How to use Lipschitzian modelling

[1]:

import numpy as np
import pandas as pd
from desdeo_problem.surrogatemodels.lipschitzian import LipschitzianRegressor
import matplotlib.pyplot as plt

[2]:

def y_func(x):
    return(np.sin(x) + np.sin(2*x))

[3]:

num_points = 20
x = np.linspace(0, 2 * np.pi, num_points).reshape(-1,1)
y = y_func(x)
data = pd.DataFrame(np.hstack((x,y)), columns = ['x','y'])

[4]:

model = LipschitzianRegressor()

[5]:

model.fit(X=data['x'], y = data['y'])

[6]:

model.L

[6]:

2.8392177826759726

[7]:

model.y

[7]:

array([[ 0.00000000e+00],
       [ 9.38912182e-01],
       [ 1.58361298e+00],
       [ 1.75293980e+00],
       [ 1.44534766e+00],
       [ 8.31989903e-01],
       [ 1.80049416e-01],
       [-2.60860582e-01],
       [-3.61219085e-01],
       [-1.60104879e-01],
       [ 1.60104879e-01],
       [ 3.61219085e-01],
       [ 2.60860582e-01],
       [-1.80049416e-01],
       [-8.31989903e-01],
       [-1.44534766e+00],
       [-1.75293980e+00],
       [-1.58361298e+00],
       [-9.38912182e-01],
       [-7.34788079e-16]])

[8]:

x_new = np.linspace(0, 2*np.pi, 1000).reshape(-1,1)
y_new_true = y_func(x_new)
y_mean, y_delta = model.predict(x_new)

[9]:

plt.scatter(x_new, y_new_true, marker='.')
plt.scatter(x_new, y_mean, marker='.')
plt.scatter(x_new, y_mean + y_delta, marker='.')
plt.scatter(x_new, y_mean - y_delta, marker='.')

[9]:

<matplotlib.collections.PathCollection at 0x2c4d3b5d9c8>

../_images/notebooks_Lipschitzian_modelling_9_1.png

[10]:

def y_func2d(x):
    return(np.sin(x[:,0]) + np.sin(2*x[:,1]))

[11]:

x = np.random.rand(200,2)
y = y_func2d(x).reshape(-1,1)
data = pd.DataFrame(np.hstack((x,y)), columns = ['x1', 'x2','y'])

[12]:

model = LipschitzianRegressor()
model.fit(X=data[['x1', 'x2']], y = data['y'])

[13]:

x_new = np.random.rand(2000,2)
y_new_true = y_func2d(x_new).reshape(-1,1)
y_predict, y_delta = model.predict(x_new)

[14]:

line = np.linspace(y_new_true.min(),y_new_true.max(),200)
plt.scatter(y_new_true, y_predict.reshape(-1,1), marker=".")
plt.scatter(y_new_true, (y_predict+y_delta).reshape(-1,1), marker=".", alpha=0.3)
plt.scatter(y_new_true, (y_predict-y_delta).reshape(-1,1), marker=".", alpha=0.3)
plt.scatter(line,line, marker='.')

[14]:

<matplotlib.collections.PathCollection at 0x2c4d4c56c08>

../_images/notebooks_Lipschitzian_modelling_14_1.png

[ ]: