Issue #18606: Add the new "statistics" module (PEP 450). Contributed
by Steven D'Aprano.
diff --git a/Doc/library/numeric.rst b/Doc/library/numeric.rst
index 2732a84..7c76a47 100644
--- a/Doc/library/numeric.rst
+++ b/Doc/library/numeric.rst
@@ -23,3 +23,4 @@
decimal.rst
fractions.rst
random.rst
+ statistics.rst
diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst
new file mode 100644
index 0000000..4f5b759
--- /dev/null
+++ b/Doc/library/statistics.rst
@@ -0,0 +1,463 @@
+:mod:`statistics` --- Mathematical statistics functions
+=======================================================
+
+.. module:: statistics
+ :synopsis: mathematical statistics functions
+.. moduleauthor:: Steven D'Aprano <steve+python@pearwood.info>
+.. sectionauthor:: Steven D'Aprano <steve+python@pearwood.info>
+
+.. versionadded:: 3.4
+
+.. testsetup:: *
+
+ from statistics import *
+ __name__ = '<doctest>'
+
+**Source code:** :source:`Lib/statistics.py`
+
+--------------
+
+This module provides functions for calculating mathematical statistics of
+numeric (:class:`Real`-valued) data.
+
+Averages and measures of central location
+-----------------------------------------
+
+These functions calculate an average or typical value from a population
+or sample.
+
+======================= =============================================
+:func:`mean` Arithmetic mean ("average") of data.
+:func:`median` Median (middle value) of data.
+:func:`median_low` Low median of data.
+:func:`median_high` High median of data.
+:func:`median_grouped` Median, or 50th percentile, of grouped data.
+:func:`mode` Mode (most common value) of discrete data.
+======================= =============================================
+
+:func:`mean`
+~~~~~~~~~~~~
+
+The :func:`mean` function calculates the arithmetic mean, commonly known
+as the average, of its iterable argument:
+
+.. function:: mean(data)
+
+ Return the sample arithmetic mean of *data*, a sequence or iterator
+ of real-valued numbers.
+
+ The arithmetic mean is the sum of the data divided by the number of
+ data points. It is commonly called "the average", although it is only
+ one of many different mathematical averages. It is a measure of the
+ central location of the data.
+
+ Some examples of use:
+
+ .. doctest::
+
+ >>> mean([1, 2, 3, 4, 4])
+ 2.8
+ >>> mean([-1.0, 2.5, 3.25, 5.75])
+ 2.625
+
+ >>> from fractions import Fraction as F
+ >>> mean([F(3, 7), F(1, 21), F(5, 3), F(1, 3)])
+ Fraction(13, 21)
+
+ >>> from decimal import Decimal as D
+ >>> mean([D("0.5"), D("0.75"), D("0.625"), D("0.375")])
+ Decimal('0.5625')
+
+ .. note::
+
+ The mean is strongly effected by outliers and is not a robust
+ estimator for central location: the mean is not necessarily a
+ typical example of the data points. For more robust, although less
+ efficient, measures of central location, see :func:`median` and
+ :func:`mode`. (In this case, "efficient" refers to statistical
+ efficiency rather than computational efficiency.)
+
+ The sample mean gives an unbiased estimate of the true population
+ mean, which means that, taken on average over all the possible
+ samples, ``mean(sample)`` converges on the true mean of the entire
+ population. If *data* represents the entire population rather than
+ a sample, then ``mean(data)`` is equivalent to calculating the true
+ population mean μ.
+
+ If ``data`` is empty, :exc:`StatisticsError` will be raised.
+
+:func:`median`
+~~~~~~~~~~~~~~
+
+The :func:`median` function calculates the median, or middle, data point,
+using the common "mean of middle two" method.
+
+ .. seealso::
+
+ :func:`median_low`
+
+ :func:`median_high`
+
+ :func:`median_grouped`
+
+.. function:: median(data)
+
+ Return the median (middle value) of numeric data.
+
+ The median is a robust measure of central location, and is less affected
+ by the presence of outliers in your data. When the number of data points
+ is odd, the middle data point is returned:
+
+ .. doctest::
+
+ >>> median([1, 3, 5])
+ 3
+
+ When the number of data points is even, the median is interpolated by
+ taking the average of the two middle values:
+
+ .. doctest::
+
+ >>> median([1, 3, 5, 7])
+ 4.0
+
+ This is suited for when your data is discrete, and you don't mind that
+ the median may not be an actual data point.
+
+ If data is empty, :exc:`StatisticsError` is raised.
+
+:func:`median_low`
+~~~~~~~~~~~~~~~~~~
+
+The :func:`median_low` function calculates the low median without
+interpolation.
+
+.. function:: median_low(data)
+
+ Return the low median of numeric data.
+
+ The low median is always a member of the data set. When the number
+ of data points is odd, the middle value is returned. When it is
+ even, the smaller of the two middle values is returned.
+
+ .. doctest::
+
+ >>> median_low([1, 3, 5])
+ 3
+ >>> median_low([1, 3, 5, 7])
+ 3
+
+ Use the low median when your data are discrete and you prefer the median
+ to be an actual data point rather than interpolated.
+
+ If data is empty, :exc:`StatisticsError` is raised.
+
+:func:`median_high`
+~~~~~~~~~~~~~~~~~~~
+
+The :func:`median_high` function calculates the high median without
+interpolation.
+
+.. function:: median_high(data)
+
+ Return the high median of data.
+
+ The high median is always a member of the data set. When the number of
+ data points is odd, the middle value is returned. When it is even, the
+ larger of the two middle values is returned.
+
+ .. doctest::
+
+ >>> median_high([1, 3, 5])
+ 3
+ >>> median_high([1, 3, 5, 7])
+ 5
+
+ Use the high median when your data are discrete and you prefer the median
+ to be an actual data point rather than interpolated.
+
+ If data is empty, :exc:`StatisticsError` is raised.
+
+:func:`median_grouped`
+~~~~~~~~~~~~~~~~~~~~~~
+
+The :func:`median_grouped` function calculates the median of grouped data
+as the 50th percentile, using interpolation.
+
+.. function:: median_grouped(data [, interval])
+
+ Return the median of grouped continuous data, calculated as the
+ 50th percentile.
+
+ .. doctest::
+
+ >>> median_grouped([52, 52, 53, 54])
+ 52.5
+
+ In the following example, the data are rounded, so that each value
+ represents the midpoint of data classes, e.g. 1 is the midpoint of the
+ class 0.5-1.5, 2 is the midpoint of 1.5-2.5, 3 is the midpoint of
+ 2.5-3.5, etc. With the data given, the middle value falls somewhere in
+ the class 3.5-4.5, and interpolation is used to estimate it:
+
+ .. doctest::
+
+ >>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
+ 3.7
+
+ Optional argument ``interval`` represents the class interval, and
+ defaults to 1. Changing the class interval naturally will change the
+ interpolation:
+
+ .. doctest::
+
+ >>> median_grouped([1, 3, 3, 5, 7], interval=1)
+ 3.25
+ >>> median_grouped([1, 3, 3, 5, 7], interval=2)
+ 3.5
+
+ This function does not check whether the data points are at least
+ ``interval`` apart.
+
+ .. impl-detail::
+
+ Under some circumstances, :func:`median_grouped` may coerce data
+ points to floats. This behaviour is likely to change in the future.
+
+ .. seealso::
+
+ * "Statistics for the Behavioral Sciences", Frederick J Gravetter
+ and Larry B Wallnau (8th Edition).
+
+ * Calculating the `median <http://www.ualberta.ca/~opscan/median.html>`_.
+
+ * The `SSMEDIAN <https://projects.gnome.org/gnumeric/doc/gnumeric-function-SSMEDIAN.shtml>`_
+ function in the Gnome Gnumeric spreadsheet, including
+ `this discussion <https://mail.gnome.org/archives/gnumeric-list/2011-April/msg00018.html>`_.
+
+ If data is empty, :exc:`StatisticsError` is raised.
+
+:func:`mode`
+~~~~~~~~~~~~
+
+The :func:`mode` function calculates the mode, or most common element, of
+discrete or nominal data. The mode (when it exists) is the most typical
+value, and is a robust measure of central location.
+
+.. function:: mode(data)
+
+ Return the most common data point from discrete or nominal data.
+
+ ``mode`` assumes discrete data, and returns a single value. This is the
+ standard treatment of the mode as commonly taught in schools:
+
+ .. doctest::
+
+ >>> mode([1, 1, 2, 3, 3, 3, 3, 4])
+ 3
+
+ The mode is unique in that it is the only statistic which also applies
+ to nominal (non-numeric) data:
+
+ .. doctest::
+
+ >>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
+ 'red'
+
+ If data is empty, or if there is not exactly one most common value,
+ :exc:`StatisticsError` is raised.
+
+Measures of spread
+------------------
+
+These functions calculate a measure of how much the population or sample
+tends to deviate from the typical or average values.
+
+======================= =============================================
+:func:`pstdev` Population standard deviation of data.
+:func:`pvariance` Population variance of data.
+:func:`stdev` Sample standard deviation of data.
+:func:`variance` Sample variance of data.
+======================= =============================================
+
+:func:`pstdev`
+~~~~~~~~~~~~~~
+
+The :func:`pstdev` function calculates the standard deviation of a
+population. The standard deviation is equivalent to the square root of
+the variance.
+
+.. function:: pstdev(data [, mu])
+
+ Return the square root of the population variance. See :func:`pvariance`
+ for arguments and other details.
+
+ .. doctest::
+
+ >>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
+ 0.986893273527251
+
+:func:`pvariance`
+~~~~~~~~~~~~~~~~~
+
+The :func:`pvariance` function calculates the variance of a population.
+Variance, or second moment about the mean, is a measure of the variability
+(spread or dispersion) of data. A large variance indicates that the data is
+spread out; a small variance indicates it is clustered closely around the
+mean.
+
+.. function:: pvariance(data [, mu])
+
+ Return the population variance of *data*, a non-empty iterable of
+ real-valued numbers.
+
+ If the optional second argument *mu* is given, it should be the mean
+ of *data*. If it is missing or None (the default), the mean is
+ automatically caclulated.
+
+ Use this function to calculate the variance from the entire population.
+ To estimate the variance from a sample, the :func:`variance` function is
+ usually a better choice.
+
+ Examples:
+
+ .. doctest::
+
+ >>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
+ >>> pvariance(data)
+ 1.25
+
+ If you have already calculated the mean of your data, you can pass
+ it as the optional second argument *mu* to avoid recalculation:
+
+ .. doctest::
+
+ >>> mu = mean(data)
+ >>> pvariance(data, mu)
+ 1.25
+
+ This function does not attempt to verify that you have passed the actual
+ mean as *mu*. Using arbitrary values for *mu* may lead to invalid or
+ impossible results.
+
+ Decimals and Fractions are supported:
+
+ .. doctest::
+
+ >>> from decimal import Decimal as D
+ >>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
+ Decimal('24.815')
+
+ >>> from fractions import Fraction as F
+ >>> pvariance([F(1, 4), F(5, 4), F(1, 2)])
+ Fraction(13, 72)
+
+ .. note::
+
+ When called with the entire population, this gives the population
+ variance σ². When called on a sample instead, this is the biased
+ sample variance s², also known as variance with N degrees of freedom.
+
+ If you somehow know the true population mean μ, you may use this
+ function to calculate the variance of a sample, giving the known
+ population mean as the second argument. Provided the data points are
+ representative (e.g. independent and identically distributed), the
+ result will be an unbiased estimate of the population variance.
