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# Running an optimization to find the best number of line segments
# import our libraries
import numpy as np
import matplotlib.pyplot as plt
import pwlf
from GPyOpt.methods import BayesianOptimization
# your data
y = np.array([0.00000000e+00, 9.69801700e-03, 2.94350340e-02,
4.39052750e-02, 5.45343950e-02, 6.74104940e-02,
8.34831790e-02, 1.02580042e-01, 1.22767939e-01,
1.42172312e-01, 0.00000000e+00, 8.58600000e-06,
8.31543400e-03, 2.34184100e-02, 3.39709150e-02,
4.03581990e-02, 4.53545600e-02, 5.02345260e-02,
5.55253360e-02, 6.14750770e-02, 6.82125120e-02,
7.55892510e-02, 8.38356810e-02, 9.26413070e-02,
1.02039790e-01, 1.11688258e-01, 1.21390666e-01,
1.31196948e-01, 0.00000000e+00, 1.56706510e-02,
3.54628780e-02, 4.63739040e-02, 5.61442590e-02,
6.78542550e-02, 8.16388310e-02, 9.77756110e-02,
1.16531753e-01, 1.37038283e-01, 0.00000000e+00,
1.16951050e-02, 3.12089850e-02, 4.41776550e-02,
5.42877590e-02, 6.63321350e-02, 8.07655920e-02,
9.70363280e-02, 1.15706975e-01, 1.36687642e-01,
0.00000000e+00, 1.50144640e-02, 3.44519970e-02,
4.55907760e-02, 5.59556700e-02, 6.88450940e-02,
8.41374060e-02, 1.01254006e-01, 1.20605073e-01,
1.41881288e-01, 1.62618058e-01])
x = np.array([0.00000000e+00, 8.82678000e-03, 3.25615100e-02,
5.66106800e-02, 7.95549800e-02, 1.00936330e-01,
1.20351520e-01, 1.37442010e-01, 1.51858250e-01,
1.64433570e-01, 0.00000000e+00, -2.12600000e-05,
7.03872000e-03, 1.85494500e-02, 3.00926700e-02,
4.17617000e-02, 5.37279600e-02, 6.54941000e-02,
7.68092100e-02, 8.76596300e-02, 9.80525800e-02,
1.07961810e-01, 1.17305210e-01, 1.26063930e-01,
1.34180360e-01, 1.41725010e-01, 1.48629710e-01,
1.55374770e-01, 0.00000000e+00, 1.65610200e-02,
3.91016100e-02, 6.18679400e-02, 8.30997400e-02,
1.02132890e-01, 1.19011260e-01, 1.34620080e-01,
1.49429370e-01, 1.63539960e-01, -0.00000000e+00,
1.01980300e-02, 3.28642800e-02, 5.59461900e-02,
7.81388400e-02, 9.84458400e-02, 1.16270210e-01,
1.31279040e-01, 1.45437090e-01, 1.59627540e-01,
0.00000000e+00, 1.63404300e-02, 4.00086000e-02,
6.34390200e-02, 8.51085900e-02, 1.04787860e-01,
1.22120350e-01, 1.36931660e-01, 1.50958760e-01,
1.65299640e-01, 1.79942720e-01])
# initialize piecewise linear fit with your x and y data
my_pwlf = pwlf.PiecewiseLinFit(x, y)
# define your objective function
def my_obj(x):
# define some penalty parameter l
# you'll have to arbitrarily pick this
# it depends upon the noise in your data,
# and the value of your sum of square of residuals
l = y.mean()*0.001
f = np.zeros(x.shape[0])
for i, j in enumerate(x):
my_pwlf.fit(j[0])
f[i] = my_pwlf.ssr + (l*j[0])
return f
# define the lower and upper bound for the number of line segements
bounds = [{'name': 'var_1', 'type': 'discrete', 'domain': np.arange(2, 40)}]
np.random.seed(12121)
myBopt = BayesianOptimization(my_obj, domain=bounds, model_type='GP',
initial_design_numdata=10,
initial_design_type='latin',
exact_feval=True, verbosity=True,
verbosity_model=False)
max_iter = 30
# perform the bayesian optimization to find the optimum number of line segments
myBopt.run_optimization(max_iter=max_iter, verbosity=True)
print('\n \n Opt found \n')
print('Optimum number of line segments:', myBopt.x_opt)
print('Function value:', myBopt.fx_opt)
myBopt.plot_acquisition()
myBopt.plot_convergence()
# perform the fit for the optimum
my_pwlf.fit(myBopt.x_opt)
# predict for the determined points
xHat = np.linspace(min(x), max(x), num=10000)
yHat = my_pwlf.predict(xHat)
# plot the results
plt.figure()
plt.plot(x, y, 'o')
plt.plot(xHat, yHat, '-')
plt.show()
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