def obj_fun(x):
return 0.5 * np.linalg.norm(b - A.dot(x)) ** 2 / A.shape[0] + 0.5 * l2_reg * x.dot(x)
def grad(x):
return - A.T.dot(b - A.dot(x)) / A.shape[0] + l2_reg * x
f, ax = plt.subplots(2, 3, sharey=False)
all_alphas = [1e-6, 1e-3, 1e-1]
xlim = [0.02, 0.02, 0.1]
for i, alpha in enumerate(all_alphas):
max_iter = 5000
trace_three = Trace(lambda x: obj_fun(x) + alpha * TV(x))
out_tos = three_split(
obj_fun, grad, prox_tv1d_rows, prox_tv1d_cols, np.zeros(n_features),
alpha=alpha, beta=alpha, g_prox_args=(n_rows, n_cols), h_prox_args=(n_rows, n_cols),
callback=trace_three, max_iter=max_iter, tol=1e-16)
trace_gd = Trace(lambda x: obj_fun(x) + alpha * TV(x))
out_gd = proximal_gradient(
obj_fun, grad, prox_tv2d, np.zeros(n_features),
alpha=alpha, g_prox_args=(n_rows, n_cols, 1000, 1e-1),
max_iter=max_iter, callback=trace_gd)
ax[0, i].set_title(r'$\lambda=%s$' % alpha)
ax[0, i].imshow(out_tos.x.reshape((n_rows, n_cols)),
interpolation='nearest', cmap=plt.cm.Blues)
ax[0, i].set_xticks(())
ax[0, i].set_yticks(())
fmin = min(np.min(trace_three.values), np.min(trace_gd.values))