def penalty_matrix(self, basis):
r"""
Return a penalty matrix for ordinary least squares.
"""
return self.regularization_parameter * gramian_matrix(
self.linear_operator, basis)
def _test_penalty(self, basis, linear_diff_op, atol=0, result=None):
operator = LinearDifferentialOperator(linear_diff_op)
penalty = gramian_matrix(operator, basis)
numerical_penalty = gramian_matrix_numerical(operator, basis)
np.testing.assert_allclose(penalty, numerical_penalty, atol=atol)
if result is not None:
np.testing.assert_allclose(penalty, result, atol=atol)
def test_bspline_penalty_special_case(self):
basis = BSpline(n_basis=5)
res = np.array([[1152., -2016., 1152., -288., 0.],
[-2016., 3600., -2304., 1008., -288.],
[1152., -2304., 2304., -2304., 1152.],
[-288., 1008., -2304., 3600., -2016.],
[0., -288., 1152., -2016., 1152.]])
operator = LinearDifferentialOperator(basis.order - 1)
penalty = gramian_matrix(operator, basis)
numerical_penalty = gramian_matrix_numerical(operator, basis)
np.testing.assert_allclose(penalty, res)
np.testing.assert_allclose(numerical_penalty, res)