Move statistical functions in bisect script to their own module.

tools/auto_bisect/math_utils.py

Index: tools/auto_bisect/math_utils.py
diff --git a/tools/auto_bisect/math_utils.py b/tools/auto_bisect/math_utils.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe94f53583bd255f7ecb07902ab114f863e4380e
--- /dev/null
+++ b/tools/auto_bisect/math_utils.py
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+# Copyright 2014 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
+
+
+def TruncatedMean(data_set, truncate_percent):
+  """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_percent: The % from the upper and lower portions of the data set
+        to discard, expressed as a value in [0, 1].
+
+  Returns:
+    The truncated mean as a float.
+
+  Raises:
+    TypeError: The data set was empty after discarding values.
+  """
+  if len(data_set) > 2:
+    data_set = sorted(data_set)
+
+    discard_num_float = len(data_set) * truncate_percent
+    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
+
+
+def Mean(values):
+  """Calculates the arithmetic mean of a list of values."""
+  return TruncatedMean(values, 0.0)
+
+
+def StandardDeviation(values):
+  """Calculates the sample standard deviation of the given list of values."""
+  if len(values) == 1:
+    return 0.0
+
+  mean = 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)
+  std_dev = math.sqrt(variance)
+
+  return std_dev
+
+
+def RelativeChange(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)
+
+
+def PooledStandardError(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 = StandardDeviation(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)
+
+
+# Redefining built-in 'StandardError'
+# pylint: disable=W0622
+def StandardError(values):
+  """Calculates the standard error of a list of values."""
+  if len(values) <= 1:
+    return 0.0
+  std_dev = StandardDeviation(values)
+  return std_dev / math.sqrt(len(values))