def test_nucnorm():
pen = 1.
rho = 0.1
tol = 1.
op = proxops.nucnorm(pen)
X = 2*np.outer(np.random.randn(50), np.random.randn(25))
V = X + 0.5 * np.random.randn(50,25)
nn = lambda A: np.linalg.svd(A, compute_uv=False).sum()
assert np.abs(nn(X) - nn(op(X, rho)) - pen / rho) <= tol
def test_lowrank_matrix_approx():
"""
Test low rank matrix approximation
"""
Xobs, Xtrue = generate_lowrank_matrix()
# helper function to test relative error of given parameters
def test_error(Xhat):
test_err = np.linalg.norm(Xhat - Xtrue, 'fro')
naive_err = np.linalg.norm(Xobs - Xtrue, 'fro')
err_ratio = test_err / naive_err
assert err_ratio <= 0.5
# proximal algorithm for low rank matrix approximation
opt = ProximalConsensus(Xobs)
opt.add('squared_error', Xobs)
opt.add('nucnorm', 0.2)
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):
grad = X - Xtrue
obj = 0.5 * np.linalg.norm(grad.ravel()) ** 2
return obj, grad
# sparsity penalty
proxop = nucnorm(0.2)
# optimizer
opt = algorithm(f_df, Xobs, proxop, learning_rate=0.005)
opt.display = None
opt.storage = None
opt.run(maxiter=5000)
# test
test_error(opt.theta)
