Skip to content

bpo-20499: Rounding error in statistics.pvariance #28230

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
rhettinger merged 12 commits into from
Sep 9, 2021
Merged

bpo-20499: Rounding error in statistics.pvariance #28230

Changes from 1 commit
Commits
Show all changes
12 commits
Select commit Hold shift + click to select a range
0a1d350
Incorrect first draft
rhettinger Sep 8, 2021
d8714cc
Exact ss
rhettinger Sep 8, 2021
2108d4d
Add test
rhettinger Sep 8, 2021
da6c6cb
Add blurb
rhettinger Sep 8, 2021
69387c6
Remove superfluous comment
rhettinger Sep 8, 2021
39973fd
Add another test
rhettinger Sep 8, 2021
829d5ec
Improve clairity
rhettinger Sep 8, 2021
cc78aaf
Beautify the order of terms
rhettinger Sep 8, 2021
c0b1560
Removed unused "start" argument from internal function
rhettinger Sep 8, 2021
c746482
Modernize and speed-up _exact_ratio() internal function
rhettinger Sep 8, 2021
e7c46fa
Remove unnecessary sort
rhettinger Sep 8, 2021
117ad6b
Add accuracy comments to stdev() and pstdev().
rhettinger Sep 8, 2021
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
Next Next commit
Incorrect first draft
  • Loading branch information
@rhettinger
rhettinger committed Sep 8, 2021
commit 0a1d35050453aeda84c42c5acf1cfa326ed837d0
33 changes: 20 additions & 13 deletions Lib/statistics.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -188,7 +188,7 @@ def _sum(data, start=0):
partials = {d: n}
partials_get = partials.get
T = _coerce(int, type(start))
for typ, values in groupby(data, type):
for typ, values in groupby(data, type): # XXX Are these sorted
T = _coerce(T, typ) # or raise TypeError
for n, d in map(_exact_ratio, values):
count += 1
Expand Down Expand Up @@ -730,18 +730,25 @@ def _ss(data, c=None):
if c is not None:
T, total, count = _sum((d := x - c) * d for x in data)
return (T, total)
# Compute the mean accurate to within 1/2 ulp
c = mean(data)
# Initial computation for the sum of square deviations
T, total, count = _sum((d := x - c) * d for x in data)
# Correct any remaining inaccuracy in the mean c.
# The following sum should mathematically equal zero,
# but due to the final rounding of the mean, it may not.
U, error, count2 = _sum((x - c) for x in data)
assert count == count2
correction = error * error / len(data)
total -= correction
assert not total < 0, 'negative sum of square deviations: %f' % total
T, total, count = _sum(data)
c = total / count # Exact fraction
cn = c.numerator
cd = c.denominator
partials = {}
partials_get = partials.get
for n, d in map(_exact_ratio, data):
dev_numerator = n * cd - cn * d
dev_denominator = d * cd
dev_numerator *= dev_numerator
dev_denominator *= dev_denominator
partials[d] = partials_get(dev_denominator, 0) + dev_numerator
if None in partials:
# The sum will be a NAN or INF. We can ignore all the finite
# partials, and just look at this special one.
total = partials[None]
assert not _isfinite(total)
else:
total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
return (T, total)


Expand Down