def test_conjugate_l1norm():
'''
this test verifies that numerically computing the conjugate
is essentially the same as using the smooth_conjugate
of the atom
'''
q = rr.identity_quadratic(1.2,0,0,0)
l1 = rr.l1norm(4, lagrange=0.3)
pen2 = copy(l1)
pen2.set_quadratic(q)
v1 = rr.smooth_conjugate(l1, q)
v2 = rr.conjugate(l1, q, tol=1.e-12, min_its=100)
v3 = rr.conjugate(pen2, None, tol=1.e-12, min_its=100)
w = np.random.standard_normal(4)
u11, u12 = v1.smooth_objective(w)
u21, u22 = v2.smooth_objective(w)
u31, u32 = v3.smooth_objective(w)
np.testing.assert_approx_equal(u11, u21)
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
np.testing.assert_approx_equal(u11, u31)
np.testing.assert_allclose(u12, u32, rtol=1.0e-05)
v2.smooth_objective(w, mode='func')
v2.smooth_objective(w, mode='grad')
nt.assert_raises(ValueError, v2.smooth_objective, w, 'blah')
def test_conjugate_sqerror():
"""
This verifies the conjugate class can compute the conjugate
of a quadratic function.
"""
ridge_coef = 0.4
X = np.random.standard_normal((10,4))
Y = np.random.standard_normal(10)
l = rr.squared_error(X, Y)
q = rr.identity_quadratic(ridge_coef,0,0,0)
atom_conj = rr.conjugate(l, q, tol=1.e-12, min_its=100)
w = np.random.standard_normal(4)
u11, u12 = atom_conj.smooth_objective(w)
# check that objective is half of squared error
np.testing.assert_allclose(l.smooth_objective(w, mode='func'), 0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
np.testing.assert_allclose(atom_conj.atom.smooth_objective(w, mode='func'), 0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
XTX = np.dot(X.T, X)
XTXi = np.linalg.pinv(XTX)
quadratic_term = XTX + ridge_coef * np.identity(4)
linear_term = np.dot(X.T, Y) + w
b = u22 = np.linalg.solve(quadratic_term, linear_term)
u21 = (w*u12).sum() - l.smooth_objective(u12, mode='func') - q.objective(u12, mode='func')
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
np.testing.assert_approx_equal(u11, u21)
def test_conjugate_sqerror():
X = np.random.standard_normal((10,4))
Y = np.random.standard_normal(10)
l = rr.quadratic.affine(X,-Y, coef=0.5)
v = rr.conjugate(l, rr.identity_quadratic(0.3,None,None,0), tol=1.e-12)
w=np.random.standard_normal(4)
u11, u12 = v.smooth_objective(w)
XTX = np.dot(X.T, X)
b = u22 = np.linalg.solve(XTX + 0.3 * np.identity(4), np.dot(X.T, Y) + w)
u21 = - np.dot(b.T, np.dot(XTX + 0.3 * np.identity(4), b)) / 2. + (w*b).sum() + (np.dot(X.T, Y) * b).sum() - np.linalg.norm(Y)**2/2.
np.testing.assert_approx_equal(u11, u21)
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
def test_conjugate_l1norm():
'''
this test verifies that numerically computing the conjugate
is essentially the same as using the smooth_conjugate
of the atom
'''
l1 = rr.l1norm(4, lagrange=0.3)
v1=rr.smooth_conjugate(l1, rr.identity_quadratic(0.3,None,None,0))
v2 = rr.conjugate(l1, rr.identity_quadratic(0.3,None,None,0), tol=1.e-12)
w=np.random.standard_normal(4)
u11, u12 = v1.smooth_objective(w)
u21, u22 = v2.smooth_objective(w)
np.testing.assert_approx_equal(u11, u21)
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
def test_conjugate_sqerror():
"""
This verifies the conjugate class can compute the conjugate
of a quadratic function.
"""
X = np.random.standard_normal((10, 4))
Y = np.random.standard_normal(10)
l = rr.quadratic.affine(X, -Y, coef=0.5)
v = rr.conjugate(l, rr.identity_quadratic(0.3, 0, 0, 0), tol=1.e-12)
w = np.random.standard_normal(4)
u11, u12 = v.smooth_objective(w)
XTX = np.dot(X.T, X)
b = u22 = np.linalg.solve(XTX + 0.3 * np.identity(4), np.dot(X.T, Y) + w)
u21 = -np.dot(b.T, np.dot(XTX + 0.3 * np.identity(4), b)) / 2. + (
w * b).sum() + (np.dot(X.T, Y) * b).sum() - np.linalg.norm(Y)**2 / 2.
np.testing.assert_approx_equal(u11, u21)
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
def test_conjugate_l1norm():
'''
this test verifies that numerically computing the conjugate
is essentially the same as using the smooth_conjugate
of the atom
'''
l1 = rr.l1norm(4, lagrange=0.3)
v1 = rr.smooth_conjugate(l1, rr.identity_quadratic(0.3, None, None, 0))
v2 = rr.conjugate(l1,
rr.identity_quadratic(0.3, None, None, 0),
tol=1.e-12)
w = np.random.standard_normal(4)
u11, u12 = v1.smooth_objective(w)
u21, u22 = v2.smooth_objective(w)
np.testing.assert_approx_equal(u11, u21)
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
