云数据点的加权一维插值

Question

I have a cloud of data points (x,y) that I would like to interpolate and smooth.

Currently, I am using scipy :

from scipy.interpolate import interp1d
from scipy.signal import savgol_filter

spl = interp1d(Cloud[:,1], Cloud[:,0]) # interpolation
x = np.linspace(Cloud[:,1].min(), Cloud[:,1].max(), 1000)
smoothed = savgol_filter(spl(x), 21, 1) #smoothing

This is working pretty well, except that I would like to give some weights to the data points given at interp1d . Any suggestion for another function that is handling this ?

Basically, I thought that I could just multiply the occurrence of each point of the cloud according to its weight, but that is not very optimized as it increases a lot the number of points to interpolate, and slows down the algorithm ..

Answer 1

The default interp1d uses linear interpolation , ie, it simply computes a line between two points. A weighted interpolation does not make much sense mathematically in such scenario - there is only one way in euclidean space to make a straight line between two points.

Depending on your goal, you can look into other methods of interpolation, eg, B-splines . Then you can use scipy's scipy.interpolate.splrep and set the w argument:

w - Strictly positive rank-1 array of weights the same length as x and y. The weights are used in computing the weighted least-squares spline fit. If the errors in the y values have standard-deviation given by the vector d, then w should be 1/d. Default is ones(len(x)).