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In [1]:



    


import numpy as np
import pwlf
# generate sin wave data
x = np.linspace(0, 10, num=100)
y = np.sin(x * np.pi / 2)
# add noise to the data
y = np.random.normal(0, 0.05, 100) + y
my_pwlf_2 = pwlf.PiecewiseLinFit(x, y, degree=2)
res2 = my_pwlf_2.fitfast(5, pop=50)



    











In [2]:



    


import matplotlib.pyplot as plt
%matplotlib inline
# first line
xhat = np.linspace(my_pwlf_2.fit_breaks[0], my_pwlf_2.fit_breaks[1], 100)
yhat = my_pwlf_2.beta[0] + my_pwlf_2.beta[1]*(xhat-my_pwlf_2.fit_breaks[0]) + my_pwlf_2.beta[6]*(xhat-my_pwlf_2.fit_breaks[0])**2
plt.figure()
plt.plot(x, y, 'o')
plt.plot(xhat, yhat, '-.', label='First segment')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()



    


















    
























In [3]:



    


# second segment
xhat2 = np.linspace(my_pwlf_2.fit_breaks[1], my_pwlf_2.fit_breaks[2], 100)
yhat2 = (my_pwlf_2.beta[0] +
         (my_pwlf_2.beta[1])*(xhat2-my_pwlf_2.fit_breaks[0]) +
         (my_pwlf_2.beta[2])*(xhat2-my_pwlf_2.fit_breaks[1]) +
         (my_pwlf_2.beta[6])*(xhat2-my_pwlf_2.fit_breaks[0])**2 +
         (my_pwlf_2.beta[7])*(xhat2-my_pwlf_2.fit_breaks[1])**2)
plt.plot(x, y, 'o')
plt.plot(xhat, yhat, '-.', label='First segment')
plt.plot(xhat2, yhat2, '-.', label='Second segment')

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()



    


















    
























In [4]:



    


# Third segment
xhat3 = np.linspace(my_pwlf_2.fit_breaks[2], my_pwlf_2.fit_breaks[3], 100)
yhat3 = (my_pwlf_2.beta[0] +
         (my_pwlf_2.beta[1])*(xhat3-my_pwlf_2.fit_breaks[0]) +
         (my_pwlf_2.beta[2])*(xhat3-my_pwlf_2.fit_breaks[1]) +
         (my_pwlf_2.beta[3])*(xhat3-my_pwlf_2.fit_breaks[2]) +
         (my_pwlf_2.beta[6])*(xhat3-my_pwlf_2.fit_breaks[0])**2 +
         (my_pwlf_2.beta[7])*(xhat3-my_pwlf_2.fit_breaks[1])**2 +
         (my_pwlf_2.beta[8])*(xhat3-my_pwlf_2.fit_breaks[2])**2)
plt.plot(x, y, 'o')
plt.plot(xhat, yhat, '-.', label='First segment')
plt.plot(xhat2, yhat2, '-.', label='Second segment')
plt.plot(xhat3, yhat3, '-.', label='Third segment')

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()



    


















    
























In [5]:



    


# Fourth segment
xhat4 = np.linspace(my_pwlf_2.fit_breaks[3], my_pwlf_2.fit_breaks[4], 100)
yhat4 = (my_pwlf_2.beta[0] +
         (my_pwlf_2.beta[1])*(xhat4-my_pwlf_2.fit_breaks[0]) +
         (my_pwlf_2.beta[2])*(xhat4-my_pwlf_2.fit_breaks[1]) +
         (my_pwlf_2.beta[3])*(xhat4-my_pwlf_2.fit_breaks[2]) +
         (my_pwlf_2.beta[4])*(xhat4-my_pwlf_2.fit_breaks[3]) +
         (my_pwlf_2.beta[6])*(xhat4-my_pwlf_2.fit_breaks[0])**2 +
         (my_pwlf_2.beta[7])*(xhat4-my_pwlf_2.fit_breaks[1])**2 +
         (my_pwlf_2.beta[8])*(xhat4-my_pwlf_2.fit_breaks[2])**2 +
         (my_pwlf_2.beta[9])*(xhat4-my_pwlf_2.fit_breaks[3])**2)
plt.plot(x, y, 'o')
plt.plot(xhat, yhat, '-.', label='First')
plt.plot(xhat2, yhat2, '-.', label='Second')
plt.plot(xhat3, yhat3, '-.', label='Third')
plt.plot(xhat4, yhat4, '-.', label='Fourth')

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()



    


















    
























In [6]:



    


