def test_vandermond_matrix_type(cell):
points = np.ones((4, cell.dim))
v = vandermonde_matrix(cell, 2, points)
assert isinstance(v, np.ndarray), \
"vandermonde matrix must return a numpy array, not a %s" % type(v)
def test_vandermond_matrix_rank(cell):
points = np.ones((4, cell.dim))
v = vandermonde_matrix(cell, 2, points)
assert len(v.shape) == 2, \
"vandermonde matrix must return a rank 2 array, not rank %s" % len(v.shape)
def test_init_finite_element(cell):
nodes = cell.vertices
fe = FiniteElement(cell, 1, nodes)
v = vandermonde_matrix(cell, 1, nodes)
assert (np.round(np.dot(fe.basis_coefs, v) -
np.eye(cell.dim + 1)) == 0).all()
def test_vandermonde_matrix_size(cell, degree):
points = np.ones((1, cell.dim))
shape = vandermonde_matrix(cell, degree, points).shape
correct_shape = (1, np.round(comb(degree + cell.dim, cell.dim)))
assert shape == correct_shape, \
"vandermonde matrix should have returned an array of shape %s, not %s"\
% (correct_shape, shape)
def test_vandermonde_matrix_values_1D(degree):
points = np.array([[0.], [1.], [2.]])
V = vandermonde_matrix(ReferenceInterval, degree, points)
V_t = np.array([[1] + [0] * (V.shape[1] - 1), [1] * V.shape[1],
[2**d for d in range(V.shape[1])]])
print "Vandermonde matrix is:"
print V
print "Correct answer is:"
print V_t
assert (V == V_t).all()
def test_vandermonde_matrix_grad_values_1D(degree):
points = np.array([[0], [1]])
V = vandermonde_matrix(ReferenceInterval, degree, points, grad=True)
V_t = np.array([[0] + ([1] if degree > 0 else []) + [0] * (V.shape[1]-2),
range(V.shape[1])]).reshape((2, V.shape[1], 1))
print "Vandermonde matrix is:"
print V
print "Correct answer is:"
print V_t
assert (V == V_t).all()
def test_vandermonde_matrix_values_2D(degree):
points = np.array([[0., 0.], [1., 1.], [1., 0.], [0., 1.]])
V = vandermonde_matrix(ReferenceTriangle, degree, points)
V_t = np.array([[1] + [0] * (V.shape[1] - 1),
[1] * V.shape[1],
[1 if p == 0 else 0 for d in range(degree+1) for p in range(d+1)],
[1 if p == d else 0 for d in range(degree+1) for p in range(d+1)]])
print("Vandermonde matrix is:")
print(V)
print("Correct answer is:")
print(V_t)
assert (V == V_t).all()
def test_vandermonde_matrix_grad_values_2D(degree):
points = np.array([[0., 0.], [1., 0.], [0., 1.]])
V = vandermonde_matrix(ReferenceTriangle, degree, points, grad=True)
V_t = np.array([[[0, 0]] + ([[1, 0], [0, 1]] if degree > 0 else [])
+ [[0, 0]] * (V.shape[1] - 3),
[[d, 0] if p == 0 else [0, 1] if p == 1 else [0, 0] for d in range(degree+1) for p in range(d+1)],
[[0, d] if p == d else [1, 0] if p == d - 1 else [0, 0] for d in range(degree+1) for p in range(d+1)]])
print "Vandermonde matrix is:"
print V
print "Correct answer is:"
print V_t
assert (V == V_t).all()
