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 gradient descent and Accelerated proximal gradient descent
for algorithm in ['sgd', 'nag']:
# objective
def f_df(X):
grad = X - Xtrue
obj = 0.5 * np.linalg.norm(grad.ravel()) ** 2
return obj, grad
# optimizer
opt = getattr(algorithms, algorithm)(lr=5e-3)
opt.operators.append(nucnorm(0.2))
# run it
res = opt.minimize(f_df, Xobs, maxiter=5000, display=None)
# test
test_error(res.x)
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 gradient descent and Accelerated proximal gradient descent
for algorithm in ['sgd', 'nag']:
# objective
def f_df(X):
grad = X - Xtrue
obj = 0.5 * np.linalg.norm(grad.ravel()) ** 2
return obj, grad
# optimizer
opt = GradientDescent(Xobs, f_df, algorithm, {'lr': 5e-3}, proxop=nucnorm(0.2), rho=1.0)
opt.callbacks = []
opt.run(maxiter=5000)
# test
test_error(opt.theta)
def test_nucnorm():
pen = 1.
rho = 0.1
tol = 1.
X = 2 * np.outer(np.random.randn(50), np.random.randn(25))
V = X + 0.5 * np.random.randn(50, 25)
# compute the nuclear norm
def nn(A):
return np.linalg.svd(A, compute_uv=False).sum()
# test nucnorm
op = proxops.nucnorm(pen)
assert np.abs(nn(X) - nn(op(V, rho)) - pen / rho) <= tol
# test nucnorm (w/ reshape)
op = proxops.nucnorm(pen, newshape=(50, 25))
v = op(V.ravel(), rho)
assert v.shape == (50 * 25, )
assert np.abs(nn(X) - nn(v.reshape(X.shape)) - pen / rho) <= tol
def test_nucnorm():
pen = 1.
rho = 0.1
tol = 1.
X = 2 * np.outer(np.random.randn(50), np.random.randn(25))
V = X + 0.5 * np.random.randn(50, 25)
# compute the nuclear norm
def nn(A):
return np.linalg.svd(A, compute_uv=False).sum()
# test nucnorm
op = proxops.nucnorm(pen)
assert np.abs(nn(X) - nn(op(V, rho)) - pen / rho) <= tol
# test nucnorm (w/ reshape)
op = proxops.nucnorm(pen, newshape=(50, 25))
v = op(V.ravel(), rho)
assert v.shape == (50*25,)
assert np.abs(nn(X) - nn(v.reshape(X.shape)) - pen / rho) <= tol
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
