Interpolation method that does not add unnecessary extremums

Question

This question is half programming but also half mathematics. I want to interpolate a set of points by a curve without adding unnecessary extremums staying \"close to the lin

Answer 1

You can use the linear interpolation and then filter it (with a mean filter) :

size = 51.0;    
fun = interpolate.interp1d(xp, yp,kind='linear');
filt = (1/size)*np.ones(size);
yc = signal.convolve( fun(xc),filt,'same');

With the parameter sizeyou can control the smoothing degree.

This is the integrated code:

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt
from scipy import interpolate,signal

fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

list_points=[(-3,0.1),(-2,0.15),(0,4),(2,-6),(4,-2),(7,-0.15),(8,-0.1)]
(xp,yp)=zip(*list_points)
xc=np.linspace(min(xp),max(xp),300)

########################################################
size = 41.0;#Put here any odd number
fun = interpolate.interp1d(xp, yp,kind='linear');
filt = (1/size)*np.ones(size);
yc = signal.convolve(fun(xc),filt,'same');
########################################################

plt.plot(xp,yp,'o',color='black',ms=5)
plt.plot(xc,yc)
plt.plot(xc,fun(xc))
plt.show()