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Merge pull request #29 from betatim/benchmarks
Benchmark functions were locked into one of the tests
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"""A collection of benchmark problems""" | ||
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import numpy as np | ||
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def branin(x, a=1, b=5.1 / (4 * np.pi**2), c=5. / np.pi, | ||
r=6, s=10, t=1. / (8 * np.pi)): | ||
"""Branin-Hoo function is defined on the square x1 ∈ [-5, 10], x2 ∈ [0, 15]. | ||
It has three minima with f(x*) = 0.397887 at x* = (-pi, 12.275), | ||
(+pi, 2.275), and (9.42478, 2.475). | ||
More details: <http://www.sfu.ca/~ssurjano/branin.html> | ||
""" | ||
return (a * (x[1] - b * x[0]**2 + c * x[0] - r)**2 + | ||
s * (1 - t) * np.cos(x[0]) + s) | ||
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def hartmann_6(x, | ||
alpha=np.asarray([1.0, 1.2, 3.0, 3.2]), | ||
P=10**-4 * np.asarray([[1312, 1696, 5569, 124, 8283, 5886], | ||
[2329, 4135, 8307, 3736, 1004, 9991], | ||
[2348, 1451, 3522, 2883, 3047, 6650], | ||
[4047, 8828, 8732, 5743, 1091, 381]]), | ||
A=np.asarray([[10, 3, 17, 3.50, 1.7, 8], | ||
[0.05, 10, 17, 0.1, 8, 14], | ||
[3, 3.5, 1.7, 10, 17, 8], | ||
[17, 8, 0.05, 10, 0.1, 14]])): | ||
"""The six dimensional Hartmann function is defined on the unit hypercube. | ||
It has six local minima and one global minimum f(x*) = -3.32237 at | ||
x* = (0.20169, 0.15001, 0.476874, 0.275332, 0.311652, 0.6573). | ||
More details: <http://www.sfu.ca/~ssurjano/hart6.html> | ||
""" | ||
return -np.sum(alpha * np.exp(-np.sum(A * (x - P)**2, axis=1))) |
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import numpy as np | ||
from sklearn.utils.testing import assert_array_almost_equal | ||
from sklearn.utils.testing import assert_almost_equal | ||
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from skopt.benchmarks import branin | ||
from skopt.benchmarks import hartmann_6 | ||
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def test_branin(): | ||
xstars = np.asarray([(-np.pi, 12.275), (+np.pi, 2.275), (9.42478, 2.475)]) | ||
f_at_xstars = np.asarray([branin(xstar) for xstar in xstars]) | ||
branin_min = np.array([0.397887] * xstars.shape[0]) | ||
assert_array_almost_equal(f_at_xstars, branin_min) | ||
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def test_hartmann6(): | ||
assert_almost_equal(hartmann_6((0.20169, 0.15001, 0.476874, | ||
0.275332, 0.311652, 0.6573)), | ||
-3.32237, | ||
decimal=5) |
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