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The Mann-Whitney test can be used to compare samples taken from non-normal distributions, and so can more accurately reflect performance changes than a T-test. This patch does not remove t-tests from the benchmark reporting, it just supplements them by including the Mann-Whitney test result as well. Change-Id: I8d6631ebeba1422b832def5cd68537624f672fa0 Reviewed-on: http://gerrit.cloudera.org:8080/11194 Reviewed-by: Jim Apple <jbapple-impala@apache.org> Tested-by: Impala Public Jenkins <impala-public-jenkins@cloudera.com>
92 lines
3.2 KiB
Python
92 lines
3.2 KiB
Python
# Licensed to the Apache Software Foundation (ASF) under one
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# or more contributor license agreements. See the NOTICE file
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# distributed with this work for additional information
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# regarding copyright ownership. The ASF licenses this file
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# to you under the Apache License, Version 2.0 (the
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# "License"); you may not use this file except in compliance
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# with the License. You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing,
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# software distributed under the License is distributed on an
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# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
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# KIND, either express or implied. See the License for the
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# specific language governing permissions and limitations
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# under the License.
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#
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# Utility functions for calculating common mathematical measurements. Note that although
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# some of these functions are available in external python packages (ex. numpy), these
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# are simple enough that it is better to implement them ourselves to avoid extra
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# dependencies.
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import math
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import random
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import string
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def calculate_avg(values):
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return sum(values) / float(len(values))
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def calculate_stddev(values):
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"""Return the standard deviation of a numeric iterable."""
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avg = calculate_avg(values)
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return math.sqrt(calculate_avg([(val - avg)**2 for val in values]))
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def calculate_median(values):
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"""Return the median of a numeric iterable."""
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if all([v is None for v in values]): return None
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sorted_values = sorted(values)
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length = len(sorted_values)
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if length % 2 == 0:
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return (sorted_values[length / 2] + sorted_values[length / 2 - 1]) / 2
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else:
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return sorted_values[length / 2]
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def calculate_geomean(values):
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""" Calculates the geometric mean of the given collection of numerics """
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if len(values) > 0:
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product = 1.0
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exponent = 1.0 / len(values)
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for value in values:
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product *= value ** exponent
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return product
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def calculate_tval(avg, stddev, iters, ref_avg, ref_stddev, ref_iters):
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"""
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Calculates the t-test t value for the given result and refrence.
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Uses the Welch's t-test formula. For more information see:
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http://en.wikipedia.org/wiki/Student%27s_t-distribution#Table_of_selected_values
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http://en.wikipedia.org/wiki/Student's_t-test
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"""
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# SEM (standard error mean) = sqrt(var1/N1 + var2/N2)
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# t = (X1 - X2) / SEM
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sem = math.sqrt((math.pow(stddev, 2) / iters) + (math.pow(ref_stddev, 2) / ref_iters))
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return (avg - ref_avg) / sem
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def get_random_id(length):
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return ''.join(
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random.choice(string.ascii_uppercase + string.digits) for _ in range(length))
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def calculate_mwu(samples, ref_samples):
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"""
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Calculates the Mann-Whitney U Test Z value for the given samples and reference.
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"""
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tag_a = [(s, 'A') for s in samples]
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tab_b = [(s, 'B') for s in ref_samples]
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ab = tag_a + tab_b
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ab.sort()
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# Assume no ties
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u = 0
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count_b = 0
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for v in ab:
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if v[1] == 'A':
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u += count_b
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else:
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count_b += 1
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# u is normally distributed with the following mean and standard deviation:
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mean = len(samples) * len(ref_samples) / 2.0
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stddev = math.sqrt(len(samples) * len(ref_samples) * (1 + len(ab)) / 12.0)
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return (u - mean) / stddev
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