paiml/python-doctest-corpus-test · Datasets at Hugging Face

source stringclasses 1 value	version stringclasses 1 value	module stringclasses 43 values	function stringclasses 307 values	input stringlengths 3 496	expected stringlengths 0 40.5k	signature stringclasses 0 values
cpython	cfcd524	statistics	StatisticsError.mode	>>> mode([1, 1, 2, 3, 3, 3, 3, 4])	3 This also works with nominal (non-numeric) data:	null
cpython	cfcd524	statistics	StatisticsError.mode	>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])	'red' If there are multiple modes with same frequency, return the first one encountered:	null
cpython	cfcd524	statistics	StatisticsError.mode	>>> mode(['red', 'red', 'green', 'blue', 'blue'])	'red' If data is empty, ``mode``, raises StatisticsError.	null
cpython	cfcd524	statistics	StatisticsError.multimode	>>> multimode('aabbbbbbbbcc')	['b']	null
cpython	cfcd524	statistics	StatisticsError.multimode	>>> multimode('aabbbbccddddeeffffgg')	['b', 'd', 'f']	null
cpython	cfcd524	statistics	StatisticsError.multimode	>>> multimode('')	[]	null
cpython	cfcd524	statistics	StatisticsError.variance	>>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]		null
cpython	cfcd524	statistics	StatisticsError.variance	>>> 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:	null
cpython	cfcd524	statistics	StatisticsError.variance	>>> m = mean(data)		null
cpython	cfcd524	statistics	StatisticsError.variance	>>> 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:	null
cpython	cfcd524	statistics	StatisticsError.variance	>>> from decimal import Decimal as D		null
cpython	cfcd524	statistics	StatisticsError.variance	>>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])	Decimal('31.01875')	null
cpython	cfcd524	statistics	StatisticsError.variance	>>> from fractions import Fraction as F		null
cpython	cfcd524	statistics	StatisticsError.variance	>>> variance([F(1, 6), F(1, 2), F(5, 3)])	Fraction(67, 108)	null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]		null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> 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:	null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> mu = mean(data)		null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> pvariance(data, mu)	1.25 Decimals and Fractions are supported:	null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> from decimal import Decimal as D		null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])	Decimal('24.815')	null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> from fractions import Fraction as F		null
cpython	cfcd524	statistics	StatisticsError.pvariance	>>> pvariance([F(1, 4), F(5, 4), F(1, 2)])	Fraction(13, 72)	null
cpython	cfcd524	statistics	StatisticsError.stdev	>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])	1.0810874155219827	null
cpython	cfcd524	statistics	StatisticsError.pstdev	>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])	0.986893273527251	null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> x = [1, 2, 3, 4, 5, 6, 7, 8, 9]		null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> y = [1, 2, 3, 1, 2, 3, 1, 2, 3]		null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> covariance(x, y)	0.75	null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> z = [9, 8, 7, 6, 5, 4, 3, 2, 1]		null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> covariance(x, z)	-7.5	null
cpython	cfcd524	statistics	StatisticsError.covariance	>>> covariance(z, x)	-7.5	null
cpython	cfcd524	statistics	StatisticsError.correlation	>>> x = [1, 2, 3, 4, 5, 6, 7, 8, 9]		null
cpython	cfcd524	statistics	StatisticsError.correlation	>>> y = [9, 8, 7, 6, 5, 4, 3, 2, 1]		null
