def test_sample_2D(self):
N, d = 20, 2
jacobi_params = - 0.5 * np.ones((d, 2))
dpp = MultivariateJacobiOPE(N, jacobi_params)
sampl = dpp.sample(random_state=self.seed) # seed = 0
expected_sample = np.array([[-0.44929357, -0.92988338],
[0.07128896, -0.98828901],
[-0.43895328, -0.64850438],
[-0.56491996, 0.43632636],
[0.33859341, 0.6642957],
[-0.89437538, -0.98384996],
[0.93451148, -0.42788073],
[-0.81846092, 0.57000777],
[-0.42084694, 0.98065145],
[0.97651548, 0.94243444],
[0.11753084, 0.96240585],
[-0.12183308, -0.14093164],
[-0.9940169, 0.16811198],
[-0.76730512, -0.05402772],
[0.99984566, -0.95942833],
[0.99996511, -0.01959666],
[0.05053165, -0.40778628],
[0.82158181, 0.58501064],
[-0.97396649, 0.90805501],
[-0.99808676, -0.49690354]])
self.assertTrue(np.allclose(sampl, expected_sample))
def test_sample_2D(self):
N, d = 20, 2
jacobi_params = -0.5 * np.ones((d, 2))
dpp = MultivariateJacobiOPE(N, jacobi_params)
sampl = dpp.sample(random_state=self.seed)
# seed = 0
expected_sample = np.array([[-0.44929357, -0.92988338],
[-0.38287518, 0.20141371],
[-0.82081218, 0.71370281],
[0.54434591, -0.40548681],
[0.83560033, 0.99975326],
[0.58479869, -0.97294791],
[-0.97140965, -0.9958691],
[0.73176809, 0.0462124],
[0.99999994, 0.62478638],
[-0.995107, 0.6146506],
[0.99956026, -0.54696107],
[-0.73400973, 0.99976412],
[-0.9940169, 0.16811198],
[0.26219327, 0.71667124],
[-0.76730512, -0.05402772],
[0.99910531, 0.90729924],
[0.99984566, -0.95942833],
[0.99996511, -0.01959666],
[0.05053165, -0.40778628],
[0.11004152, 0.99337928]])
self.assertTrue(np.allclose(sampl, expected_sample))
def test_sample_1D(self):
N, d = 20, 1
jacobi_params = - 0.5 * np.ones((d, 2))
dpp = MultivariateJacobiOPE(N, jacobi_params)
sampl = dpp.sample(random_state=self.seed) # seed = 0
expected_sample = np.array([[0.9995946],
[0.98944808],
[0.97485733],
[0.86576265],
[0.7958162],
[0.64406931],
[0.53459294],
[0.4259159],
[0.1784497],
[0.12319757],
[-0.13340743],
[-0.28758726],
[-0.40275405],
[-0.68282936],
[-0.76523971],
[-0.82355336],
[-0.88258742],
[-0.94587727],
[-0.96426474],
[-0.99658163]])
self.assertTrue(np.allclose(sampl, expected_sample))
def test_kernel_gram_matrix(self):
"""
K(x) == phi_x.dot(phi_x)
K(x, y) == phi_x.dot(phi_y)
K(x, Y) == K(Y, x) = [phi_x.dot(phi_y) for y in Y]
K(X) == [phi_x.dot(phi_x) for x in X]
K(X, Y) == [phi_x.dot(phi_y) for x, y in zip(X, Y)]
"""
N = 100
dims = np.arange(2, 5)
for d in dims:
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
x, y = np.random.rand(d), np.random.rand(d)
phi_x = dpp.eval_poly_multiD(x, normalize='norm')
phi_y = dpp.eval_poly_multiD(y, normalize='norm')
X, Y = np.random.rand(5, d), np.random.rand(5, d)
phi_X = dpp.eval_poly_multiD(X, normalize='norm').T
phi_Y = dpp.eval_poly_multiD(Y, normalize='norm').T
self.assertTrue(np.allclose(dpp.K(x), inner1d(phi_x)))
self.assertTrue(np.allclose(dpp.K(X), inner1d(phi_X)))
self.assertTrue(np.allclose(dpp.K(x, y), inner1d(phi_x, phi_y)))
self.assertTrue(np.allclose(dpp.K(x, Y), phi_x.dot(phi_Y)))
self.assertTrue(np.allclose(dpp.K(X, Y), inner1d(phi_X, phi_Y)))
def test_square_norms(self):
N = 100
dims = np.arange(2, 5)
max_deg = 50 # to avoid quad warning in dimension 1
for d in dims:
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
pol_2_eval = dpp.poly_1D_degrees[:max_deg]
quad_square_norms =\
[[quad(lambda x:
(1-x)**a * (1+x)**b * eval_jacobi(n, a, b, x)**2,
-1, 1)[0]
for n, a, b in zip(deg,
dpp.jacobi_params[:, 0],
dpp.jacobi_params[:, 1])]
for deg in pol_2_eval]
self.assertTrue(
np.allclose(
dpp.poly_1D_square_norms[pol_2_eval,
range(dpp.dim)],
quad_square_norms))
def test_kernel_evaluations(self):
N = 100
dims = np.arange(2, 5)
for d in dims:
with self.subTest(dimension=d):
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
X = np.random.rand(20, d)
Y = np.random.rand(20, d)
K_XX = is_symmetric(dpp.K(X, X))
K_xx = np.diag(K_XX)
K_xy = np.ravel([dpp.K(x, y) for x, y in zip(X, Y)])
checks = ((dpp.K(X), K_XX),
(dpp.K(X, X, eval_pointwise=True), K_xx),
(dpp.K(X, Y, eval_pointwise=True), K_xy))
for idx, (a, b) in enumerate(checks):
with self.subTest(idx=idx):
self.assertTrue(np.allclose(a, b),
'a={}, b={}'.format(a, b))
def test_Gautschi_bounds(self):
"""Test if bounds computed w/wo log scale coincide"""
N = 100
dims = np.arange(2, 5)
for d in dims:
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
with_log_scale = compute_Gautschi_bounds(dpp.jacobi_params,
dpp.ordering,
log_scale=True)
without_log_scale = compute_Gautschi_bounds(dpp.jacobi_params,
dpp.ordering,
log_scale=False)
self.assertTrue(np.allclose(with_log_scale, without_log_scale))
def test_kernel_symmetry(self):
"""
K(x) == K(x, x)
K(x, y) == K(y, x)
K(x, Y) == K(Y, x) = [K(x, y) for y in Y]
K(X) == [K(x, x) for x in X]
K(X, Y) == [K(x, y) for x, y in zip(X, Y)]
"""
N = 100
dims = np.arange(2, 5)
for d in dims:
jacobi_params = 0.5 - np.random.rand(d, 2)
jacobi_params[0, :] = -0.5
dpp = MultivariateJacobiOPE(N, jacobi_params)
x, y = np.random.rand(d), np.random.rand(d)
X, Y = np.random.rand(5, d), np.random.rand(5, d)
self.assertTrue(np.allclose(dpp.K(x), dpp.K(x, x)))
self.assertTrue(
np.allclose(np.array([dpp.K(x) for x in X]),
np.concatenate([dpp.K(x, x) for x in X])))
self.assertTrue(np.allclose(dpp.K(X), dpp.K(X, X)))
self.assertTrue(np.allclose(dpp.K(x, y), dpp.K(y, x)))
self.assertTrue(
np.allclose(dpp.K(x, Y),
np.concatenate([dpp.K(x, y) for y in Y])))
self.assertTrue(np.allclose(dpp.K(x, Y), dpp.K(Y, x)))
self.assertTrue(np.allclose(dpp.K(X, Y), dpp.K(Y, X)))
import numpy as np
import matplotlib.pyplot as plt
from dppy.multivariate_jacobi_ope import MultivariateJacobiOPE
# The .plot() method outputs smtg only in dimension d=1 or 2
# Number of points / dimension
N, d = 200, 2
# Jacobi parameters in [-0.5, 0.5]^{d x 2}
jac_params = np.array([[0.5, 0.5], [-0.3, 0.4]])
dpp = MultivariateJacobiOPE(N, jac_params)
# Get an exact sample
sampl = dpp.sample()
# Display
# the cloud of points
# the base probability densities
# the marginal empirical histograms
dpp.plot(sample=sampl, weighted=False)
plt.tight_layout()
dpp.plot(sample=sampl, weighted='BH')
plt.tight_layout()
dpp.plot(sample=sampl, weighted='EZ')
plt.tight_layout()