| # 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)) |