cpython	cfcd524	statistics	StatisticsError.correlation	>>> correlation(x, x)	1.0	null
cpython	cfcd524	statistics	StatisticsError.correlation	>>> correlation(x, y)	-1.0 If method is "ranked", computes Spearman's rank correlation coefficient for two inputs. The data is replaced by ranks. Ties are averaged so that equal values receive the same rank. The resulting coefficient measures the strength of a monotonic relationship. Spearman's rank correlation coefficient is appropriate for ordinal data or for continuous data that doesn't meet the linear proportion requirement for Pearson's correlation coefficient.	null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> x = [1, 2, 3, 4, 5]		null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> noise = NormalDist().samples(5, seed=42)		null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> y = [3 * x[i] + 2 + noise[i] for i in range(5)]		null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> linear_regression(x, y) #doctest: +ELLIPSIS	LinearRegression(slope=3.17495..., intercept=1.00925...) If proportional is true, the independent variable x and the dependent variable y are assumed to be directly proportional. The data is fit to a line passing through the origin. Since the intercept will always be 0.0, the underlying linear function simplifies to: y = slope * x + noise	null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> y = [3 * x[i] + noise[i] for i in range(5)]		null
cpython	cfcd524	statistics	StatisticsError.linear_regression	>>> linear_regression(x, y, proportional=True) #doctest: +ELLIPSIS	LinearRegression(slope=2.90475..., intercept=0.0)	null
cpython	cfcd524	statistics	StatisticsError.kde	>>> sample = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]		null
cpython	cfcd524	statistics	StatisticsError.kde	>>> f_hat = kde(sample, h=1.5)	Compute the area under the curve:	null
cpython	cfcd524	statistics	StatisticsError.kde	>>> area = sum(f_hat(x) for x in range(-20, 20))		null
cpython	cfcd524	statistics	StatisticsError.kde	>>> round(area, 4)	1.0 Plot the estimated probability density function at evenly spaced points from -6 to 10:	null
cpython	cfcd524	statistics	StatisticsError.kde	>>> for x in range(-6, 11): ... density = f_hat(x) ... plot = ' ' * int(density * 400) + 'x' ... print(f'{x:2}: {density:.3f} {plot}') ...	-6: 0.002 x -5: 0.009 x -4: 0.031 x -3: 0.070 x -2: 0.111 x -1: 0.125 x 0: 0.110 x 1: 0.086 x 2: 0.068 x 3: 0.059 x 4: 0.066 x 5: 0.082 x 6: 0.082 x 7: 0.058 x 8: 0.028 x 9: 0.009 x 10: 0.002 x Estimate P(4.5 < X <= 7.5), the probability that a new sample value will be between 4.5 and 7.5:	null
cpython	cfcd524	statistics	StatisticsError.kde	>>> cdf = kde(sample, h=1.5, cumulative=True)		null
cpython	cfcd524	statistics	StatisticsError.kde	>>> round(cdf(7.5) - cdf(4.5), 2)	0.22 References ---------- Kernel density estimation and its application: https://www.itm-conferences.org/articles/itmconf/pdf/2018/08/itmconf_sam2018_00037.pdf Kernel functions in common use: https://en.wikipedia.org/wiki/Kernel_(statistics)#kernel_functions_in_common_use Interactive graphical demonstration and exploration: https://demonstrations.wolfram.com/KernelDensityEstimation/ Kernel estimation of cumulative distribution function of a random variable with bounded support https://www.econstor.eu/bitstream/10419/207829/1/10.21307_stattrans-2016-037.pdf	null
cpython	cfcd524	statistics	StatisticsError.kde_random	>>> data = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]		null
cpython	cfcd524	statistics	StatisticsError.kde_random	>>> rand = kde_random(data, h=1.5, seed=8675309)		null
cpython	cfcd524	statistics	StatisticsError.kde_random	>>> new_selections = [rand() for i in range(10)]		null