+
+ Raises :exc:`StatisticsError` if *data* is empty.
+
+:func:`stdev`
+~~~~~~~~~~~~~~
+
+The :func:`stdev` function calculates the standard deviation of a sample.
+The standard deviation is equivalent to the square root of the variance.
+
+.. function:: stdev(data [, xbar])
+
+ Return the square root of the sample variance. See :func:`variance` for
+ arguments and other details.
+
+ .. doctest::
+
+ >>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
+ 1.0810874155219827
+
+:func:`variance`
+~~~~~~~~~~~~~~~~~
+
+The :func:`variance` function calculates the variance of a sample. Variance,
+or second moment about the mean, is a measure of the variability (spread or
+dispersion) of data. A large variance indicates that the data is spread out;
+a small variance indicates it is clustered closely around the mean.
+
+.. function:: variance(data [, xbar])
+
+ Return the sample variance of *data*, an iterable of at least two
+ real-valued numbers.
+
+ If the optional second argument *xbar* is given, it should be the mean
+ of *data*. If it is missing or None (the default), the mean is
+ automatically caclulated.
+
+ Use this function when your data is a sample from a population. To
+ calculate the variance from the entire population, see :func:`pvariance`.
+
+ Examples:
+
+ .. doctest::
+
+ >>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
+ >>> variance(data)
+ 1.3720238095238095
+
+ If you have already calculated the mean of your data, you can pass
+ it as the optional second argument *xbar* to avoid recalculation:
+
+ .. doctest::
+
+ >>> m = mean(data)
+ >>> variance(data, m)
+ 1.3720238095238095
+
+ This function does not attempt to verify that you have passed the actual
+ mean as *xbar*. Using arbitrary values for *xbar* can lead to invalid or
+ impossible results.
+
+ Decimal and Fraction values are supported:
+
+ .. doctest::
+
+ >>> from decimal import Decimal as D
+ >>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
+ Decimal('31.01875')
+
+ >>> from fractions import Fraction as F
+ >>> variance([F(1, 6), F(1, 2), F(5, 3)])
+ Fraction(67, 108)
+
+ .. note::
+
+ This is the sample variance s² with Bessel's correction, also known
+ as variance with N-1 degrees of freedom. Provided that the data
+ points are representative (e.g. independent and identically
+ distributed), the result should be an unbiased estimate of the true
+ population variance.
+
+ If you somehow know the actual population mean μ you should pass it
+ to the :func:`pvariance` function as the *mu* parameter to get
+ the variance of a sample.
+
+ Raises :exc:`StatisticsError` if *data* has fewer than two values.
+
+Exceptions
+----------
+
+A single exception is defined:
+
+:exc:`StatisticsError`
+
+Subclass of :exc:`ValueError` for statistics-related exceptions.
+
+..
+ # This modelines must appear within the last ten lines of the file.
+ kate: indent-width 3; remove-trailing-space on; replace-tabs on; encoding utf-8;
diff --git a/Lib/statistics.py b/Lib/statistics.py
new file mode 100644
index 0000000..a18241b
--- /dev/null
+++ b/Lib/statistics.py
@@ -0,0 +1,612 @@
+## Module statistics.py
+##
+## Copyright (c) 2013 Steven D'Aprano <steve+python@pearwood.info>.
+##
+## Licensed under the Apache License, Version 2.0 (the "License");
+## you may not use this file except in compliance with the License.
+## You may obtain a copy of the License at
+##
+## http://www.apache.org/licenses/LICENSE-2.0
+##
+## Unless required by applicable law or agreed to in writing, software
+## distributed under the License is distributed on an "AS IS" BASIS,
+## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+## See the License for the specific language governing permissions and
+## limitations under the License.
+
+
+"""
+Basic statistics module.
+
+This module provides functions for calculating statistics of data, including
+averages, variance, and standard deviation.
+
+Calculating averages
+--------------------
+
+================== =============================================
+Function Description
+================== =============================================
+mean Arithmetic mean (average) of data.
+median Median (middle value) of data.
+median_low Low median of data.
+median_high High median of data.
+median_grouped Median, or 50th percentile, of grouped data.
+mode Mode (most common value) of data.
+================== =============================================
+
+Calculate the arithmetic mean ("the average") of data:
+
+>>> mean([-1.0, 2.5, 3.25, 5.75])
+2.625
+
+
+Calculate the standard median of discrete data:
+
+>>> median([2, 3, 4, 5])
+3.5
+
+
+Calculate the median, or 50th percentile, of data grouped into class intervals
+centred on the data values provided. E.g. if your data points are rounded to
+the nearest whole number:
+
+>>> median_grouped([2, 2, 3, 3, 3, 4]) #doctest: +ELLIPSIS
+2.8333333333...
+
+This should be interpreted in this way: you have two data points in the class
+interval 1.5-2.5, three data points in the class interval 2.5-3.5, and one in
+the class interval 3.5-4.5. The median of these data points is 2.8333...
+
+
+Calculating variability or spread
+---------------------------------
+
+================== =============================================
+Function Description
+================== =============================================
+pvariance Population variance of data.
+variance Sample variance of data.
+pstdev Population standard deviation of data.
+stdev Sample standard deviation of data.
+================== =============================================
+
+Calculate the standard deviation of sample data:
+
+>>> stdev([2.5, 3.25, 5.5, 11.25, 11.75]) #doctest: +ELLIPSIS
+4.38961843444...
+
+If you have previously calculated the mean, you can pass it as the optional
+second argument to the four "spread" functions to avoid recalculating it:
+
+>>> data = [1, 2, 2, 4, 4, 4, 5, 6]
+>>> mu = mean(data)
+>>> pvariance(data, mu)
+2.5
+
+
+Exceptions
+----------
+
+A single exception is defined: StatisticsError is a subclass of ValueError.
+
+"""
+
+__all__ = [ 'StatisticsError',
+ 'pstdev', 'pvariance', 'stdev', 'variance',
+ 'median', 'median_low', 'median_high', 'median_grouped',
+ 'mean', 'mode',
+ ]
+
+
+import collections
+import math
+import numbers
+import operator
+
+from fractions import Fraction
+from decimal import Decimal
+
+
+# === Exceptions ===
+
+class StatisticsError(ValueError):
+ pass
+
+
+# === Private utilities ===
+
+def _sum(data, start=0):
+ """_sum(data [, start]) -> value
+
+ Return a high-precision sum of the given numeric data. If optional
+ argument ``start`` is given, it is added to the total. If ``data`` is
+ empty, ``start`` (defaulting to 0) is returned.
+
+
+ Examples
+ --------
+
+ >>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75)
+ 11.0
+
+ Some sources of round-off error will be avoided:
+
+ >>> _sum([1e50, 1, -1e50] * 1000) # Built-in sum returns zero.
+ 1000.0
+
+ Fractions and Decimals are also supported:
+
+ >>> from fractions import Fraction as F
+ >>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])
+ Fraction(63, 20)
+
+ >>> from decimal import Decimal as D
+ >>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]
+ >>> _sum(data)
+ Decimal('0.6963')
+
+ """
+ n, d = _exact_ratio(start)
+ T = type(start)
+ partials = {d: n} # map {denominator: sum of numerators}
+ # Micro-optimizations.
+ coerce_types = _coerce_types
+ exact_ratio = _exact_ratio
+ partials_get = partials.get
+ # Add numerators for each denominator, and track the "current" type.
+ for x in data:
+ T = _coerce_types(T, type(x))
+ n, d = exact_ratio(x)
+ partials[d] = partials_get(d, 0) + n
+ if None in partials:
+ assert issubclass(T, (float, Decimal))
+ assert not math.isfinite(partials[None])
+ return T(partials[None])
+ total = Fraction()
+ for d, n in sorted(partials.items()):
+ total += Fraction(n, d)
+ if issubclass(T, int):
+ assert total.denominator == 1
+ return T(total.numerator)
+ if issubclass(T, Decimal):
+ return T(total.numerator)/total.denominator
+ return T(total)
+
+
+def _exact_ratio(x):
+ """Convert Real number x exactly to (numerator, denominator) pair.
+
+ >>> _exact_ratio(0.25)
+ (1, 4)
+
+ x is expected to be an int, Fraction, Decimal or float.
+ """
+ try:
+ try:
+ # int, Fraction
+ return (x.numerator, x.denominator)
+ except AttributeError:
+ # float
+ try:
+ return x.as_integer_ratio()
+ except AttributeError:
+ # Decimal
+ try:
+ return _decimal_to_ratio(x)
+ except AttributeError:
+ msg = "can't convert type '{}' to numerator/denominator"
+ raise TypeError(msg.format(type(x).__name__)) from None
+ except (OverflowError, ValueError):
+ # INF or NAN
+ if __debug__:
+ # Decimal signalling NANs cannot be converted to float :-(
+ if isinstance(x, Decimal):
+ assert not x.is_finite()
+ else:
+ assert not math.isfinite(x)
+ return (x, None)
+
+
+# FIXME This is faster than Fraction.from_decimal, but still too slow.
+def _decimal_to_ratio(d):
+ """Convert Decimal d to exact integer ratio (numerator, denominator).
+
+ >>> from decimal import Decimal
+ >>> _decimal_to_ratio(Decimal("2.6"))
+ (26, 10)
+
+ """
+ sign, digits, exp = d.as_tuple()
+ if exp in ('F', 'n', 'N'): # INF, NAN, sNAN
+ assert not d.is_finite()
+ raise ValueError
+ num = 0
+ for digit in digits:
+ num = num*10 + digit
+ if sign:
+ num = -num
+ den = 10**-exp
+ return (num, den)
+
+
+def _coerce_types(T1, T2):
+ """Coerce types T1 and T2 to a common type.
+
+ >>> _coerce_types(int, float)
+ <class 'float'>
+
+ Coercion is performed according to this table, where "N/A" means
+ that a TypeError exception is raised.
+
+ +----------+-----------+-----------+-----------+----------+
+ | | int | Fraction | Decimal | float |
+ +----------+-----------+-----------+-----------+----------+
+ | int | int | Fraction | Decimal | float |
+ | Fraction | Fraction | Fraction | N/A | float |
+ | Decimal | Decimal | N/A | Decimal | float |
+ | float | float | float | float | float |
+ +----------+-----------+-----------+-----------+----------+
+
+ Subclasses trump their parent class; two subclasses of the same
+ base class will be coerced to the second of the two.
+
+ """
+ # Get the common/fast cases out of the way first.
+ if T1 is T2: return T1
+ if T1 is int: return T2
+ if T2 is int: return T1
+ # Subclasses trump their parent class.
+ if issubclass(T2, T1): return T2
+ if issubclass(T1, T2): return T1
+ # Floats trump everything else.
+ if issubclass(T2, float): return T2
+ if issubclass(T1, float): return T1
+ # Subclasses of the same base class give priority to the second.
+ if T1.__base__ is T2.__base__: return T2
+ # Otherwise, just give up.
+ raise TypeError('cannot coerce types %r and %r' % (T1, T2))
+
+
+def _counts(data):
+ # Generate a table of sorted (value, frequency) pairs.
+ if data is None:
+ raise TypeError('None is not iterable')
+ table = collections.Counter(data).most_common()
+ if not table:
+ return table
+ # Extract the values with the highest frequency.
+ maxfreq = table[0][1]
+ for i in range(1, len(table)):
+ if table[i][1] != maxfreq:
+ table = table[:i]
+ break
+ return table
+
+
+# === Measures of central tendency (averages) ===
+
+def mean(data):
+ """Return the sample arithmetic mean of data.
