def test_proximal_nonsmooth():
# Minimize ||x||_1.
oracle = oracles.create_lasso_prox_oracle(np.zeros([2, 2]),
np.zeros(2),
regcoef=1.0)
x_0 = np.array([2.0, -1.0])
[x_star, status, hist] = optimization.proximal_gradient_descent(
oracle, x_0, trace=True)
eq_(status, 'success')
ok_(np.allclose(x_star, np.array([0.0, 0.0])))
ok_(np.allclose(np.array(hist['func']), np.array([3.0, 1.0, 0.0])))
def test_proximal_gd_one_step():
# Simple smooth quadratic task.
A = np.eye(2)
b = np.array([1.0, 0.0])
oracle = oracles.create_lasso_prox_oracle(A, b, regcoef=0.0)
x_0 = np.zeros(2)
[x_star, status, hist] = optimization.proximal_gradient_descent(
oracle, x_0, trace=True)
eq_(status, 'success')
ok_(np.allclose(x_star, np.array([1.0, 0.0])))
ok_(np.allclose(np.array(hist['func']), np.array([0.5, 0.0])))
def test_proximal_nonsmooth2():
oracle = oracles.create_lasso_prox_oracle(np.array([[1, 2, 3], [4, 5, 6]]),
np.array([1, 4]),
regcoef=1.0)
x_0 = np.array([1, 1, -1])
[x_star, status, hist] = optimization.proximal_gradient_descent(oracle,
x_0,
trace=True,
max_iter=3)
eq_(status, 'iterations_exceeded')
ok_(np.allclose(x_star, np.array([1.02216721, 1.05131721, -0.85703278])))
ok_(
np.allclose(
np.array(hist['func']),
np.array(
[[4.0, 3.219970703125, 3.1220934763550758,
3.0507238902373501]])))
x_star, msg, hist = optimization.subgradient_method(oracle, x_0, alpha_0=a_0, trace=True, max_iter=10**4)
res.append(len(hist['func']))
plt.plot([a / 10 for a in range(1, 50)], res)
plt.xlabel("Alpha")
plt.ylabel("Iterations")
plt.savefig("exp1/{}.png".format(label))
# ------------------ Experiment 2
for n in [5, 50]:
A = np.random.rand(n, n)
b = np.random.rand(n)
r = 1/n
oracle = oracles.create_lasso_prox_oracle(A, b, r)
x_star, msg, hist = optimization.proximal_gradient_descent(oracle, np.zeros(n), trace=True)
plt.clf()
plt.plot(range(len(hist['line_counter'])), hist['line_counter'])
plt.xlabel("Iteration")
plt.ylabel("Line search counter")
plt.savefig("exp2/LCounter{}.png".format(n))
# ------------------- Experiment 3
for n in [50, 1000]:
for eps, eps_name in zip([10**-2, 10**-7], ["low", "high"]):
A = np.random.rand(n, n)
b = np.random.rand(n)
r = 1
x_0 = np.zeros(n)
u_0 = np.ones(n) * 50