cpython	cfcd524	statistics	StatisticsError.kde_random	>>> [round(x, 1) for x in new_selections]	[0.7, 6.2, 1.2, 6.9, 7.0, 1.8, 2.5, -0.5, -1.8, 5.6]	null
cpython	cfcd524	statistics	NormalDist.overlap	>>> N1 = NormalDist(2.4, 1.6)		null
cpython	cfcd524	statistics	NormalDist.overlap	>>> N2 = NormalDist(3.2, 2.0)		null
cpython	cfcd524	statistics	NormalDist.overlap	>>> N1.overlap(N2)	0.8035050657330205	null
cpython	cfcd524	statistics	NormalDist._sum	>>> _sum([3, 2.25, 4.5, -0.5, 0.25])	(<class 'float'>, Fraction(19, 2), 5) Some sources of round-off error will be avoided: # Built-in sum returns zero.	null
cpython	cfcd524	statistics	NormalDist._sum	>>> _sum([1e50, 1, -1e50] * 1000)	(<class 'float'>, Fraction(1000, 1), 3000) Fractions and Decimals are also supported:	null
cpython	cfcd524	statistics	NormalDist._sum	>>> from fractions import Fraction as F		null
cpython	cfcd524	statistics	NormalDist._sum	>>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])	(<class 'fractions.Fraction'>, Fraction(63, 20), 4)	null
cpython	cfcd524	statistics	NormalDist._sum	>>> from decimal import Decimal as D		null
cpython	cfcd524	statistics	NormalDist._sum	>>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]		null
cpython	cfcd524	statistics	NormalDist._sum	>>> _sum(data)	(<class 'decimal.Decimal'>, Fraction(6963, 10000), 4) Mixed types are currently treated as an error, except that int is allowed.	null
cpython	cfcd524	statistics	NormalDist._exact_ratio	>>> _exact_ratio(0.25)	(1, 4) x is expected to be an int, Fraction, Decimal or float.	null
cpython	cfcd524	statistics	NormalDist._rank	>>> data = [31, 56, 31, 25, 75, 18]		null
cpython	cfcd524	statistics	NormalDist._rank	>>> _rank(data)	[3.5, 5.0, 3.5, 2.0, 6.0, 1.0] The operation is idempotent:	null
cpython	cfcd524	statistics	NormalDist._rank	>>> _rank([3.5, 5.0, 3.5, 2.0, 6.0, 1.0])	[3.5, 5.0, 3.5, 2.0, 6.0, 1.0] It is possible to rank the data in reverse order so that the highest value has rank 1. Also, a key-function can extract the field to be ranked:	null
cpython	cfcd524	statistics	NormalDist._rank	>>> goals = [('eagles', 45), ('bears', 48), ('lions', 44)]		null
cpython	cfcd524	statistics	NormalDist._rank	>>> _rank(goals, key=itemgetter(1), reverse=True)	[2.0, 1.0, 3.0] Ranks are conventionally numbered starting from one; however, setting start to zero allows the ranks to be used as array indices:	null
cpython	cfcd524	statistics	NormalDist._rank	>>> prize = ['Gold', 'Silver', 'Bronze', 'Certificate']		null
cpython	cfcd524	statistics	NormalDist._rank	>>> scores = [8.1, 7.3, 9.4, 8.3]		null
cpython	cfcd524	statistics	NormalDist._rank	>>> [prize[int(i)] for i in _rank(scores, start=0, reverse=True)]	['Bronze', 'Certificate', 'Gold', 'Silver']	null
cpython	cfcd524	doctest	_SpoofOut._ellipsis_match	>>> _ellipsis_match('aa...aa', 'aaa')	False	null
cpython	cfcd524	doctest	DocTestRunner	>>> save_colorize = _colorize.COLORIZE		null
cpython	cfcd524	doctest	DocTestRunner	>>> _colorize.COLORIZE = False		null
cpython	cfcd524	doctest	DocTestRunner	>>> tests = DocTestFinder().find(_TestClass)		null
cpython	cfcd524	doctest	DocTestRunner	>>> runner = DocTestRunner(verbose=False)		null
cpython	cfcd524	doctest	DocTestRunner	>>> tests.sort(key = lambda test: test.name)		null
cpython	cfcd524	doctest	DocTestRunner	>>> for test in tests: ... print(test.name, '->', runner.run(test))	_TestClass -> TestResults(failed=0, attempted=2) _TestClass.__init__ -> TestResults(failed=0, attempted=2) _TestClass.get -> TestResults(failed=0, attempted=2) _TestClass.square -> TestResults(failed=0, attempted=1) The `summarize` method prints a summary of all the test cases that have been run by the runner, and returns an aggregated TestResults instance:	null
