def test_nesta_lasso():
n, p = 1000, 20
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 30
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X,Y)
penalty = rr.l1norm(p, lagrange=2.)
# using nesta
z = rr.zero(p)
primal, dual = rr.nesta(loss, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p))
# using simple problem
problem = rr.simple_problem(loss, penalty)
problem.solve()
nt.assert_true(np.linalg.norm(primal - problem.coefs) / np.linalg.norm(problem.coefs) < 1.e-3)
# test None as smooth_atom
rr.nesta(None, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p))
# using coefficients to stop
rr.nesta(loss, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p),
coef_stop=True)
def test_nesta_lasso():
n, p = 1000, 20
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 30
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X, Y)
penalty = rr.l1norm(p, lagrange=4.)
# using nesta
z = rr.zero(p)
primal, dual = rr.nesta(loss,
z,
penalty,
tol=1.e-10,
epsilon=2.**(-np.arange(30)))
# using simple problem
problem = rr.simple_problem(loss, penalty)
problem.solve()
nt.assert_true(
np.linalg.norm(primal - problem.coefs) /
np.linalg.norm(problem.coefs) < 1.e-3)
def test_quadratic():
l = rr.quadratic(5, coef=3., offset=np.arange(5))
l.quadratic = rr.identity_quadratic(1, np.ones(5), 2 * np.ones(5), 3.)
c1 = l.get_conjugate(as_quadratic=True)
q1 = rr.identity_quadratic(3, -np.arange(5), 0, 0)
q2 = q1 + l.quadratic
c2 = rr.zero(5, quadratic=q2.collapsed()).conjugate
ww = np.random.standard_normal(5)
np.testing.assert_almost_equal(c2.smooth_objective(ww, 'grad'),
c1.smooth_objective(ww, 'grad'))
np.testing.assert_almost_equal(c2.objective(ww), c1.objective(ww))
np.testing.assert_almost_equal(
c2.smooth_objective(ww, 'func') + c2.nonsmooth_objective(ww),
c1.smooth_objective(ww, 'func') + c1.nonsmooth_objective(ww))
def test_quadratic():
l = rr.quadratic(5, coef=3., offset=np.arange(5))
l.quadratic = rr.identity_quadratic(1,np.ones(5), 2*np.ones(5), 3.)
c1 = l.get_conjugate(as_quadratic=True)
q1 = rr.identity_quadratic(3, -np.arange(5), 0, 0)
q2 = q1 + l.quadratic
c2 = rr.zero(5, quadratic=q2.collapsed()).conjugate
ww = np.random.standard_normal(5)
np.testing.assert_almost_equal(c2.smooth_objective(ww, 'grad'),
c1.smooth_objective(ww, 'grad'))
np.testing.assert_almost_equal(c2.objective(ww),
c1.objective(ww))
np.testing.assert_almost_equal(c2.smooth_objective(ww, 'func') +
c2.nonsmooth_objective(ww),
c1.smooth_objective(ww, 'func') +
c1.nonsmooth_objective(ww))
