使用scipy curve_fit的absolute_sigma参数时触发ValueError错误

我编写了如下Python代码，用于通过模拟数据做线性拟合：

import numpy as np
from scipy.optimize import curve_fit

def lin_func(x, a, b):
    return a * x + b

a = 0.005/4
b = 10000/4
N = 10000

position_list = np.array([-100,-50,-20,0,20,50,100]) 

def get_params(N):
    counts_list = np.zeros(len(position_list))
    for i in range(len(position_list)):
        position_0 = position_list[i]
        counts = 0
        for j in range(N):
            position = np.random.normal(position_0,10)
            p = 0.5+a+b*position*10**(-6) 
            counts = counts + np.sum(np.random.binomial(1000, p, 1)) 
        counts_list[i] = counts
    print(np.sqrt(counts_list))
    popt, pcov = curve_fit(lin_func, position_list*10**(-6), counts_list, absolute_sigma = np.sqrt(counts_list))
    return popt[1]/(N*1000)

K = 100
params_list = np.zeros(K)
for i in range(K):
    params_list[i] = get_params(N)-0.5
    print(params_list[i])

程序运行后触发如下错误：

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

该错误仅在添加absolute_sigma = np.sqrt(counts_list)参数时出现，移除该参数则运行正常，出错前打印的counts_list数值无异常。完整报错栈信息如下：

ValueError                                Traceback (most recent call last)
Cell In[10], line 4
      2 params_list = np.zeros(K)
      3 for i in range(K):
----> 4     params_list[i] = get_params(N)-0.5
      5     print(params_list[i])

Cell In[9], line 13, in get_params(N)
     11     counts_list[i] = counts
     12 print(np.sqrt(counts_list))
---> 13 popt, pcov = curve_fit(lin_func, position_list*10**(-6), counts_list, absolute_sigma = np.sqrt(counts_list))
     14 return popt[1]/(N*1000)

File ~/miniforge3/lib/python3.10/site-packages/scipy/optimize/_minpack_py.py:897, in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, full_output, **kwargs)
    895     pcov.fill(inf)
    896     warn_cov = True
--> 897 elif not absolute_sigma:
    898     if ysize > p0.size:
    899         s_sq = cost / (ysize - p0.size)

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

解决方案 #

问题出在参数传错了：

• absolute_sigma是一个布尔值参数，作用是指定sigma参数传入的误差是绝对误差还是相对权重；
• 你要传入的误差数组np.sqrt(counts_list)应该传给sigma参数，而不是absolute_sigma。

修正后的curve_fit调用代码如下：

popt, pcov = curve_fit(lin_func, position_list*10**(-6), counts_list, sigma=np.sqrt(counts_list), absolute_sigma=True)

这样既传入了每个数据点的误差数组，又通过absolute_sigma=True声明这是绝对误差，就不会触发布尔值判断的歧义错误了。

内容的提问来源于stack exchange，提问作者Alex Marshall