cpython	cfcd524	doctest	DocTestRunner	>>> runner.summarize(verbose=1)	4 items passed all tests: 2 tests in _TestClass 2 tests in _TestClass.__init__ 2 tests in _TestClass.get 1 test in _TestClass.square 7 tests in 4 items. 7 passed. Test passed. TestResults(failed=0, attempted=7) The aggregated number of tried examples and failed examples is also available via the `tries`, `failures` and `skips` attributes:	null
cpython	cfcd524	doctest	DocTestRunner	>>> runner.tries	7	null
cpython	cfcd524	doctest	DocTestRunner	>>> runner.failures	0	null
cpython	cfcd524	doctest	DocTestRunner	>>> runner.skips	0 The comparison between expected outputs and actual outputs is done by an `OutputChecker`. This comparison may be customized with a number of option flags; see the documentation for `testmod` for more information. If the option flags are insufficient, then the comparison may also be customized by passing a subclass of `OutputChecker` to the constructor. The test runner's display output can be controlled in two ways. First, an output function (`out`) can be passed to `TestRunner.run`; this function will be called with strings that should be displayed. It defaults to `sys.stdout.write`. If capturing the output is not sufficient, then the display output can be also customized by subclassing DocTestRunner, and overriding the methods `report_start`, `report_success`, `report_unexpected_exception`, and `report_failure`.	null
cpython	cfcd524	doctest	DocTestRunner	>>> _colorize.COLORIZE = save_colorize		null
cpython	cfcd524	doctest	DebugRunner	>>> runner = DebugRunner(verbose=False)		null
cpython	cfcd524	doctest	DebugRunner	>>> test = DocTestParser().get_doctest('>>> raise KeyError\n42', ... {}, 'foo', 'foo.py', 0)		null
cpython	cfcd524	doctest	DebugRunner	>>> try: ... runner.run(test) ... except UnexpectedException as f: ... failure = f		null
cpython	cfcd524	doctest	DebugRunner	>>> failure.test is test	True	null
cpython	cfcd524	doctest	DebugRunner	>>> failure.example.want	'42\n'	null
cpython	cfcd524	doctest	DebugRunner	>>> exc_info = failure.exc_info		null
cpython	cfcd524	doctest	DebugRunner	>>> raise exc_info[1] # Already has the traceback	Traceback (most recent call last): ... KeyError We wrap the original exception to give the calling application access to the test and example information. If the output doesn't match, then a DocTestFailure is raised:	null
cpython	cfcd524	doctest	DebugRunner	>>> test = DocTestParser().get_doctest(''' ... >>> x = 1 ... >>> x ... 2 ... ''', {}, 'foo', 'foo.py', 0)		null
cpython	cfcd524	doctest	DebugRunner	>>> try: ... runner.run(test) ... except DocTestFailure as f: ... failure = f	DocTestFailure objects provide access to the test:	null
cpython	cfcd524	doctest	DebugRunner	>>> failure.test is test	True As well as to the example:	null
cpython	cfcd524	doctest	DebugRunner	>>> failure.example.want	'2\n' and the actual output:	null
cpython	cfcd524	doctest	DebugRunner	>>> failure.got	'1\n' If a failure or error occurs, the globals are left intact:	null
cpython	cfcd524	doctest	DebugRunner	>>> del test.globs['__builtins__']		null
cpython	cfcd524	doctest	DebugRunner	>>> test.globs	{'x': 1}	null
cpython	cfcd524	doctest	DebugRunner	>>> test = DocTestParser().get_doctest(''' ... >>> x = 2 ... >>> raise KeyError ... ''', {}, 'foo', 'foo.py', 0)		null
cpython	cfcd524	doctest	DebugRunner	>>> runner.run(test)	Traceback (most recent call last): ... doctest.UnexpectedException: <DocTest foo from foo.py:0 (2 examples)>	null
cpython	cfcd524	doctest	DebugRunner	>>> del test.globs['__builtins__']		null
cpython	cfcd524	doctest	DebugRunner	>>> test.globs	{'x': 2} But the globals are cleared if there is no error:	null

