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import pytest
from iminuit import minimize
import numpy as np
from numpy.testing import assert_allclose, assert_equal
opt = pytest.importorskip("scipy.optimize")
def func(x, *args):
c = args[0] if args else 1
return c + x[0] ** 2 + (x[1] - 1) ** 2 + (x[2] - 2) ** 2
def grad(x, *args):
return 2 * (x - (0, 1, 2))
def test_simple():
result = minimize(func, (1, 1, 1))
assert_allclose(result.x, (0, 1, 2), atol=1e-8)
assert_allclose(result.fun, 1)
assert result.nfev > 0
assert result.njev == 0
def test_gradient():
result = minimize(func, (1, 1, 1), jac=grad)
assert_allclose(result.x, (0, 1, 2), atol=1e-8)
assert_allclose(result.fun, 1)
assert result.nfev > 0
assert result.njev > 0
def test_args():
result = minimize(func, np.ones(3), args=(5,))
assert_allclose(result.x, (0, 1, 2), atol=1e-8)
assert_allclose(result.fun, 5)
assert result.nfev > 0
assert result.njev == 0
def test_callback():
trace = []
result = minimize(func, np.ones(3), callback=lambda x: trace.append(x.copy()))
assert_allclose(result.x, (0, 1, 2), atol=1e-8)
assert_allclose(result.fun, 1)
assert result.nfev == len(trace)
assert_allclose(trace[0], np.ones(3), atol=1e-2)
assert_allclose(trace[-1], result.x, atol=1e-2)
def test_tol():
ref = np.ones(2)
def rosen(par):
x, y = par
return (1 - x) ** 2 + 100 * (y - x**2) ** 2
r1 = minimize(rosen, (0, 0), tol=1)
r2 = minimize(rosen, (0, 0), tol=1e-6)
assert max(np.abs(r2.x - ref)) < max(np.abs(r1.x - ref))
def test_disp(capsys):
minimize(lambda x: np.sum(x**2), 0)
assert capsys.readouterr()[0] == ""
minimize(lambda x: np.sum(x**2), 0, options={"disp": True})
assert capsys.readouterr()[0] != ""
def test_hessinv():
r = minimize(func, (1, 1, 1))
href = np.zeros((3, 3))
for i in range(3):
href[i, i] = 0.5
assert_allclose(r.hess_inv, href, atol=1e-8)
def test_unsupported():
with pytest.raises(ValueError):
minimize(func, (1, 1, 1), constraints=[])
with pytest.raises(ValueError):
minimize(func, (1, 1, 1), jac=True)
def test_call_limit():
ref = minimize(func, (1, 1, 1))
with pytest.warns(UserWarning):
r1 = minimize(func, (1, 1, 1), options={"maxiter": 1})
assert r1.nfev < ref.nfev
assert not r1.success
assert "Call limit" in r1.message
with pytest.warns(DeprecationWarning):
r2 = minimize(func, (1, 1, 1), options={"maxfev": 1})
assert not r2.success
assert r2.nfev == r1.nfev
r3 = minimize(func, (1, 1, 1), options={"maxfun": 1})
assert not r3.success
assert r3.nfev == r1.nfev
def test_eps():
ref = minimize(func, (1, 1, 1))
r = minimize(func, (1, 1, 1), options={"eps": 1e-10})
assert np.any(ref.x != r.x)
assert_allclose(r.x, ref.x, atol=1e-9)
def test_bad_function():
class Fcn:
n = 0
def __call__(self, x):
self.n += 1
return np.sum(x**2 + 1e-2 * (self.n % 3))
r = minimize(Fcn(), [1], options={"maxfun": 100000000})
assert not r.success
assert "Estimated distance to minimum too large" in r.message
def test_bounds():
r1 = minimize(func, (1.5, 1.7, 1.5), bounds=opt.Bounds((1, 1.5, 1), (2, 2, 2)))
assert r1.success
assert_allclose(r1.x, (1, 1.5, 2), atol=1e-2)
r2 = minimize(func, (1.5, 1.7, 1.5), bounds=((1, 2), (1.5, 2), (1, 2)))
assert r2.success
assert_equal(r1.x, r2.x)
def test_method_warn():
with pytest.raises(ValueError):
minimize(func, (1.5, 1.7, 1.5), method="foo")
def test_hess_warn():
with pytest.warns(UserWarning):
minimize(func, (1.5, 1.7, 1.5), hess=True)
def test_unreliable_uncertainties():
r = minimize(func, (1.5, 1.7, 1.5), options={"stra": 0})
assert (
r.message
== "Optimization terminated successfully, but uncertainties are unrealiable."
)
def test_simplex():
r = minimize(func, (1.5, 1.7, 1.5), method="simplex", tol=1e-4)
assert r.success
assert_allclose(r.x, (0, 1, 2), atol=2e-3)
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