Fix exponential_moving_average for window_size=1 - #15452
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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.
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Describe your change
For
window_size=1the 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_sizeso the exponential recurrence applies from the second value onward, and adds a doctest pinning thewindow_size=1behavior. The existingwindow_size=3doctest is unchanged and still passes.Verified with the module doctests plus the issue's repro.
Checklist
Fixes #15449. (Supersedes #15451, which the keeper bot closed before the checklist was filled in.)