Question

I’m having a weird problem trying to interpolate data using the UnivariateSpline function. Interpolating through all the points (s=0) and the spline function does not give a result on the entire set of data. The result for s>=1 is also very weird. As I think it is related to the data I’m using, I join them in attachement.
I’m stuck, so if anyone have a good idea on a solution, I will really appreciate.

Thanks,

here part of the code:

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

def openfile(infilename):
    ifile = open(infilename, 'r') # open file for reading
    lines = ifile.readlines()
    ifile.close()
    return lines

def extractData(lines):
    data=[]
    CV=[]

    for i in range(len(lines)):
        item=lines[i].split()
        for j in range(len(item)):
            item[j]=float(item[j])
            data.append(item[j])

    CV=np.array(data)
    CV.shape = (len(CV)/3,3)
    return CV

if __name__ == "__main__":

    lines=openfile("D:\capamos\LOCOS\cap15L1_rec_mod.csv")
    CV=extractData(lines)
    Vg1=CV[:,0]
    C1=CV[:,1]
    Cmax=C1.max()
    Cmin=C1.min()
    S=0.002
    Cfb=compute(Cmax,Cmin,S) #compute the flat band capacitance
    print "Cfb=",Cfb

    splineCV= UnivariateSpline(Vg1,C1,s=0)
    x = linspace(-5, 5, 1000)   # just to draw the spline function
    y=splineCV(x)
    Vfb=splineCV(Cfb)  # find the flat band voltage at Cfb
    print "Vfb=",Vfb
    print y

    plt.figure(1)
    p1=plot(Vg1,C1,'b',label='edge')
    p2=plot(x,y,'g')
    plt.axis([-6,6,1e-11,80e-12])

And here the datas:

