def test_vector_valued_smoothing(self):
X, _ = skfda.datasets.fetch_weather(return_X_y=True)
basis_dim = skfda.representation.basis.Fourier(
n_basis=7, domain_range=X.domain_range)
basis = skfda.representation.basis.VectorValued([basis_dim] * 2)
for method in smoothing.BasisSmoother.SolverMethod:
with self.subTest(method=method):
basis_smoother = smoothing.BasisSmoother(
basis,
regularization=TikhonovRegularization(
LinearDifferentialOperator(2)),
return_basis=True,
smoothing_parameter=1,
method=method)
basis_smoother_dim = smoothing.BasisSmoother(
basis_dim,
regularization=TikhonovRegularization(
LinearDifferentialOperator(2)),
return_basis=True,
smoothing_parameter=1,
method=method)
X_basis = basis_smoother.fit_transform(X)
self.assertEqual(X_basis.dim_codomain, 2)
self.assertEqual(X_basis.coordinates[0].basis, basis_dim)
np.testing.assert_allclose(
X_basis.coordinates[0].coefficients,
basis_smoother_dim.fit_transform(
X.coordinates[0]).coefficients)
self.assertEqual(X_basis.coordinates[1].basis, basis_dim)
np.testing.assert_allclose(
X_basis.coordinates[1].coefficients,
basis_smoother_dim.fit_transform(
X.coordinates[1]).coefficients)
def test_qr(self):
t = np.linspace(0, 1, 5)
x = np.sin(2 * np.pi * t) + np.cos(2 * np.pi * t)
basis = BSpline((0, 1), n_basis=5)
fd = FDataGrid(data_matrix=x, sample_points=t)
smoother = smoothing.BasisSmoother(basis=basis,
smoothing_parameter=10,
penalty=2,
method='qr',
return_basis=True)
fd_basis = smoother.fit_transform(fd)
np.testing.assert_array_almost_equal(
fd_basis.coefficients.round(2),
np.array([[0.60, 0.47, 0.20, -0.07, -0.20]]))
def test_cholesky(self):
t = np.linspace(0, 1, 5)
x = np.sin(2 * np.pi * t) + np.cos(2 * np.pi * t)
basis = BSpline((0, 1), n_basis=5)
fd = FDataGrid(data_matrix=x, sample_points=t)
smoother = smoothing.BasisSmoother(
basis=basis,
smoothing_parameter=10,
regularization=TikhonovRegularization(
LinearDifferentialOperator(2)),
method='cholesky',
return_basis=True)
fd_basis = smoother.fit_transform(fd)
np.testing.assert_array_almost_equal(
fd_basis.coefficients.round(2),
np.array([[0.60, 0.47, 0.20, -0.07, -0.20]]))
def test_monomial_smoothing(self):
# It does not have much sense to apply smoothing in this basic case
# where the fit is very good but its just for testing purposes
t = np.linspace(0, 1, 5)
x = np.sin(2 * np.pi * t) + np.cos(2 * np.pi * t)
basis = Monomial(n_basis=4)
fd = FDataGrid(data_matrix=x, sample_points=t)
smoother = smoothing.BasisSmoother(basis=basis,
smoothing_parameter=1,
penalty=2,
return_basis=True)
fd_basis = smoother.fit_transform(fd)
# These results where extracted from the R package fda
np.testing.assert_array_almost_equal(
fd_basis.coefficients.round(2),
np.array([[0.61, -0.88, 0.06, 0.02]]))