File size: 8,143 Bytes
7885a28 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 |
import numpy as np
import pytest
import threading
from numpy.testing import assert_allclose, assert_equal
from scipy.optimize import (
Bounds,
LinearConstraint,
NonlinearConstraint,
OptimizeResult,
minimize,
)
class TestCOBYQA:
def setup_method(self):
self.x0 = [4.95, 0.66]
self.options = {'maxfev': 100}
@staticmethod
def fun(x, c=1.0):
return x[0]**2 + c * abs(x[1])**3
@staticmethod
def con(x):
return x[0]**2 + x[1]**2 - 25.0
def test_minimize_simple(self):
class Callback:
def __init__(self):
self.lock = threading.Lock()
self.n_calls = 0
def __call__(self, x):
assert isinstance(x, np.ndarray)
with self.lock:
self.n_calls += 1
class CallbackNewSyntax:
def __init__(self):
self.lock = threading.Lock()
self.n_calls = 0
def __call__(self, intermediate_result):
assert isinstance(intermediate_result, OptimizeResult)
with self.lock:
self.n_calls += 1
x0 = [4.95, 0.66]
callback = Callback()
callback_new_syntax = CallbackNewSyntax()
# Minimize with method='cobyqa'.
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
sol = minimize(
self.fun,
x0,
method='cobyqa',
constraints=constraints,
callback=callback,
options=self.options,
)
sol_new = minimize(
self.fun,
x0,
method='cobyqa',
constraints=constraints,
callback=callback_new_syntax,
options=self.options,
)
solution = [np.sqrt(25.0 - 4.0 / 9.0), 2.0 / 3.0]
assert_allclose(sol.x, solution, atol=1e-4)
assert sol.success, sol.message
assert sol.maxcv < 1e-8, sol
assert sol.nfev <= 100, sol
assert sol.fun < self.fun(solution) + 1e-3, sol
assert sol.nfev == callback.n_calls, \
"Callback is not called exactly once for every function eval."
assert_equal(sol.x, sol_new.x)
assert sol_new.success, sol_new.message
assert sol.fun == sol_new.fun
assert sol.maxcv == sol_new.maxcv
assert sol.nfev == sol_new.nfev
assert sol.nit == sol_new.nit
assert sol_new.nfev == callback_new_syntax.n_calls, \
"Callback is not called exactly once for every function eval."
def test_minimize_bounds(self):
def fun_check_bounds(x):
assert np.all(bounds.lb <= x) and np.all(x <= bounds.ub)
return self.fun(x)
# Case where the bounds are not active at the solution.
bounds = Bounds([4.5, 0.6], [5.0, 0.7])
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
sol = minimize(
fun_check_bounds,
self.x0,
method='cobyqa',
bounds=bounds,
constraints=constraints,
options=self.options,
)
solution = [np.sqrt(25.0 - 4.0 / 9.0), 2.0 / 3.0]
assert_allclose(sol.x, solution, atol=1e-4)
assert sol.success, sol.message
assert sol.maxcv < 1e-8, sol
assert np.all(bounds.lb <= sol.x) and np.all(sol.x <= bounds.ub), sol
assert sol.nfev <= 100, sol
assert sol.fun < self.fun(solution) + 1e-3, sol
# Case where the bounds are active at the solution.
bounds = Bounds([5.0, 0.6], [5.5, 0.65])
sol = minimize(
fun_check_bounds,
self.x0,
method='cobyqa',
bounds=bounds,
constraints=constraints,
options=self.options,
)
assert not sol.success, sol.message
assert sol.maxcv > 0.35, sol
assert np.all(bounds.lb <= sol.x) and np.all(sol.x <= bounds.ub), sol
assert sol.nfev <= 100, sol
def test_minimize_linear_constraints(self):
constraints = LinearConstraint([1.0, 1.0], 1.0, 1.0)
sol = minimize(
self.fun,
self.x0,
method='cobyqa',
constraints=constraints,
options=self.options,
)
solution = [(4 - np.sqrt(7)) / 3, (np.sqrt(7) - 1) / 3]
assert_allclose(sol.x, solution, atol=1e-4)
assert sol.success, sol.message
assert sol.maxcv < 1e-8, sol
assert sol.nfev <= 100, sol
assert sol.fun < self.fun(solution) + 1e-3, sol
def test_minimize_args(self):
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
sol = minimize(
self.fun,
self.x0,
args=(2.0,),
method='cobyqa',
constraints=constraints,
options=self.options,
)
solution = [np.sqrt(25.0 - 4.0 / 36.0), 2.0 / 6.0]
assert_allclose(sol.x, solution, atol=1e-4)
assert sol.success, sol.message
assert sol.maxcv < 1e-8, sol
assert sol.nfev <= 100, sol
assert sol.fun < self.fun(solution, 2.0) + 1e-3, sol
def test_minimize_array(self):
def fun_array(x, dim):
f = np.array(self.fun(x))
return np.reshape(f, (1,) * dim)
# The argument fun can return an array with a single element.
bounds = Bounds([4.5, 0.6], [5.0, 0.7])
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
sol = minimize(
self.fun,
self.x0,
method='cobyqa',
bounds=bounds,
constraints=constraints,
options=self.options,
)
for dim in [0, 1, 2]:
sol_array = minimize(
fun_array,
self.x0,
args=(dim,),
method='cobyqa',
bounds=bounds,
constraints=constraints,
options=self.options,
)
assert_equal(sol.x, sol_array.x)
assert sol_array.success, sol_array.message
assert sol.fun == sol_array.fun
assert sol.maxcv == sol_array.maxcv
assert sol.nfev == sol_array.nfev
assert sol.nit == sol_array.nit
# The argument fun cannot return an array with more than one element.
with pytest.raises(TypeError):
minimize(
lambda x: np.array([self.fun(x), self.fun(x)]),
self.x0,
method='cobyqa',
bounds=bounds,
constraints=constraints,
options=self.options,
)
def test_minimize_maxfev(self):
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
options = {'maxfev': 2}
sol = minimize(
self.fun,
self.x0,
method='cobyqa',
constraints=constraints,
options=options,
)
assert not sol.success, sol.message
assert sol.nfev <= 2, sol
def test_minimize_maxiter(self):
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
options = {'maxiter': 2}
sol = minimize(
self.fun,
self.x0,
method='cobyqa',
constraints=constraints,
options=options,
)
assert not sol.success, sol.message
assert sol.nit <= 2, sol
def test_minimize_f_target(self):
constraints = NonlinearConstraint(self.con, 0.0, 0.0)
sol_ref = minimize(
self.fun,
self.x0,
method='cobyqa',
constraints=constraints,
options=self.options,
)
options = dict(self.options)
options['f_target'] = sol_ref.fun
sol = minimize(
self.fun,
self.x0,
method='cobyqa',
constraints=constraints,
options=options,
)
assert sol.success, sol.message
assert sol.maxcv < 1e-8, sol
assert sol.nfev <= sol_ref.nfev, sol
assert sol.fun <= sol_ref.fun, sol
|