+
+ >>> mean([1, 2, 3, 4, 4])
+ 2.8
+
+ >>> from fractions import Fraction as F
+ >>> mean([F(3, 7), F(1, 21), F(5, 3), F(1, 3)])
+ Fraction(13, 21)
+
+ >>> from decimal import Decimal as D
+ >>> mean([D("0.5"), D("0.75"), D("0.625"), D("0.375")])
+ Decimal('0.5625')
+
+ If ``data`` is empty, StatisticsError will be raised.
+ """
+ if iter(data) is data:
+ data = list(data)
+ n = len(data)
+ if n < 1:
+ raise StatisticsError('mean requires at least one data point')
+ return _sum(data)/n
+
+
+# FIXME: investigate ways to calculate medians without sorting? Quickselect?
+def median(data):
+ """Return the median (middle value) of numeric data.
+
+ When the number of data points is odd, return the middle data point.
+ When the number of data points is even, the median is interpolated by
+ taking the average of the two middle values:
+
+ >>> median([1, 3, 5])
+ 3
+ >>> median([1, 3, 5, 7])
+ 4.0
+
+ """
+ data = sorted(data)
+ n = len(data)
+ if n == 0:
+ raise StatisticsError("no median for empty data")
+ if n%2 == 1:
+ return data[n//2]
+ else:
+ i = n//2
+ return (data[i - 1] + data[i])/2
+
+
+def median_low(data):
+ """Return the low median of numeric data.
+
+ When the number of data points is odd, the middle value is returned.
+ When it is even, the smaller of the two middle values is returned.
+
+ >>> median_low([1, 3, 5])
+ 3
+ >>> median_low([1, 3, 5, 7])
+ 3
+
+ """
+ data = sorted(data)
+ n = len(data)
+ if n == 0:
+ raise StatisticsError("no median for empty data")
+ if n%2 == 1:
+ return data[n//2]
+ else:
+ return data[n//2 - 1]
+
+
+def median_high(data):
+ """Return the high median of data.
+
+ When the number of data points is odd, the middle value is returned.
+ When it is even, the larger of the two middle values is returned.
+
+ >>> median_high([1, 3, 5])
+ 3
+ >>> median_high([1, 3, 5, 7])
+ 5
+
+ """
+ data = sorted(data)
+ n = len(data)
+ if n == 0:
+ raise StatisticsError("no median for empty data")
+ return data[n//2]
+
+
+def median_grouped(data, interval=1):
+ """"Return the 50th percentile (median) of grouped continuous data.
+
+ >>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
+ 3.7
+ >>> median_grouped([52, 52, 53, 54])
+ 52.5
+
+ This calculates the median as the 50th percentile, and should be
+ used when your data is continuous and grouped. In the above example,
+ the values 1, 2, 3, etc. actually represent the midpoint of classes
+ 0.5-1.5, 1.5-2.5, 2.5-3.5, etc. The middle value falls somewhere in
+ class 3.5-4.5, and interpolation is used to estimate it.
+
+ Optional argument ``interval`` represents the class interval, and
+ defaults to 1. Changing the class interval naturally will change the
+ interpolated 50th percentile value:
+
+ >>> median_grouped([1, 3, 3, 5, 7], interval=1)
+ 3.25
+ >>> median_grouped([1, 3, 3, 5, 7], interval=2)
+ 3.5
+
+ This function does not check whether the data points are at least
+ ``interval`` apart.
+ """
+ data = sorted(data)
+ n = len(data)
+ if n == 0:
+ raise StatisticsError("no median for empty data")
+ elif n == 1:
+ return data[0]
+ # Find the value at the midpoint. Remember this corresponds to the
+ # centre of the class interval.
+ x = data[n//2]
+ for obj in (x, interval):
+ if isinstance(obj, (str, bytes)):
+ raise TypeError('expected number but got %r' % obj)
+ try:
+ L = x - interval/2 # The lower limit of the median interval.
+ except TypeError:
+ # Mixed type. For now we just coerce to float.
+ L = float(x) - float(interval)/2
+ cf = data.index(x) # Number of values below the median interval.
+ # FIXME The following line could be more efficient for big lists.
+ f = data.count(x) # Number of data points in the median interval.
+ return L + interval*(n/2 - cf)/f
+
+
+def mode(data):
+ """Return the most common data point from discrete or nominal data.
+
+ ``mode`` assumes discrete data, and returns a single value. This is the
+ standard treatment of the mode as commonly taught in schools:
+
+ >>> mode([1, 1, 2, 3, 3, 3, 3, 4])
+ 3
+
+ This also works with nominal (non-numeric) data:
+
+ >>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
+ 'red'
+
+ If there is not exactly one most common value, ``mode`` will raise
+ StatisticsError.
+ """
+ # Generate a table of sorted (value, frequency) pairs.
+ table = _counts(data)
+ if len(table) == 1:
+ return table[0][0]
+ elif table:
+ raise StatisticsError(
+ 'no unique mode; found %d equally common values' % len(table)
+ )
+ else:
+ raise StatisticsError('no mode for empty data')
+
+
+# === Measures of spread ===
+
+# See http://mathworld.wolfram.com/Variance.html
+# http://mathworld.wolfram.com/SampleVariance.html
+# http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
+#
+# Under no circumstances use the so-called "computational formula for
+# variance", as that is only suitable for hand calculations with a small
+# amount of low-precision data. It has terrible numeric properties.
+#
+# See a comparison of three computational methods here:
+# http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/
+
+def _ss(data, c=None):
+ """Return sum of square deviations of sequence data.
+
+ If ``c`` is None, the mean is calculated in one pass, and the deviations
+ from the mean are calculated in a second pass. Otherwise, deviations are
+ calculated from ``c`` as given. Use the second case with care, as it can
+ lead to garbage results.
+ """
+ if c is None:
+ c = mean(data)
+ ss = _sum((x-c)**2 for x in data)
+ # The following sum should mathematically equal zero, but due to rounding
+ # error may not.
+ ss -= _sum((x-c) for x in data)**2/len(data)
+ assert not ss < 0, 'negative sum of square deviations: %f' % ss
+ return ss
+
+
+def variance(data, xbar=None):
+ """Return the sample variance of data.
+
+ data should be an iterable of Real-valued numbers, with at least two
+ values. The optional argument xbar, if given, should be the mean of
+ the data. If it is missing or None, the mean is automatically calculated.
+
+ Use this function when your data is a sample from a population. To
+ calculate the variance from the entire population, see ``pvariance``.
+
+ Examples:
+
+ >>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
+ >>> variance(data)
+ 1.3720238095238095
+
+ If you have already calculated the mean of your data, you can pass it as
+ the optional second argument ``xbar`` to avoid recalculating it:
+
+ >>> m = mean(data)
+ >>> variance(data, m)
+ 1.3720238095238095
+
+ This function does not check that ``xbar`` is actually the mean of
+ ``data``. Giving arbitrary values for ``xbar`` may lead to invalid or
+ impossible results.
+
+ Decimals and Fractions are supported:
+
+ >>> from decimal import Decimal as D
+ >>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
+ Decimal('31.01875')
+
+ >>> from fractions import Fraction as F
+ >>> variance([F(1, 6), F(1, 2), F(5, 3)])
+ Fraction(67, 108)
+
+ """
+ if iter(data) is data:
+ data = list(data)
+ n = len(data)
+ if n < 2:
+ raise StatisticsError('variance requires at least two data points')
+ ss = _ss(data, xbar)
+ return ss/(n-1)
+
+
+def pvariance(data, mu=None):
+ """Return the population variance of ``data``.
+
+ data should be an iterable of Real-valued numbers, with at least one
+ value. The optional argument mu, if given, should be the mean of
+ the data. If it is missing or None, the mean is automatically calculated.
+
+ Use this function to calculate the variance from the entire population.
+ To estimate the variance from a sample, the ``variance`` function is
+ usually a better choice.
+
+ Examples:
+
+ >>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
+ >>> pvariance(data)
+ 1.25
+
+ If you have already calculated the mean of the data, you can pass it as
+ the optional second argument to avoid recalculating it:
+
+ >>> mu = mean(data)
+ >>> pvariance(data, mu)
+ 1.25
+
+ This function does not check that ``mu`` is actually the mean of ``data``.
+ Giving arbitrary values for ``mu`` may lead to invalid or impossible
+ results.
+
+ Decimals and Fractions are supported:
+
+ >>> from decimal import Decimal as D
+ >>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
+ Decimal('24.815')
+
+ >>> from fractions import Fraction as F
+ >>> pvariance([F(1, 4), F(5, 4), F(1, 2)])
+ Fraction(13, 72)
+
+ """
+ if iter(data) is data:
+ data = list(data)
+ n = len(data)
+ if n < 1:
+ raise StatisticsError('pvariance requires at least one data point')
+ ss = _ss(data, mu)
+ return ss/n
+
+
+def stdev(data, xbar=None):
+ """Return the square root of the sample variance.
+
+ See ``variance`` for arguments and other details.
+
+ >>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
+ 1.0810874155219827
+
+ """
+ var = variance(data, xbar)
+ try:
+ return var.sqrt()
+ except AttributeError:
+ return math.sqrt(var)
+
+
+def pstdev(data, mu=None):
+ """Return the square root of the population variance.
+
+ See ``pvariance`` for arguments and other details.
+
+ >>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
+ 0.986893273527251
+
+ """
+ var = pvariance(data, mu)
+ try:
+ return var.sqrt()
+ except AttributeError:
+ return math.sqrt(var)
diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
new file mode 100644
index 0000000..71b3654
--- /dev/null
+++ b/Lib/test/test_statistics.py
@@ -0,0 +1,1534 @@
+"""Test suite for statistics module, including helper NumericTestCase and
+approx_equal function.
+
+"""
+
+import collections
+import decimal
+import doctest
+import math
+import random
+import types
+import unittest
+
+from decimal import Decimal
+from fractions import Fraction
+
+
+# Module to be tested.
+import statistics
+
+
+# === Helper functions and class ===
+
+def _calc_errors(actual, expected):
+ """Return the absolute and relative errors between two numbers.
+
+ >>> _calc_errors(100, 75)
+ (25, 0.25)
+ >>> _calc_errors(100, 100)
+ (0, 0.0)
+
+ Returns the (absolute error, relative error) between the two arguments.
+ """
+ base = max(abs(actual), abs(expected))
+ abs_err = abs(actual - expected)
+ rel_err = abs_err/base if base else float('inf')
+ return (abs_err, rel_err)
+
+
+def approx_equal(x, y, tol=1e-12, rel=1e-7):
+ """approx_equal(x, y [, tol [, rel]]) => True|False
+
+ Return True if numbers x and y are approximately equal, to within some
+ margin of error, otherwise return False. Numbers which compare equal
+ will also compare approximately equal.
+
+ x is approximately equal to y if the difference between them is less than
+ an absolute error tol or a relative error rel, whichever is bigger.
+
+ If given, both tol and rel must be finite, non-negative numbers. If not
+ given, default values are tol=1e-12 and rel=1e-7.
+
+ >>> approx_equal(1.2589, 1.2587, tol=0.0003, rel=0)
+ True
+ >>> approx_equal(1.2589, 1.2587, tol=0.0001, rel=0)
+ False
+
+ Absolute error is defined as abs(x-y); if that is less than or equal to
+ tol, x and y are considered approximately equal.
