def test_quadratic_function_of_one_variable(self):
"""Minimize f(x)=x^2 (one-dimensional)"""
def func(x):
return x * x
def grad(x):
return 2.0 * x
def hess(x):
return 2.0
nr = NewtonRaphson(iterations=10)
x = nr.optimize(x0=100, func=func, grad=grad, hess=hess)
self.assertAlmostEqual(x, 0.0)
def test_quadratic_function_of_several_variables(self):
"""Minimize f(x)=||x||^2 (multi-dimensional)"""
def func(x):
return np.dot(x, x)
func.grad = lambda x: 2. * np.asarray(x)
func.hess = lambda x: 2. * np.identity(np.size(x))
nr = NewtonRaphson(iterations=10)
n_tests = 100
for _ in range(n_tests):
size = np.random.randint(low=1, high=100)
loc = np.random.uniform(-1000, 1000)
scale = np.random.uniform(10, 10000)
x0 = np.random.normal(loc=loc, scale=scale, size=size)
x = nr.optimize(x0=x0, func=func)
np.testing.assert_almost_equal(x, np.zeros(size))