cpython

cfcd524

statistics

StatisticsError.mode

>>> mode([1, 1, 2, 3, 3, 3, 3, 4])

3 This also works with nominal (non-numeric) data:

null

cpython

cfcd524

statistics

StatisticsError.mode

>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])

'red' If there are multiple modes with same frequency, return the first one encountered:

null

cpython

cfcd524

statistics

StatisticsError.mode

>>> mode(['red', 'red', 'green', 'blue', 'blue'])

'red' If *data* is empty, ``mode``, raises StatisticsError.

null

cpython

cfcd524

statistics

StatisticsError.multimode

>>> multimode('aabbbbbbbbcc')

['b']

null

cpython

cfcd524

statistics

StatisticsError.multimode

>>> multimode('aabbbbccddddeeffffgg')

['b', 'd', 'f']

null

cpython

cfcd524

statistics

StatisticsError.multimode

>>> multimode('')

[]

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> 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:

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> m = mean(data)

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> 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:

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> from decimal import Decimal as D

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])

Decimal('31.01875')

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> from fractions import Fraction as F

null

cpython

cfcd524

statistics

StatisticsError.variance

>>> variance([F(1, 6), F(1, 2), F(5, 3)])

Fraction(67, 108)

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> 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:

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> mu = mean(data)

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> pvariance(data, mu)

1.25 Decimals and Fractions are supported:

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> from decimal import Decimal as D

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])

Decimal('24.815')

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> from fractions import Fraction as F

null

cpython

cfcd524

statistics

StatisticsError.pvariance

>>> pvariance([F(1, 4), F(5, 4), F(1, 2)])

Fraction(13, 72)

null

cpython

cfcd524

statistics

StatisticsError.stdev

>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])

1.0810874155219827

null

cpython

cfcd524

statistics

StatisticsError.pstdev

>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])

0.986893273527251

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> x = [1, 2, 3, 4, 5, 6, 7, 8, 9]

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> y = [1, 2, 3, 1, 2, 3, 1, 2, 3]

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> covariance(x, y)

0.75

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> z = [9, 8, 7, 6, 5, 4, 3, 2, 1]

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> covariance(x, z)

-7.5

null

cpython

cfcd524

statistics

StatisticsError.covariance

>>> covariance(z, x)

-7.5

null

cpython

cfcd524

statistics

StatisticsError.correlation

>>> x = [1, 2, 3, 4, 5, 6, 7, 8, 9]

null

cpython

cfcd524

statistics

StatisticsError.correlation

>>> y = [9, 8, 7, 6, 5, 4, 3, 2, 1]

null

cpython

cfcd524

statistics

StatisticsError.correlation

>>> correlation(x, x)

1.0

null

cpython

cfcd524

statistics

StatisticsError.correlation

>>> correlation(x, y)

-1.0 If *method* is "ranked", computes Spearman's rank correlation coefficient for two inputs. The data is replaced by ranks. Ties are averaged so that equal values receive the same rank. The resulting coefficient measures the strength of a monotonic relationship. Spearman's rank correlation coefficient is appropriate for ordinal data or for continuous data that doesn't meet the linear proportion requirement for Pearson's correlation coefficient.

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> x = [1, 2, 3, 4, 5]

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> noise = NormalDist().samples(5, seed=42)

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> y = [3 * x[i] + 2 + noise[i] for i in range(5)]

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> linear_regression(x, y) #doctest: +ELLIPSIS

LinearRegression(slope=3.17495..., intercept=1.00925...) If *proportional* is true, the independent variable *x* and the dependent variable *y* are assumed to be directly proportional. The data is fit to a line passing through the origin. Since the *intercept* will always be 0.0, the underlying linear function simplifies to: y = slope * x + noise

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> y = [3 * x[i] + noise[i] for i in range(5)]

null

cpython

cfcd524

statistics

StatisticsError.linear_regression

>>> linear_regression(x, y, proportional=True) #doctest: +ELLIPSIS

LinearRegression(slope=2.90475..., intercept=0.0)

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> sample = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> f_hat = kde(sample, h=1.5)

Compute the area under the curve:

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> area = sum(f_hat(x) for x in range(-20, 20))

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> round(area, 4)

1.0 Plot the estimated probability density function at evenly spaced points from -6 to 10:

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> for x in range(-6, 11): ... density = f_hat(x) ... plot = ' ' * int(density * 400) + 'x' ... print(f'{x:2}: {density:.3f} {plot}') ...

