def test_apply():
N = 4
#a = [ConstFunction(1.0), SimpleFunction(np.sin), SimpleFunction(np.cos)]
mean_func = ConstFunction(2.0)
a = [ConstFunction(3.0), ConstFunction(4.0)]
rvs = [UniformRV(), NormalRV(mu=0.5)]
coeff_field = ListCoefficientField(mean_func, a, rvs)
A = MultiOperator(coeff_field, diag_assemble)
mis = [Multiindex([0]),
Multiindex([1]),
Multiindex([0, 1]),
Multiindex([0, 2])]
vecs = [FlatVector(np.random.random(N), SimpleProjectBasis(N)),
FlatVector(np.random.random(N), SimpleProjectBasis(N)),
FlatVector(np.random.random(N), SimpleProjectBasis(N)),
FlatVector(np.random.random(N), SimpleProjectBasis(N))]
w = MultiVectorWithProjection()
for i in range(len(mis)):
w[mis[i]] = vecs[i]
v = A * w
L = LegendrePolynomials(normalised=True)
H = StochasticHermitePolynomials(mu=0.5, normalised=True)
v0_ex = (2 * vecs[0] +
3 * (L.get_beta(0)[1] * vecs[1] - L.get_beta(0)[0] * vecs[0]) +
4 * (H.get_beta(0)[1] * vecs[2] - H.get_beta(0)[0] * vecs[0]))
v2_ex = (2 * vecs[2] + 4 * (H.get_beta(1)[1] * vecs[3] -
H.get_beta(1)[0] * vecs[2] +
H.get_beta(1)[-1] * vecs[0]))
assert_equal(v[mis[0]], v0_ex)
assert_equal(v[mis[2]], v2_ex)
def test_fenics_vector():
def mult_assemble(a, basis):
return MultiplicationOperator(a(0), basis)
mean_func = ConstFunction(2)
a = [ConstFunction(3), ConstFunction(4)]
rvs = [UniformRV(), NormalRV(mu=0.5)]
coeff_field = ListCoefficientField(mean_func, a, rvs)
A = MultiOperator(coeff_field, mult_assemble)
mis = [Multiindex([0]),
Multiindex([1]),
Multiindex([0, 1]),
Multiindex([0, 2])]
mesh = UnitSquare(4, 4)
fs = FunctionSpace(mesh, "CG", 4)
F = [interpolate(Expression("*".join(["x[0]"] * i)), fs) for i in range(1, 5)]
vecs = [FEniCSVector(f) for f in F]
w = MultiVectorWithProjection()
for mi, vec in zip(mis, vecs):
w[mi] = vec
v = A * w
L = LegendrePolynomials(normalised=True)
H = StochasticHermitePolynomials(mu=0.5, normalised=True)
ex0 = Expression("2*x[0] + 3*(l01*x[0]*x[0]-l00*x[0]) + 4*(h01*x[0]*x[0]*x[0]-h00*x[0])",
l01=L.get_beta(0)[1], l00=L.get_beta(0)[0],
h01=H.get_beta(0)[1], h00=H.get_beta(0)[0])
vec0 = FEniCSVector(interpolate(ex0, fs))
assert_almost_equal(v[mis[0]].array, vec0.array)
# ======================================================================
# test with different meshes
# ======================================================================
N = len(mis)
meshes = [UnitSquare(i + 3, i + 3) for i in range(N)]
fss = [FunctionSpace(mesh, "CG", 4) for mesh in meshes]
F = [interpolate(Expression("*".join(["x[0]"] * (i + 1))), fss[i]) for i in range(N)]
vecs = [FEniCSVector(f) for f in F]
w = MultiVectorWithProjection()
for mi, vec in zip(mis, vecs):
w[mi] = vec
v = A * w
L = LegendrePolynomials(normalised=True)
H = StochasticHermitePolynomials(mu=0.5, normalised=True)
ex0 = Expression("2*x[0] + 3*(l01*x[0]*x[0]-l00*x[0]) + 4*(h01*x[0]*x[0]*x[0]-h00*x[0])",
l01=L.get_beta(0)[1], l00=L.get_beta(0)[0],
h01=H.get_beta(0)[1], h00=H.get_beta(0)[0])
ex2 = Expression("2*x[0]*x[0]*x[0] + 4*(h11*x[0]*x[0]*x[0]*x[0] - h10*x[0]*x[0]*x[0] + h1m1*x[0])",
h11=H.get_beta(1)[1], h10=H.get_beta(1)[0], h1m1=H.get_beta(1)[-1])
vec0 = FEniCSVector(interpolate(ex0, fss[0]))
vec2 = FEniCSVector(interpolate(ex2, fss[2]))
assert_almost_equal(v[mis[0]].array, vec0.array)
assert_almost_equal(v[mis[2]].array, vec2.array)