is there an easy way in python to apply a gaussian filter to a set of points (x,y), or more specifically (x,f(x)) that are not regularly spaced along the x-axis? In response to the request for clarification on what I mean, maybe a better way to describe what I'm looking for is as a "gaussian-weighted average", F_gwa(X_j), of a series of points (X_i,F(X_i)) where for each point in the provided series (X_i,F(X_i)) a sum essentially is taken over all the provided points such that

F_gwa(X_j)    =    Σ_i [ e^{-[(X_j-X_i)/σ]^2} * F(X_i) ]    /    Σ_i [ exp^{-[(X_j-X_i)/σ]^2} ]

(Note - if the points in (X_i,F(X_i)) happen to be evenly spaced, I believe that the end result of the above definition would be the same as what "scipy.ndimage.filters.gaussian_filter1d" does). Is there a nice, already-optimized, numpy or scipy way to do this?

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This looks like Nadaraya-Watson Kernel Regression, and one available python implementation is in the statsmodels package.

You can do a similar kernel smoothing operation with pandas rolling window.

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