Smoothing a curve with vectors made by few elements?

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I have 4 curves that are represented by these vectors:

x = [300, 700, 1000, 1500]
y1 = [-1.0055394199673442, -0.11221578805214968, -1.502661406039569, 1.0216939169819494]
y2 = [-1.0200777228890747, -0.6951505674297687, -2.832988761335546, 1.0253075071285915]
y3 = [2.0502387421569463, -1.3363305947335058, 0.2893545237634795, 0.8692051683379767]
y4 = [1.8676528391899183, -1.7554177636905024, 0.2364994810496486, 0.9811885784744991]

and when I plot them I obtain something like this:

enter image description here

As you can see, the few values of those vectors cause these curves to be of a zigzag shape and I would like them to be more smooth. I tried different methods, both in Python and Matlab. For instance, in python I used the numpy methods like:

xp = np.linspace(300,1500,100,endpoint=True)
z1 = np.polyfit(x,  y1, 3)
p1 = np.poly1d(z1)
z2 = np.polyfit(x, y2, 3)
p2 = np.poly1d(z2)
z3 = np.polyfit(x,y3, 3)
p3 = np.poly1d(z3)
z4 = np.polyfit(x, y4, 3)
p4 = np.poly1d(z4)

and I obtained this:

enter image description here

but in this way, there are minima and maxima points that I'm not sure are present for the value in between the x vector. Also, I tried the "smooth" function in Matlab with different smoothing values but they also change the value inside the vectors that are no more like the original ones, i.e. they are meaningless for the concept I want to explain. I would like just to smooth a little bit the zigzag parts of the plot to make the curve more pleasant to the view..can you help me please? Python or Matlab is the same for me, I'm open to everything! :)

smoothing curve-fitting matlab numpy python
1 Answers

Alright, so what I'm proposing here is cheating and inventing data, but at least it makes the curves look a little more like you (or your supervisor) want.

x =  [300,      700,      1000,       1500] # your original x
x2 = [300, 500, 700, 850, 1000, 1250, 1500] # add points in between

# interpolate your data for the new points in x2
p1 = np.interp(x2,x,y1)
p2 = np.interp(x2,x,y2)
p3 = np.interp(x2,x,y3)
p4 = np.interp(x2,x,y4)

# cubic spline interpolation on xp, so it looks smooth
p1 = scipy.interpolate.CubicSpline(x2,p1)
p2 = scipy.interpolate.CubicSpline(x2,p2)
p3 = scipy.interpolate.CubicSpline(x2,p3)
p4 = scipy.interpolate.CubicSpline(x2,p4)

Here's what it looks like:

smooth curves

If you're not satisfied with the way this looks, you can try different values in x2.

EDIT:

Here is the full code to produce the plot:

import numpy as np
from scipy.interpolate import CubicSpline
import matplotlib.pyplot as plt

x =  [300,      700,      1000,       1500] # your orginial x
x2 = [300, 500, 700, 850, 1000, 1250, 1500] # add points in between
xp = np.linspace(300,1500,100,endpoint=True) # your x-axis for smooth curve plot

# your orginal data
y1 = [-1.0055394199673442, -0.11221578805214968, -1.502661406039569, 1.0216939169819494]
y2 = [-1.0200777228890747, -0.6951505674297687, -2.832988761335546, 1.0253075071285915]
y3 = [2.0502387421569463, -1.3363305947335058, 0.2893545237634795, 0.8692051683379767]
y4 = [1.8676528391899183, -1.7554177636905024, 0.2364994810496486, 0.9811885784744991]

for yi in [y1,y2,y3,y4]:
    # Piecewise linear interpolation of data y over the points x2
    y_interpolated_over_x2 = np.interp(x2,x,yi)

    # Make a cubic spline from the manipulated data
    y_cubic_spline = CubicSpline(x2, y_interpolated_over_x2)

    # The smooth curve is the cubic spline evaluated at points xp
    y_smooth = y_cubic_spline(xp)

    plt.plot(xp, y_smooth) # plot the smooth curve
    plt.scatter(x, yi) # plot the original data points

plt.show()
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