Python: 如何将一条线拟合到特定的数据区间？

Question

我正在尝试为我的数据集的 9.0 到 10.0 um 范围拟合一条线。这是我的情节：

不幸的是，这是一个散点图，其中 x 值没有从小数字到大数字进行索引，所以我不能只将 optimize.curve_fit 函数应用于特定范围的索引来获得x 值中的所需范围。

以下是我进行曲线拟合的首选程序。我将如何修改它以仅适合 9.0 到 10.0 um x 值范围（在我的例子中，x_dist 变量），该范围内的点随机分布在整个索引中？

    def func(x,a,b):                                # Define your fitting function
    return a*x+b                                  
  
initialguess = [-14.0, 0.05]                     # initial guess for the parameters of the function func

fit, covariance = optimize.curve_fit(             # call to the fitting routine curve_fit.  Returns optimal values of the fit parameters, and their estimated variance
        func,                                     # function to fit
        x_dist,                                    # data for independant variable
        xdiff_norm,                                    # data for dependant variable
        initialguess,                             # initial guess of fit parameters
        )                                     # uncertainty in dependant variable

print("linear coefficient:",fit[0],"+-",np.sqrt(covariance[0][0])) #print value and one std deviation of first fit parameter
print("offset coefficient:",fit[1],"+-",np.sqrt(covariance[1][1]))     #print value and one std deviation of second fit parameter

print(covariance)

Answer 1

您正确地确定问题的出现是因为您的 x 值数据未排序。您可以用不同的方式解决这个问题。一种方法是使用布尔掩码来过滤掉不需要的值。我试图尽可能接近你的例子：

from matplotlib import pyplot as plt
import numpy as np
from scipy import optimize

#fake data generation
np.random.seed(1234)
arr = np.linspace(0, 15, 100).reshape(2, 50)
arr[1, :] = np.random.random(50)
arr[1, 20:45] += 2 * arr[0, 20:45] -5
rng = np.random.default_rng()
rng.shuffle(arr, axis = 1)
x_dist = arr[0, :]
xdiff_norm = arr[1, :]

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

initialguess = [5, 3]
mask = (x_dist>2.5) & (x_dist<6.6)
fit, covariance = optimize.curve_fit(           
        func,                                     
        x_dist[mask],   
        xdiff_norm[mask],    
        initialguess)   

plt.scatter(x_dist, xdiff_norm, label="data")
x_fit = np.linspace(x_dist[mask].min(), x_dist[mask].max(), 100)
y_fit = func(x_fit, *fit)
plt.plot(x_fit, y_fit, c="red", label="fit")
plt.legend()
plt.show()

示例输出：

此方法不会修改 x_dist 和 xdiff_norm，这对于进一步的数据评估可能是好事，也可能不是好事。如果您想使用折线图而不是散点图，提前对数组进行排序可能会很有用（尝试使用上述方法绘制折线图以了解原因）：

from matplotlib import pyplot as plt
import numpy as np
from scipy import optimize

#fake data generation
np.random.seed(1234)
arr = np.linspace(0, 15, 100).reshape(2, 50)
arr[1, :] = np.random.random(50)
arr[1, 20:45] += 2 * arr[0, 20:45] -5
rng = np.random.default_rng()
rng.shuffle(arr, axis = 1)
x_dist = arr[0, :]
xdiff_norm = arr[1, :]

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

#find indexes of a sorted x_dist array, then sort both arrays based on this index
ind = x_dist.argsort()
x_dist = x_dist[ind]
xdiff_norm = xdiff_norm[ind]

#identify index where linear range starts for normal array indexing
start = np.argmax(x_dist>2.5)
stop = np.argmax(x_dist>6.6)

initialguess = [5, 3]
fit, covariance = optimize.curve_fit(           
        func,                                     
        x_dist[start:stop],   
        xdiff_norm[start:stop],    
        initialguess)   

plt.plot(x_dist, xdiff_norm, label="data")
x_fit = np.linspace(x_dist[start], x_dist[stop], 100)
y_fit = func(x_fit, *fit)
plt.plot(x_fit, y_fit, c="red", ls="--", label="fit")
plt.legend()
plt.show()

示例输出（不出所料，差别不大）：

Python: 如何将一条线拟合到特定的数据区间？

Python: How do I fit a line to a specific interval of data?

python

curve-fitting

scipy

scipy-optimize