def test_change_of_basis_matrix_linear():
knots = [[0, 0, 1 / 3, 2 / 3, 1, 1]]
d = [1]
dim = 1
T = HierarchicalSpace(knots, d, dim)
cells = {0: [1]}
T = refine(T, cells)
C = T.get_basis_conversion_matrix(0)
np.testing.assert_allclose(
C.toarray(),
np.array([[1, 0, 0, 0], [0.5, 0.5, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0],
[0, 0, 1, 0], [0, 0, 0.5, 0.5], [0, 0, 0, 1]]))
def create_subdivision_matrix(hspace: HierarchicalSpace) -> dict:
"""
Returns hspace.nlevels-1 matrices used for representing coarse B-splines in terms of the finer B-splines.
:param hspace: HierarchicalSpace containing the needed information
:return: a dictionary mapping
"""
mesh = hspace.mesh
C = {}
C[0] = sp.identity(hspace.spaces[0].nfuncs, format='lil')
C[0] = C[0][:, hspace.afunc_level[0]]
for level in range(1, hspace.nlevels):
I = sp.identity(hspace.spaces[level].nfuncs, format='lil')
aux = sp.lil_matrix(hspace.get_basis_conversion_matrix(level - 1))
C[level] = sp.hstack(
[aux @ C[level - 1], I[:, hspace.afunc_level[level]]])
return C