def best_hermite(self):
d = 2
def function(X):
return np.ones(shape=(X.shape[0], 1)) # np.prod(np.sin(3 * X), axis=1)
ups = UnivariatePolynomialSpace(measure='h')
ps = TensorPolynomialSpace(ups=ups, c_var=2, sampler='optimal')
P = WeightedPolynomialApproximator(function=function, ps=ps)
sparseindices = cartesian_product([range(2)] * d)
P.expand(sparseindices)
# P.plot_sampling_measure(N=200,L=10)
P.plot_xy()
P.plot()
M = 100
sparseindices = cartesian_product([range(3)] * d)
P.expand(sparseindices)
# P.plot_sampling_measure(N=200,L=10)
P.plot_xy()
P.plot(L=5)
sparseindices = indices.simplex(6, n=d)
P.expand(sparseindices)
# P.plot_sampling_measure(N=200,L=20)
P.plot_xy()
P.plot(L=5)
X = np.random.rand(M, d)
Y = function(X.reshape((X.shape[0], d))).reshape((X.shape[0], 1))
self.assertLess(np.linalg.norm(P(X) - Y) / np.sqrt(M), 0.1)
def test_cartesian_product(self):
T = [[1, 2], [3, 4], [2]]
TT = cartesian_product(T)
self.assertEqual([mi.full_tuple() for mi in TT], [(1, 3, 2), (1, 4, 2),
(2, 3, 2),
(2, 4, 2)])
TT = cartesian_product(T, (1, 3, 4))
self.assertEqual([mi.full_tuple() for mi in TT], [(0, 1, 0, 3, 2),
(0, 1, 0, 4, 2),
(0, 2, 0, 3, 2),
(0, 2, 0, 4, 2)])
def adaptive(self, measure):
def function(X):
return np.prod(np.sin(3 * X), axis=1)
ups = UnivariatePolynomialSpace(measure=measure)
P = WeightedPolynomialApproximator(function, ps=ups)
sparseindices = cartesian_product([range(4)] * 1)
P.expand(sparseindices)
ps = TensorPolynomialSpace(ups=ups,c_var=1)
self.assertAlmostEqual(ps.plot_optimal_distribution(N=200), 1, delta=0.2)
P.plot_xy()
M = 100
sparseindices = cartesian_product([range(4)] * 2)
P.expand(sparseindices)
self.assertAlmostEqual(P.plot_sampling_measure(N=200), 1, delta=0.2)
P.plot_xy()
X = np.random.rand(M, 2)
Y = function(X.reshape((X.shape[0], 2))).reshape((X.shape[0], 1))
self.assertLess(np.linalg.norm(P(X) - Y) / np.sqrt(M), 0.01)
def test_rectangle(self):
self.assertCountEqual(indices.rectangle(L=[4, 4], n=2),
[mi for mi in cartesian_product([range(4)] * 2)])
self.assertCountEqual(indices.rectangle(L=2, n=2), [
MultiIndex(),
MultiIndex((1, 0)),
MultiIndex((0, 1)),
MultiIndex((1, 1))
])
def test_returnshapes(self):
cRandomTests = 100
for __ in range(cRandomTests):
A = []
cSets = randint(0, 5)
cElements = []
for j in range(cSets):
cElements.append(randint(0, 5))
A.append(rand(cElements[j]))
C = cartesian_product(A)
self.assertEqual(len(C), np.prod(cElements))
def _pols_from_mi(self, mi):
'''
Convert multi-index to corresponding polynomials
:param mi: Multi-index
:return: List of polynomials corresponding to mi
'''
if self.reparametrization is True:
if mi == MultiIndex():
return [mi]
else:
univariate_entries = []
for dimension in mi.active_dims():
init_range = 2 ** (mi[dimension])-1
end_range = 2 ** (mi[dimension]+1)-1
univariate_entries.append(range(init_range, end_range))
return cartesian_product(univariate_entries, mi.active_dims())
elif self.reparametrization is False:
return [mi]
else:
return self.reparametrization(mi)
def test_rectangles(self):
d = 5
L = 5
sparseindices = cartesian_product([range(L)] * d)
CR = combination_rule(sparseindices)
self.assertEqual([mi for mi in CR], [MultiIndex((L - 1, ) * d)])