Python中如何查找绘制曲线的极小值点对应的x和y坐标

方法1：直接找全局最小值（适配你当前的单谷曲线） #

你的数据是单调递减后单调递增的，只有一个全局极小值，直接用np.argmin获取最小值对应的下标即可：

import numpy as np
import matplotlib.pyplot as plt

# 你的原有数据
a_list = [0.019514047519378953, 0.019688745408747047, 0.019863443298115138, 0.020038141187483233, 0.020212839076851324, 0.020387536966219415, 0.02056223485558751, 0.0207369327449556, 0.020911630634323698, 0.021086328523691786, 0.02126102641305988, 0.02143572430242797, 0.021610422191796066, 0.021785120081164157, 0.02195981797053225, 0.022134515859900342, 0.022309213749268433, 0.022483911638636528, 0.02265860952800462, 0.02283330741737271, 0.023008005306740804, 0.0231827031961089, 0.023357401085476993, 0.02353209897484508, 0.023706796864213175, 0.02388149475358127, 0.02405619264294936, 0.024230890532317455, 0.024405588421685546, 0.024580286311053638, 0.02475498420042173, 0.024929682089789823, 0.025104379979157914, 0.02527907786852601, 0.025453775757894103, 0.025628473647262194, 0.02580317153663029, 0.025977869425998376, 0.02615256731536647, 0.02632726520473456, 0.026501963094102656, 0.02667666098347075, 0.02685135887283884, 0.027026056762206936, 0.027200754651575027, 0.02737545254094312, 0.02755015043031121, 0.027724848319679304, 0.027899546209047395]
b_list = [0.998835898052097, 0.9977458605969758, 0.996730130628437, 0.9957889355330694, 0.9949224868405108, 0.994130979989584, 0.9934145941108957, 0.9927734918264597, 0.992207819066857, 0.9917177049064095, 0.9913032614168004, 0.9909645835395204, 0.9907017489774841, 0.9905148181060986, 0.9904038339040244, 0.9903688219038117, 0.990409790162546, 0.99052672925258, 0.9907196122723776, 0.9909883948774414, 0.9913330153312387, 0.991753394575993, 0.9922494363231483, 0.992821027163268, 0.993468036695076, 0.9941903176732974, 0.9949877061749134, 0.9958600217833934, 0.9968070677904258, 0.99782863141463, 0.998924484036687, 1.000094381450296, 1.0013380641283243, 1.0026552575034904, 1.0040456722628917, 1.0055090046556592, 1.0070449368130043, 1.0086531370798995, 1.0103332603576196, 1.0120849484563605, 1.0139078304571334, 1.0158015230821371, 1.017765631072797, 1.019799747574664, 1.0219034545283667, 1.0240763230658112, 1.0263179139108383, 1.028627777783547, 1.031005455807516]

# 转成numpy数组方便操作
a_arr = np.array(a_list)
b_arr = np.array(b_list)

# 找最小值的索引
min_idx = np.argmin(b_arr)
# 获取对应坐标
min_x = a_arr[min_idx]
min_y = b_arr[min_idx]

print(f"极小值点坐标：x = {min_x}, y = {min_y}")

# 绘图验证
plt.plot(a_arr, b_arr, label='原始曲线')
plt.scatter(min_x, min_y, color='red', s=50, label=f'极小值点 ({min_x:.4f}, {min_y:.4f})')
plt.xlabel("A")
plt.ylabel("B")
plt.legend()
plt.show()

运行后输出的极小值坐标为：
x = 0.022134515859900342, y = 0.9903688219038117

方法2：查找所有局部极小值（适配多谷曲线） #

如果你的曲线存在多个局部极小值，可以用scipy.signal.find_peaks实现，原理是把y值取反后找峰值，对应原数据的极小值：

from scipy.signal import find_peaks

# 对b_arr取反，找峰值就是原数据的极小值
peaks, _ = find_peaks(-b_arr)
# 所有局部极小值的坐标
local_min_x = a_arr[peaks]
local_min_y = b_arr[peaks]

print("所有局部极小值坐标：")
for x, y in zip(local_min_x, local_min_y):
    print(f"x = {x}, y = {y}")

如果数据有噪声，可以给find_peaks加distance、height等参数过滤误识别的极小值点。

内容的提问来源于stack exchange，提问作者SDGAL