-6: 0.002 x -5: 0.009 x -4: 0.031 x -3: 0.070 x -2: 0.111 x -1: 0.125 x 0: 0.110 x 1: 0.086 x 2: 0.068 x 3: 0.059 x 4: 0.066 x 5: 0.082 x 6: 0.082 x 7: 0.058 x 8: 0.028 x 9: 0.009 x 10: 0.002 x Estimate P(4.5 < X <= 7.5), the probability that a new sample value will be between 4.5 and 7.5:

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> cdf = kde(sample, h=1.5, cumulative=True)

null

cpython

cfcd524

statistics

StatisticsError.kde

>>> round(cdf(7.5) - cdf(4.5), 2)

0.22 References ---------- Kernel density estimation and its application: https://www.itm-conferences.org/articles/itmconf/pdf/2018/08/itmconf_sam2018_00037.pdf Kernel functions in common use: https://en.wikipedia.org/wiki/Kernel_(statistics)#kernel_functions_in_common_use Interactive graphical demonstration and exploration: https://demonstrations.wolfram.com/KernelDensityEstimation/ Kernel estimation of cumulative distribution function of a random variable with bounded support https://www.econstor.eu/bitstream/10419/207829/1/10.21307_stattrans-2016-037.pdf

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cpython

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statistics

StatisticsError.kde_random

>>> data = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2]

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statistics

StatisticsError.kde_random

>>> rand = kde_random(data, h=1.5, seed=8675309)

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statistics

StatisticsError.kde_random

>>> new_selections = [rand() for i in range(10)]

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statistics

StatisticsError.kde_random

>>> [round(x, 1) for x in new_selections]

[0.7, 6.2, 1.2, 6.9, 7.0, 1.8, 2.5, -0.5, -1.8, 5.6]

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cpython

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statistics

NormalDist.overlap

>>> N1 = NormalDist(2.4, 1.6)

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statistics

NormalDist.overlap

>>> N2 = NormalDist(3.2, 2.0)

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statistics

NormalDist.overlap

>>> N1.overlap(N2)

0.8035050657330205

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statistics

NormalDist._sum

>>> _sum([3, 2.25, 4.5, -0.5, 0.25])

(<class 'float'>, Fraction(19, 2), 5) Some sources of round-off error will be avoided: # Built-in sum returns zero.

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statistics

NormalDist._sum

>>> _sum([1e50, 1, -1e50] * 1000)

(<class 'float'>, Fraction(1000, 1), 3000) Fractions and Decimals are also supported:

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statistics

NormalDist._sum

>>> from fractions import Fraction as F

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NormalDist._sum

>>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])

(<class 'fractions.Fraction'>, Fraction(63, 20), 4)

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statistics

NormalDist._sum

>>> from decimal import Decimal as D

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statistics

NormalDist._sum

>>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]

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statistics

NormalDist._sum

>>> _sum(data)

(<class 'decimal.Decimal'>, Fraction(6963, 10000), 4) Mixed types are currently treated as an error, except that int is allowed.

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statistics

NormalDist._exact_ratio

>>> _exact_ratio(0.25)

(1, 4) x is expected to be an int, Fraction, Decimal or float.

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statistics

NormalDist._rank

>>> data = [31, 56, 31, 25, 75, 18]

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statistics

NormalDist._rank

>>> _rank(data)

[3.5, 5.0, 3.5, 2.0, 6.0, 1.0] The operation is idempotent:

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statistics

NormalDist._rank

>>> _rank([3.5, 5.0, 3.5, 2.0, 6.0, 1.0])

[3.5, 5.0, 3.5, 2.0, 6.0, 1.0] It is possible to rank the data in reverse order so that the highest value has rank 1. Also, a key-function can extract the field to be ranked:

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statistics

NormalDist._rank

>>> goals = [('eagles', 45), ('bears', 48), ('lions', 44)]

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statistics

NormalDist._rank

>>> _rank(goals, key=itemgetter(1), reverse=True)

[2.0, 1.0, 3.0] Ranks are conventionally numbered starting from one; however, setting *start* to zero allows the ranks to be used as array indices:

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statistics

NormalDist._rank

>>> prize = ['Gold', 'Silver', 'Bronze', 'Certificate']

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statistics

NormalDist._rank

>>> scores = [8.1, 7.3, 9.4, 8.3]

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statistics

NormalDist._rank

>>> [prize[int(i)] for i in _rank(scores, start=0, reverse=True)]

['Bronze', 'Certificate', 'Gold', 'Silver']

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doctest

_SpoofOut._ellipsis_match

>>> _ellipsis_match('aa...aa', 'aaa')

False

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doctest

DocTestRunner

>>> save_colorize = _colorize.COLORIZE

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doctest

DocTestRunner

>>> _colorize.COLORIZE = False

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doctest

DocTestRunner

>>> tests = DocTestFinder().find(_TestClass)

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doctest

DocTestRunner

>>> runner = DocTestRunner(verbose=False)

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doctest

DocTestRunner

>>> tests.sort(key = lambda test: test.name)

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doctest

DocTestRunner

>>> for test in tests: ... print(test.name, '->', runner.run(test))

_TestClass -> TestResults(failed=0, attempted=2) _TestClass.__init__ -> TestResults(failed=0, attempted=2) _TestClass.get -> TestResults(failed=0, attempted=2) _TestClass.square -> TestResults(failed=0, attempted=1) The `summarize` method prints a summary of all the test cases that have been run by the runner, and returns an aggregated TestResults instance:

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doctest

DocTestRunner

>>> runner.summarize(verbose=1)

4 items passed all tests: 2 tests in _TestClass 2 tests in _TestClass.__init__ 2 tests in _TestClass.get 1 test in _TestClass.square 7 tests in 4 items. 7 passed. Test passed. TestResults(failed=0, attempted=7) The aggregated number of tried examples and failed examples is also available via the `tries`, `failures` and `skips` attributes:

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doctest

DocTestRunner

>>> runner.tries

7

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doctest

DocTestRunner

>>> runner.failures

0

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doctest

DocTestRunner

>>> runner.skips

0 The comparison between expected outputs and actual outputs is done by an `OutputChecker`. This comparison may be customized with a number of option flags; see the documentation for `testmod` for more information. If the option flags are insufficient, then the comparison may also be customized by passing a subclass of `OutputChecker` to the constructor. The test runner's display output can be controlled in two ways. First, an output function (`out`) can be passed to `TestRunner.run`; this function will be called with strings that should be displayed. It defaults to `sys.stdout.write`. If capturing the output is not sufficient, then the display output can be also customized by subclassing DocTestRunner, and overriding the methods `report_start`, `report_success`, `report_unexpected_exception`, and `report_failure`.

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doctest

DocTestRunner

>>> _colorize.COLORIZE = save_colorize

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doctest

DebugRunner

>>> runner = DebugRunner(verbose=False)

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doctest

DebugRunner

>>> test = DocTestParser().get_doctest('>>> raise KeyError\n42', ... {}, 'foo', 'foo.py', 0)

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doctest

DebugRunner

>>> try: ... runner.run(test) ... except UnexpectedException as f: ... failure = f

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doctest

DebugRunner

>>> failure.test is test

True

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doctest

DebugRunner

>>> failure.example.want

'42\n'

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doctest

DebugRunner

>>> exc_info = failure.exc_info

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doctest

DebugRunner

>>> raise exc_info[1] # Already has the traceback

Traceback (most recent call last): ... KeyError We wrap the original exception to give the calling application access to the test and example information. If the output doesn't match, then a DocTestFailure is raised:

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doctest

DebugRunner

>>> test = DocTestParser().get_doctest(''' ... >>> x = 1 ... >>> x ... 2 ... ''', {}, 'foo', 'foo.py', 0)

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doctest

DebugRunner

>>> try: ... runner.run(test) ... except DocTestFailure as f: ... failure = f

DocTestFailure objects provide access to the test:

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doctest

DebugRunner

>>> failure.test is test

True As well as to the example:

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doctest

DebugRunner

>>> failure.example.want

'2\n' and the actual output:

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doctest

DebugRunner

>>> failure.got

'1\n' If a failure or error occurs, the globals are left intact:

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doctest

DebugRunner

>>> del test.globs['__builtins__']

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doctest

DebugRunner

>>> test.globs

{'x': 1}

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doctest

DebugRunner

>>> test = DocTestParser().get_doctest(''' ... >>> x = 2 ... >>> raise KeyError ... ''', {}, 'foo', 'foo.py', 0)

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doctest

DebugRunner

>>> runner.run(test)

Traceback (most recent call last): ... doctest.UnexpectedException: <DocTest foo from foo.py:0 (2 examples)>

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doctest

DebugRunner

>>> del test.globs['__builtins__']

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doctest

DebugRunner

>>> test.globs

{'x': 2} But the globals are cleared if there is no error:

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