["python","numpy","scipy","curve-fitting","piecewise"]
How to apply piecewise linear fit in Python?

I am trying to fit piecewise linear fit as shown in fig.1 for a data set 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'\textit{y_a}') plot.plot(x, y_fit, linestyle = ':', linewidth = 0.25, markeredgecolor='none', marker = '', label = r'\textit{y_b}') plot.set_ylabel('Y', labelpad = 6) plot.set_xlabel('X', labelpad = 6) figure.savefig('test.pdf', box_inches='tight') plt.close() 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. I want the code to recognize and fit two linear fits in the appropriate range. How can this be done in Python?
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)) the output: For an N parts fitting, please reference segments_fit.ipynb