def test_fixedpoint():
"""
Test that the minimum of a quadratic is a fixed point
"""
def grad(x):
return x
xstar = np.array([0., 0.])
xinit = xstar
algorithm = sgd(xinit)
xnext = algorithm(grad(xstar))
assert np.allclose(xnext, xstar)
def test_fixedpoint():
"""
Test that the minimum of a quadratic is a fixed point
"""
def grad(x):
return x
xstar = np.array([0., 0.])
xinit = xstar
opt = sgd()
_ = opt.algorithm.send(xinit)
xnext = opt.algorithm.send(grad(xstar))
assert np.allclose(xnext, xstar)
def test_quadratic_bowl():
"""
Test optimization in a quadratic bowl
"""
t = np.linspace(0, 2 * np.pi, 100)
tol = 1e-3
theta_true = [np.sin(t), np.cos(t)]
theta_init = [np.cos(t), np.sin(t)]
def f_df(theta):
obj = 0.5 * (theta[0] - theta_true[0])**2 + 0.5 * (theta[1] - theta_true[1])**2
grad = [theta[0] - theta_true[0], theta[1] - theta_true[1]]
return np.sum(obj), grad
# opt = GradientDescent(theta_init, f_df, 'sgd', {'lr': 1e-2})
opt = sgd(lr=1e-2)
res = opt.minimize(f_df, theta_init, display=None, maxiter=1e3)
for theta in zip(res.x, theta_true):
assert np.linalg.norm(theta[0] - theta[1]) <= tol
def test_quadratic_bowl():
"""
Test optimization in a quadratic bowl
"""
t = np.linspace(0, 2 * np.pi, 100)
tol = 1e-3
theta_true = [np.sin(t), np.cos(t)]
theta_init = [np.cos(t), np.sin(t)]
def f_df(theta):
obj = 0.5 * (theta[0] - theta_true[0])**2 + 0.5 * (theta[1] -
theta_true[1])**2
grad = [theta[0] - theta_true[0], theta[1] - theta_true[1]]
return np.sum(obj), grad
# opt = GradientDescent(theta_init, f_df, 'sgd', {'lr': 1e-2})
opt = sgd(lr=1e-2)
res = opt.minimize(f_df, theta_init, display=None, maxiter=1e3)
for theta in zip(res.x, theta_true):
assert np.linalg.norm(theta[0] - theta[1]) <= tol
