def test_values_quadratic_basis():
"""
tests that the polynomial pieces and the numerical splines evaluate to the same value over all the
subtriangles.
"""
X, Y = sy.symbols('X Y')
triangle = np.array([[0, 0], [1, 0], [0, 1]])
S = SplineSpace(triangle, 2)
for basis_num in range(12):
b_num = S.basis()[basis_num]
b_sym = polynomial_pieces(triangle,
KNOT_MULTIPLICITIES_QUADRATIC[basis_num])
subtriangles = ps12_sub_triangles(triangle)
for k in range(12):
t = subtriangles[k]
points = sample_triangle(t, 1)
num_b_sym = sy.lambdify([X, Y], b_sym[k])
for p in points:
np.testing.assert_almost_equal(b_num(p), num_b_sym(p[0], p[1]))
def test_laplacian_quadratic_basis_functions():
X, Y = sy.symbols('X Y')
triangle = np.array([[0, 0], [1, 0], [0, 1]])
S = SplineSpace(triangle, 2)
points = sample_triangle(triangle, 10)
for basis_num in range(12):
b_num = S.basis()[basis_num]
b_sym = polynomial_pieces(triangle,
KNOT_MULTIPLICITIES_QUADRATIC[basis_num])
for p in points:
b = barycentric_coordinates(triangle, p)
k = determine_sub_triangle(b)[0]
b_lapl = sy.diff(b_sym[k], X, X) + sy.diff(b_sym[k], Y, Y)
num_b_sym = sy.lambdify([X, Y], b_lapl)
np.testing.assert_almost_equal(b_num.lapl(p),
num_b_sym(p[0], p[1]))