import math

def gaussfilt(xdata, ydata, sigma, xfilt=None, M=None, extrap=None):

if xfilt is None:

xfilt = xdata

if M is None:

M = 3 * sigma

if extrap is None:

extrap = 0

yfilt = [0] * len(xfilt)

for i in range(0, len(xfilt), 1):

indices = [k for k, x in enumerate(xdata) if x > (xfilt[i] - M) and x < (xfilt[i] + M)]

if indices:

x = []

for ind in indices:

x.append(xdata[ind] - xfilt[i])

gaussfactors = gausskernel(x, sigma)

y = []

yd = []

for ind in indices:

yd.append(ydata[ind])

for j in range(0, len(gaussfactors), 1):

y.append(gaussfactors[j] * yd[j])

yfilt[i] = sum(y) / sum(gaussfactors)

if not indices:

yfilt[i] = extrap

return yfilt

def gausskernel(x, sigma):

res = []

for element in x:

res.append(1 / (sigma * math.sqrt(2 * math.pi)) * math.exp(-0.5 * pow((element / sigma), 2)))

return res