用枢轴点拟合曲线Python [英] Fitting a curve with a pivot point Python

问题描述

我有下面的图，我想用2条线拟合.使用python，我设法适应了上面的部分:

I have the plot below and I want to fit it with 2 lines. Using python I manage to fit the upper part:

def func(x,a,b):
    x=np.array(x)
    return a*(x**b)
popt,pcov=curve_fit(func,up_x,up_y)

我想在下部用另一条线拟合，但是我希望该线穿过红色的一颗星星的点，因此我可以具有连续的功能.所以我的问题是，如何通过给定函数必须通过的点来使用curve_fit，而让直线的斜率由python计算呢? (或其他任何能够执行此操作的python软件包)

And I want to fit the lower part with another line, but I want the line to pass through the point where the red one stars, so I can have a continuous function. So my question is how can I use curve_fit by giving a point the function has to pass through, but leaving the slope of the line to be calculated by python? (Or any other python package able to do it)

推荐答案

在日志空间中对模型进行可能的逐步参数化是这样的:

A possible stepwise parametrisation of your model in log-space is something like:

(x>q)*((x-q)*a)+(x<q)*((x-q)*c)+b

其中q是纽结的位置，a和c是两个零件的斜率，b是全局y偏移.由于模型具有不连续性，因此基于梯度的最小化器可能不是找到最佳拟合的最佳选择.尽管如此，我同时尝试了scipy.optimize.leastsq和scipy.odr并获得了良好的结果.

Where q is the position of the kink, a, and c are the slopes of both parts and b is a global y-offset. Since the model has a discontinuity a gradient based minimizer might not be the best choice to find a best fit. Nevertheless I tried both scipy.optimize.leastsq and scipy.odr and got good results.

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