在scipy python中使用UnivariateSpline擬合數據

Question

我有一個試驗數據，我試圖用scipy中的UnivariateSpline函數擬合曲線。數據是這樣的：

x   y 
13 2.404070 
12 1.588134 
11 1.760112 
10 1.771360 
09 1.860087 
08 1.955789 
07 1.910408 
06 1.655911 
05 1.778952 
04 2.624719 
03 1.698099 
02 3.022607 
01 3.303135  

下面是我在做什麼：

import matplotlib.pyplot as plt 
from scipy import interpolate 
yinterp = interpolate.UnivariateSpline(x, y, s = 5e8)(x) 
plt.plot(x, y, 'bo', label = 'Original') 
plt.plot(x, yinterp, 'r', label = 'Interpolated') 
plt.show() 

這是它的外觀：

如果任何人有其他曲線以爲我不知道scipy可能有哪些適合的選項？我對scipy比較陌生。

謝謝！

Answer 1

有幾個問題。

第一個問題是x值的順序。從scipy.interpolate.UnivariateSpline的文檔，我們發現

x : (N,) array_like 
    1-D array of independent input data. MUST BE INCREASING. 

強調由我添加。對於你給出的數據，x是相反的順序。 要調試此功能，使用「正常」樣條來確保一切都合理有用。

第二個問題與您的問題更直接相關，與s參數有關。它有什麼作用？再次從文檔，我們發現

s : float or None, optional 
    Positive smoothing factor used to choose the number of knots. Number 
    of knots will be increased until the smoothing condition is satisfied: 

    sum((w[i]*(y[i]-s(x[i])))**2,axis=0) <= s 

    If None (default), s=len(w) which should be a good value if 1/w[i] is 
    an estimate of the standard deviation of y[i]. If 0, spline will 
    interpolate through all data points. 

所以小號決定了插值曲線必須多接近來數據點，在最小二乘意義。如果我們將該值設置得非常大，則樣條線不需要靠近數據點。

作爲一個完整的例子考慮以下

import scipy.interpolate as inter 
import numpy as np 
import pylab as plt 

x = np.array([13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) 
y = np.array([2.404070, 1.588134, 1.760112, 1.771360, 1.860087, 
      1.955789, 1.910408, 1.655911, 1.778952, 2.624719, 
      1.698099, 3.022607, 3.303135]) 
xx = np.arange(1,13.01,0.1) 
s1 = inter.InterpolatedUnivariateSpline (x, y) 
s1rev = inter.InterpolatedUnivariateSpline (x[::-1], y[::-1]) 
# Use a smallish value for s 
s2 = inter.UnivariateSpline (x[::-1], y[::-1], s=0.1) 
s2crazy = inter.UnivariateSpline (x[::-1], y[::-1], s=5e8) 
plt.plot (x, y, 'bo', label='Data') 
plt.plot (xx, s1(xx), 'k-', label='Spline, wrong order') 
plt.plot (xx, s1rev(xx), 'k--', label='Spline, correct order') 
plt.plot (xx, s2(xx), 'r-', label='Spline, fit') 
# Uncomment to get the poor fit. 
#plt.plot (xx, s2crazy(xx), 'r--', label='Spline, fit, s=5e8') 
plt.minorticks_on() 
plt.legend() 
plt.xlabel('x') 
plt.ylabel('y') 
plt.show()