In [1]:
import numpy as np
import matplotlib.pyplot as plt
import pwlf
pwlf.__version__
%matplotlib inline
This jupyter notebook uses SLSQP to apply a constraint function to force a minimum line segment length. You'll need to supply a starting point (or guess) to start the optimization. If you don't know what is a good starting point, check out how I use Latin Hypercube random sampling to run multiple optimizations in the fitfast function.
A constraint function could look like:
def my_con(var):
var = np.sort(var)
distances = np.zeros(number_of_line_segments)
distances[0] = var[0] - my_pwlf.break_0
distances[-1] = my_pwlf.break_n - var[-1]
for i in range(number_of_line_segments - 2):
distances[i+1] = var[i+1] - var[i]
# element must be greater or equal to 0.0
# in a successfully optimized problem
return np.array((distances.min() - min_length))
This is a single constraint for the minimum length of all segments. It's possible that the min() in this function will create issues with the gradient of the constraint. If you run into issues with this, you may want to investigate using a separate constraint for each line segment. That could be done by changing:
return np.array((distances.min() - min_length))
to
return distances - min_length
In [2]:
# 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])
In [3]:
# initialize piecewise linear fit with your x and y data
my_pwlf = pwlf.PiecewiseLinFit(x, y)
# initialize custom optimization
number_of_line_segments = 3
my_pwlf.use_custom_opt(number_of_line_segments)
# minium length of a segment
min_length = 0.05
In [4]:
def my_con(var):
var = np.sort(var)
distances = np.zeros(number_of_line_segments)
distances[0] = var[0] - my_pwlf.break_0
distances[-1] = my_pwlf.break_n - var[-1]
for i in range(number_of_line_segments - 2):
distances[i+1] = var[i+1] - var[i]
# element must be greater or equal to 0.0
# in a successfully optimized problem
return np.array((distances.min() - min_length))
In [5]:
from scipy.optimize import fmin_slsqp
# i have number_of_line_segments - 1 number of variables
# let's guess the correct location of the two unknown variables
# (the program defaults to have end segments at x0= min(x)
# and xn=max(x)
xGuess = np.zeros(number_of_line_segments - 1)
xGuess[0] = 0.06
xGuess[1] = 0.13
bounds = np.zeros((number_of_line_segments - 1, 2))
bounds[:, 0] = my_pwlf.break_0
bounds[:, 1] = my_pwlf.break_n
res = fmin_slsqp(my_pwlf.fit_with_breaks_opt, xGuess, f_ieqcons=my_con,
bounds=bounds, iter=100, acc=1e-06, iprint=1,
epsilon=1.4901161193847656e-08)
In [6]:
# set up the break point locations
x0 = np.zeros(number_of_line_segments + 1)
x0[0] = np.min(x)
x0[-1] = np.max(x)
x0[1:-1] = res
# calculate the parameters based on the optimal break point locations
my_pwlf.fit_with_breaks(x0)
# predict for the determined points
xHat = np.linspace(min(x), max(x), num=10000)
yHat = my_pwlf.predict(xHat)
plt.figure()
plt.plot(x, y, 'o')
plt.plot(xHat, yHat, '-')
plt.show()
In [ ]: