def test_multivariate_penalty():
alphas = [1, 2]
weights = [1, 1]
np.random.seed(1)
x, y, pol = multivariate_sample_data()
univ_pol1 = UnivariatePolynomialSmoother(x[:, 0], degree=pol.degrees[0])
univ_pol2 = UnivariatePolynomialSmoother(x[:, 1], degree=pol.degrees[1])
gp1 = UnivariateGamPenalty(alpha=alphas[0], univariate_smoother=univ_pol1)
gp2 = UnivariateGamPenalty(alpha=alphas[1], univariate_smoother=univ_pol2)
mgp = MultivariateGamPenalty(multivariate_smoother=pol, alpha=alphas,
weights=weights)
for i in range(10):
params1 = np.random.randint(-3, 3, pol.smoothers[0].dim_basis)
params2 = np.random.randint(-3, 3, pol.smoothers[1].dim_basis)
params = np.concatenate([params1, params2])
c1 = gp1.func(params1)
c2 = gp2.func(params2)
c = mgp.func(params)
assert_allclose(c, c1 + c2, atol=1.e-10, rtol=1.e-10)
d1 = gp1.deriv(params1)
d2 = gp2.deriv(params2)
d12 = np.concatenate([d1, d2])
d = mgp.deriv(params)
assert_allclose(d, d12)
h1 = gp1.deriv2(params1)
h2 = gp2.deriv2(params2)
h12 = block_diag(h1, h2)
h = mgp.deriv2(params)
assert_allclose(h, h12)
def test_multivariate_penalty():
alphas = [1, 2]
weights = [1, 1]
np.random.seed(1)
x, y, pol = multivariate_sample_data()
univ_pol1 = UnivariatePolynomialSmoother(x[:, 0], degree=pol.degrees[0])
univ_pol2 = UnivariatePolynomialSmoother(x[:, 1], degree=pol.degrees[1])
gp1 = UnivariateGamPenalty(alpha=alphas[0], univariate_smoother=univ_pol1)
gp2 = UnivariateGamPenalty(alpha=alphas[1], univariate_smoother=univ_pol2)
mgp = MultivariateGamPenalty(multivariate_smoother=pol,
alpha=alphas,
weights=weights)
for i in range(10):
params1 = np.random.randint(-3, 3, pol.smoothers[0].dim_basis)
params2 = np.random.randint(-3, 3, pol.smoothers[1].dim_basis)
params = np.concatenate([params1, params2])
c1 = gp1.func(params1)
c2 = gp2.func(params2)
c = mgp.func(params)
assert_allclose(c, c1 + c2, atol=1.e-10, rtol=1.e-10)
d1 = gp1.deriv(params1)
d2 = gp2.deriv(params2)
d12 = np.concatenate([d1, d2])
d = mgp.deriv(params)
assert_allclose(d, d12)
h1 = gp1.deriv2(params1)
h2 = gp2.deriv2(params2)
h12 = block_diag(h1, h2)
h = mgp.deriv2(params)
assert_allclose(h, h12)
def test_gam_hessian():
# test the deriv2 method of the gam penalty
np.random.seed(1)
pol, y = polynomial_sample_data()
univ_pol = pol.smoothers[0]
alpha = 1
gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=univ_pol)
for _ in range(10):
params = np.random.randint(-2, 2, 5)
gam_der2 = gp.deriv2(params)
hess = hessian(params)
hess = np.flipud(hess)
hess = np.fliplr(hess)
assert_allclose(gam_der2, hess, atol=1.e-13, rtol=1.e-3)
def test_gam_hessian():
# test the deriv2 method of the gam penalty
np.random.seed(1)
pol, y = polynomial_sample_data()
univ_pol = pol.smoothers[0]
alpha = 1
gp = UnivariateGamPenalty(alpha=alpha, univariate_smoother=univ_pol)
for _ in range(10):
params = np.random.randint(-2, 2, 5)
gam_der2 = gp.deriv2(params)
hess = hessian(params)
hess = np.flipud(hess)
hess = np.fliplr(hess)
assert_allclose(gam_der2, hess, atol=1.e-13, rtol=1.e-3)