python - 为什么包络曲线一开始就是错误的？

Question

我实现了一个给出离散值包络曲线的函数。我认为可能存在错误，因为当我在帖子底部提供的日期进行测试时，我得到了真实数据点与包络曲线之间的差异，如下图所示

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

def enveloppe(s):
    u_x = [0,]        
    u_y = [s[0],]
    q_u = np.zeros(s.shape)
    for k in xrange(1,len(s)-1):
        if (np.sign(s[k]-s[k-1])==1) and (np.sign(s[k]-s[k+1])==1):
            u_x.append(k)
            u_y.append(s[k])
    u_x.append(len(s)-1)
    u_y.append(s[-1]) 
    u_p = interp1d(u_x,u_y, kind = 'cubic',bounds_error = False, fill_value=0.0)
    #Evaluate each model over the domain of (s)
    for k in xrange(0,len(s)):
        q_u[k] = u_p(k)
    return q_u   

fig, ax = plt.subplots()
ax.plot(S, '-o', label = 'magnitude')
ax.plot(envelope(S), '-o', label = 'enveloppe magnitude')
ax.legend()

<小时/>

Data S : array([  9.12348621e-11,   6.69568658e-10,   6.55973768e-09,
         1.26822485e-06,   4.50553316e-09,   5.06526113e-07,
         2.96728433e-09,   2.36088205e-07,   1.90802318e-09,
         1.15867354e-07,   1.18504790e-09,   5.72888034e-08,
         6.98672478e-10,   2.75361324e-08,   3.82391643e-10,
         1.25393143e-08,   1.96697343e-10,   5.96979943e-09,
         1.27009013e-10,   4.46365555e-09,   1.31769958e-10,
         4.42024233e-09,   1.42514400e-10,   4.17757107e-09,
         1.41640360e-10,   3.65170558e-09,   1.29784598e-10,
         2.99790514e-09,   1.11732461e-10])

Answer 1

我会对你的信封函数进行两项修改以获得更单调的输出

这个想法是避免将左端和右端隐式添加到用于构造包络的峰值列表中

def enveloppe(s):
    u_x = [] # do not add 0
    u_y = []
    q_u = np.zeros(s.shape)
    for k in range(1,len(s)-1):
        if (np.sign(s[k]-s[k-1])==1) and (np.sign(s[k]-s[k+1])==1):
            u_x.append(k)
            u_y.append(s[k])
    print(u_x)
    u_p = interp1d(u_x,u_y, kind = 'cubic',
              bounds_error = False, 
              fill_value="extrapolate") # use fill_value="extrapolate"
    for k in range(0,len(s)):
        q_u[k] = u_p(k)
    return q_u