如何在 Python 中应用分段线性拟合? [英] How to apply piecewise linear fit in Python?

问题描述

我正在尝试对数据集进行分段线性拟合，如图 1 所示

I am trying to fit piecewise linear fit as shown in fig.1 for a data set

这个数字是通过设置在线获得的.我尝试使用代码应用分段线性拟合:

This figure was obtained by setting on the lines. I attempted to apply a piecewise linear fit using the code:

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


x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15])
y = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03])


def linear_fit(x, a, b):
    return a * x + b
fit_a, fit_b = optimize.curve_fit(linear_fit, x[0:5], y[0:5])[0]
y_fit = fit_a * x[0:7] + fit_b
fit_a, fit_b = optimize.curve_fit(linear_fit, x[6:14], y[6:14])[0]
y_fit = np.append(y_fit, fit_a * x[6:14] + fit_b)


figure = plt.figure(figsize=(5.15, 5.15))
figure.clf()
plot = plt.subplot(111)
ax1 = plt.gca()
plot.plot(x, y, linestyle = '', linewidth = 0.25, markeredgecolor='none', marker = 'o', label = r'	extit{y_a}')
plot.plot(x, y_fit, linestyle = ':', linewidth = 0.25, markeredgecolor='none', marker = '', label = r'	extit{y_b}')
plot.set_ylabel('Y', labelpad = 6)
plot.set_xlabel('X', labelpad = 6)
figure.savefig('test.pdf', box_inches='tight')
plt.close()    

但这给了我图 1 中的形式的拟合.2，我尝试使用这些值，但没有任何变化，我无法正确拟合上线.对我来说最重要的需求是如何让Python获得梯度变化点.本质上，我希望 Python 能够识别并在适当的范围内拟合两个线性拟合.如何在 Python 中完成此操作?

But this gave me fitting of the form in fig. 2, I tried playing with the values but no change I can't get the fit of the upper line proper. The most important requirement for me is how can I get Python to get the gradient change point. In essence I want Python to recognize and fit two linear fits in the appropriate range. How can this be done in Python?

推荐答案

您可以使用 numpy.piecewise() 创建分段函数，然后使用 curve_fit(), 这是代码

You can use numpy.piecewise() to create the piecewise function and then use curve_fit(), Here is the code

from scipy import optimize
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline

x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15], dtype=float)
y = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03])

def piecewise_linear(x, x0, y0, k1, k2):
    return np.piecewise(x, [x < x0], [lambda x:k1*x + y0-k1*x0, lambda x:k2*x + y0-k2*x0])

p , e = optimize.curve_fit(piecewise_linear, x, y)
xd = np.linspace(0, 15, 100)
plt.plot(x, y, "o")
plt.plot(xd, piecewise_linear(xd, *p))

输出:

N个零件拟合请参考segments_fit.ipynb

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