def test_minimize(self):
"""
Tests maximizing a function with and without constraints, taken from the
scipy `minimize` tutorial. Compare the symfit result with the scipy
result.
https://docs.scipy.org/doc/scipy-0.18.1/reference/tutorial/optimize.html#constrained-minimization-of-multivariate-scalar-functions-minimize
"""
x = Parameter(-1.0)
y = Parameter(1.0)
z = Variable()
model = {z: 2*x*y + 2*x - x**2 - 2*y**2}
constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
def func(x, sign=1.0):
""" Objective function """
return sign*(2*x[0]*x[1] + 2*x[0] - x[0]**2 - 2*x[1]**2)
def func_deriv(x, sign=1.0):
""" Derivative of objective function """
dfdx0 = sign*(-2*x[0] + 2*x[1] + 2)
dfdx1 = sign*(2*x[0] - 4*x[1])
return np.array([ dfdx0, dfdx1 ])
cons = (
{'type': 'eq',
'fun' : lambda x: np.array([x[0]**3 - x[1]]),
'jac' : lambda x: np.array([3.0*(x[0]**2.0), -1.0])},
{'type': 'ineq',
'fun' : lambda x: np.array([x[1] - 1]),
'jac' : lambda x: np.array([0.0, 1.0])})
# Unconstrained fit
res = minimize(func, [-1.0,1.0], args=(-1.0,), jac=func_deriv,
method='SLSQP', options={'disp': False})
fit = Maximize(model)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(x), res.x[0])
self.assertAlmostEqual(fit_result.value(y), res.x[1])
# Same test, but with constraints in place.
res = minimize(func, [-1.0,1.0], args=(-1.0,), jac=func_deriv,
constraints=cons, method='SLSQP', options={'disp': False})
fit = Maximize(model, constraints=constraints)
self.assertEqual(fit.constraints[0].constraint_type, Ge)
self.assertEqual(fit.constraints[1].constraint_type, Eq)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(x), res.x[0])
self.assertAlmostEqual(fit_result.value(y), res.x[1])
def test_constraint_types(self):
x = Parameter(-1.0)
y = Parameter(1.0)
z = Variable()
model = {z: 2 * x * y + 2 * x - x**2 - 2 * y**2}
# These types are not allowed constraints.
for relation in [Lt, Gt, Ne]:
with self.assertRaises(ModelError):
Maximize(model, constraints=[relation(x, y)])
# Should execute without problems.
for relation in [Eq, Ge, Le]:
Maximize(model, constraints=[relation(x, y)])
fit = Maximize(model, constraints=[Le(x, y)])
# Le should be transformed to Ge
self.assertIs(fit.constraints[0].constraint_type, Ge)
# Redo the standard test as a Le
constraints = [
Le(-y + 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
std_constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
fit = Maximize(model, constraints=constraints)
std_fit = Maximize(model, constraints=std_constraints)
self.assertEqual(fit.constraints[0].constraint_type, Ge)
self.assertEqual(fit.constraints[1].constraint_type, Eq)
fit_result = fit.execute()
std_result = std_fit.execute()
self.assertAlmostEqual(fit_result.value(x), std_result.value(x))
self.assertAlmostEqual(fit_result.value(y), std_result.value(y))
def test_constraint_types(self):
x = Parameter(-1.0)
y = Parameter(1.0)
z = Variable()
model = {z: 2*x*y + 2*x - x**2 - 2*y**2}
# These types are not allowed constraints.
for relation in [Lt, Gt, Ne]:
with self.assertRaises(ModelError):
Maximize(model, constraints=[relation(x, y)])
# Should execute without problems.
for relation in [Eq, Ge, Le]:
Maximize(model, constraints=[relation(x, y)])
fit = Maximize(model, constraints=[Le(x, y)])
# Le should be transformed to Ge
self.assertIs(fit.constraints[0].constraint_type, Ge)
# Redo the standard test as a Le
constraints = [
Le(- y + 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
std_constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
fit = Maximize(model, constraints=constraints)
std_fit = Maximize(model, constraints=std_constraints)
self.assertEqual(fit.constraints[0].constraint_type, Ge)
self.assertEqual(fit.constraints[1].constraint_type, Eq)
fit_result = fit.execute()
std_result = std_fit.execute()
self.assertAlmostEqual(fit_result.value(x), std_result.value(x))
self.assertAlmostEqual(fit_result.value(y), std_result.value(y))
def test_minimize(self):
"""
Tests maximizing a function with and without constraints, taken from the
scipy `minimize` tutorial. Compare the symfit result with the scipy
result.
https://docs.scipy.org/doc/scipy-0.18.1/reference/tutorial/optimize.html#constrained-minimization-of-multivariate-scalar-functions-minimize
"""
x = Parameter(-1.0)
y = Parameter(1.0)
z = Variable()
model = {z: 2 * x * y + 2 * x - x**2 - 2 * y**2}
constraints = [
Ge(y - 1, 0), # y - 1 >= 0,
Eq(x**3 - y, 0), # x**3 - y == 0,
]
def func(x, sign=1.0):
""" Objective function """
return sign * (2 * x[0] * x[1] + 2 * x[0] - x[0]**2 - 2 * x[1]**2)
def func_deriv(x, sign=1.0):
""" Derivative of objective function """
dfdx0 = sign * (-2 * x[0] + 2 * x[1] + 2)
dfdx1 = sign * (2 * x[0] - 4 * x[1])
return np.array([dfdx0, dfdx1])
cons = ({
'type': 'eq',
'fun': lambda x: np.array([x[0]**3 - x[1]]),
'jac': lambda x: np.array([3.0 * (x[0]**2.0), -1.0])
}, {
'type': 'ineq',
'fun': lambda x: np.array([x[1] - 1]),
'jac': lambda x: np.array([0.0, 1.0])
})
# Unconstrained fit
res = minimize(func, [-1.0, 1.0],
args=(-1.0, ),
jac=func_deriv,
method='SLSQP',
options={'disp': False})
fit = Maximize(model)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(x), res.x[0])
self.assertAlmostEqual(fit_result.value(y), res.x[1])
# Same test, but with constraints in place.
res = minimize(func, [-1.0, 1.0],
args=(-1.0, ),
jac=func_deriv,
constraints=cons,
method='SLSQP',
options={'disp': False})
fit = Maximize(model, constraints=constraints)
self.assertEqual(fit.constraints[0].constraint_type, Ge)
self.assertEqual(fit.constraints[1].constraint_type, Eq)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(x), res.x[0])
self.assertAlmostEqual(fit_result.value(y), res.x[1])