# Fifth segment
xhat5 = np.linspace(my_pwlf_2.fit_breaks[4], my_pwlf_2.fit_breaks[5], 100)
yhat5 = (my_pwlf_2.beta[0] +
         (my_pwlf_2.beta[1])*(xhat5-my_pwlf_2.fit_breaks[0]) +
         (my_pwlf_2.beta[2])*(xhat5-my_pwlf_2.fit_breaks[1]) +
         (my_pwlf_2.beta[3])*(xhat5-my_pwlf_2.fit_breaks[2]) +
         (my_pwlf_2.beta[4])*(xhat5-my_pwlf_2.fit_breaks[3]) +
         (my_pwlf_2.beta[5])*(xhat5-my_pwlf_2.fit_breaks[4]) +
         (my_pwlf_2.beta[6])*(xhat5-my_pwlf_2.fit_breaks[0])**2 +
         (my_pwlf_2.beta[7])*(xhat5-my_pwlf_2.fit_breaks[1])**2 +
         (my_pwlf_2.beta[8])*(xhat5-my_pwlf_2.fit_breaks[2])**2 +
         (my_pwlf_2.beta[9])*(xhat5-my_pwlf_2.fit_breaks[3])**2 +
         (my_pwlf_2.beta[10])*(xhat5-my_pwlf_2.fit_breaks[4])**2)
plt.plot(x, y, 'o')
plt.plot(xhat, yhat, '-.', label='First')
plt.plot(xhat2, yhat2, '-.', label='Second')
plt.plot(xhat3, yhat3, '-.', label='Third')
plt.plot(xhat4, yhat4, '-.', label='Fourth')
plt.plot(xhat5, yhat5, '-.', label='Fifth')

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()



    


















    
























In [7]:



    


from sympy import Symbol
from sympy.utilities import lambdify
x = Symbol('x')

def get_symbolic_eqn(pwlf_, segment_number):
    if pwlf_.degree < 1:
        raise ValueError('Degree must be at least 1')
    if segment_number < 1 or segment_number > pwlf_.n_segments:
        raise ValueError('segment_number not possible')
    # assemble degree = 1 first
    for line in range(segment_number):
        if line == 0:
            my_eqn = pwlf_.beta[0] + (pwlf_.beta[1])*(x-pwlf_.fit_breaks[0])
        else:
            my_eqn += (pwlf_.beta[line+1])*(x-pwlf_.fit_breaks[line])
    # assemble all other degrees
    if pwlf_.degree > 1:
        for k in range(2, pwlf_.degree + 1):
            for line in range(segment_number):
                beta_index = pwlf_.n_segments*(k-1) + line + 1 
                my_eqn += (pwlf_.beta[beta_index])*(x-pwlf_.fit_breaks[line])**k
    return my_eqn.simplify()

eqn1 = get_symbolic_eqn(my_pwlf_2, 1)



    











In [8]:



    


eqn_list = []
f_list = []
for i in range(my_pwlf_2.n_segments):
    eqn_list.append(get_symbolic_eqn(my_pwlf_2, i + 1))
    print('Equation number: ', i + 1)
    print(eqn_list[-1])
    f_list.append(lambdify(x, eqn_list[-1]))



    


















    






Equation number:  1
-0.953964059782599*x**2 + 1.89945177490653*x + 0.00538634182565454
Equation number:  2
0.951561315686298*x**2 - 5.69747505830914*x + 7.5772216545711
Equation number:  3
-0.949735350431857*x**2 + 9.48218236957122*x - 22.720785454735
Equation number:  4
0.926850298824217*x**2 - 12.9824424358344*x + 44.5102742956827
Equation number:  5
-1.03016230425747*x**2 + 18.5306546317065*x - 82.3508513333073

















In [9]:



    


yhat1 = f_list[0](xhat)
yhat2 = f_list[1](xhat2)
yhat3 = f_list[2](xhat3)
yhat4 = f_list[3](xhat4)
yhat5 = f_list[4](xhat5)
xtemp = np.linspace(0,10, 1000)
plt.plot(my_pwlf_2.x_data, my_pwlf_2.y_data, 'o')
plt.plot(xtemp, my_pwlf_2.predict(xtemp), '-k', label='Predict')
plt.plot(xhat, yhat1, '-.', label='First')
plt.plot(xhat2, yhat2, '-.', label='Second')
plt.plot(xhat3, yhat3, '-.', label='Third')
plt.plot(xhat4, yhat4, '-.', label='Fourth')
plt.plot(xhat5, yhat5, '-.', label='Fifth')

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

Content source: cjekel/piecewise_linear_fit_py

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