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a.py
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a.py
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# lsqfitgp/examples/a.py
#
# Copyright (c) 2020, 2022, Giacomo Petrillo
#
# This file is part of lsqfitgp.
#
# lsqfitgp is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# lsqfitgp is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with lsqfitgp. If not, see <http://www.gnu.org/licenses/>.
"""
EXAMPLE A.
Where the oscillating nature of an unknown function is revealed
from but a few points, though only to a certain distance.
"""
import lsqfitgp as lgp
from matplotlib import pyplot as plt
import numpy as np
import gvar
xdata = np.linspace(0, 10, 10)
xpred = np.linspace(-15, 25, 300)
y = np.sin(xdata)
u = (lgp
.GP(lgp.ExpQuad(scale=3))
.addx(xdata, 'pere')
.addx(xpred, 'banane')
.predfromdata({'pere': y}, 'banane')
)
m = gvar.mean(u)
s = gvar.sdev(u)
cov = gvar.evalcov(u)
fig, ax = plt.subplots(num='a', clear=True)
patch = ax.fill_between(xpred, m - s, m + s, label='pred', alpha=0.5)
color = patch.get_facecolor()[0]
simulated_lines = np.random.multivariate_normal(m, cov, size=10)
ax.plot(xpred, simulated_lines.T, '-', color=color)
ax.plot(xdata, y, 'k.', label='data')
ax.legend(loc='best')
fig.show()