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Fix exponential_moving_average for window_size=1 - #15452

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intertermux-code:fix/ema-window-size-1
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intertermux-code wants to merge 1 commit into
TheAlgorithms:masterfrom
intertermux-code:fix/ema-window-size-1

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Describe your change

  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests?

For window_size=1 the documented smoothing factor is alpha = 2/(1+1) = 1, so the recurrence should return each input unchanged. Instead the warmup branch (i <= window_size) averaged the second price: [10.0, 20.0, 30.0] came out [10.0, 15.0, 30.0].

This narrows the warmup to i < window_size so the exponential recurrence applies from the second value onward, and adds a doctest pinning the window_size=1 behavior. The existing window_size=3 doctest is unchanged and still passes.

Verified with the module doctests plus the issue's repro.

Checklist

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues, then the description above includes the issue number(s) with a closing keyword: "Fixes exponential_moving_average returns an incorrect second value when window_size=1 #15449".

Fixes #15449. (Supersedes #15451, which the keeper bot closed before the checklist was filled in.)

The warmup branch used `i <= window_size`, so with window_size=1 the
second price was averaged ((10+20)*0.5=15) instead of applying the
documented smoothing factor alpha=2/(1+1)=1, which must return each
input unchanged. Narrowing the warmup to `i < window_size` applies
the exponential recurrence from the second value onward, and adds a
doctest pinning the window_size=1 behavior.
@algorithms-keeper algorithms-keeper Bot added awaiting reviews This PR is ready to be reviewed enhancement This PR modified some existing files labels Sep 27, 2026

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exponential_moving_average returns an incorrect second value when window_size=1

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