使用 scipy.optimize.curve_fit 执行加权线性拟合

Question

我想执行加权线性拟合以提取方程 y = mx+c 中的参数 m 和 c。我要进行拟合的数据是：

xdata = [661.657, 1173.228, 1332.492, 511.0, 1274.537]

ydata = [242.604, 430.086, 488.825, 186.598, 467.730]

yerr = [0.08, 0.323, 0.249, 0.166, 0.223]

我想使用 scipy.optimize.curve_fit 但我不知道如何在每个 y 数据点都有与之关联的错误时使用它。

Answer 1

IIUC 那么您正在寻找的是 sigma 关键字参数。

sigma: None or M-length sequence or MxM array, optional

Determines the uncertainty in ydata. If we define residuals as r = ydata - f(xdata, *popt), 
then the interpretation of sigma depends on its number of dimensions:
A 1-d sigma should contain values of standard deviations of errors in ydata. 
In this case, the optimized function is chisq = sum((r / sigma) ** 2).

None (default) is equivalent of 1-d sigma filled with ones.

那么代码会变成：

def func(x, m, c):
    return m * x + c

curve_fit(func, xdata, ydata, sigma=yerr)

使用 scipy.optimize.curve_fit 执行加权线性拟合

Performing a weighted linear fit with scipy.optimize.curve_fit

python

curve-fitting

scipy

linear-regression

least-squares