2.552, 2.878, 3.197, 3.610, 3.922],
-      19: [0, 1.328, 1.729, 2.093, 2.539, 2.861, 3.174, 3.579, 3.883],
-      20: [0, 1.325, 1.725, 2.086, 2.528, 2.845, 3.153, 3.552, 3.850],
-      21: [0, 1.323, 1.721, 2.080, 2.518, 2.831, 3.135, 3.527, 3.819],
-      22: [0, 1.321, 1.717, 2.074, 2.508, 2.819, 3.119, 3.505, 3.792],
-      23: [0, 1.319, 1.714, 2.069, 2.500, 2.807, 3.104, 3.485, 3.768],
-      24: [0, 1.318, 1.711, 2.064, 2.492, 2.797, 3.090, 3.467, 3.745],
-      25: [0, 1.316, 1.708, 2.060, 2.485, 2.787, 3.078, 3.450, 3.725],
-      26: [0, 1.315, 1.706, 2.056, 2.479, 2.779, 3.067, 3.435, 3.707],
-      27: [0, 1.314, 1.703, 2.052, 2.473, 2.771, 3.057, 3.421, 3.690],
-      28: [0, 1.313, 1.701, 2.048, 2.467, 2.763, 3.047, 3.408, 3.674],
-      29: [0, 1.311, 1.699, 2.045, 2.462, 2.756, 3.038, 3.396, 3.659],
-      30: [0, 1.310, 1.697, 2.042, 2.457, 2.750, 3.030, 3.385, 3.646],
-      31: [0, 1.309, 1.695, 2.040, 2.453, 2.744, 3.022, 3.375, 3.633],
-      32: [0, 1.309, 1.694, 2.037, 2.449, 2.738, 3.015, 3.365, 3.622],
-      33: [0, 1.308, 1.692, 2.035, 2.445, 2.733, 3.008, 3.356, 3.611],
-      34: [0, 1.307, 1.691, 2.032, 2.441, 2.728, 3.002, 3.348, 3.601],
-      35: [0, 1.306, 1.690, 2.030, 2.438, 2.724, 2.996, 3.340, 3.591],
-      36: [0, 1.306, 1.688, 2.028, 2.434, 2.719, 2.991, 3.333, 3.582],
-      37: [0, 1.305, 1.687, 2.026, 2.431, 2.715, 2.985, 3.326, 3.574],
-      38: [0, 1.304, 1.686, 2.024, 2.429, 2.712, 2.980, 3.319, 3.566],
-      39: [0, 1.304, 1.685, 2.023, 2.426, 2.708, 2.976, 3.313, 3.558],
-      40: [0, 1.303, 1.684, 2.021, 2.423, 2.704, 2.971, 3.307, 3.551],
-      42: [0, 1.302, 1.682, 2.018, 2.418, 2.698, 2.963, 3.296, 3.538],
-      44: [0, 1.301, 1.680, 2.015, 2.414, 2.692, 2.956, 3.286, 3.526],
-      46: [0, 1.300, 1.679, 2.013, 2.410, 2.687, 2.949, 3.277, 3.515],
-      48: [0, 1.299, 1.677, 2.011, 2.407, 2.682, 2.943, 3.269, 3.505],
-      50: [0, 1.299, 1.676, 2.009, 2.403, 2.678, 2.937, 3.261, 3.496],
-      60: [0, 1.296, 1.671, 2.000, 2.390, 2.660, 2.915, 3.232, 3.460],
-      70: [0, 1.294, 1.667, 1.994, 2.381, 2.648, 2.899, 3.211, 3.435],
-      80: [0, 1.292, 1.664, 1.990, 2.374, 2.639, 2.887, 3.195, 3.416],
-      90: [0, 1.291, 1.662, 1.987, 2.369, 2.632, 2.878, 3.183, 3.402],
-      100: [0, 1.290, 1.660, 1.984, 2.364, 2.626, 2.871, 3.174, 3.391],
-      120: [0, 1.289, 1.658, 1.980, 2.358, 2.617, 2.860, 3.160, 3.373],
-      150: [0, 1.287, 1.655, 1.976, 2.351, 2.609, 2.849, 3.145, 3.357],
-      200: [0, 1.286, 1.652, 1.972, 2.345, 2.601, 2.839, 3.131, 3.340],
-      300: [0, 1.284, 1.650, 1.968, 2.339, 2.592, 2.828, 3.118, 3.323],
-      500: [0, 1.283, 1.648, 1.965, 2.334, 2.586, 2.820, 3.107, 3.310],
-  }
-
-  @staticmethod
-  def _lookup_p_value(t, df):
-    """Looks up a p-value in a t-distribution table.
-
-    Args:
-      t: A t statistic value; the result of a t-test.
-      df: Number of degrees of freedom.
-
-    Returns:
-      A p-value, which represents the likelihood of obtaining a result at least
-      as extreme as the one observed just by chance (the null hypothesis).
-    """
-    assert df >= 1, 'Degrees of freedom must be positive'
-
-    # We ignore the negative sign on the t-value because our null hypothesis
-    # is that the two samples are the same; our alternative hypothesis is that
-    # the second sample is lesser OR greater than the first.
-    t = abs(t)
-
-    def greatest_smaller(nums, target):
-      """Returns the largest number that is <= the target number."""
-      lesser_equal = [n for n in nums if n <= target]
-      assert lesser_equal, 'No number in number list <= target.'
-      return max(lesser_equal)
-
-    df_key = greatest_smaller(MathUtilsApi.TABLE.keys(), df)
-    t_table_row = MathUtilsApi.TABLE[df_key]
-    approximate_t_value = greatest_smaller(t_table_row, t)
-    t_value_index = t_table_row.index(approximate_t_value)
-
-    return MathUtilsApi.TWO_TAIL[t_value_index]