如何找到函数的所有极值点（最小值和最大值）

Question

我想找出一个函数的所有极值点。

这是我目前尝试过的方法：

import matplotlib.pyplot as plt
from scipy.signal import find_peaks

scale_factor = 0.01 
peaks, _ = find_peaks(derivation)
plt.plot(x_values[:-2], derivation)
plt.plot(peaks*scale_factor, derivation[peaks], "x")
plt.show()

这是输出：

问题是我想要所有的极值点而不仅仅是最大值。有人可以向我解释我如何才能做到这一点吗？因为接下来我打算将极值点相互比较。因此我也需要 y 值。但是 peaks 只给我 x 位置。有人可以帮我吗？非常感谢。

这是我的数据：

derivation=[   9.88,   -2.12,   29.88,   -2.12,    9.88,   16.88,    9.88,
          4.88,    9.88,   -2.12,    9.88,   16.88,   10.88,    9.88,
         10.88,    9.88,    4.88,    3.88,   -2.12,    9.88,    3.88,
         10.88,   10.88,    9.88,    9.88,   10.88,   10.88,   15.88,
         16.88,   16.88,   22.88,   34.88,   41.88,   53.88,   60.88,
         -2.12,   72.88,   84.88,   97.88,  110.88,  128.88,  141.88,
        159.88,  172.88,  191.88,  203.88,  222.88,  241.88,  266.88,
        272.88,  297.88,  303.88,  322.88,  303.88,  279.88,  240.88,
        166.88,   97.88,   22.88,  -46.12,  -64.12,  -90.12, -139.12,
       -134.12, -164.12, -190.12,   -2.12, -202.12, -226.12, -221.12,
       -227.12, -234.12, -214.12, -214.12, -215.12, -215.12, -208.12,
       -196.12, -189.12, -183.12, -184.12, -189.12, -183.12, -177.12,
       -165.12, -152.12, -146.12,   -2.12, -152.12, -170.12, -171.12,
       -177.12, -171.12, -177.12, -170.12, -159.12, -133.12, -108.12,
        -77.12,  -52.12,  -27.12,   -8.12,   21.88,   47.88,   -2.12,
         73.88,   84.88,   91.88,  109.88,  122.88,  103.88,  110.88,
        110.88,  109.88,  109.88,  110.88,   91.88,   78.88,   66.88,
         53.88,   47.88,   34.88,   29.88,   -2.12,   22.88,   22.88,
         15.88,   16.88,   10.88,    3.88,    9.88,    4.88,   -2.12,
         16.88,   -2.12,    3.88,  -15.12,   -8.12,  -15.12,   -8.12,
         -8.12,   -2.12,   -8.12,   -8.12,   -9.12,   -8.12,   -8.12,
         -2.12,   -9.12]

和

x_values=[0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,
       0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,
       0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,
       0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,
       0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,
       0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,
       0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,
       0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,
       0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,
       0.99, 1.  , 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09,
       1.1 , 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.2 ,
       1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.3 , 1.31,
       1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39, 1.4 , 1.41, 1.42,
       1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.5]

Answer 1

我们可以编写少量代码来找到派生列表中的峰。然后我们就可以收集对应的指数了。

编辑：如果没有现有的库，这将是最好的方法

# store indexes
idx = []
for i, v in enumerate(derivation):
    # left and right can not be peaks
    if i > 0 and i < len(derivation)-1:
        # if local max then add to index list
        if derivation[i-1] < v < derivation[i+1]:
            idx.append(i)

# all local maximas
local_max = [derivation[i] for i in idx]
# corresponding x_values
local_max_idx = [x_values[i] for i in idx]

Answer 2

这样的事情对你有用吗？

xdata = [1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.8, 2.1, 2.5] 
ydata = [0.0, 0.1, 0.2, 0.1, 0.3, 0.4, 0.8, 0.3, -0.1] #random data with min and max


max_indices = []
min_indices = []
for i in range(1,len(ydata)-1):
    
    if ydata[i]>ydata[i-1] and ydata[i]>ydata[i+1]:
        max_indices.append(i)
    
    
    if ydata[i]<ydata[i-1] and ydata[i]<ydata[i+1]:
        min_indices.append(i)


max_x_vals = []        
max_y_vals = []
for j in max_indices:
    max_x_vals.append(xdata[j])
    max_y_vals.append(ydata[j])
    
min_x_vals = []
min_y_vals = []
for k in min_indices:
    min_x_vals.append(xdata[k])
    min_y_vals.append(ydata[k])
    

print(max_x_vals)
print(max_y_vals)

print(min_x_vals)
print(min_y_vals)


output: 
[1.3, 1.8]
[0.2, 0.8]
[1.4]
[0.1]

下面的绘图代码。

import matplotlib.pyplot as plt

plt.plot(xdata, ydata)
plt.scatter(max_x_vals, max_y_vals, color = 'red')
plt.scatter(min_x_vals, min_y_vals, color = 'orange')

Output plot

Answer 3

抱歉，如果我误解了您在评论中的意思；您可以使用 scipy.signal.argrelextrema 来计算最大值和最小值：

import matplotlib.pyplot as plt
import numpy as np
from scipy.signal import find_peaks, argrelextrema

derivation = np.array(derivation)
x_values = np.array(x_values)

scale_factor = 0.01
maxima = argrelextrema(derivation, np.greater)
minima = argrelextrema(derivation, np.less)
extrema = np.concatenate([maxima, minima], axis=None)
plt.plot(x_values[:-2], derivation)
plt.plot(extrema*scale_factor, derivation[extrema], "x")
plt.show()

并且您始终可以在原始文件中使用 derivation[extrema] 或 derivation[peaks] 来获取与每个峰关联的 y 值。

如何找到函数的所有极值点（最小值和最大值）

How can I find all extreme points of the function (minimun and maximum)

python

signals

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