def test_matrixization():
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(1, 1)
fs = FunctionSpace(mesh, "CG", 2)
F = [interpolate(Expression("*".join(["x[0]"] * i)), fs) for i in range(1, 5)]
vecs = [FEniCSVector(f) for f in F]
w = MultiVector()
for mi, vec in zip(mis, vecs):
w[mi] = vec
P = w.to_euclidian_operator
Q = w.from_euclidian_operator
Pw = P.apply(w)
assert type(Pw) == np.ndarray and len(Pw) == sum((v for v in w.dim.values()))
QPw = Q.apply(Pw)
assert w.active_indices() == QPw.active_indices()
for mu in w.active_indices():
assert_equal(w[mu].array, QPw[mu].array)
A_linear = P * A * Q
A_mat = evaluate_operator_matrix(A_linear)
def test_symmetry(A=None, w0=None, **kwargs):
from spuq.linalg.operator import evaluate_operator_matrix
v = w0
P = v.to_euclidian_operator
Q = v.from_euclidian_operator
print "Computing the matrix. This may take a while..."
A_mat = evaluate_operator_matrix(P * A * Q)
import scipy.linalg as la
print "norm(A-A^T) = %s" % la.norm(A_mat - A_mat.T)
print "norm(A) = %s" % la.norm(A_mat)
B = 0.5 * (A_mat + A_mat.T)
lam = la.eig(B)[0]
print "l_min = %s, l_max = %s" % (min(lam), max(lam))