How to force the fit process to have a fixed Intercept?

[riemanncode]

is it possible to choose the value of the intercept for the first segment? In a simple linear regression this can be done easily, but I don't know how to specify a "fixed intercept" here.

considering your main example, you have the intercept of this fitted data that is b0=5.

import numpy as np
import matplotlib.pyplot as plt
import pwlf

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])

my_pwlf = pwlf.PiecewiseLinFit(x, y)
breaks = my_pwlf.fit(2)
print(breaks)

Can I force the fitting process to have the intercept value equal to 6?
Something like..

breaks1 = my_pwlf.fit(2,fixed_b0=6)

That would be helpful. Thank you

[cjekel]

What you can do in the meantime is use constraints x_c and y_c.

It's not the same solution as what you would do to explicitly fix the intercept, because technically the intercept is still a model parameter this way. The constrained least squares fit should figure out how to solve the constrain by fixing the intercept easily. However, this constrained least squares fit is less robust than a method that explicitly fixes the intercept.

import numpy as np
import matplotlib.pyplot as plt
import pwlf
import matplotlib.pyplot as plt

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])

my_pwlf = pwlf.PiecewiseLinFit(x, y)
breaks = my_pwlf.fit(2, x_c=[0.0], y_c=[6.0])
print(breaks)

print(my_pwlf.predict([0.0]))

x_hat = np.linspace(-1.0, 20, 100)
y_hat = my_pwlf.predict(x_hat)

plt.figure()
plt.plot(x_hat, y_hat)
plt.plot([0.0],[6.0], '*k')
plt.show()