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GH-102670: Use sumprod() to simplify, speed up, and improve accuracy of statistics functions by rhettinger · Pull Request #102649 · python/cpython · GitHub

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GH-102670: Use sumprod() to simplify, speed up, and improve accuracy of statistics functions #102649

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Merged
rhettinger merged 11 commits into from
Mar 14, 2023
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GH-102670: Use sumprod() to simplify, speed up, and improve accuracy of statistics functions #102649

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3f2fd8d
Use sumprod() to speed-up and improve accuracy of correlation()
rhettinger Mar 13, 2023
3241045
Only compute differences once
rhettinger Mar 13, 2023
52c7584
Use sumprod() in covariance().
rhettinger Mar 13, 2023
16b2745
Use sumprod() in linear_regression().
rhettinger Mar 13, 2023
b9eeee5
Can skip centering if xbar or ybar is already zero
rhettinger Mar 13, 2023
c51e520
Factor-out common logic in linear_regression
rhettinger Mar 13, 2023
39be9f8
Factor-out common logic in linear_regression
rhettinger Mar 13, 2023
a448615
Use generator for y array in linear_regression()
rhettinger Mar 13, 2023
c9a4e4d
Coerce result to a float
rhettinger Mar 13, 2023
5fe1be5
Add test for the result type being a float.
rhettinger Mar 13, 2023
45ffe7e
Add blurb
rhettinger Mar 13, 2023
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26 changes: 14 additions & 12 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1036,7 +1036,7 @@ def covariance(x, y, /):
raise StatisticsError('covariance requires at least two data points')
xbar = fsum(x) / n
ybar = fsum(y) / n
sxy = fsum((xi - xbar) * (yi - ybar) for xi, yi in zip(x, y))
sxy = sumprod((xi - xbar for xi in x), (yi - ybar for yi in y))
return sxy / (n - 1)


Expand Down Expand Up @@ -1074,11 +1074,14 @@ def correlation(x, y, /, *, method='linear'):
start = (n - 1) / -2 # Center rankings around zero
x = _rank(x, start=start)
y = _rank(y, start=start)
xbar = fsum(x) / n
ybar = fsum(y) / n
sxy = fsum((xi - xbar) * (yi - ybar) for xi, yi in zip(x, y))
sxx = fsum((d := xi - xbar) * d for xi in x)
syy = fsum((d := yi - ybar) * d for yi in y)
else:
xbar = fsum(x) / n
ybar = fsum(y) / n
x = [xi - xbar for xi in x]
y = [yi - ybar for yi in y]
sxy = sumprod(x, y)
sxx = sumprod(x, x)
syy = sumprod(y, y)
try:
return sxy / sqrt(sxx * syy)
except ZeroDivisionError:
Expand Down Expand Up @@ -1131,14 +1134,13 @@ def linear_regression(x, y, /, *, proportional=False):
raise StatisticsError('linear regression requires that both inputs have same number of data points')
if n < 2:
raise StatisticsError('linear regression requires at least two data points')
if proportional:
sxy = fsum(xi * yi for xi, yi in zip(x, y))
sxx = fsum(xi * xi for xi in x)
else:
if not proportional:
xbar = fsum(x) / n
ybar = fsum(y) / n
sxy = fsum((xi - xbar) * (yi - ybar) for xi, yi in zip(x, y))
sxx = fsum((d := xi - xbar) * d for xi in x)
x = [xi - xbar for xi in x] # List because used three times below
y = (yi - ybar for yi in y) # Generator because only used once below
sxy = sumprod(x, y) + 0.0 # Add zero to coerce result to a float
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sxx = sumprod(x, x)
try:
slope = sxy / sxx # equivalent to: covariance(x, y) / variance(x)
except ZeroDivisionError:
Expand Down
12 changes: 11 additions & 1 deletion Lib/test/test_statistics.py
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@@ -1,4 +1,4 @@
"""Test suite for statistics module, including helper NumericTestCase and
x = """Test suite for statistics module, including helper NumericTestCase and

alexanderGerbik Mar 23, 2023 •
edited
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Choose a reason Spam Abuse Off Topic Outdated Duplicate Resolved Low Quality

Is this a typo or some kind of black magic?
approx_equal function.

"""
Expand Down Expand Up @@ -2610,6 +2610,16 @@ def test_proportional(self):
self.assertAlmostEqual(slope, 20 + 1/150)
self.assertEqual(intercept, 0.0)

def test_float_output(self):
x = [Fraction(2, 3), Fraction(3, 4)]
y = [Fraction(4, 5), Fraction(5, 6)]
slope, intercept = statistics.linear_regression(x, y)
self.assertTrue(isinstance(slope, float))
self.assertTrue(isinstance(intercept, float))
slope, intercept = statistics.linear_regression(x, y, proportional=True)
self.assertTrue(isinstance(slope, float))
self.assertTrue(isinstance(intercept, float))

class TestNormalDist:

# General note on precision: The pdf(), cdf(), and overlap() methods
Expand Down
2 changes: 2 additions & 0 deletions Misc/NEWS.d/next/Library/2023-03-13-18-27-00.gh-issue-102670.GyoThv.rst
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Original file line number Diff line number Diff line change
@@ -0,0 +1,2 @@
Optimized fmean(), correlation(), covariance(), and linear_regression()
using the new math.sumprod() function.
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