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SCIPY 数据相关的 UnivariateSpline 插值问题

发布于 2024-11-02 06:54:29 字数 7361 浏览 5 评论 0原文

我在尝试使用 UnivariateSpline 函数插入数据时遇到一个奇怪的问题。对所有点 (s=0) 和样条函数进行插值不会给出整个数据集的结果。 s>=1 的结果也很奇怪。因为我认为这与我正在使用的数据有关，所以我将它们加入到附件中。
我被困住了，所以如果有人对解决方案有好主意，我将非常感激。

谢谢，

这里是部分代码：

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])

这里是数据：

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
原文

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

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温馨耳语 2024-11-09 06:54:29

您的问题是您输入的 x 坐标按递减顺序排列。 UnivariateSpline 期望它们按递增顺序排列。

这是上面代码的更紧凑版本，它重现了您遇到的问题。 （您问题中的数据预计位于名为 data.txt 的文件中）。

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()

在此处输入图像描述

显然，这不起作用。

但是，如果您查看输入数据，您的“x”坐标将按降序排列。如果我们简单地反转输入“x”和“y”数据，它就可以完美工作。

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()

在此处输入图像描述

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()

enter image description here

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()

enter image description here

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