def extend_with_zeros_left_side(xIn, fIn, xOut, enforcePositive=False):
"""Extending a function to another domain, with zeros where it was not originally defined.
The domains xIn and xOut should satsify xOut[0] < xIn[0] and xOut[-1] < xIn[0]. The output
domain is "to the left" of the input domain.
This function operates by resampling within the overlapping region, and then extending with zeros.
Sometimes, interpolation might produce negative values when zero is the minimum for physical reasons.
The diffusion coefficient is one example where one wants to maintain positivity. In this case, one
can optionally enforce positivity of the returned value by zeroing out negative values.
Inputs:
xIn independent variable on the input domain (array)
fIn dependent variable on the input domain (array)
xOut independent variable on the new domain (array)
enforcePositive (optional) If True, set any negative values to zero before returning (boolean)
Outputs:
fOut dependent variable on the new domain (array)
"""
assert xOut[0] <= xIn[0] and xOut[-1] <= xIn[-1]
fOut = np.zeros_like(xOut) # initialize with zeros
# resample within the overlapping region
ind = np.where(xOut > xIn[0])
indstart = ind[0][0]
xOutTemp = xOut[indstart:]
interpolate = scipy.interpolate.InterpolatedUnivariateSpline(xIn, fIn)
fOut[indstart:] = interpolate(xOutTemp)
# extend with zeros -- automatically performed because fOut was initialized with zeros
if enforcePositive == True:
ind = fOut < 0
fOut[ind] = 0
return fOut
###################################################
#### Functions for extrapolation ####
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