def test_projected_gradient_descent():
"""Test sparse regression"""
A, y, x_true, xls, ls_error = generate_sparse_system()
# helper function to test relative error
def test_error(xhat):
assert relative_error(xhat, x_true, ls_error) <= 0.01
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in ['sgd', 'nag']:
# 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
# optimizer
opt = getattr(algorithms, algorithm)(lr=5e-3)
opt.add(sparse(10.0))
# run it
res = opt.minimize(f_df, xls, display=None, maxiter=5000)
# test
test_error(res.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
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in ['sgd', 'nag']:
# 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
# optimizer
opt = GradientDescent(xls, f_df, algorithm, {'lr': 5e-3}, proxop=sparse(10.0), rho=1.0)
opt.run(maxiter=5000)
# test
test_error(opt.theta)
def test_projected_gradient_descent():
"""Test sparse regression"""
A, y, x_true, xls, ls_error = generate_sparse_system()
# helper function to test relative error
def test_error(xhat):
assert relative_error(xhat, x_true, ls_error) <= 0.01
# Proximal gradient descent and Accelerated proximal gradient descent
for algorithm in ['sgd', 'nag']:
# 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
# optimizer
opt = getattr(algorithms, algorithm)(lr=5e-3)
opt.add(sparse(10.0))
# run it
res = opt.minimize(f_df, xls, display=None, maxiter=5000)
# test
test_error(res.x)
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():
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_consensus():
"""Test the consensus optimizer (ADMM)"""
A, y, x_true, xls, ls_error = generate_sparse_system()
# optimizer
opt = Consensus()
opt.add(linsys(A, y))
opt.add(sparse(10.0))
# run it
res = opt.minimize(xls, display=None, maxiter=5000)
# test
assert relative_error(res.x, x_true, ls_error) <= 0.05
def test_consensus():
"""Test the consensus optimizer (ADMM)"""
A, y, x_true, xls, ls_error = generate_sparse_system()
# optimizer
opt = Consensus()
opt.add(linsys(A, y))
opt.add(sparse(10.0))
# run it
res = opt.minimize(xls, display=None, maxiter=5000)
# test
assert relative_error(res.x, x_true, ls_error) <= 0.05
