Smoothing function with fixed end points (decreasing window size near boundary)

I would like either

a link to a smoothing function from existing library or
a 'reasonably performant' python function

that performs simple boxcar smoothing but with the catch that it accepts a boundary condition like this:

Suppose an array of length 9, with a rolling window of 5

target source indices

  1       1
  2     1 2 3
  3   1 2 3 4 5
  4   2 3 4 5 6
  5   3 4 5 6 7
  6   4 5 6 7 8
  7   5 6 7 8 9
  8     7 8 9
  9       9

So the rolling window get smaller near the boundaries, thereby preserving the end point values.

I have looked at: https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.uniform_filter1d.html https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.rolling.html

Solution

I would smooth the valid part first and then fix the boundary conditions. You could apply something like this:

import numpy as np

x = np.linspace(1, 9, 9)

def rolling_average(x: np.ndarray, n: int) -> np.ndarray:
    boundary_values = n // 2

    y = np.zeros_like(x)
    y[boundary_values: -boundary_values] = np.convolve(x, np.ones(n)/n, mode='valid')

    for i in range(boundary_values):
        y[i] = np.mean(x[:i*2 + 1])
        y[-1 - i] = np.mean(x[-i*2 - 1:])
    return y

print(rolling_average(x, 5))

>>> [1. 2. 3. 4. 5. 6. 7. 8. 9.]