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"""
Unit test for DIRECT optimization algorithm.
"""
from numpy.testing import (assert_allclose,
assert_array_less)
import pytest
import numpy as np
from scipy.optimize import direct, Bounds
import threading
class TestDIRECT:
def setup_method(self):
self.fun_calls = threading.local()
self.bounds_sphere = 4*[(-2, 3)]
self.optimum_sphere_pos = np.zeros((4, ))
self.optimum_sphere = 0.0
self.bounds_stylinski_tang = Bounds([-4., -4.], [4., 4.])
self.maxiter = 1000
# test functions
def sphere(self, x):
if not hasattr(self.fun_calls, 'c'):
self.fun_calls.c = 0
self.fun_calls.c += 1
return np.square(x).sum()
def inv(self, x):
if np.sum(x) == 0:
raise ZeroDivisionError()
return 1/np.sum(x)
def nan_fun(self, x):
return np.nan
def inf_fun(self, x):
return np.inf
def styblinski_tang(self, pos):
x, y = pos
return 0.5 * (x**4 - 16 * x**2 + 5 * x + y**4 - 16 * y**2 + 5 * y)
@pytest.mark.parametrize("locally_biased", [True, False])
def test_direct(self, locally_biased):
res = direct(self.sphere, self.bounds_sphere,
locally_biased=locally_biased)
# test accuracy
assert_allclose(res.x, self.optimum_sphere_pos,
rtol=1e-3, atol=1e-3)
assert_allclose(res.fun, self.optimum_sphere, atol=1e-5, rtol=1e-5)
# test that result lies within bounds
_bounds = np.asarray(self.bounds_sphere)
assert_array_less(_bounds[:, 0], res.x)
assert_array_less(res.x, _bounds[:, 1])
# test number of function evaluations. Original DIRECT overshoots by
# up to 500 evaluations in last iteration
assert res.nfev <= 1000 * (len(self.bounds_sphere) + 1)
# test that number of function evaluations is correct
assert res.nfev == self.fun_calls.c
# test that number of iterations is below supplied maximum
assert res.nit <= self.maxiter
@pytest.mark.parametrize("locally_biased", [True, False])
def test_direct_callback(self, locally_biased):
# test that callback does not change the result
res = direct(self.sphere, self.bounds_sphere,
locally_biased=locally_biased)
def callback(x):
x = 2*x
dummy = np.square(x)
print("DIRECT minimization algorithm callback test")
return dummy
res_callback = direct(self.sphere, self.bounds_sphere,
locally_biased=locally_biased,
callback=callback)
assert_allclose(res.x, res_callback.x)
assert res.nit == res_callback.nit
assert res.nfev == res_callback.nfev
assert res.status == res_callback.status
assert res.success == res_callback.success
assert res.fun == res_callback.fun
assert_allclose(res.x, res_callback.x)
assert res.message == res_callback.message
# test accuracy
assert_allclose(res_callback.x, self.optimum_sphere_pos,
rtol=1e-3, atol=1e-3)
assert_allclose(res_callback.fun, self.optimum_sphere,
atol=1e-5, rtol=1e-5)
@pytest.mark.parametrize("locally_biased", [True, False])
def test_exception(self, locally_biased):
bounds = 4*[(-10, 10)]
with pytest.raises(ZeroDivisionError):
direct(self.inv, bounds=bounds,
locally_biased=locally_biased)
@pytest.mark.parametrize("locally_biased", [True, False])
def test_nan(self, locally_biased):
bounds = 4*[(-10, 10)]
direct(self.nan_fun, bounds=bounds,
locally_biased=locally_biased)
@pytest.mark.parametrize("len_tol", [1e-3, 1e-4])
@pytest.mark.parametrize("locally_biased", [True, False])
def test_len_tol(self, len_tol, locally_biased):
bounds = 4*[(-10., 10.)]
res = direct(self.sphere, bounds=bounds, len_tol=len_tol,
vol_tol=1e-30, locally_biased=locally_biased)
assert res.status == 5
assert res.success
assert_allclose(res.x, np.zeros((4, )))
message = ("The side length measure of the hyperrectangle containing "
"the lowest function value found is below "
f"len_tol={len_tol}")
assert res.message == message
@pytest.mark.parametrize("vol_tol", [1e-6, 1e-8])
@pytest.mark.parametrize("locally_biased", [True, False])
def test_vol_tol(self, vol_tol, locally_biased):
bounds = 4*[(-10., 10.)]
res = direct(self.sphere, bounds=bounds, vol_tol=vol_tol,
len_tol=0., locally_biased=locally_biased)
assert res.status == 4
assert res.success
assert_allclose(res.x, np.zeros((4, )))
message = ("The volume of the hyperrectangle containing the lowest "
f"function value found is below vol_tol={vol_tol}")
assert res.message == message
@pytest.mark.parametrize("f_min_rtol", [1e-3, 1e-5, 1e-7])
@pytest.mark.parametrize("locally_biased", [True, False])
def test_f_min(self, f_min_rtol, locally_biased):
# test that desired function value is reached within
# relative tolerance of f_min_rtol
f_min = 1.
bounds = 4*[(-2., 10.)]
