def test_sparse():
pen = 0.1
rho = 0.1
v = np.linspace(-5, 5, 1e3)
gamma = pen / rho
x = (v - gamma * np.sign(v)) * (np.abs(v) > gamma)
op = proxops.sparse(pen)
assert np.allclose(op(v, rho), x)
def test_sparse_regression():
"""
Test sparse regression
"""
A, y, x_true = generate_sparse_system()
# least squares solution
xls = np.linalg.lstsq(A, y)[0]
# helper function to test relative error
def test_error(xhat):
test_err = np.linalg.norm(xhat - x_true, 2)
naive_err = np.linalg.norm(xls - x_true, 2)
err_ratio = test_err / naive_err
assert err_ratio <= 0.01
# ProximalConsensus
opt = ProximalConsensus(xls)
opt.add('linsys', A=A, b=y)
opt.add('sparse', 1.)
opt.display = None
opt.storage = None
opt.run(maxiter=100)
# test error
test_error(opt.theta)
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in [ProximalGradientDescent, AcceleratedProximalGradient]:
# objective
def f_df(x):
err = A.dot(x) - y
obj = 0.5 * np.linalg.norm(err) ** 2
grad = A.T.dot(err)
return obj, grad
# sparsity penalty
proxop = sparse(1.)
# optimizer
opt = algorithm(f_df, xls, proxop, learning_rate=0.005)
opt.display = None
opt.storage = None
opt.run(maxiter=5000)
# test
test_error(opt.theta)
