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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 2020-2026 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
Example applying mystic to sklearn
Use a linear regression to fit sparse data generated from:
f(x) = a*x3**3 + b*x2**2 + c*x1 + d*x0
a,b,c,d = 0.661, -1.234, 2.983, -16.5571
Where the following information is utilized:
f(x) is a polynomial of order=3
3*b + c > -0.75
4.5*b - d > 11.0
"""
import numpy as np
from sklearn import preprocessing as pre
from sklearn import linear_model as lin
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.constraints import vectorize
from mystic import random_seed
random_seed(123)
# define a model
a,b,c,d = 0.661, -1.234, 2.983, -16.5571
def model(x):
x0,x1,x2,x3 = x
return a*x3**3 + b*x2**2 + c*x1 + d*x0
# generate some sparse training data
xtrain = np.random.uniform(0,100, size=(10,4))
target = model(xtrain.T).T
# generate sparse test data outside the training region
xtest = np.random.uniform(100,200, size=(10,4))
test = model(xtest.T).T
# define some model constraints
equations = """
3*b + c > -0.75
4.5*b - d > 11.0
"""
var = list('abcd')
equations = simplify(equations, variables=var)
cf = generate_constraint(generate_solvers(equations, variables=var))
if __name__ == '__main__':
# build a kernel-transformed regressor
ta = pre.FunctionTransformer(func=vectorize(cf, axis=1))
tp = pre.PolynomialFeatures(degree=3)
e = lin.LinearRegression()
# build a pipeline, then train
from sklearn.pipeline import Pipeline
pipe = Pipeline([('ta', ta), ('tp', tp), ('e', e)])
pipe = pipe.fit(xtrain, target)
# get training score and test score
assert 1.0 == pipe.score(xtrain, target)
assert 1 - pipe.score(xtest, test) <= 1e-2
# EOF
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