5   6.35E-011   -4.79E-010
4.95    6.35E-011   -1.91E-010
4.9 6.35E-011   -2.19E-010
4.85    6.35E-011   -4.57E-010
4.8 6.35E-011   -1.24E-010
4.75    6.35E-011   -3.50E-010
4.7 6.35E-011   -4.15E-010
4.65    6.34E-011   2.37E-010
4.6 6.35E-011   -2.84E-010
4.55    6.34E-011   -2.18E-010
4.5 6.35E-011   1.90E-010
4.45    6.34E-011   -7.71E-011
4.4 6.34E-011   -6.89E-010
4.35    6.34E-011   -2.79E-010
4.3 6.33E-011   -3.37E-010
4.25    6.33E-011   -4.32E-010
4.2 6.33E-011   -7.29E-010
4.15    6.33E-011   -2.17E-012
4.1 6.33E-011   1.62E-010
4.05    6.32E-011   -1.63E-010
4   6.32E-011   -2.73E-010
3.95    6.33E-011   -9.93E-011
3.9 6.32E-011   1.77E-010
3.85    6.32E-011   -3.26E-010
3.8 6.32E-011   -2.47E-010 
3.75    6.32E-011   -1.59E-010
3.7 6.30E-011   -1.03E-010
3.65    6.30E-011   -7.15E-011
3.6 6.31E-011   -3.02E-010
3.55    6.30E-011   2.52E-010
3.5 6.31E-011   -2.98E-010
3.45    6.29E-011   -1.21E-010
3.4 6.29E-011   -1.97E-010
3.35    6.29E-011   -6.97E-011
3.3 6.29E-011   -1.68E-010
3.25    6.28E-011   2.52E-010
3.2 6.28E-011   -2.66E-010
3.15    6.28E-011   -6.52E-010
3.1 6.27E-011   2.78E-011
3.05    6.27E-011   -4.69E-010
3   6.27E-011   -2.63E-010
2.95    6.26E-011   -3.00E-010
2.9 6.26E-011   -2.23E-010
2.85    6.25E-011   -4.05E-010
2.8 6.25E-011   -2.68E-010
2.75    6.25E-011   -5.19E-010
2.7 6.23E-011   9.14E-011
2.65    6.24E-011   -5.05E-010
2.6 6.22E-011   -4.39E-010
2.55    6.21E-011   -4.11E-010
2.5 6.21E-011   1.71E-010
2.45    6.20E-011   2.35E-010
2.4 6.19E-011   -1.20E-010
2.35    6.18E-011   -9.91E-012
2.3 6.18E-011   -6.99E-011
2.25    6.17E-011   -2.35E-010
2.2 6.15E-011   -6.35E-010
2.15    6.14E-011   -2.10E-010
2.1 6.13E-011   -3.70E-010
2.05    6.11E-011   -2.89E-010
2   6.10E-011   1.06E-010
1.95    6.09E-011   -3.23E-010
1.9 6.07E-011   1.37E-010
1.85    6.05E-011   -2.40E-010
1.8 6.03E-011   -1.04E-010
1.75    6.00E-011   -1.72E-010
1.7 5.98E-011   -4.59E-011
1.65    5.96E-011   -4.71E-010
1.6 5.91E-011   -4.40E-010
1.55    5.88E-011   -2.11E-010
1.5 5.84E-011   -3.97E-010
1.45    5.78E-011   -1.37E-010
1.4 5.74E-011   -2.56E-010
1.35    5.66E-011   -3.33E-010  
1.3 5.58E-011   -1.61E-011
1.25    5.50E-011   -3.73E-011
1.2 5.39E-011   -2.02E-010 
1.15    5.27E-011   2.62E-011
1.1 5.12E-011   1.48E-010
1.05    4.94E-011   -5.94E-011 
1   4.75E-011   -2.22E-010
0.95    4.52E-011   5.05E-011
0.9 4.27E-011   -2.08E-010
0.85    4.02E-011   -3.30E-011
0.8 3.77E-011   2.84E-010
0.75    3.52E-011   -2.50E-010
0.7 3.30E-011   7.79E-010
0.65    3.11E-011   9.33E-010
0.6 2.93E-011   9.51E-010
0.55    2.78E-011   7.86E-010
0.5 2.65E-011   5.22E-010
0.45    2.54E-011   7.77E-011
0.4 2.44E-011   7.67E-011
0.35    2.36E-011   -2.22E-010
0.3 2.28E-011   -1.93E-010
0.25    2.21E-011   -1.78E-010
0.2 2.15E-011   4.91E-011
0.15    2.09E-011   -1.97E-010
0.1 2.04E-011   -4.07E-010
0.05    1.99E-011   -1.37E-0 10
0   1.95E-011   -1.58E-010
-0.05   1.91E-011   -2.27E-010
-0.1    1.88E-011   -4.24E-010
-0.15   1.86E-011   -3.00E-010
-0.2    1.83E-011   2.35E-010
-0.25   1.81E-011   2.87E-010
-0.3    1.79E-011   -7.89E-011
-0.35   1.78E-011   5.05E-010
-0.4    1.77E-011   8.43E-011
-0.45   1.76E-011   -1.67E-010
-0.5    1.75E-011   -3.21E-010
-0.55   1.74E-011   -1.39E-010
-0.6    1.74E-011   -2.56E-010
-0.65   1.73E-011   6.28E-011
-0.7    1.72E-011   -1.39E-010
-0.75   1.71E-011   1.07E-010
-0.8    1.70E-011   2.98E-010
-0.85   1.69E-011   -4.11E-011
-0.9    1.68E-011   -2.59E-010
-0.95   1.68E-011   -4.53E-010 
-1  1.67E-011   -4.97E-010
-1.05   1.66E-011   -3.11E-010
-1.1    1.65E-011   1.02E-010
-1.15   1.64E-011   3.58E-010
-1.2    1.64E-011   2.33E-011
-1.25   1.63E-011   -1.96E-011
-1.3    1.62E-011   -2.55E-010
-1.35   1.61E-011   -1.24E-010
-1.4    1.60E-011   9.76E-011
-1.45   1.60E-011   -1.30E-010
-1.5    1.59E-011   -1.94E-010
-1.55   1.59E-011   3.96E-010
-1.6    1.58E-011   -9.73E-013
-1.65   1.58E-011   -3.42E-011
-1.7    1.56E-011   2.40E-010
-1.75   1.56E-011   -2.59E-010
-1.8    1.55E-011   -2.25E-010
-1.85   1.55E-011   -2.09E-010
-1.9    1.54E-011   6.10E-011
-1.95   1.54E-011   -1.91E-010  
-2  1.53E-011   -5.28E-011
-2.05   1.52E-011   -1.15E-010
-2.1    1.52E-011   -1.54E-010
-2.15   1.51E-011   -9.81E-011
-2.2    1.51E-011   -2.18E-011
-2.25   1.50E-011   -4.79E-011
-2.3    1.50E-011   4.71E-011
-2.35   1.50E-011   -3.73E-010
-2.4    1.49E-011   1.50E-010
-2.45   1.48E-011   1.08E-010
-2.5    1.48E-011   -1.51E-010
-2.55   1.48E-011   1.72E-010
-2.6    1.47E-011   -3.49E-011
-2.65   1.47E-011   -2.53E-010
-2.7    1.46E-011   -1.64E-010  
-2.75   1.46E-011   -2.40E-011
-2.8    1.45E-011   -7.15E-011
-2.85   1.45E-011   -2.91E-010
-2.9    1.45E-011   6.30E-011
-2.95   1.45E-011   -2.76E-010
-3  1.45E-011   2.01E-010
-3.05   1.44E-011   -2.15E-010
-3.1    1.44E-011   -9.85E-011  
-3.15   1.43E-011   2.53E-011
-3.2    1.44E-011   5.78E-012
-3.25   1.43E-011   -3.54E-010
-3.3    1.43E-011   3.60E-011
-3.35   1.44E-011   -1.14E-010
-3.4    1.44E-011   -2.33E-010
-3.45   1.44E-011   -3.83E-010 
-3.5    1.44E-011   -3.10E-010
-3.55   1.43E-011   -9.04E-011
-3.6    1.43E-011   -1.86E-010
-3.65   1.43E-011   -3.67E-010
-3.7    1.44E-011   8.13E-011
-3.75   1.43E-011   -1.46E-010
-3.8    1.43E-011   2.34E-010
-3.85   1.44E-011   -1.07E-011
-3.9    1.44E-011   -2.10E-010
-3.95   1.44E-011   -1.86E-010
-4  1.45E-011   -4.67E-011
-4.05   1.44E-011   -1.51E-010
-4.1    1.45E-011   1.09E-010
-4.15   1.44E-011   1.94E-010
-4.2    1.45E-011   -8.02E-011
-4.25   1.45E-011   -1.25E-010
-4.3    1.46E-011   -1.47E-010
-4.35   1.46E-011   -2.76E-010
-4.4    1.46E-011   5.60E-011
-4.45   1.47E-011   -6.24E-011
-4.5    1.48E-011   1.79E-010
-4.55   1.49E-011   -1.71E-010
-4.6    1.49E-011   1.49E-010
-4.65   1.50E-011   -4.05E-011
-4.7    1.50E-011   8.56E-012
-4.75   1.51E-011   -3.71E-010
-4.8    1.52E-011   2.12E-010
-4.85   1.53E-011   -2.04E-010
-4.9    1.54E-011   -1.97E-012
-4.95   1.56E-011   -4.94E-010
-5  1.58E-011   -2.03E-010

Answer 1

Your problem is that your input x-coordinates are in decreasing order. UnivariateSpline expects them to be in increasing order.

Here’s a more compact version of your code above that reproduces the problems you were having. (The data you had in your question is expected to be in a file called data.txt).

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

data = np.loadtxt('data.txt')
x = data[:,0]
y = data[:,1]

spline = UnivariateSpline(x, y, s=0)
xi = np.linspace(x.min(), x.max(), 1000)
yi = spline(xi) 

p1 = plt.plot(x, y, 'bo', label='Original Points')
p2 = plt.plot(xi, yi, 'g', label='Interpolated Points')
plt.legend()
plt.show()

Obviously, that didn’t work right.

However, if you take a look at your input data, your “x” coordinates are in decreasing order. If we simply reverse the input “x” and “y” data, it works perfectly.

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

data = np.loadtxt('data.txt')
x = data[:,0][::-1] # Reversing the input data...
y = data[:,1][::-1]

spline = UnivariateSpline(x, y, s=0)
xi = np.linspace(x.min(), x.max(), 1000)
yi = spline(xi) 

p1 = plt.plot(x, y, 'bo', label='Original Points')
p2 = plt.plot(xi, yi, 'g', label='Interpolated Points')
plt.legend()
plt.show()