+
+ Relative error is defined as abs((x-y)/x) or abs((x-y)/y), whichever is
+ smaller, provided x or y are not zero. If that figure is less than or
+ equal to rel, x and y are considered approximately equal.
+
+ Complex numbers are not directly supported. If you wish to compare to
+ complex numbers, extract their real and imaginary parts and compare them
+ individually.
+
+ NANs always compare unequal, even with themselves. Infinities compare
+ approximately equal if they have the same sign (both positive or both
+ negative). Infinities with different signs compare unequal; so do
+ comparisons of infinities with finite numbers.
+ """
+ if tol < 0 or rel < 0:
+ raise ValueError('error tolerances must be non-negative')
+ # NANs are never equal to anything, approximately or otherwise.
+ if math.isnan(x) or math.isnan(y):
+ return False
+ # Numbers which compare equal also compare approximately equal.
+ if x == y:
+ # This includes the case of two infinities with the same sign.
+ return True
+ if math.isinf(x) or math.isinf(y):
+ # This includes the case of two infinities of opposite sign, or
+ # one infinity and one finite number.
+ return False
+ # Two finite numbers.
+ actual_error = abs(x - y)
+ allowed_error = max(tol, rel*max(abs(x), abs(y)))
+ return actual_error <= allowed_error
+
+
+# This class exists only as somewhere to stick a docstring containing
+# doctests. The following docstring and tests were originally in a separate
+# module. Now that it has been merged in here, I need somewhere to hang the.
+# docstring. Ultimately, this class will die, and the information below will
+# either become redundant, or be moved into more appropriate places.
+class _DoNothing:
+ """
+ When doing numeric work, especially with floats, exact equality is often
+ not what you want. Due to round-off error, it is often a bad idea to try
+ to compare floats with equality. Instead the usual procedure is to test
+ them with some (hopefully small!) allowance for error.
+
+ The ``approx_equal`` function allows you to specify either an absolute
+ error tolerance, or a relative error, or both.
+
+ Absolute error tolerances are simple, but you need to know the magnitude
+ of the quantities being compared:
+
+ >>> approx_equal(12.345, 12.346, tol=1e-3)
+ True
+ >>> approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small.
+ False
+
+ Relative errors are more suitable when the values you are comparing can
+ vary in magnitude:
+
+ >>> approx_equal(12.345, 12.346, rel=1e-4)
+ True
+ >>> approx_equal(12.345e6, 12.346e6, rel=1e-4)
+ True
+
+ but a naive implementation of relative error testing can run into trouble
+ around zero.
+
+ If you supply both an absolute tolerance and a relative error, the
+ comparison succeeds if either individual test succeeds:
+
+ >>> approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4)
+ True
+
+ """
+ pass
+
+
+
+# We prefer this for testing numeric values that may not be exactly equal,
+# and avoid using TestCase.assertAlmostEqual, because it sucks :-)
+
+class NumericTestCase(unittest.TestCase):
+ """Unit test class for numeric work.
+
+ This subclasses TestCase. In addition to the standard method
+ ``TestCase.assertAlmostEqual``, ``assertApproxEqual`` is provided.
+ """
+ # By default, we expect exact equality, unless overridden.
+ tol = rel = 0
+
+ def assertApproxEqual(
+ self, first, second, tol=None, rel=None, msg=None
+ ):
+ """Test passes if ``first`` and ``second`` are approximately equal.
+
+ This test passes if ``first`` and ``second`` are equal to
+ within ``tol``, an absolute error, or ``rel``, a relative error.
+
+ If either ``tol`` or ``rel`` are None or not given, they default to
+ test attributes of the same name (by default, 0).
+
+ The objects may be either numbers, or sequences of numbers. Sequences
+ are tested element-by-element.
+
+ >>> class MyTest(NumericTestCase):
+ ... def test_number(self):
+ ... x = 1.0/6
+ ... y = sum([x]*6)
+ ... self.assertApproxEqual(y, 1.0, tol=1e-15)
+ ... def test_sequence(self):
+ ... a = [1.001, 1.001e-10, 1.001e10]
+ ... b = [1.0, 1e-10, 1e10]
+ ... self.assertApproxEqual(a, b, rel=1e-3)
+ ...
+ >>> import unittest
+ >>> from io import StringIO # Suppress test runner output.
+ >>> suite = unittest.TestLoader().loadTestsFromTestCase(MyTest)
+ >>> unittest.TextTestRunner(stream=StringIO()).run(suite)
+ <unittest.runner.TextTestResult run=2 errors=0 failures=0>
+
+ """
+ if tol is None:
+ tol = self.tol
+ if rel is None:
+ rel = self.rel
+ if (
+ isinstance(first, collections.Sequence) and
+ isinstance(second, collections.Sequence)
+ ):
+ check = self._check_approx_seq
+ else:
+ check = self._check_approx_num
+ check(first, second, tol, rel, msg)
+
+ def _check_approx_seq(self, first, second, tol, rel, msg):
+ if len(first) != len(second):
+ standardMsg = (
+ "sequences differ in length: %d items != %d items"
+ % (len(first), len(second))
+ )
+ msg = self._formatMessage(msg, standardMsg)
+ raise self.failureException(msg)
+ for i, (a,e) in enumerate(zip(first, second)):
+ self._check_approx_num(a, e, tol, rel, msg, i)
+
+ def _check_approx_num(self, first, second, tol, rel, msg, idx=None):
+ if approx_equal(first, second, tol, rel):
+ # Test passes. Return early, we are done.
+ return None
+ # Otherwise we failed.
+ standardMsg = self._make_std_err_msg(first, second, tol, rel, idx)
+ msg = self._formatMessage(msg, standardMsg)
+ raise self.failureException(msg)
+
+ @staticmethod
+ def _make_std_err_msg(first, second, tol, rel, idx):
+ # Create the standard error message for approx_equal failures.
+ assert first != second
+ template = (
+ ' %r != %r\n'
+ ' values differ by more than tol=%r and rel=%r\n'
+ ' -> absolute error = %r\n'
+ ' -> relative error = %r'
+ )
+ if idx is not None:
+ header = 'numeric sequences first differ at index %d.\n' % idx
+ template = header + template
+ # Calculate actual errors:
+ abs_err, rel_err = _calc_errors(first, second)
+ return template % (first, second, tol, rel, abs_err, rel_err)
+
+
+# ========================
+# === Test the helpers ===
+# ========================
+
+
+# --- Tests for approx_equal ---
+
+class ApproxEqualSymmetryTest(unittest.TestCase):
+ # Test symmetry of approx_equal.
+
+ def test_relative_symmetry(self):
+ # Check that approx_equal treats relative error symmetrically.
+ # (a-b)/a is usually not equal to (a-b)/b. Ensure that this
+ # doesn't matter.
+ #
+ # Note: the reason for this test is that an early version
+ # of approx_equal was not symmetric. A relative error test
+ # would pass, or fail, depending on which value was passed
+ # as the first argument.
+ #
+ args1 = [2456, 37.8, -12.45, Decimal('2.54'), Fraction(17, 54)]
+ args2 = [2459, 37.2, -12.41, Decimal('2.59'), Fraction(15, 54)]
+ assert len(args1) == len(args2)
+ for a, b in zip(args1, args2):
+ self.do_relative_symmetry(a, b)
+
+ def do_relative_symmetry(self, a, b):
+ a, b = min(a, b), max(a, b)
+ assert a < b
+ delta = b - a # The absolute difference between the values.
+ rel_err1, rel_err2 = abs(delta/a), abs(delta/b)
+ # Choose an error margin halfway between the two.
+ rel = (rel_err1 + rel_err2)/2
+ # Now see that values a and b compare approx equal regardless of
+ # which is given first.
+ self.assertTrue(approx_equal(a, b, tol=0, rel=rel))
+ self.assertTrue(approx_equal(b, a, tol=0, rel=rel))
+
+ def test_symmetry(self):
+ # Test that approx_equal(a, b) == approx_equal(b, a)
+ args = [-23, -2, 5, 107, 93568]
+ delta = 2
+ for x in args:
+ for type_ in (int, float, Decimal, Fraction):
+ x = type_(x)*100
+ y = x + delta
+ r = abs(delta/max(x, y))
+ # There are five cases to check:
+ # 1) actual error <= tol, <= rel
+ self.do_symmetry_test(x, y, tol=delta, rel=r)
+ self.do_symmetry_test(x, y, tol=delta+1, rel=2*r)
+ # 2) actual error > tol, > rel
+ self.do_symmetry_test(x, y, tol=delta-1, rel=r/2)
+ # 3) actual error <= tol, > rel
+ self.do_symmetry_test(x, y, tol=delta, rel=r/2)
+ # 4) actual error > tol, <= rel
+ self.do_symmetry_test(x, y, tol=delta-1, rel=r)
+ self.do_symmetry_test(x, y, tol=delta-1, rel=2*r)
+ # 5) exact equality test
+ self.do_symmetry_test(x, x, tol=0, rel=0)
+ self.do_symmetry_test(x, y, tol=0, rel=0)
+
+ def do_symmetry_test(self, a, b, tol, rel):
+ template = "approx_equal comparisons don't match for %r"
+ flag1 = approx_equal(a, b, tol, rel)
+ flag2 = approx_equal(b, a, tol, rel)
+ self.assertEqual(flag1, flag2, template.format((a, b, tol, rel)))
+
+
+class ApproxEqualExactTest(unittest.TestCase):
+ # Test the approx_equal function with exactly equal values.
+ # Equal values should compare as approximately equal.
+ # Test cases for exactly equal values, which should compare approx
+ # equal regardless of the error tolerances given.
+
+ def do_exactly_equal_test(self, x, tol, rel):
+ result = approx_equal(x, x, tol=tol, rel=rel)
+ self.assertTrue(result, 'equality failure for x=%r' % x)
+ result = approx_equal(-x, -x, tol=tol, rel=rel)
+ self.assertTrue(result, 'equality failure for x=%r' % -x)
+
+ def test_exactly_equal_ints(self):
+ # Test that equal int values are exactly equal.
+ for n in [42, 19740, 14974, 230, 1795, 700245, 36587]:
+ self.do_exactly_equal_test(n, 0, 0)
+
+ def test_exactly_equal_floats(self):
+ # Test that equal float values are exactly equal.
+ for x in [0.42, 1.9740, 1497.4, 23.0, 179.5, 70.0245, 36.587]:
+ self.do_exactly_equal_test(x, 0, 0)
+
+ def test_exactly_equal_fractions(self):
+ # Test that equal Fraction values are exactly equal.
+ F = Fraction
+ for f in [F(1, 2), F(0), F(5, 3), F(9, 7), F(35, 36), F(3, 7)]:
+ self.do_exactly_equal_test(f, 0, 0)
+
+ def test_exactly_equal_decimals(self):
+ # Test that equal Decimal values are exactly equal.
+ D = Decimal
+ for d in map(D, "8.2 31.274 912.04 16.745 1.2047".split()):
+ self.do_exactly_equal_test(d, 0, 0)
+
+ def test_exactly_equal_absolute(self):
+ # Test that equal values are exactly equal with an absolute error.
+ for n in [16, 1013, 1372, 1198, 971, 4]:
+ # Test as ints.
+ self.do_exactly_equal_test(n, 0.01, 0)
+ # Test as floats.
+ self.do_exactly_equal_test(n/10, 0.01, 0)
+ # Test as Fractions.
