def test_04_Townsend(self):
(vars, domain) = make_domain([("x", -2.25, 2.5), ("y", -2.5, 1.75)])
[x, y] = vars
def objective(x, y):
return -(cos((x - 0.1) * y))**2 - x * sin(3 * x + y)
constraints = logical_and(
domain, x**2 + y**2 <
(2 * cos(atan2(x, y)) - 0.5 * cos(2 * atan2(x, y)) -
0.25 * cos(3 * atan2(x, y)) - 0.125 * cos(4 * atan2(x, y)))**2 +
(2 * sin(atan2(x, y)))**2)
sol = Minimize(objective(*vars), constraints, self.config)
self.global_min = -2.0239884
self.assertIsNotNone(sol)
self.found_min = compute_min(objective, sol, vars)
self.assertAlmostEqual(self.found_min,
self.global_min,
delta=self.config.precision * 2)
def test_functions_with_expression(self):
self.assertEqual(str(abs(e_x)), "abs(x)")
self.assertEqual(str(exp(e_x)), "exp(x)")
self.assertEqual(str(sqrt(e_x)), "sqrt(x)")
self.assertEqual(str(pow(e_x, e_y)), "pow(x, y)")
self.assertEqual(str(sin(e_x)), "sin(x)")
self.assertEqual(str(cos(e_x)), "cos(x)")
self.assertEqual(str(tan(e_x)), "tan(x)")
self.assertEqual(str(asin(e_x)), "asin(x)")
self.assertEqual(str(acos(e_x)), "acos(x)")
self.assertEqual(str(atan(e_x)), "atan(x)")
self.assertEqual(str(atan2(e_x, e_y)), "atan2(x, y)")
self.assertEqual(str(sinh(e_x)), "sinh(x)")
self.assertEqual(str(cosh(e_x)), "cosh(x)")
self.assertEqual(str(tanh(e_x)), "tanh(x)")
self.assertEqual(str(min(e_x, e_y)), "min(x, y)")
self.assertEqual(str(max(e_x, e_y)), "max(x, y)")
self.assertEqual(str(if_then_else(e_x > e_y, e_x, e_y)),
"(if (x > y) then x else y)")
def test_functions_with_variable(self):
self.assertEqual(str(abs(x)), "abs(x)")
self.assertEqual(str(exp(x)), "exp(x)")
self.assertEqual(str(sqrt(x)), "sqrt(x)")
self.assertEqual(str(pow(x, y)), "pow(x, y)")
self.assertEqual(str(sin(x)), "sin(x)")
self.assertEqual(str(cos(x)), "cos(x)")
self.assertEqual(str(tan(x)), "tan(x)")
self.assertEqual(str(asin(x)), "asin(x)")
self.assertEqual(str(acos(x)), "acos(x)")
self.assertEqual(str(atan(x)), "atan(x)")
self.assertEqual(str(atan2(x, y)), "atan2(x, y)")
self.assertEqual(str(sinh(x)), "sinh(x)")
self.assertEqual(str(cosh(x)), "cosh(x)")
self.assertEqual(str(tanh(x)), "tanh(x)")
self.assertEqual(str(min(x, y)), "min(x, y)")
self.assertEqual(str(max(x, y)), "max(x, y)")
self.assertEqual(str(if_then_else(x > y, x, y)),
"(if (x > y) then x else y)")
def test_functions_with_float(self):
v_x = 1.0
v_y = 1.0
self.assertEqual(abs(v_x), math.fabs(v_x))
self.assertEqual(exp(v_x), math.exp(v_x))
self.assertEqual(sqrt(v_x), math.sqrt(v_x))
self.assertEqual(pow(v_x, v_y), v_x**v_y)
self.assertEqual(sin(v_x), math.sin(v_x))
self.assertEqual(cos(v_x), math.cos(v_x))
self.assertEqual(tan(v_x), math.tan(v_x))
self.assertEqual(asin(v_x), math.asin(v_x))
self.assertEqual(acos(v_x), math.acos(v_x))
self.assertEqual(atan(v_x), math.atan(v_x))
self.assertEqual(atan2(v_x, v_y), math.atan2(v_x, v_y))
self.assertEqual(sinh(v_x), math.sinh(v_x))
self.assertEqual(cosh(v_x), math.cosh(v_x))
self.assertEqual(tanh(v_x), math.tanh(v_x))
self.assertEqual(min(v_x, v_y), min(v_x, v_y))
self.assertEqual(max(v_x, v_y), max(v_x, v_y))
self.assertEqual(
if_then_else(Expression(v_x) > Expression(v_y), v_x, v_y),
v_x if v_x > v_y else v_y)