res = direct(self.sphere, bounds=bounds, f_min=f_min,
f_min_rtol=f_min_rtol,
locally_biased=locally_biased)
assert res.status == 3
assert res.success
assert res.fun < f_min * (1. + f_min_rtol)
message = ("The best function value found is within a relative "
f"error={f_min_rtol} of the (known) global optimum f_min")
assert res.message == message
def circle_with_args(self, x, a, b):
return np.square(x[0] - a) + np.square(x[1] - b).sum()
@pytest.mark.parametrize("locally_biased", [True, False])
def test_f_circle_with_args(self, locally_biased):
bounds = 2*[(-2.0, 2.0)]
res = direct(self.circle_with_args, bounds, args=(1, 1), maxfun=1250,
locally_biased=locally_biased)
assert_allclose(res.x, np.array([1., 1.]), rtol=1e-5)
@pytest.mark.parametrize("locally_biased", [True, False])
def test_failure_maxfun(self, locally_biased):
# test that if optimization runs for the maximal number of
# evaluations, success = False is returned
maxfun = 100
result = direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxfun=maxfun, locally_biased=locally_biased)
assert result.success is False
assert result.status == 1
assert result.nfev >= maxfun
message = ("Number of function evaluations done is "
f"larger than maxfun={maxfun}")
assert result.message == message
@pytest.mark.parametrize("locally_biased", [True, False])
def test_failure_maxiter(self, locally_biased):
# test that if optimization runs for the maximal number of
# iterations, success = False is returned
maxiter = 10
result = direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxiter=maxiter, locally_biased=locally_biased)
assert result.success is False
assert result.status == 2
assert result.nit >= maxiter
message = f"Number of iterations is larger than maxiter={maxiter}"
assert result.message == message
@pytest.mark.parametrize("locally_biased", [True, False])
def test_bounds_variants(self, locally_biased):
# test that new and old bounds yield same result
lb = [-6., 1., -5.]
ub = [-1., 3., 5.]
x_opt = np.array([-1., 1., 0.])
bounds_old = list(zip(lb, ub))
bounds_new = Bounds(lb, ub)
res_old_bounds = direct(self.sphere, bounds_old,
locally_biased=locally_biased)
res_new_bounds = direct(self.sphere, bounds_new,
locally_biased=locally_biased)
assert res_new_bounds.nfev == res_old_bounds.nfev
assert res_new_bounds.message == res_old_bounds.message
assert res_new_bounds.success == res_old_bounds.success
assert res_new_bounds.nit == res_old_bounds.nit
assert_allclose(res_new_bounds.x, res_old_bounds.x)
assert_allclose(res_new_bounds.x, x_opt, rtol=1e-2)
@pytest.mark.parametrize("locally_biased", [True, False])
@pytest.mark.parametrize("eps", [1e-5, 1e-4, 1e-3])
def test_epsilon(self, eps, locally_biased):
result = direct(self.styblinski_tang, self.bounds_stylinski_tang,
eps=eps, vol_tol=1e-6,
locally_biased=locally_biased)
assert result.status == 4
assert result.success
@pytest.mark.xslow
@pytest.mark.parametrize("locally_biased", [True, False])
def test_no_segmentation_fault(self, locally_biased):
# test that an excessive number of function evaluations
# does not result in segmentation fault
bounds = [(-5., 20.)] * 100
result = direct(self.sphere, bounds, maxfun=10000000,
maxiter=1000000, locally_biased=locally_biased)
assert result is not None
@pytest.mark.parametrize("locally_biased", [True, False])
def test_inf_fun(self, locally_biased):
# test that an objective value of infinity does not crash DIRECT
bounds = [(-5., 5.)] * 2
result = direct(self.inf_fun, bounds,
locally_biased=locally_biased)
assert result is not None
@pytest.mark.parametrize("len_tol", [-1, 2])
def test_len_tol_validation(self, len_tol):
error_msg = "len_tol must be between 0 and 1."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
len_tol=len_tol)
@pytest.mark.parametrize("vol_tol", [-1, 2])
def test_vol_tol_validation(self, vol_tol):
error_msg = "vol_tol must be between 0 and 1."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
vol_tol=vol_tol)
@pytest.mark.parametrize("f_min_rtol", [-1, 2])
def test_fmin_rtol_validation(self, f_min_rtol):
error_msg = "f_min_rtol must be between 0 and 1."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
f_min_rtol=f_min_rtol, f_min=0.)
@pytest.mark.parametrize("maxfun", [1.5, "string", (1, 2)])
def test_maxfun_wrong_type(self, maxfun):
error_msg = "maxfun must be of type int."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxfun=maxfun)
@pytest.mark.parametrize("maxiter", [1.5, "string", (1, 2)])
def test_maxiter_wrong_type(self, maxiter):
error_msg = "maxiter must be of type int."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxiter=maxiter)
def test_negative_maxiter(self):
error_msg = "maxiter must be > 0."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxiter=-1)
def test_negative_maxfun(self):
error_msg = "maxfun must be > 0."
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
maxfun=-1)
@pytest.mark.parametrize("bounds", ["bounds", 2., 0])
def test_invalid_bounds_type(self, bounds):
error_msg = ("bounds must be a sequence or "
"instance of Bounds class")
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, bounds)
@pytest.mark.parametrize("bounds",
[Bounds([-1., -1], [-2, 1]),
Bounds([-np.nan, -1], [-2, np.nan]),
]
)
def test_incorrect_bounds(self, bounds):
error_msg = 'Bounds are not consistent min < max'
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, bounds)
def test_inf_bounds(self):
error_msg = 'Bounds must not be inf.'
bounds = Bounds([-np.inf, -1], [-2, np.inf])
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, bounds)
@pytest.mark.parametrize("locally_biased", ["bias", [0, 0], 2.])
def test_locally_biased_validation(self, locally_biased):
error_msg = 'locally_biased must be True or False.'
with pytest.raises(ValueError, match=error_msg):
direct(self.styblinski_tang, self.bounds_stylinski_tang,
locally_biased=locally_biased)
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