+ f = Fraction(n, 1234)
+ self.do_exactly_equal_test(f, 0.01, 0)
+
+ def test_exactly_equal_absolute_decimals(self):
+ # Test equal Decimal values are exactly equal with an absolute error.
+ self.do_exactly_equal_test(Decimal("3.571"), Decimal("0.01"), 0)
+ self.do_exactly_equal_test(-Decimal("81.3971"), Decimal("0.01"), 0)
+
+ def test_exactly_equal_relative(self):
+ # Test that equal values are exactly equal with a relative error.
+ for x in [8347, 101.3, -7910.28, Fraction(5, 21)]:
+ self.do_exactly_equal_test(x, 0, 0.01)
+ self.do_exactly_equal_test(Decimal("11.68"), 0, Decimal("0.01"))
+
+ def test_exactly_equal_both(self):
+ # Test that equal values are equal when both tol and rel are given.
+ for x in [41017, 16.742, -813.02, Fraction(3, 8)]:
+ self.do_exactly_equal_test(x, 0.1, 0.01)
+ D = Decimal
+ self.do_exactly_equal_test(D("7.2"), D("0.1"), D("0.01"))
+
+
+class ApproxEqualUnequalTest(unittest.TestCase):
+ # Unequal values should compare unequal with zero error tolerances.
+ # Test cases for unequal values, with exact equality test.
+
+ def do_exactly_unequal_test(self, x):
+ for a in (x, -x):
+ result = approx_equal(a, a+1, tol=0, rel=0)
+ self.assertFalse(result, 'inequality failure for x=%r' % a)
+
+ def test_exactly_unequal_ints(self):
+ # Test unequal int values are unequal with zero error tolerance.
+ for n in [951, 572305, 478, 917, 17240]:
+ self.do_exactly_unequal_test(n)
+
+ def test_exactly_unequal_floats(self):
+ # Test unequal float values are unequal with zero error tolerance.
+ for x in [9.51, 5723.05, 47.8, 9.17, 17.24]:
+ self.do_exactly_unequal_test(x)
+
+ def test_exactly_unequal_fractions(self):
+ # Test that unequal Fractions are unequal with zero error tolerance.
+ F = Fraction
+ for f in [F(1, 5), F(7, 9), F(12, 11), F(101, 99023)]:
+ self.do_exactly_unequal_test(f)
+
+ def test_exactly_unequal_decimals(self):
+ # Test that unequal Decimals are unequal with zero error tolerance.
+ for d in map(Decimal, "3.1415 298.12 3.47 18.996 0.00245".split()):
+ self.do_exactly_unequal_test(d)
+
+
+class ApproxEqualInexactTest(unittest.TestCase):
+ # Inexact test cases for approx_error.
+ # Test cases when comparing two values that are not exactly equal.
+
+ # === Absolute error tests ===
+
+ def do_approx_equal_abs_test(self, x, delta):
+ template = "Test failure for x={!r}, y={!r}"
+ for y in (x + delta, x - delta):
+ msg = template.format(x, y)
+ self.assertTrue(approx_equal(x, y, tol=2*delta, rel=0), msg)
+ self.assertFalse(approx_equal(x, y, tol=delta/2, rel=0), msg)
+
+ def test_approx_equal_absolute_ints(self):
+ # Test approximate equality of ints with an absolute error.
+ for n in [-10737, -1975, -7, -2, 0, 1, 9, 37, 423, 9874, 23789110]:
+ self.do_approx_equal_abs_test(n, 10)
+ self.do_approx_equal_abs_test(n, 2)
+
+ def test_approx_equal_absolute_floats(self):
+ # Test approximate equality of floats with an absolute error.
+ for x in [-284.126, -97.1, -3.4, -2.15, 0.5, 1.0, 7.8, 4.23, 3817.4]:
+ self.do_approx_equal_abs_test(x, 1.5)
+ self.do_approx_equal_abs_test(x, 0.01)
+ self.do_approx_equal_abs_test(x, 0.0001)
+
+ def test_approx_equal_absolute_fractions(self):
+ # Test approximate equality of Fractions with an absolute error.
+ delta = Fraction(1, 29)
+ numerators = [-84, -15, -2, -1, 0, 1, 5, 17, 23, 34, 71]
+ for f in (Fraction(n, 29) for n in numerators):
+ self.do_approx_equal_abs_test(f, delta)
+ self.do_approx_equal_abs_test(f, float(delta))
+
+ def test_approx_equal_absolute_decimals(self):
+ # Test approximate equality of Decimals with an absolute error.
+ delta = Decimal("0.01")
+ for d in map(Decimal, "1.0 3.5 36.08 61.79 7912.3648".split()):
+ self.do_approx_equal_abs_test(d, delta)
+ self.do_approx_equal_abs_test(-d, delta)
+
+ def test_cross_zero(self):
+ # Test for the case of the two values having opposite signs.
+ self.assertTrue(approx_equal(1e-5, -1e-5, tol=1e-4, rel=0))
+
+ # === Relative error tests ===
+
+ def do_approx_equal_rel_test(self, x, delta):
+ template = "Test failure for x={!r}, y={!r}"
+ for y in (x*(1+delta), x*(1-delta)):
+ msg = template.format(x, y)
+ self.assertTrue(approx_equal(x, y, tol=0, rel=2*delta), msg)
+ self.assertFalse(approx_equal(x, y, tol=0, rel=delta/2), msg)
+
+ def test_approx_equal_relative_ints(self):
+ # Test approximate equality of ints with a relative error.
+ self.assertTrue(approx_equal(64, 47, tol=0, rel=0.36))
+ self.assertTrue(approx_equal(64, 47, tol=0, rel=0.37))
+ # ---
+ self.assertTrue(approx_equal(449, 512, tol=0, rel=0.125))
+ self.assertTrue(approx_equal(448, 512, tol=0, rel=0.125))
+ self.assertFalse(approx_equal(447, 512, tol=0, rel=0.125))
+
+ def test_approx_equal_relative_floats(self):
+ # Test approximate equality of floats with a relative error.
+ for x in [-178.34, -0.1, 0.1, 1.0, 36.97, 2847.136, 9145.074]:
+ self.do_approx_equal_rel_test(x, 0.02)
+ self.do_approx_equal_rel_test(x, 0.0001)
+
+ def test_approx_equal_relative_fractions(self):
+ # Test approximate equality of Fractions with a relative error.
+ F = Fraction
+ delta = Fraction(3, 8)
+ for f in [F(3, 84), F(17, 30), F(49, 50), F(92, 85)]:
+ for d in (delta, float(delta)):
+ self.do_approx_equal_rel_test(f, d)
+ self.do_approx_equal_rel_test(-f, d)
+
+ def test_approx_equal_relative_decimals(self):
+ # Test approximate equality of Decimals with a relative error.
+ for d in map(Decimal, "0.02 1.0 5.7 13.67 94.138 91027.9321".split()):
+ self.do_approx_equal_rel_test(d, Decimal("0.001"))
+ self.do_approx_equal_rel_test(-d, Decimal("0.05"))
+
+ # === Both absolute and relative error tests ===
+
+ # There are four cases to consider:
+ # 1) actual error <= both absolute and relative error
+ # 2) actual error <= absolute error but > relative error
+ # 3) actual error <= relative error but > absolute error
+ # 4) actual error > both absolute and relative error
+
+ def do_check_both(self, a, b, tol, rel, tol_flag, rel_flag):
+ check = self.assertTrue if tol_flag else self.assertFalse
+ check(approx_equal(a, b, tol=tol, rel=0))
+ check = self.assertTrue if rel_flag else self.assertFalse
+ check(approx_equal(a, b, tol=0, rel=rel))
+ check = self.assertTrue if (tol_flag or rel_flag) else self.assertFalse
+ check(approx_equal(a, b, tol=tol, rel=rel))
+
+ def test_approx_equal_both1(self):
+ # Test actual error <= both absolute and relative error.
+ self.do_check_both(7.955, 7.952, 0.004, 3.8e-4, True, True)
+ self.do_check_both(-7.387, -7.386, 0.002, 0.0002, True, True)
+
+ def test_approx_equal_both2(self):
+ # Test actual error <= absolute error but > relative error.
+ self.do_check_both(7.955, 7.952, 0.004, 3.7e-4, True, False)
+
+ def test_approx_equal_both3(self):
+ # Test actual error <= relative error but > absolute error.
+ self.do_check_both(7.955, 7.952, 0.001, 3.8e-4, False, True)
+
+ def test_approx_equal_both4(self):
+ # Test actual error > both absolute and relative error.
+ self.do_check_both(2.78, 2.75, 0.01, 0.001, False, False)
+ self.do_check_both(971.44, 971.47, 0.02, 3e-5, False, False)
+
+
+class ApproxEqualSpecialsTest(unittest.TestCase):
+ # Test approx_equal with NANs and INFs and zeroes.
+
+ def test_inf(self):
+ for type_ in (float, Decimal):
+ inf = type_('inf')
+ self.assertTrue(approx_equal(inf, inf))
+ self.assertTrue(approx_equal(inf, inf, 0, 0))
+ self.assertTrue(approx_equal(inf, inf, 1, 0.01))
+ self.assertTrue(approx_equal(-inf, -inf))
+ self.assertFalse(approx_equal(inf, -inf))
+ self.assertFalse(approx_equal(inf, 1000))
+
+ def test_nan(self):
+ for type_ in (float, Decimal):
+ nan = type_('nan')
+ for other in (nan, type_('inf'), 1000):
+ self.assertFalse(approx_equal(nan, other))
+
+ def test_float_zeroes(self):
+ nzero = math.copysign(0.0, -1)
+ self.assertTrue(approx_equal(nzero, 0.0, tol=0.1, rel=0.1))
+
+ def test_decimal_zeroes(self):
+ nzero = Decimal("-0.0")
+ self.assertTrue(approx_equal(nzero, Decimal(0), tol=0.1, rel=0.1))
+
+
+class TestApproxEqualErrors(unittest.TestCase):
+ # Test error conditions of approx_equal.
+
+ def test_bad_tol(self):
+ # Test negative tol raises.
+ self.assertRaises(ValueError, approx_equal, 100, 100, -1, 0.1)
+
+ def test_bad_rel(self):
+ # Test negative rel raises.
+ self.assertRaises(ValueError, approx_equal, 100, 100, 1, -0.1)
+
+
+# --- Tests for NumericTestCase ---
+
+# The formatting routine that generates the error messages is complex enough
+# that it too needs testing.
+
+class TestNumericTestCase(unittest.TestCase):
+ # The exact wording of NumericTestCase error messages is *not* guaranteed,
+ # but we need to give them some sort of test to ensure that they are
+ # generated correctly. As a compromise, we look for specific substrings
+ # that are expected to be found even if the overall error message changes.
+
+ def do_test(self, args):
+ actual_msg = NumericTestCase._make_std_err_msg(*args)
+ expected = self.generate_substrings(*args)
+ for substring in expected:
+ self.assertIn(substring, actual_msg)
+
+ def test_numerictestcase_is_testcase(self):
+ # Ensure that NumericTestCase actually is a TestCase.
+ self.assertTrue(issubclass(NumericTestCase, unittest.TestCase))
+
+ def test_error_msg_numeric(self):
+ # Test the error message generated for numeric comparisons.
+ args = (2.5, 4.0, 0.5, 0.25, None)
+ self.do_test(args)
+
+ def test_error_msg_sequence(self):
+ # Test the error message generated for sequence comparisons.
