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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
Fit linear and quadratic polynomial to noisy data:
y(x) ~ a + b * x --or-- y(x) ~ a + b * x + c * x**2
where:
0 >= x >= 4
y(x) = y0(x) + yn
y0(x) = 1.5 * exp(-0.2 * x) + 0.3
yn = 0.1 * Normal(0,1)
"""
from numpy import polyfit, poly1d, linspace, exp
from numpy.random import normal
from mystic.math import polyeval
from mystic import reduced
# Create clean data.
x = linspace(0, 4.0, 100)
y0 = 1.5 * exp(-0.2 * x) + 0.3
# Add a bit of noise.
noise = 0.1 * normal(size=100)
y = y0 + noise
@reduced(lambda x,y: abs(x)+abs(y))
def objective(coeffs, x, y):
return polyeval(coeffs, x) - y
bounds = [(None, None), (None, None)]
bounds_ = [(None, None), (None, None), (None, None)]
args = (x, y)
# 'solution' is:
xs = polyfit(x, y, 1)
xs_ = polyfit(x, y, 2)
ys = objective(xs, x, y)
ys_ = objective(xs_, x, y)
if __name__ == '__main__':
from mystic.solvers import diffev2, fmin_powell
from mystic.math import almostEqual
# from mystic.monitors import VerboseMonitor
# mon = VerboseMonitor(10)
result = diffev2(objective, args=args, x0=bounds, bounds=bounds, npop=40, ftol=1e-8, gtol=100, disp=False, full_output=True)#, itermon=mon)
# print("%s %s" % (result[0], xs))
assert almostEqual(result[0], xs, rel=1e-1)
assert almostEqual(result[1], ys, rel=1e-1)
result = fmin_powell(objective, args=args, x0=[0.0,0.0], bounds=bounds, disp=False, full_output=True)
# print("%s %s" % (result[0], xs))
assert almostEqual(result[0], xs, rel=1e-1)
assert almostEqual(result[1], ys, rel=1e-1)
# mon = VerboseMonitor(10)
result = diffev2(objective, args=args, x0=bounds_, bounds=bounds_, npop=40, ftol=1e-8, gtol=100, disp=False, full_output=True)#, itermon=mon)
# print("%s %s" % (result[0], xs_))
assert almostEqual(result[0], xs_, tol=1e-1)
assert almostEqual(result[1], ys_, rel=1e-1)
result = fmin_powell(objective, args=args, x0=[0.0,0.0,0.0], bounds=bounds_, disp=False, full_output=True)
# print("%s %s" % (result[0], xs_))
assert almostEqual(result[0], xs_, tol=1e-1)
assert almostEqual(result[1], ys_, rel=1e-1)
# EOF
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