+ args = (3.75, 8.25, 1.25, 0.5, 7)
+ self.do_test(args)
+
+ def generate_substrings(self, first, second, tol, rel, idx):
+ """Return substrings we expect to see in error messages."""
+ abs_err, rel_err = _calc_errors(first, second)
+ substrings = [
+ 'tol=%r' % tol,
+ 'rel=%r' % rel,
+ 'absolute error = %r' % abs_err,
+ 'relative error = %r' % rel_err,
+ ]
+ if idx is not None:
+ substrings.append('differ at index %d' % idx)
+ return substrings
+
+
+# =======================================
+# === Tests for the statistics module ===
+# =======================================
+
+
+class GlobalsTest(unittest.TestCase):
+ module = statistics
+ expected_metadata = ["__doc__", "__all__"]
+
+ def test_meta(self):
+ # Test for the existence of metadata.
+ for meta in self.expected_metadata:
+ self.assertTrue(hasattr(self.module, meta),
+ "%s not present" % meta)
+
+ def test_check_all(self):
+ # Check everything in __all__ exists and is public.
+ module = self.module
+ for name in module.__all__:
+ # No private names in __all__:
+ self.assertFalse(name.startswith("_"),
+ 'private name "%s" in __all__' % name)
+ # And anything in __all__ must exist:
+ self.assertTrue(hasattr(module, name),
+ 'missing name "%s" in __all__' % name)
+
+
+class DocTests(unittest.TestCase):
+ def test_doc_tests(self):
+ failed, tried = doctest.testmod(statistics)
+ self.assertGreater(tried, 0)
+ self.assertEqual(failed, 0)
+
+class StatisticsErrorTest(unittest.TestCase):
+ def test_has_exception(self):
+ errmsg = (
+ "Expected StatisticsError to be a ValueError, but got a"
+ " subclass of %r instead."
+ )
+ self.assertTrue(hasattr(statistics, 'StatisticsError'))
+ self.assertTrue(
+ issubclass(statistics.StatisticsError, ValueError),
+ errmsg % statistics.StatisticsError.__base__
+ )
+
+
+# === Tests for private utility functions ===
+
+class ExactRatioTest(unittest.TestCase):
+ # Test _exact_ratio utility.
+
+ def test_int(self):
+ for i in (-20, -3, 0, 5, 99, 10**20):
+ self.assertEqual(statistics._exact_ratio(i), (i, 1))
+
+ def test_fraction(self):
+ numerators = (-5, 1, 12, 38)
+ for n in numerators:
+ f = Fraction(n, 37)
+ self.assertEqual(statistics._exact_ratio(f), (n, 37))
+
+ def test_float(self):
+ self.assertEqual(statistics._exact_ratio(0.125), (1, 8))
+ self.assertEqual(statistics._exact_ratio(1.125), (9, 8))
+ data = [random.uniform(-100, 100) for _ in range(100)]
+ for x in data:
+ num, den = statistics._exact_ratio(x)
+ self.assertEqual(x, num/den)
+
+ def test_decimal(self):
+ D = Decimal
+ _exact_ratio = statistics._exact_ratio
+ self.assertEqual(_exact_ratio(D("0.125")), (125, 1000))
+ self.assertEqual(_exact_ratio(D("12.345")), (12345, 1000))
+ self.assertEqual(_exact_ratio(D("-1.98")), (-198, 100))
+
+
+class DecimalToRatioTest(unittest.TestCase):
+ # Test _decimal_to_ratio private function.
+
+ def testSpecialsRaise(self):
+ # Test that NANs and INFs raise ValueError.
+ # Non-special values are covered by _exact_ratio above.
+ for d in (Decimal('NAN'), Decimal('sNAN'), Decimal('INF')):
+ self.assertRaises(ValueError, statistics._decimal_to_ratio, d)
+
+
+
+# === Tests for public functions ===
+
+class UnivariateCommonMixin:
+ # Common tests for most univariate functions that take a data argument.
+
+ def test_no_args(self):
+ # Fail if given no arguments.
+ self.assertRaises(TypeError, self.func)
+
+ def test_empty_data(self):
+ # Fail when the data argument (first argument) is empty.
+ for empty in ([], (), iter([])):
+ self.assertRaises(statistics.StatisticsError, self.func, empty)
+
+ def prepare_data(self):
+ """Return int data for various tests."""
+ data = list(range(10))
+ while data == sorted(data):
+ random.shuffle(data)
+ return data
+
+ def test_no_inplace_modifications(self):
+ # Test that the function does not modify its input data.
+ data = self.prepare_data()
+ assert len(data) != 1 # Necessary to avoid infinite loop.
+ assert data != sorted(data)
+ saved = data[:]
+ assert data is not saved
+ _ = self.func(data)
+ self.assertListEqual(data, saved, "data has been modified")
+
+ def test_order_doesnt_matter(self):
+ # Test that the order of data points doesn't change the result.
+
+ # CAUTION: due to floating point rounding errors, the result actually
+ # may depend on the order. Consider this test representing an ideal.
+ # To avoid this test failing, only test with exact values such as ints
+ # or Fractions.
+ data = [1, 2, 3, 3, 3, 4, 5, 6]*100
+ expected = self.func(data)
+ random.shuffle(data)
+ actual = self.func(data)
+ self.assertEqual(expected, actual)
+
+ def test_type_of_data_collection(self):
+ # Test that the type of iterable data doesn't effect the result.
+ class MyList(list):
+ pass
+ class MyTuple(tuple):
+ pass
+ def generator(data):
+ return (obj for obj in data)
+ data = self.prepare_data()
+ expected = self.func(data)
+ for kind in (list, tuple, iter, MyList, MyTuple, generator):
+ result = self.func(kind(data))
+ self.assertEqual(result, expected)
+
+ def test_range_data(self):
+ # Test that functions work with range objects.
+ data = range(20, 50, 3)
+ expected = self.func(list(data))
+ self.assertEqual(self.func(data), expected)
+
+ def test_bad_arg_types(self):
+ # Test that function raises when given data of the wrong type.
+
+ # Don't roll the following into a loop like this:
+ # for bad in list_of_bad:
+ # self.check_for_type_error(bad)
+ #
+ # Since assertRaises doesn't show the arguments that caused the test
+ # failure, it is very difficult to debug these test failures when the
+ # following are in a loop.
+ self.check_for_type_error(None)
+ self.check_for_type_error(23)
+ self.check_for_type_error(42.0)
+ self.check_for_type_error(object())
+
+ def check_for_type_error(self, *args):
+ self.assertRaises(TypeError, self.func, *args)
+
+ def test_type_of_data_element(self):
+ # Check the type of data elements doesn't affect the numeric result.
+ # This is a weaker test than UnivariateTypeMixin.testTypesConserved,
+ # because it checks the numeric result by equality, but not by type.
+ class MyFloat(float):
+ def __truediv__(self, other):
+ return type(self)(super().__truediv__(other))
+ def __add__(self, other):
+ return type(self)(super().__add__(other))
+ __radd__ = __add__
+
+ raw = self.prepare_data()
+ expected = self.func(raw)
+ for kind in (float, MyFloat, Decimal, Fraction):
+ data = [kind(x) for x in raw]
+ result = type(expected)(self.func(data))
+ self.assertEqual(result, expected)
+
+
+class UnivariateTypeMixin:
+ """Mixin class for type-conserving functions.
+
+ This mixin class holds test(s) for functions which conserve the type of
+ individual data points. E.g. the mean of a list of Fractions should itself
+ be a Fraction.
+
+ Not all tests to do with types need go in this class. Only those that
+ rely on the function returning the same type as its input data.
+ """
+ def test_types_conserved(self):
+ # Test that functions keeps the same type as their data points.
+ # (Excludes mixed data types.) This only tests the type of the return
+ # result, not the value.
+ class MyFloat(float):
+ def __truediv__(self, other):
+ return type(self)(super().__truediv__(other))
+ def __sub__(self, other):
+ return type(self)(super().__sub__(other))
+ def __rsub__(self, other):
+ return type(self)(super().__rsub__(other))
+ def __pow__(self, other):
+ return type(self)(super().__pow__(other))
+ def __add__(self, other):
+ return type(self)(super().__add__(other))
+ __radd__ = __add__
+
+ data = self.prepare_data()
+ for kind in (float, Decimal, Fraction, MyFloat):
+ d = [kind(x) for x in data]
+ result = self.func(d)
+ self.assertIs(type(result), kind)
+
+
+class TestSum(NumericTestCase, UnivariateCommonMixin, UnivariateTypeMixin):
+ # Test cases for statistics._sum() function.
+
+ def setUp(self):
+ self.func = statistics._sum
+
+ def test_empty_data(self):
+ # Override test for empty data.
+ for data in ([], (), iter([])):
+ self.assertEqual(self.func(data), 0)
+ self.assertEqual(self.func(data, 23), 23)
+ self.assertEqual(self.func(data, 2.3), 2.3)
+
+ def test_ints(self):
+ self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]), 60)
+ self.assertEqual(self.func([4, 2, 3, -8, 7], 1000), 1008)
+
+ def test_floats(self):
+ self.assertEqual(self.func([0.25]*20), 5.0)
+ self.assertEqual(self.func([0.125, 0.25, 0.5, 0.75], 1.5), 3.125)
+
+ def test_fractions(self):
+ F = Fraction
+ self.assertEqual(self.func([Fraction(1, 1000)]*500), Fraction(1, 2))
+
+ def test_decimals(self):
+ D = Decimal
+ data = [D("0.001"), D("5.246"), D("1.702"), D("-0.025"),
+ D("3.974"), D("2.328"), D("4.617"), D("2.843"),
+ ]
+ self.assertEqual(self.func(data), Decimal("20.686"))
+
+ def test_compare_with_math_fsum(self):
+ # Compare with the math.fsum function.
+ # Ideally we ought to get the exact same result, but sometimes
+ # we differ by a very slight amount :-(
+ data = [random.uniform(-100, 1000) for _ in range(1000)]
+ self.assertApproxEqual(self.func(data), math.fsum(data), rel=2e-16)
+
+ def test_start_argument(self):
+ # Test that the optional start argument works correctly.
+ data = [random.uniform(1, 1000) for _ in range(100)]
+ t = self.func(data)
+ self.assertEqual(t+42, self.func(data, 42))
+ self.assertEqual(t-23, self.func(data, -23))
+ self.assertEqual(t+1e20, self.func(data, 1e20))
+
+ def test_strings_fail(self):
+ # Sum of strings should fail.
+ self.assertRaises(TypeError, self.func, [1, 2, 3], '999')
+ self.assertRaises(TypeError, self.func, [1, 2, 3, '999'])
+
+ def test_bytes_fail(self):
+ # Sum of bytes should fail.
+ self.assertRaises(TypeError, self.func, [1, 2, 3], b'999')
+ self.assertRaises(TypeError, self.func, [1, 2, 3, b'999'])
+
+ def test_mixed_sum(self):
+ # Mixed sums are allowed.
+
+ # Careful here: order matters. Can't mix Fraction and Decimal directly,
+ # only after they're converted to float.
+ data = [1, 2, Fraction(1, 2), 3.0, Decimal("0.25")]
+ self.assertEqual(self.func(data), 6.75)
+
+
+class SumInternalsTest(NumericTestCase):
+ # Test internals of the sum function.
+
+ def test_ignore_instance_float_method(self):
+ # Test that __float__ methods on data instances are ignored.
+
+ # Python typically calls __dunder__ methods on the class, not the
+ # instance. The ``sum`` implementation calls __float__ directly. To
+ # better match the behaviour of Python, we call it only on the class,
+ # not the instance. This test will fail if somebody "fixes" that code.
+
+ # Create a fake __float__ method.
+ def __float__(self):
+ raise AssertionError('test fails')
+
+ # Inject it into an instance.
+ class MyNumber(Fraction):
+ pass
+ x = MyNumber(3)
+ x.__float__ = types.MethodType(__float__, x)
+
+ # Check it works as expected.
+ self.assertRaises(AssertionError, x.__float__)
+ self.assertEqual(float(x), 3.0)
+ # And now test the function.
+ self.assertEqual(statistics._sum([1.0, 2.0, x, 4.0]), 10.0)
+
+
+class SumTortureTest(NumericTestCase):
+ def test_torture(self):
+ # Tim Peters' torture test for sum, and variants of same.
+ self.assertEqual(statistics._sum([1, 1e100, 1, -1e100]*10000), 20000.0)
+ self.assertEqual(statistics._sum([1e100, 1, 1, -1e100]*10000), 20000.0)
+ self.assertApproxEqual(
+ statistics._sum([1e-100, 1, 1e-100, -1]*10000), 2.0e-96, rel=5e-16
+ )
+
+
+class SumSpecialValues(NumericTestCase):
+ # Test that sum works correctly with IEEE-754 special values.
+
+ def test_nan(self):
+ for type_ in (float, Decimal):
+ nan = type_('nan')
+ result = statistics._sum([1, nan, 2])
+ self.assertIs(type(result), type_)
+ self.assertTrue(math.isnan(result))
+
+ def check_infinity(self, x, inf):
+ """Check x is an infinity of the same type and sign as inf."""
+ self.assertTrue(math.isinf(x))
+ self.assertIs(type(x), type(inf))
+ self.assertEqual(x > 0, inf > 0)
+ assert x == inf
+
+ def do_test_inf(self, inf):
+ # Adding a single infinity gives infinity.
+ result = statistics._sum([1, 2, inf, 3])
+ self.check_infinity(result, inf)
+ # Adding two infinities of the same sign also gives infinity.
+ result = statistics._sum([1, 2, inf, 3, inf, 4])
+ self.check_infinity(result, inf)
+
+ def test_float_inf(self):
+ inf = float('inf')
+ for sign in (+1, -1):
+ self.do_test_inf(sign*inf)
+
+ def test_decimal_inf(self):
+ inf = Decimal('inf')
+ for sign in (+1, -1):
+ self.do_test_inf(sign*inf)
+
+ def test_float_mismatched_infs(self):
+ # Test that adding two infinities of opposite sign gives a NAN.
+ inf = float('inf')
+ result = statistics._sum([1, 2, inf, 3, -inf, 4])
+ self.assertTrue(math.isnan(result))
+
+ def test_decimal_mismatched_infs_to_nan(self):
+ # Test adding Decimal INFs with opposite sign returns NAN.
+ inf = Decimal('inf')
+ data = [1, 2, inf, 3, -inf, 4]
+ with decimal.localcontext(decimal.ExtendedContext):
+ self.assertTrue(math.isnan(statistics._sum(data)))
+
+ def test_decimal_mismatched_infs_to_nan(self):
+ # Test adding Decimal INFs with opposite sign raises InvalidOperation.
+ inf = Decimal('inf')
+ data = [1, 2, inf, 3, -inf, 4]
+ with decimal.localcontext(decimal.BasicContext):
+ self.assertRaises(decimal.InvalidOperation, statistics._sum, data)
+
+ def test_decimal_snan_raises(self):
+ # Adding sNAN should raise InvalidOperation.
+ sNAN = Decimal('sNAN')
+ data = [1, sNAN, 2]
+ self.assertRaises(decimal.InvalidOperation, statistics._sum, data)
+
+
+# === Tests for averages ===
+
+class AverageMixin(UnivariateCommonMixin):
+ # Mixin class holding common tests for averages.
+
+ def test_single_value(self):
+ # Average of a single value is the value itself.
+ for x in (23, 42.5, 1.3e15, Fraction(15, 19), Decimal('0.28')):
+ self.assertEqual(self.func([x]), x)
+
+ def test_repeated_single_value(self):
+ # The average of a single repeated value is the value itself.
+ for x in (3.5, 17, 2.5e15, Fraction(61, 67), Decimal('4.9712')):
+ for count in (2, 5, 10, 20):
+ data = [x]*count
+ self.assertEqual(self.func(data), x)
+
+
+class TestMean(NumericTestCase, AverageMixin, UnivariateTypeMixin):
+ def setUp(self):
+ self.func = statistics.mean
+
+ def test_torture_pep(self):
+ # "Torture Test" from PEP-450.
+ self.assertEqual(self.func([1e100, 1, 3, -1e100]), 1)
+
+ def test_ints(self):
+ # Test mean with ints.
+ data = [0, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 7, 7, 8, 9]
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 4.8125)
+
+ def test_floats(self):
+ # Test mean with floats.
+ data = [17.25, 19.75, 20.0, 21.5, 21.75, 23.25, 25.125, 27.5]
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 22.015625)
+
+ def test_decimals(self):
+ # Test mean with ints.
+ D = Decimal
+ data = [D("1.634"), D("2.517"), D("3.912"), D("4.072"), D("5.813")]
+ random.shuffle(data)
+ self.assertEqual(self.func(data), D("3.5896"))
+
+ def test_fractions(self):
+ # Test mean with Fractions.
+ F = Fraction
+ data = [F(1, 2), F(2, 3), F(3, 4), F(4, 5), F(5, 6), F(6, 7), F(7, 8)]
+ random.shuffle(data)
+ self.assertEqual(self.func(data), F(1479, 1960))
+
+ def test_inf(self):
+ # Test mean with infinities.
+ raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later.
+ for kind in (float, Decimal):
+ for sign in (1, -1):
+ inf = kind("inf")*sign
+ data = raw + [inf]
+ result = self.func(data)
+ self.assertTrue(math.isinf(result))
+ self.assertEqual(result, inf)
+
+ def test_mismatched_infs(self):
+ # Test mean with infinities of opposite sign.
+ data = [2, 4, 6, float('inf'), 1, 3, 5, float('-inf')]
+ result = self.func(data)
+ self.assertTrue(math.isnan(result))
+
+ def test_nan(self):
+ # Test mean with NANs.
+ raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later.
+ for kind in (float, Decimal):
+ inf = kind("nan")
+ data = raw + [inf]
+ result = self.func(data)
+ self.assertTrue(math.isnan(result))
+
+ def test_big_data(self):
+ # Test adding a large constant to every data point.
+ c = 1e9
+ data = [3.4, 4.5, 4.9, 6.7, 6.8, 7.2, 8.0, 8.1, 9.4]
+ expected = self.func(data) + c
+ assert expected != c
+ result = self.func([x+c for x in data])
+ self.assertEqual(result, expected)
+
+ def test_doubled_data(self):
+ # Mean of [a,b,c...z] should be same as for [a,a,b,b,c,c...z,z].
+ data = [random.uniform(-3, 5) for _ in range(1000)]
+ expected = self.func(data)
+ actual = self.func(data*2)
+ self.assertApproxEqual(actual, expected)
+
+
+class TestMedian(NumericTestCase, AverageMixin):
+ # Common tests for median and all median.* functions.
+ def setUp(self):
+ self.func = statistics.median
+
+ def prepare_data(self):
+ """Overload method from UnivariateCommonMixin."""
+ data = super().prepare_data()
+ if len(data)%2 != 1:
+ data.append(2)
+ return data
+
+ def test_even_ints(self):
+ # Test median with an even number of int data points.
+ data = [1, 2, 3, 4, 5, 6]
+ assert len(data)%2 == 0
+ self.assertEqual(self.func(data), 3.5)
+
+ def test_odd_ints(self):
+ # Test median with an odd number of int data points.
+ data = [1, 2, 3, 4, 5, 6, 9]
+ assert len(data)%2 == 1
+ self.assertEqual(self.func(data), 4)
+
+ def test_odd_fractions(self):
+ # Test median works with an odd number of Fractions.
+ F = Fraction
+ data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7)]
+ assert len(data)%2 == 1
+ random.shuffle(data)
+ self.assertEqual(self.func(data), F(3, 7))
+
+ def test_even_fractions(self):
+ # Test median works with an even number of Fractions.
+ F = Fraction
+ data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), F(1, 2))
+
+ def test_odd_decimals(self):
+ # Test median works with an odd number of Decimals.
+ D = Decimal
+ data = [D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')]
+ assert len(data)%2 == 1
+ random.shuffle(data)
+ self.assertEqual(self.func(data), D('4.2'))
+
+ def test_even_decimals(self):
+ # Test median works with an even number of Decimals.
+ D = Decimal
+ data = [D('1.2'), D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), D('3.65'))
+
+
+class TestMedianDataType(NumericTestCase, UnivariateTypeMixin):
+ # Test conservation of data element type for median.
+ def setUp(self):
+ self.func = statistics.median
+
+ def prepare_data(self):
+ data = list(range(15))
+ assert len(data)%2 == 1
+ while data == sorted(data):
+ random.shuffle(data)
+ return data
+
+
+class TestMedianLow(TestMedian, UnivariateTypeMixin):
+ def setUp(self):
+ self.func = statistics.median_low
+
+ def test_even_ints(self):
+ # Test median_low with an even number of ints.
+ data = [1, 2, 3, 4, 5, 6]
+ assert len(data)%2 == 0
+ self.assertEqual(self.func(data), 3)
+
+ def test_even_fractions(self):
+ # Test median_low works with an even number of Fractions.
+ F = Fraction
+ data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), F(3, 7))
+
+ def test_even_decimals(self):
+ # Test median_low works with an even number of Decimals.
+ D = Decimal
+ data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), D('3.3'))
+
+
+class TestMedianHigh(TestMedian, UnivariateTypeMixin):
+ def setUp(self):
+ self.func = statistics.median_high
+
+ def test_even_ints(self):
+ # Test median_high with an even number of ints.
+ data = [1, 2, 3, 4, 5, 6]
+ assert len(data)%2 == 0
+ self.assertEqual(self.func(data), 4)
+
+ def test_even_fractions(self):
+ # Test median_high works with an even number of Fractions.
+ F = Fraction
+ data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), F(4, 7))
+
+ def test_even_decimals(self):
+ # Test median_high works with an even number of Decimals.
+ D = Decimal
+ data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), D('4.4'))
+
+
+class TestMedianGrouped(TestMedian):
+ # Test median_grouped.
+ # Doesn't conserve data element types, so don't use TestMedianType.
+ def setUp(self):
+ self.func = statistics.median_grouped
+
+ def test_odd_number_repeated(self):
+ # Test median.grouped with repeated median values.
+ data = [12, 13, 14, 14, 14, 15, 15]
+ assert len(data)%2 == 1
+ self.assertEqual(self.func(data), 14)
+ #---
+ data = [12, 13, 14, 14, 14, 14, 15]
+ assert len(data)%2 == 1
+ self.assertEqual(self.func(data), 13.875)
+ #---
+ data = [5, 10, 10, 15, 20, 20, 20, 20, 25, 25, 30]
+ assert len(data)%2 == 1
+ self.assertEqual(self.func(data, 5), 19.375)
+ #---
+ data = [16, 18, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 26, 28]
+ assert len(data)%2 == 1
+ self.assertApproxEqual(self.func(data, 2), 20.66666667, tol=1e-8)
+
+ def test_even_number_repeated(self):
+ # Test median.grouped with repeated median values.
+ data = [5, 10, 10, 15, 20, 20, 20, 25, 25, 30]
+ assert len(data)%2 == 0
+ self.assertApproxEqual(self.func(data, 5), 19.16666667, tol=1e-8)
+ #---
+ data = [2, 3, 4, 4, 4, 5]
+ assert len(data)%2 == 0
+ self.assertApproxEqual(self.func(data), 3.83333333, tol=1e-8)
+ #---
+ data = [2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6]
+ assert len(data)%2 == 0
+ self.assertEqual(self.func(data), 4.5)
+ #---
+ data = [3, 4, 4, 4, 5, 5, 5, 5, 6, 6]
+ assert len(data)%2 == 0
+ self.assertEqual(self.func(data), 4.75)
+
+ def test_repeated_single_value(self):
+ # Override method from AverageMixin.
+ # Yet again, failure of median_grouped to conserve the data type
+ # causes me headaches :-(
+ for x in (5.3, 68, 4.3e17, Fraction(29, 101), Decimal('32.9714')):
+ for count in (2, 5, 10, 20):
+ data = [x]*count
+ self.assertEqual(self.func(data), float(x))
+
+ def test_odd_fractions(self):
+ # Test median_grouped works with an odd number of Fractions.
+ F = Fraction
+ data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4)]
+ assert len(data)%2 == 1
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 3.0)
+
+ def test_even_fractions(self):
+ # Test median_grouped works with an even number of Fractions.
+ F = Fraction
+ data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4), F(17, 4)]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 3.25)
+
+ def test_odd_decimals(self):
+ # Test median_grouped works with an odd number of Decimals.
+ D = Decimal
+ data = [D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')]
+ assert len(data)%2 == 1
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 6.75)
+
+ def test_even_decimals(self):
+ # Test median_grouped works with an even number of Decimals.
+ D = Decimal
+ data = [D('5.5'), D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 6.5)
+ #---
+ data = [D('5.5'), D('5.5'), D('6.5'), D('7.5'), D('7.5'), D('8.5')]
+ assert len(data)%2 == 0
+ random.shuffle(data)
+ self.assertEqual(self.func(data), 7.0)
+
+ def test_interval(self):
+ # Test median_grouped with interval argument.
+ data = [2.25, 2.5, 2.5, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75]
+ self.assertEqual(self.func(data, 0.25), 2.875)
+ data = [2.25, 2.5, 2.5, 2.75, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75]
+ self.assertApproxEqual(self.func(data, 0.25), 2.83333333, tol=1e-8)
+ data = [220, 220, 240, 260, 260, 260, 260, 280, 280, 300, 320, 340]
+ self.assertEqual(self.func(data, 20), 265.0)
+
+
+class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin):
+ # Test cases for the discrete version of mode.
+ def setUp(self):
+ self.func = statistics.mode
+
+ def prepare_data(self):
+ """Overload method from UnivariateCommonMixin."""
+ # Make sure test data has exactly one mode.
+ return [1, 1, 1, 1, 3, 4, 7, 9, 0, 8, 2]
+
+ def test_range_data(self):
+ # Override test from UnivariateCommonMixin.
+ data = range(20, 50, 3)
+ self.assertRaises(statistics.StatisticsError, self.func, data)
+
+ def test_nominal_data(self):
+ # Test mode with nominal data.
+ data = 'abcbdb'
+ self.assertEqual(self.func(data), 'b')
+ data = 'fe fi fo fum fi fi'.split()
+ self.assertEqual(self.func(data), 'fi')
+
+ def test_discrete_data(self):
+ # Test mode with discrete numeric data.
+ data = list(range(10))
+ for i in range(10):
+ d = data + [i]
+ random.shuffle(d)
+ self.assertEqual(self.func(d), i)
+
+ def test_bimodal_data(self):
+ # Test mode with bimodal data.
+ data = [1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9]
+ assert data.count(2) == data.count(6) == 4
+ # Check for an exception.
+ self.assertRaises(statistics.StatisticsError, self.func, data)
+
+ def test_unique_data_failure(self):
+ # Test mode exception when data points are all unique.
+ data = list(range(10))
+ self.assertRaises(statistics.StatisticsError, self.func, data)
+
+ def test_none_data(self):
+ # Test that mode raises TypeError if given None as data.
+
+ # This test is necessary because the implementation of mode uses
+ # collections.Counter, which accepts None and returns an empty dict.
+ self.assertRaises(TypeError, self.func, None)
+
+
+# === Tests for variances and standard deviations ===
+
+class VarianceStdevMixin(UnivariateCommonMixin):
+ # Mixin class holding common tests for variance and std dev.
+
+ # Subclasses should inherit from this before NumericTestClass, in order
+ # to see the rel attribute below. See testShiftData for an explanation.
+
+ rel = 1e-12
+
+ def test_single_value(self):
+ # Deviation of a single value is zero.
+ for x in (11, 19.8, 4.6e14, Fraction(21, 34), Decimal('8.392')):
+ self.assertEqual(self.func([x]), 0)
+
+ def test_repeated_single_value(self):
+ # The deviation of a single repeated value is zero.
+ for x in (7.2, 49, 8.1e15, Fraction(3, 7), Decimal('62.4802')):
+ for count in (2, 3, 5, 15):
+ data = [x]*count
+ self.assertEqual(self.func(data), 0)
+
+ def test_domain_error_regression(self):
+ # Regression test for a domain error exception.
+ # (Thanks to Geremy Condra.)
+ data = [0.123456789012345]*10000
+ # All the items are identical, so variance should be exactly zero.
+ # We allow some small round-off error, but not much.
+ result = self.func(data)
+ self.assertApproxEqual(result, 0.0, tol=5e-17)
+ self.assertGreaterEqual(result, 0) # A negative result must fail.
+
+ def test_shift_data(self):
+ # Test that shifting the data by a constant amount does not affect
+ # the variance or stdev. Or at least not much.
+
+ # Due to rounding, this test should be considered an ideal. We allow
+ # some tolerance away from "no change at all" by setting tol and/or rel
+ # attributes. Subclasses may set tighter or looser error tolerances.
+ raw = [1.03, 1.27, 1.94, 2.04, 2.58, 3.14, 4.75, 4.98, 5.42, 6.78]
+ expected = self.func(raw)
+ # Don't set shift too high, the bigger it is, the more rounding error.
+ shift = 1e5
+ data = [x + shift for x in raw]
+ self.assertApproxEqual(self.func(data), expected)
+
+ def test_shift_data_exact(self):
+ # Like test_shift_data, but result is always exact.
+ raw = [1, 3, 3, 4, 5, 7, 9, 10, 11, 16]
+ assert all(x==int(x) for x in raw)
+ expected = self.func(raw)
+ shift = 10**9
+ data = [x + shift for x in raw]
+ self.assertEqual(self.func(data), expected)
+
+ def test_iter_list_same(self):
+ # Test that iter data and list data give the same result.
+
+ # This is an explicit test that iterators and lists are treated the
+ # same; justification for this test over and above the similar test
+ # in UnivariateCommonMixin is that an earlier design had variance and
+ # friends swap between one- and two-pass algorithms, which would
+ # sometimes give different results.
+ data = [random.uniform(-3, 8) for _ in range(1000)]
+ expected = self.func(data)
+ self.assertEqual(self.func(iter(data)), expected)
+
+
+class TestPVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin):
+ # Tests for population variance.
+ def setUp(self):
+ self.func = statistics.pvariance
+
+ def test_exact_uniform(self):
+ # Test the variance against an exact result for uniform data.
+ data = list(range(10000))
+ random.shuffle(data)
+ expected = (10000**2 - 1)/12 # Exact value.
+ self.assertEqual(self.func(data), expected)
+
+ def test_ints(self):
+ # Test population variance with int data.
+ data = [4, 7, 13, 16]
+ exact = 22.5
+ self.assertEqual(self.func(data), exact)
+
+ def test_fractions(self):
+ # Test population variance with Fraction data.
+ F = Fraction
+ data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)]
+ exact = F(3, 8)
+ result = self.func(data)
+ self.assertEqual(result, exact)
+ self.assertIsInstance(result, Fraction)
+
+ def test_decimals(self):
+ # Test population variance with Decimal data.
+ D = Decimal
+ data = [D("12.1"), D("12.2"), D("12.5"), D("12.9")]
+ exact = D('0.096875')
+ result = self.func(data)
+ self.assertEqual(result, exact)
+ self.assertIsInstance(result, Decimal)
+
+
+class TestVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin):
+ # Tests for sample variance.
+ def setUp(self):
+ self.func = statistics.variance
+
+ def test_single_value(self):
+ # Override method from VarianceStdevMixin.
+ for x in (35, 24.7, 8.2e15, Fraction(19, 30), Decimal('4.2084')):
+ self.assertRaises(statistics.StatisticsError, self.func, [x])
+
+ def test_ints(self):
+ # Test sample variance with int data.
+ data = [4, 7, 13, 16]
+ exact = 30
+ self.assertEqual(self.func(data), exact)
+
+ def test_fractions(self):
+ # Test sample variance with Fraction data.
+ F = Fraction
+ data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)]
+ exact = F(1, 2)
+ result = self.func(data)
+ self.assertEqual(result, exact)
+ self.assertIsInstance(result, Fraction)
+
+ def test_decimals(self):
+ # Test sample variance with Decimal data.
+ D = Decimal
+ data = [D(2), D(2), D(7), D(9)]
+ exact = 4*D('9.5')/D(3)
+ result = self.func(data)
+ self.assertEqual(result, exact)
+ self.assertIsInstance(result, Decimal)
+
+
+class TestPStdev(VarianceStdevMixin, NumericTestCase):
+ # Tests for population standard deviation.
+ def setUp(self):
+ self.func = statistics.pstdev
+
+ def test_compare_to_variance(self):
+ # Test that stdev is, in fact, the square root of variance.
+ data = [random.uniform(-17, 24) for _ in range(1000)]
+ expected = math.sqrt(statistics.pvariance(data))
+ self.assertEqual(self.func(data), expected)
+
+
+class TestStdev(VarianceStdevMixin, NumericTestCase):
+ # Tests for sample standard deviation.
+ def setUp(self):
+ self.func = statistics.stdev
+
+ def test_single_value(self):
+ # Override method from VarianceStdevMixin.
+ for x in (81, 203.74, 3.9e14, Fraction(5, 21), Decimal('35.719')):
+ self.assertRaises(statistics.StatisticsError, self.func, [x])
+
+ def test_compare_to_variance(self):
+ # Test that stdev is, in fact, the square root of variance.
+ data = [random.uniform(-2, 9) for _ in range(1000)]
+ expected = math.sqrt(statistics.variance(data))
+ self.assertEqual(self.func(data), expected)
+
+
+# === Run tests ===
+
+def load_tests(loader, tests, ignore):
+ """Used for doctest/unittest integration."""
+ tests.addTests(doctest.DocTestSuite())
+ return tests
+
+
+if __name__ == "__main__":
+ unittest.main()
diff --git a/Misc/NEWS b/Misc/NEWS
index dcf6d68..f8d2f19 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -59,6 +59,9 @@
Library
-------
+- Issue #18606: Add the new "statistics" module (PEP 450). Contributed
+ by Steven D'Aprano.
+
- Issue #12866: The audioop module now supports 24-bit samples.
- Issue #19254: Provide an optimized Python implementation of pbkdf2_hmac.